/* * msvcrt.dll math functions * * Copyright 2000 Jon Griffiths * * This library is free software; you can redistribute it and/or * modify it under the terms of the GNU Lesser General Public * License as published by the Free Software Foundation; either * version 2.1 of the License, or (at your option) any later version. * * This library is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU * Lesser General Public License for more details. * * You should have received a copy of the GNU Lesser General Public * License along with this library; if not, write to the Free Software * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA * * * For functions copied from musl libc (http://musl.libc.org/): * ==================================================== * Copyright 2005-2020 Rich Felker, et al. * * Permission is hereby granted, free of charge, to any person obtaining * a copy of this software and associated documentation files (the * "Software"), to deal in the Software without restriction, including * without limitation the rights to use, copy, modify, merge, publish, * distribute, sublicense, and/or sell copies of the Software, and to * permit persons to whom the Software is furnished to do so, subject to * the following conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * ==================================================== */ #include #include #include #include #include #include #include #include #include "msvcrt.h" #include "winternl.h" #include "wine/asm.h" #include "wine/debug.h" WINE_DEFAULT_DEBUG_CHANNEL(msvcrt); #undef div #undef ldiv #define _DOMAIN 1 /* domain error in argument */ #define _SING 2 /* singularity */ #define _OVERFLOW 3 /* range overflow */ #define _UNDERFLOW 4 /* range underflow */ typedef int (CDECL *MSVCRT_matherr_func)(struct _exception *); static MSVCRT_matherr_func MSVCRT_default_matherr_func = NULL; BOOL sse2_supported; static BOOL sse2_enabled; void msvcrt_init_math( void *module ) { sse2_supported = IsProcessorFeaturePresent( PF_XMMI64_INSTRUCTIONS_AVAILABLE ); #if _MSVCR_VER <=71 sse2_enabled = FALSE; #else sse2_enabled = sse2_supported; #endif } /* Copied from musl: src/internal/libm.h */ static inline float fp_barrierf(float x) { volatile float y = x; return y; } static inline double fp_barrier(double x) { volatile double y = x; return y; } static inline double ret_nan( BOOL update_sw ) { double x = 1.0; if (!update_sw) return -NAN; return (x - x) / (x - x); } #define SET_X87_CW(MASK) \ "subl $4, %esp\n\t" \ __ASM_CFI(".cfi_adjust_cfa_offset 4\n\t") \ "fnstcw (%esp)\n\t" \ "movw (%esp), %ax\n\t" \ "movw %ax, 2(%esp)\n\t" \ "testw $" #MASK ", %ax\n\t" \ "jz 1f\n\t" \ "andw $~" #MASK ", %ax\n\t" \ "movw %ax, 2(%esp)\n\t" \ "fldcw 2(%esp)\n\t" \ "1:\n\t" #define RESET_X87_CW \ "movw (%esp), %ax\n\t" \ "cmpw %ax, 2(%esp)\n\t" \ "je 1f\n\t" \ "fstpl 8(%esp)\n\t" \ "fldcw (%esp)\n\t" \ "fldl 8(%esp)\n\t" \ "fwait\n\t" \ "1:\n\t" \ "addl $4, %esp\n\t" \ __ASM_CFI(".cfi_adjust_cfa_offset -4\n\t") /********************************************************************* * _matherr (CRTDLL.@) */ int CDECL _matherr(struct _exception *e) { return 0; } static double math_error(int type, const char *name, double arg1, double arg2, double retval) { struct _exception exception = {type, (char *)name, arg1, arg2, retval}; TRACE("(%d, %s, %g, %g, %g)\n", type, debugstr_a(name), arg1, arg2, retval); if (MSVCRT_default_matherr_func && MSVCRT_default_matherr_func(&exception)) return exception.retval; switch (type) { case 0: /* don't set errno */ break; case _DOMAIN: *_errno() = EDOM; break; case _SING: case _OVERFLOW: *_errno() = ERANGE; break; case _UNDERFLOW: /* don't set errno */ break; default: ERR("Unhandled math error!\n"); } return exception.retval; } /********************************************************************* * __setusermatherr (MSVCRT.@) */ void CDECL __setusermatherr(MSVCRT_matherr_func func) { MSVCRT_default_matherr_func = func; TRACE("new matherr handler %p\n", func); } /********************************************************************* * _set_SSE2_enable (MSVCRT.@) */ int CDECL _set_SSE2_enable(int flag) { sse2_enabled = flag && sse2_supported; return sse2_enabled; } #if defined(_WIN64) # if _MSVCR_VER>=140 /********************************************************************* * _get_FMA3_enable (UCRTBASE.@) */ int CDECL _get_FMA3_enable(void) { FIXME("() stub\n"); return 0; } # endif # if _MSVCR_VER>=120 /********************************************************************* * _set_FMA3_enable (MSVCR120.@) */ int CDECL _set_FMA3_enable(int flag) { FIXME("(%x) stub\n", flag); return 0; } # endif #endif #if !defined(__i386__) || _MSVCR_VER>=120 /********************************************************************* * _chgsignf (MSVCRT.@) */ float CDECL _chgsignf( float num ) { union { float f; UINT32 i; } u = { num }; u.i ^= 0x80000000; return u.f; } /********************************************************************* * _copysignf (MSVCRT.@) * * Copied from musl: src/math/copysignf.c */ float CDECL _copysignf( float x, float y ) { union { float f; UINT32 i; } ux = { x }, uy = { y }; ux.i &= 0x7fffffff; ux.i |= uy.i & 0x80000000; return ux.f; } /********************************************************************* * _nextafterf (MSVCRT.@) * * Copied from musl: src/math/nextafterf.c */ float CDECL _nextafterf( float x, float y ) { unsigned int ix = *(unsigned int*)&x; unsigned int iy = *(unsigned int*)&y; unsigned int ax, ay, e; if (isnan(x) || isnan(y)) return x + y; if (x == y) { if (_fpclassf(y) & (_FPCLASS_ND | _FPCLASS_PD | _FPCLASS_NZ | _FPCLASS_PZ )) *_errno() = ERANGE; return y; } ax = ix & 0x7fffffff; ay = iy & 0x7fffffff; if (ax == 0) { if (ay == 0) return y; ix = (iy & 0x80000000) | 1; } else if (ax > ay || ((ix ^ iy) & 0x80000000)) ix--; else ix++; e = ix & 0x7f800000; /* raise overflow if ix is infinite and x is finite */ if (e == 0x7f800000) { fp_barrierf(x + x); *_errno() = ERANGE; } /* raise underflow if ix is subnormal or zero */ y = *(float*)&ix; if (e == 0) { fp_barrierf(x * x + y * y); *_errno() = ERANGE; } return y; } /* Copied from musl: src/math/ilogbf.c */ static int __ilogbf(float x) { union { float f; UINT32 i; } u = { x }; int e = u.i >> 23 & 0xff; if (!e) { u.i <<= 9; if (u.i == 0) return FP_ILOGB0; /* subnormal x */ for (e = -0x7f; u.i >> 31 == 0; e--, u.i <<= 1); return e; } if (e == 0xff) return u.i << 9 ? FP_ILOGBNAN : INT_MAX; return e - 0x7f; } /********************************************************************* * _logbf (MSVCRT.@) * * Copied from musl: src/math/logbf.c */ float CDECL _logbf(float x) { if (!isfinite(x)) return x * x; if (x == 0) { *_errno() = ERANGE; return -1 / (x * x); } return __ilogbf(x); } #endif /* Copied from musl: src/math/scalbn.c */ static double __scalbn(double x, int n) { union {double f; UINT64 i;} u; double y = x; if (n > 1023) { y *= 0x1p1023; n -= 1023; if (n > 1023) { y *= 0x1p1023; n -= 1023; if (n > 1023) n = 1023; } } else if (n < -1022) { /* make sure final n < -53 to avoid double rounding in the subnormal range */ y *= 0x1p-1022 * 0x1p53; n += 1022 - 53; if (n < -1022) { y *= 0x1p-1022 * 0x1p53; n += 1022 - 53; if (n < -1022) n = -1022; } } u.i = (UINT64)(0x3ff + n) << 52; x = y * u.f; return x; } /* Copied from musl: src/math/__rem_pio2_large.c */ static int __rem_pio2_large(double *x, double *y, int e0, int nx, int prec) { static const int init_jk[] = {3, 4}; static const INT32 ipio2[] = { 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, }; static const double PIo2[] = { 1.57079625129699707031e+00, 7.54978941586159635335e-08, 5.39030252995776476554e-15, 3.28200341580791294123e-22, 1.27065575308067607349e-29, 1.22933308981111328932e-36, 2.73370053816464559624e-44, 2.16741683877804819444e-51, }; INT32 jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; double z, fw, f[20], fq[20] = {0}, q[20]; /* initialize jk*/ jk = init_jk[prec]; jp = jk; /* determine jx,jv,q0, note that 3>q0 */ jx = nx - 1; jv = (e0 - 3) / 24; if(jv < 0) jv = 0; q0 = e0 - 24 * (jv + 1); /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ j = jv - jx; m = jx + jk; for (i = 0; i <= m; i++, j++) f[i] = j < 0 ? 0.0 : (double)ipio2[j]; /* compute q[0],q[1],...q[jk] */ for (i = 0; i <= jk; i++) { for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j]; q[i] = fw; } jz = jk; recompute: /* distill q[] into iq[] reversingly */ for (i = 0, j = jz, z = q[jz]; j > 0; i++, j--) { fw = (double)(INT32)(0x1p-24 * z); iq[i] = (INT32)(z - 0x1p24 * fw); z = q[j - 1] + fw; } /* compute n */ z = __scalbn(z, q0); /* actual value of z */ z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */ n = (INT32)z; z -= (double)n; ih = 0; if (q0 > 0) { /* need iq[jz-1] to determine n */ i = iq[jz - 1] >> (24 - q0); n += i; iq[jz - 1] -= i << (24 - q0); ih = iq[jz - 1] >> (23 - q0); } else if (q0 == 0) ih = iq[jz - 1] >> 23; else if (z >= 0.5) ih = 2; if (ih > 0) { /* q > 0.5 */ n += 1; carry = 0; for (i = 0; i < jz; i++) { /* compute 1-q */ j = iq[i]; if (carry == 0) { if (j != 0) { carry = 1; iq[i] = 0x1000000 - j; } } else iq[i] = 0xffffff - j; } if (q0 > 0) { /* rare case: chance is 1 in 12 */ switch(q0) { case 1: iq[jz - 1] &= 0x7fffff; break; case 2: iq[jz - 1] &= 0x3fffff; break; } } if (ih == 2) { z = 1.0 - z; if (carry != 0) z -= __scalbn(1.0, q0); } } /* check if recomputation is needed */ if (z == 0.0) { j = 0; for (i = jz - 1; i >= jk; i--) j |= iq[i]; if (j == 0) { /* need recomputation */ for (k = 1; iq[jk - k] == 0; k++); /* k = no. of terms needed */ for (i = jz + 1; i <= jz + k; i++) { /* add q[jz+1] to q[jz+k] */ f[jx + i] = (double)ipio2[jv + i]; for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j]; q[i] = fw; } jz += k; goto recompute; } } /* chop off zero terms */ if (z == 0.0) { jz -= 1; q0 -= 24; while (iq[jz] == 0) { jz--; q0 -= 24; } } else { /* break z into 24-bit if necessary */ z = __scalbn(z, -q0); if (z >= 0x1p24) { fw = (double)(INT32)(0x1p-24 * z); iq[jz] = (INT32)(z - 0x1p24 * fw); jz += 1; q0 += 24; iq[jz] = (INT32)fw; } else iq[jz] = (INT32)z; } /* convert integer "bit" chunk to floating-point value */ fw = __scalbn(1.0, q0); for (i = jz; i >= 0; i--) { q[i] = fw * (double)iq[i]; fw *= 0x1p-24; } /* compute PIo2[0,...,jp]*q[jz,...,0] */ for(i = jz; i >= 0; i--) { for (fw = 0.0, k = 0; k <= jp && k <= jz - i; k++) fw += PIo2[k] * q[i + k]; fq[jz - i] = fw; } /* compress fq[] into y[] */ switch(prec) { case 0: fw = 0.0; for (i = jz; i >= 0; i--) fw += fq[i]; y[0] = ih == 0 ? fw : -fw; break; case 1: case 2: fw = 0.0; for (i = jz; i >= 0; i--) fw += fq[i]; fw = (double)fw; y[0] = ih==0 ? fw : -fw; fw = fq[0] - fw; for (i = 1; i <= jz; i++) fw += fq[i]; y[1] = ih == 0 ? fw : -fw; break; case 3: /* painful */ for (i = jz; i > 0; i--) { fw = fq[i - 1] + fq[i]; fq[i] += fq[i - 1] - fw; fq[i - 1] = fw; } for (i = jz; i > 1; i--) { fw = fq[i - 1] + fq[i]; fq[i] += fq[i - 1] - fw; fq[i - 1] = fw; } for (fw = 0.0, i = jz; i >= 2; i--) fw += fq[i]; if (ih == 0) { y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; } else { y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; } } return n & 7; } /* Based on musl implementation: src/math/round.c */ static double __round(double x) { ULONGLONG llx = *(ULONGLONG*)&x, tmp; int e = (llx >> 52 & 0x7ff) - 0x3ff; if (e >= 52) return x; if (e < -1) return 0 * x; else if (e == -1) return signbit(x) ? -1 : 1; tmp = 0x000fffffffffffffULL >> e; if (!(llx & tmp)) return x; llx += 0x0008000000000000ULL >> e; llx &= ~tmp; return *(double*)&llx; } #if !defined(__i386__) || _MSVCR_VER >= 120 /* Copied from musl: src/math/expm1f.c */ static float __expm1f(float x) { static const float ln2_hi = 6.9313812256e-01, ln2_lo = 9.0580006145e-06, invln2 = 1.4426950216e+00, Q1 = -3.3333212137e-2, Q2 = 1.5807170421e-3; float y, hi, lo, c, t, e, hxs, hfx, r1, twopk; union {float f; UINT32 i;} u = {x}; UINT32 hx = u.i & 0x7fffffff; int k, sign = u.i >> 31; /* filter out huge and non-finite argument */ if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */ if (hx >= 0x7f800000) /* NaN */ return u.i == 0xff800000 ? -1 : x; if (sign) return math_error(_UNDERFLOW, "exp", x, 0, -1); if (hx > 0x42b17217) /* x > log(FLT_MAX) */ return math_error(_OVERFLOW, "exp", x, 0, fp_barrierf(x * FLT_MAX)); } /* argument reduction */ if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ if (!sign) { hi = x - ln2_hi; lo = ln2_lo; k = 1; } else { hi = x + ln2_hi; lo = -ln2_lo; k = -1; } } else { k = invln2 * x + (sign ? -0.5f : 0.5f); t = k; hi = x - t * ln2_hi; /* t*ln2_hi is exact here */ lo = t * ln2_lo; } x = hi - lo; c = (hi - x) - lo; } else if (hx < 0x33000000) { /* when |x|<2**-25, return x */ if (hx < 0x00800000) fp_barrierf(x * x); return x; } else k = 0; /* x is now in primary range */ hfx = 0.5f * x; hxs = x * hfx; r1 = 1.0f + hxs * (Q1 + hxs * Q2); t = 3.0f - r1 * hfx; e = hxs * ((r1 - t) / (6.0f - x * t)); if (k == 0) /* c is 0 */ return x - (x * e - hxs); e = x * (e - c) - c; e -= hxs; /* exp(x) ~ 2^k (x_reduced - e + 1) */ if (k == -1) return 0.5f * (x - e) - 0.5f; if (k == 1) { if (x < -0.25f) return -2.0f * (e - (x + 0.5f)); return 1.0f + 2.0f * (x - e); } u.i = (0x7f + k) << 23; /* 2^k */ twopk = u.f; if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ y = x - e + 1.0f; if (k == 128) y = y * 2.0f * 0x1p127f; else y = y * twopk; return y - 1.0f; } u.i = (0x7f-k) << 23; /* 2^-k */ if (k < 23) y = (x - e + (1 - u.f)) * twopk; else y = (x - (e + u.f) + 1) * twopk; return y; } /* Copied from musl: src/math/__sindf.c */ static float __sindf(double x) { static const double S1 = -0x1.5555555555555p-3, S2 = 0x1.1111111111111p-7, S3 = -0x1.a01a01a01a01ap-13, S4 = 0x1.71de3a556c734p-19; double r, s, w, z; z = x * x; if (x > -7.8175831586122513e-03 && x < 7.8175831586122513e-03) return x * (1 + S1 * z); w = z * z; r = S3 + z * S4; s = z * x; return (x + s * (S1 + z * S2)) + s * w * r; } /* Copied from musl: src/math/__cosdf.c */ static float __cosdf(double x) { static const double C0 = -0x1.0000000000000p-1, C1 = 0x1.5555555555555p-5, C2 = -0x1.6c16c16c16c17p-10, C3 = 0x1.a01a01a01a01ap-16, C4 = -0x1.27e4fb7789f5cp-22; double z; z = x * x; if (x > -7.8163146972656250e-03 && x < 7.8163146972656250e-03) return 1 + C0 * z; return 1.0 + z * (C0 + z * (C1 + z * (C2 + z * (C3 + z * C4)))); } static const UINT64 exp2f_T[] = { 0x3ff0000000000000ULL, 0x3fefd9b0d3158574ULL, 0x3fefb5586cf9890fULL, 0x3fef9301d0125b51ULL, 0x3fef72b83c7d517bULL, 0x3fef54873168b9aaULL, 0x3fef387a6e756238ULL, 0x3fef1e9df51fdee1ULL, 0x3fef06fe0a31b715ULL, 0x3feef1a7373aa9cbULL, 0x3feedea64c123422ULL, 0x3feece086061892dULL, 0x3feebfdad5362a27ULL, 0x3feeb42b569d4f82ULL, 0x3feeab07dd485429ULL, 0x3feea47eb03a5585ULL, 0x3feea09e667f3bcdULL, 0x3fee9f75e8ec5f74ULL, 0x3feea11473eb0187ULL, 0x3feea589994cce13ULL, 0x3feeace5422aa0dbULL, 0x3feeb737b0cdc5e5ULL, 0x3feec49182a3f090ULL, 0x3feed503b23e255dULL, 0x3feee89f995ad3adULL, 0x3feeff76f2fb5e47ULL, 0x3fef199bdd85529cULL, 0x3fef3720dcef9069ULL, 0x3fef5818dcfba487ULL, 0x3fef7c97337b9b5fULL, 0x3fefa4afa2a490daULL, 0x3fefd0765b6e4540ULL }; #endif /********************************************************************* * _fdclass (MSVCR120.@) * * Copied from musl: src/math/__fpclassifyf.c */ short CDECL _fdclass(float x) { union { float f; UINT32 i; } u = { x }; int e = u.i >> 23 & 0xff; if (!e) return u.i << 1 ? FP_SUBNORMAL : FP_ZERO; if (e == 0xff) return u.i << 9 ? FP_NAN : FP_INFINITE; return FP_NORMAL; } /********************************************************************* * _dclass (MSVCR120.@) * * Copied from musl: src/math/__fpclassify.c */ short CDECL _dclass(double x) { union { double f; UINT64 i; } u = { x }; int e = u.i >> 52 & 0x7ff; if (!e) return u.i << 1 ? FP_SUBNORMAL : FP_ZERO; if (e == 0x7ff) return (u.i << 12) ? FP_NAN : FP_INFINITE; return FP_NORMAL; } #ifndef __i386__ /********************************************************************* * _fpclassf (MSVCRT.@) */ int CDECL _fpclassf( float num ) { union { float f; UINT32 i; } u = { num }; int e = u.i >> 23 & 0xff; int s = u.i >> 31; switch (e) { case 0: if (u.i << 1) return s ? _FPCLASS_ND : _FPCLASS_PD; return s ? _FPCLASS_NZ : _FPCLASS_PZ; case 0xff: if (u.i << 9) return ((u.i >> 22) & 1) ? _FPCLASS_QNAN : _FPCLASS_SNAN; return s ? _FPCLASS_NINF : _FPCLASS_PINF; default: return s ? _FPCLASS_NN : _FPCLASS_PN; } } /********************************************************************* * _finitef (MSVCRT.@) */ int CDECL _finitef( float num ) { union { float f; UINT32 i; } u = { num }; return (u.i & 0x7fffffff) < 0x7f800000; } /********************************************************************* * _isnanf (MSVCRT.@) */ int CDECL _isnanf( float num ) { union { float f; UINT32 i; } u = { num }; return (u.i & 0x7fffffff) > 0x7f800000; } static float asinf_R(float z) { /* coefficients for R(x^2) */ static const float p1 = 1.66666672e-01, p2 = -5.11644611e-02, p3 = -1.21124933e-02, p4 = -3.58742251e-03, q1 = -7.56982703e-01; float p, q; p = z * (p1 + z * (p2 + z * (p3 + z * p4))); q = 1.0f + z * q1; return p / q; } /********************************************************************* * acosf (MSVCRT.@) * * Copied from musl: src/math/acosf.c */ float CDECL acosf( float x ) { static const double pio2_lo = 6.12323399573676603587e-17; float z, w, s, c, df; unsigned int hx, ix; hx = *(unsigned int*)&x; ix = hx & 0x7fffffff; /* |x| >= 1 or nan */ if (ix >= 0x3f800000) { if (ix == 0x3f800000) { if (hx >> 31) return M_PI; return 0; } if (isnan(x)) return x; return math_error(_DOMAIN, "acosf", x, 0, 0 / (x - x)); } /* |x| < 0.5 */ if (ix < 0x3f000000) { if (ix <= 0x32800000) /* |x| < 2**-26 */ return M_PI_2; return M_PI_2 - (x - (pio2_lo - x * asinf_R(x * x))); } /* x < -0.5 */ if (hx >> 31) { z = (1 + x) * 0.5f; s = sqrtf(z); return M_PI - 2 * (s + ((double)s * asinf_R(z))); } /* x > 0.5 */ z = (1 - x) * 0.5f; s = sqrtf(z); hx = *(unsigned int*)&s & 0xffff0000; df = *(float*)&hx; c = (z - df * df) / (s + df); w = asinf_R(z) * s + c; return 2 * (df + w); } /********************************************************************* * asinf (MSVCRT.@) * * Copied from musl: src/math/asinf.c */ float CDECL asinf( float x ) { static const double pio2 = 1.570796326794896558e+00; static const float pio4_hi = 0.785398125648; static const float pio2_lo = 7.54978941586e-08; float s, z, f, c; unsigned int hx, ix; hx = *(unsigned int*)&x; ix = hx & 0x7fffffff; if (ix >= 0x3f800000) { /* |x| >= 1 */ if (ix == 0x3f800000) /* |x| == 1 */ return x * pio2 + 7.5231638453e-37; /* asin(+-1) = +-pi/2 with inexact */ if (isnan(x)) return x; return math_error(_DOMAIN, "asinf", x, 0, 0 / (x - x)); } if (ix < 0x3f000000) { /* |x| < 0.5 */ /* if 0x1p-126 <= |x| < 0x1p-12, avoid raising underflow */ if (ix < 0x39800000 && ix >= 0x00800000) return x; return x + x * asinf_R(x * x); } /* 1 > |x| >= 0.5 */ z = (1 - fabsf(x)) * 0.5f; s = sqrtf(z); /* f+c = sqrt(z) */ *(unsigned int*)&f = *(unsigned int*)&s & 0xffff0000; c = (z - f * f) / (s + f); x = pio4_hi - (2 * s * asinf_R(z) - (pio2_lo - 2 * c) - (pio4_hi - 2 * f)); if (hx >> 31) return -x; return x; } /********************************************************************* * atanf (MSVCRT.@) * * Copied from musl: src/math/atanf.c */ float CDECL atanf( float x ) { static const float atanhi[] = { 4.6364760399e-01, 7.8539812565e-01, 9.8279368877e-01, 1.5707962513e+00, }; static const float atanlo[] = { 5.0121582440e-09, 3.7748947079e-08, 3.4473217170e-08, 7.5497894159e-08, }; static const float aT[] = { 3.3333328366e-01, -1.9999158382e-01, 1.4253635705e-01, -1.0648017377e-01, 6.1687607318e-02, }; float w, s1, s2, z; unsigned int ix, sign; int id; #if _MSVCR_VER == 0 if (isnan(x)) return math_error(_DOMAIN, "atanf", x, 0, x); #endif ix = *(unsigned int*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x4c800000) { /* if |x| >= 2**26 */ if (isnan(x)) return x; z = atanhi[3] + 7.5231638453e-37; return sign ? -z : z; } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ if (ix < 0x39800000) { /* |x| < 2**-12 */ if (ix < 0x00800000) /* raise underflow for subnormal x */ fp_barrierf(x*x); return x; } id = -1; } else { x = fabsf(x); if (ix < 0x3f980000) { /* |x| < 1.1875 */ if (ix < 0x3f300000) { /* 7/16 <= |x| < 11/16 */ id = 0; x = (2.0f * x - 1.0f) / (2.0f + x); } else { /* 11/16 <= |x| < 19/16 */ id = 1; x = (x - 1.0f) / (x + 1.0f); } } else { if (ix < 0x401c0000) { /* |x| < 2.4375 */ id = 2; x = (x - 1.5f) / (1.0f + 1.5f * x); } else { /* 2.4375 <= |x| < 2**26 */ id = 3; x = -1.0f / x; } } } /* end of argument reduction */ z = x * x; w = z * z; /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ s1 = z * (aT[0] + w * (aT[2] + w * aT[4])); s2 = w * (aT[1] + w * aT[3]); if (id < 0) return x - x * (s1 + s2); z = atanhi[id] - ((x * (s1 + s2) - atanlo[id]) - x); return sign ? -z : z; } /********************************************************************* * atan2f (MSVCRT.@) * * Copied from musl: src/math/atan2f.c */ float CDECL atan2f( float y, float x ) { static const float pi = 3.1415927410e+00, pi_lo = -8.7422776573e-08; float z; unsigned int m, ix, iy; if (isnan(x) || isnan(y)) return x + y; ix = *(unsigned int*)&x; iy = *(unsigned int*)&y; if (ix == 0x3f800000) /* x=1.0 */ return atanf(y); m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */ ix &= 0x7fffffff; iy &= 0x7fffffff; /* when y = 0 */ if (iy == 0) { switch (m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi; /* atan(+0,-anything) = pi */ case 3: return -pi; /* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if (ix == 0) return m & 1 ? -pi / 2 : pi / 2; /* when x is INF */ if (ix == 0x7f800000) { if (iy == 0x7f800000) { switch (m) { case 0: return pi / 4; /* atan(+INF,+INF) */ case 1: return -pi / 4; /* atan(-INF,+INF) */ case 2: return 3 * pi / 4; /*atan(+INF,-INF)*/ case 3: return -3 * pi / 4; /*atan(-INF,-INF)*/ } } else { switch (m) { case 0: return 0.0f; /* atan(+...,+INF) */ case 1: return -0.0f; /* atan(-...,+INF) */ case 2: return pi; /* atan(+...,-INF) */ case 3: return -pi; /* atan(-...,-INF) */ } } } /* |y/x| > 0x1p26 */ if (ix + (26 << 23) < iy || iy == 0x7f800000) return m & 1 ? -pi / 2 : pi / 2; /* z = atan(|y/x|) with correct underflow */ if ((m & 2) && iy + (26 << 23) < ix) /*|y/x| < 0x1p-26, x < 0 */ z = 0.0; else z = atanf(fabsf(y / x)); switch (m) { case 0: return z; /* atan(+,+) */ case 1: return -z; /* atan(-,+) */ case 2: return pi - (z - pi_lo); /* atan(+,-) */ default: /* case 3 */ return (z - pi_lo) - pi; /* atan(-,-) */ } } /* Copied from musl: src/math/__rem_pio2f.c */ static int __rem_pio2f(float x, double *y) { static const double toint = 1.5 / DBL_EPSILON, pio4 = 0x1.921fb6p-1, invpio2 = 6.36619772367581382433e-01, pio2_1 = 1.57079631090164184570e+00, pio2_1t = 1.58932547735281966916e-08; union {float f; uint32_t i;} u = {x}; double tx[1], ty[1], fn; UINT32 ix; int n, sign, e0; ix = u.i & 0x7fffffff; /* 25+53 bit pi is good enough for medium size */ if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ /* Use a specialized rint() to get fn. */ fn = fp_barrier(x * invpio2 + toint) - toint; n = (int)fn; *y = x - fn * pio2_1 - fn * pio2_1t; /* Matters with directed rounding. */ if (*y < -pio4) { n--; fn--; *y = x - fn * pio2_1 - fn * pio2_1t; } else if (*y > pio4) { n++; fn++; *y = x - fn * pio2_1 - fn * pio2_1t; } return n; } if(ix >= 0x7f800000) { /* x is inf or NaN */ *y = x - x; return 0; } /* scale x into [2^23, 2^24-1] */ sign = u.i >> 31; e0 = (ix >> 23) - (0x7f + 23); /* e0 = ilogb(|x|)-23, positive */ u.i = ix - (e0 << 23); tx[0] = u.f; n = __rem_pio2_large(tx, ty, e0, 1, 0); if (sign) { *y = -ty[0]; return -n; } *y = ty[0]; return n; } /********************************************************************* * cosf (MSVCRT.@) * * Copied from musl: src/math/cosf.c */ float CDECL cosf( float x ) { static const double c1pio2 = 1*M_PI_2, c2pio2 = 2*M_PI_2, c3pio2 = 3*M_PI_2, c4pio2 = 4*M_PI_2; double y; UINT32 ix; unsigned n, sign; ix = *(UINT32*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if (ix < 0x39800000) { /* |x| < 2**-12 */ /* raise inexact if x != 0 */ fp_barrierf(x + 0x1p120f); return 1.0f; } return __cosdf(x); } if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix > 0x4016cbe3) /* |x| ~> 3*pi/4 */ return -__cosdf(sign ? x + c2pio2 : x - c2pio2); else { if (sign) return __sindf(x + c1pio2); else return __sindf(c1pio2 - x); } } if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ if (ix > 0x40afeddf) /* |x| ~> 7*pi/4 */ return __cosdf(sign ? x + c4pio2 : x - c4pio2); else { if (sign) return __sindf(-x - c3pio2); else return __sindf(x - c3pio2); } } /* cos(Inf or NaN) is NaN */ if (isinf(x)) return math_error(_DOMAIN, "cosf", x, 0, x - x); if (ix >= 0x7f800000) return x - x; /* general argument reduction needed */ n = __rem_pio2f(x, &y); switch (n & 3) { case 0: return __cosdf(y); case 1: return __sindf(-y); case 2: return -__cosdf(y); default: return __sindf(y); } } /* Copied from musl: src/math/__expo2f.c */ static float __expo2f(float x, float sign) { static const int k = 235; static const float kln2 = 0x1.45c778p+7f; float scale; *(UINT32*)&scale = (UINT32)(0x7f + k/2) << 23; return expf(x - kln2) * (sign * scale) * scale; } /********************************************************************* * coshf (MSVCRT.@) * * Copied from musl: src/math/coshf.c */ float CDECL coshf( float x ) { UINT32 ui = *(UINT32*)&x; UINT32 sign = ui & 0x80000000; float t; /* |x| */ ui &= 0x7fffffff; x = *(float*)&ui; /* |x| < log(2) */ if (ui < 0x3f317217) { if (ui < 0x3f800000 - (12 << 23)) { fp_barrierf(x + 0x1p120f); return 1; } t = __expm1f(x); return 1 + t * t / (2 * (1 + t)); } /* |x| < log(FLT_MAX) */ if (ui < 0x42b17217) { t = expf(x); return 0.5f * (t + 1 / t); } /* |x| > log(FLT_MAX) or nan */ if (ui > 0x7f800000) *(UINT32*)&t = ui | sign | 0x400000; else t = __expo2f(x, 1.0f); return t; } /********************************************************************* * expf (MSVCRT.@) */ float CDECL expf( float x ) { static const double C[] = { 0x1.c6af84b912394p-5 / (1 << 5) / (1 << 5) / (1 << 5), 0x1.ebfce50fac4f3p-3 / (1 << 5) / (1 << 5), 0x1.62e42ff0c52d6p-1 / (1 << 5) }; static const double invln2n = 0x1.71547652b82fep+0 * (1 << 5); double kd, z, r, r2, y, s; UINT32 abstop; UINT64 ki, t; abstop = (*(UINT32*)&x >> 20) & 0x7ff; if (abstop >= 0x42b) { /* |x| >= 88 or x is nan. */ if (*(UINT32*)&x == 0xff800000) return 0.0f; if (abstop >= 0x7f8) return x + x; if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ return math_error(_OVERFLOW, "expf", x, 0, x * FLT_MAX); if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ return math_error(_UNDERFLOW, "expf", x, 0, fp_barrierf(FLT_MIN) * FLT_MIN); } /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ z = invln2n * x; /* Round and convert z to int, the result is in [-150*N, 128*N] and ideally ties-to-even rule is used, otherwise the magnitude of r can be bigger which gives larger approximation error. */ kd = __round(z); ki = (INT64)kd; r = z - kd; /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ t = exp2f_T[ki % (1 << 5)]; t += ki << (52 - 5); s = *(double*)&t; z = C[0] * r + C[1]; r2 = r * r; y = C[2] * r + 1; y = z * r2 + y; y = y * s; return y; } /********************************************************************* * fmodf (MSVCRT.@) * * Copied from musl: src/math/fmodf.c */ float CDECL fmodf( float x, float y ) { UINT32 xi = *(UINT32*)&x; UINT32 yi = *(UINT32*)&y; int ex = xi>>23 & 0xff; int ey = yi>>23 & 0xff; UINT32 sx = xi & 0x80000000; UINT32 i; if (isinf(x)) return math_error(_DOMAIN, "fmodf", x, y, (x * y) / (x * y)); if (yi << 1 == 0 || isnan(y) || ex == 0xff) return (x * y) / (x * y); if (xi << 1 <= yi << 1) { if (xi << 1 == yi << 1) return 0 * x; return x; } /* normalize x and y */ if (!ex) { for (i = xi << 9; i >> 31 == 0; ex--, i <<= 1); xi <<= -ex + 1; } else { xi &= -1U >> 9; xi |= 1U << 23; } if (!ey) { for (i = yi << 9; i >> 31 == 0; ey--, i <<= 1); yi <<= -ey + 1; } else { yi &= -1U >> 9; yi |= 1U << 23; } /* x mod y */ for (; ex > ey; ex--) { i = xi - yi; if (i >> 31 == 0) { if (i == 0) return 0 * x; xi = i; } xi <<= 1; } i = xi - yi; if (i >> 31 == 0) { if (i == 0) return 0 * x; xi = i; } for (; xi>>23 == 0; xi <<= 1, ex--); /* scale result up */ if (ex > 0) { xi -= 1U << 23; xi |= (UINT32)ex << 23; } else { xi >>= -ex + 1; } xi |= sx; return *(float*)ξ } /********************************************************************* * logf (MSVCRT.@) * * Copied from musl: src/math/logf.c src/math/logf_data.c */ float CDECL logf( float x ) { static const double Ln2 = 0x1.62e42fefa39efp-1; static const double A[] = { -0x1.00ea348b88334p-2, 0x1.5575b0be00b6ap-2, -0x1.ffffef20a4123p-2 }; static const struct { double invc, logc; } T[] = { { 0x1.661ec79f8f3bep+0, -0x1.57bf7808caadep-2 }, { 0x1.571ed4aaf883dp+0, -0x1.2bef0a7c06ddbp-2 }, { 0x1.49539f0f010bp+0, -0x1.01eae7f513a67p-2 }, { 0x1.3c995b0b80385p+0, -0x1.b31d8a68224e9p-3 }, { 0x1.30d190c8864a5p+0, -0x1.6574f0ac07758p-3 }, { 0x1.25e227b0b8eap+0, -0x1.1aa2bc79c81p-3 }, { 0x1.1bb4a4a1a343fp+0, -0x1.a4e76ce8c0e5ep-4 }, { 0x1.12358f08ae5bap+0, -0x1.1973c5a611cccp-4 }, { 0x1.0953f419900a7p+0, -0x1.252f438e10c1ep-5 }, { 0x1p+0, 0x0p+0 }, { 0x1.e608cfd9a47acp-1, 0x1.aa5aa5df25984p-5 }, { 0x1.ca4b31f026aap-1, 0x1.c5e53aa362eb4p-4 }, { 0x1.b2036576afce6p-1, 0x1.526e57720db08p-3 }, { 0x1.9c2d163a1aa2dp-1, 0x1.bc2860d22477p-3 }, { 0x1.886e6037841edp-1, 0x1.1058bc8a07ee1p-2 }, { 0x1.767dcf5534862p-1, 0x1.4043057b6ee09p-2 } }; double z, r, r2, y, y0, invc, logc; UINT32 ix, iz, tmp; int k, i; ix = *(UINT32*)&x; /* Fix sign of zero with downward rounding when x==1. */ if (ix == 0x3f800000) return 0; if (ix - 0x00800000 >= 0x7f800000 - 0x00800000) { /* x < 0x1p-126 or inf or nan. */ if (ix * 2 == 0) return math_error(_SING, "logf", x, 0, (ix & 0x80000000 ? 1.0 : -1.0) / x); if (ix == 0x7f800000) /* log(inf) == inf. */ return x; if (ix * 2 > 0xff000000) return x; if (ix & 0x80000000) return math_error(_DOMAIN, "logf", x, 0, (x - x) / (x - x)); /* x is subnormal, normalize it. */ x *= 0x1p23f; ix = *(UINT32*)&x; ix -= 23 << 23; } /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3f330000; i = (tmp >> (23 - 4)) % (1 << 4); k = (INT32)tmp >> 23; /* arithmetic shift */ iz = ix - (tmp & (0x1ffu << 23)); invc = T[i].invc; logc = T[i].logc; z = *(float*)&iz; /* log(x) = log1p(z/c-1) + log(c) + k*Ln2 */ r = z * invc - 1; y0 = logc + (double)k * Ln2; /* Pipelined polynomial evaluation to approximate log1p(r). */ r2 = r * r; y = A[1] * r + A[2]; y = A[0] * r2 + y; y = y * r2 + (y0 + r); return y; } /********************************************************************* * log10f (MSVCRT.@) */ float CDECL log10f( float x ) { static const float ivln10hi = 4.3432617188e-01, ivln10lo = -3.1689971365e-05, log10_2hi = 3.0102920532e-01, log10_2lo = 7.9034151668e-07, Lg1 = 0xaaaaaa.0p-24, Lg2 = 0xccce13.0p-25, Lg3 = 0x91e9ee.0p-25, Lg4 = 0xf89e26.0p-26; union {float f; UINT32 i;} u = {x}; float hfsq, f, s, z, R, w, t1, t2, dk, hi, lo; UINT32 ix; int k; ix = u.i; k = 0; if (ix < 0x00800000 || ix >> 31) { /* x < 2**-126 */ if (ix << 1 == 0) return math_error(_SING, "log10f", x, 0, -1 / (x * x)); if ((ix & ~(1u << 31)) > 0x7f800000) return x; if (ix >> 31) return math_error(_DOMAIN, "log10f", x, 0, (x - x) / (x - x)); /* subnormal number, scale up x */ k -= 25; x *= 0x1p25f; u.f = x; ix = u.i; } else if (ix >= 0x7f800000) { return x; } else if (ix == 0x3f800000) return 0; /* reduce x into [sqrt(2)/2, sqrt(2)] */ ix += 0x3f800000 - 0x3f3504f3; k += (int)(ix >> 23) - 0x7f; ix = (ix & 0x007fffff) + 0x3f3504f3; u.i = ix; x = u.f; f = x - 1.0f; s = f / (2.0f + f); z = s * s; w = z * z; t1= w * (Lg2 + w * Lg4); t2= z * (Lg1 + w * Lg3); R = t2 + t1; hfsq = 0.5f * f * f; hi = f - hfsq; u.f = hi; u.i &= 0xfffff000; hi = u.f; lo = f - hi - hfsq + s * (hfsq + R); dk = k; return dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi + hi * ivln10hi + dk * log10_2hi; } /* Subnormal input is normalized so ix has negative biased exponent. Output is multiplied by POWF_SCALE (where 1 << 5). */ static double powf_log2(UINT32 ix) { static const struct { double invc, logc; } T[] = { { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * (1 << 5) }, { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * (1 << 5) }, { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * (1 << 5) }, { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * (1 << 5) }, { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * (1 << 5) }, { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * (1 << 5) }, { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * (1 << 5) }, { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * (1 << 5) }, { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * (1 << 5) }, { 0x1p+0, 0x0p+0 * (1 << 4) }, { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * (1 << 5) }, { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * (1 << 5) }, { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * (1 << 5) }, { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * (1 << 5) }, { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * (1 << 5) }, { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * (1 << 5) } }; static const double A[] = { 0x1.27616c9496e0bp-2 * (1 << 5), -0x1.71969a075c67ap-2 * (1 << 5), 0x1.ec70a6ca7baddp-2 * (1 << 5), -0x1.7154748bef6c8p-1 * (1 << 5), 0x1.71547652ab82bp0 * (1 << 5) }; double z, r, r2, r4, p, q, y, y0, invc, logc; UINT32 iz, top, tmp; int k, i; /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3f330000; i = (tmp >> (23 - 4)) % (1 << 4); top = tmp & 0xff800000; iz = ix - top; k = (INT32)top >> (23 - 5); /* arithmetic shift */ invc = T[i].invc; logc = T[i].logc; z = *(float*)&iz; /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ r = z * invc - 1; y0 = logc + (double)k; /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ r2 = r * r; y = A[0] * r + A[1]; p = A[2] * r + A[3]; r4 = r2 * r2; q = A[4] * r + y0; q = p * r2 + q; y = y * r4 + q; return y; } /* The output of log2 and thus the input of exp2 is either scaled by N (in case of fast toint intrinsics) or not. The unscaled xd must be in [-1021,1023], sign_bias sets the sign of the result. */ static float powf_exp2(double xd, UINT32 sign_bias) { static const double C[] = { 0x1.c6af84b912394p-5 / (1 << 5) / (1 << 5) / (1 << 5), 0x1.ebfce50fac4f3p-3 / (1 << 5) / (1 << 5), 0x1.62e42ff0c52d6p-1 / (1 << 5) }; UINT64 ki, ski, t; double kd, z, r, r2, y, s; /* N*x = k + r with r in [-1/2, 1/2] */ kd = __round(xd); /* k */ ki = (INT64)kd; r = xd - kd; /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ t = exp2f_T[ki % (1 << 5)]; ski = ki + sign_bias; t += ski << (52 - 5); s = *(double*)&t; z = C[0] * r + C[1]; r2 = r * r; y = C[2] * r + 1; y = z * r2 + y; y = y * s; return y; } /* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is the bit representation of a non-zero finite floating-point value. */ static int powf_checkint(UINT32 iy) { int e = iy >> 23 & 0xff; if (e < 0x7f) return 0; if (e > 0x7f + 23) return 2; if (iy & ((1 << (0x7f + 23 - e)) - 1)) return 0; if (iy & (1 << (0x7f + 23 - e))) return 1; return 2; } /********************************************************************* * powf (MSVCRT.@) * * Copied from musl: src/math/powf.c src/math/powf_data.c */ float CDECL powf( float x, float y ) { UINT32 sign_bias = 0; UINT32 ix, iy; double logx, ylogx; ix = *(UINT32*)&x; iy = *(UINT32*)&y; if (ix - 0x00800000 >= 0x7f800000 - 0x00800000 || 2 * iy - 1 >= 2u * 0x7f800000 - 1) { /* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */ if (2 * iy - 1 >= 2u * 0x7f800000 - 1) { if (2 * iy == 0) return 1.0f; if (ix == 0x3f800000) return 1.0f; if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000) return x + y; if (2 * ix == 2 * 0x3f800000) return 1.0f; if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000)) return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ return y * y; } if (2 * ix - 1 >= 2u * 0x7f800000 - 1) { float x2 = x * x; if (ix & 0x80000000 && powf_checkint(iy) == 1) x2 = -x2; if (iy & 0x80000000 && x2 == 0.0) return math_error(_SING, "powf", x, y, 1 / x2); /* Without the barrier some versions of clang hoist the 1/x2 and thus division by zero exception can be signaled spuriously. */ return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2; } /* x and y are non-zero finite. */ if (ix & 0x80000000) { /* Finite x < 0. */ int yint = powf_checkint(iy); if (yint == 0) return math_error(_DOMAIN, "powf", x, y, 0 / (x - x)); if (yint == 1) sign_bias = 1 << (5 + 11); ix &= 0x7fffffff; } if (ix < 0x00800000) { /* Normalize subnormal x so exponent becomes negative. */ x *= 0x1p23f; ix = *(UINT32*)&x; ix &= 0x7fffffff; ix -= 23 << 23; } } logx = powf_log2(ix); ylogx = y * logx; /* cannot overflow, y is single prec. */ if ((*(UINT64*)&ylogx >> 47 & 0xffff) >= 0x40af800000000000llu >> 47) { /* |y*log(x)| >= 126. */ if (ylogx > 0x1.fffffffd1d571p+6 * (1 << 5)) return math_error(_OVERFLOW, "powf", x, y, (sign_bias ? -1.0 : 1.0) * 0x1p1023); if (ylogx <= -150.0 * (1 << 5)) return math_error(_UNDERFLOW, "powf", x, y, (sign_bias ? -1.0 : 1.0) / 0x1p1023); } return powf_exp2(ylogx, sign_bias); } /********************************************************************* * sinf (MSVCRT.@) * * Copied from musl: src/math/sinf.c */ float CDECL sinf( float x ) { static const double s1pio2 = 1*M_PI_2, s2pio2 = 2*M_PI_2, s3pio2 = 3*M_PI_2, s4pio2 = 4*M_PI_2; double y; UINT32 ix; int n, sign; ix = *(UINT32*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if (ix < 0x39800000) { /* |x| < 2**-12 */ /* raise inexact if x!=0 and underflow if subnormal */ fp_barrierf(ix < 0x00800000 ? x / 0x1p120f : x + 0x1p120f); return x; } return __sindf(x); } if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix <= 0x4016cbe3) { /* |x| ~<= 3pi/4 */ if (sign) return -__cosdf(x + s1pio2); else return __cosdf(x - s1pio2); } return __sindf(sign ? -(x + s2pio2) : -(x - s2pio2)); } if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ if (ix <= 0x40afeddf) { /* |x| ~<= 7*pi/4 */ if (sign) return __cosdf(x + s3pio2); else return -__cosdf(x - s3pio2); } return __sindf(sign ? x + s4pio2 : x - s4pio2); } /* sin(Inf or NaN) is NaN */ if (isinf(x)) return math_error(_DOMAIN, "sinf", x, 0, x - x); if (ix >= 0x7f800000) return x - x; /* general argument reduction needed */ n = __rem_pio2f(x, &y); switch (n&3) { case 0: return __sindf(y); case 1: return __cosdf(y); case 2: return __sindf(-y); default: return -__cosdf(y); } } /********************************************************************* * sinhf (MSVCRT.@) */ float CDECL sinhf( float x ) { UINT32 ui = *(UINT32*)&x; float t, h, absx; h = 0.5; if (ui >> 31) h = -h; /* |x| */ ui &= 0x7fffffff; absx = *(float*)&ui; /* |x| < log(FLT_MAX) */ if (ui < 0x42b17217) { t = __expm1f(absx); if (ui < 0x3f800000) { if (ui < 0x3f800000 - (12 << 23)) return x; return h * (2 * t - t * t / (t + 1)); } return h * (t + t / (t + 1)); } /* |x| > logf(FLT_MAX) or nan */ if (ui > 0x7f800000) *(DWORD*)&t = *(DWORD*)&x | 0x400000; else t = __expo2f(absx, 2 * h); return t; } static BOOL sqrtf_validate( float *x ) { short c = _fdclass(*x); if (c == FP_ZERO) return FALSE; if (c == FP_NAN) return FALSE; if (signbit(*x)) { *x = math_error(_DOMAIN, "sqrtf", *x, 0, ret_nan(TRUE)); return FALSE; } if (c == FP_INFINITE) return FALSE; return TRUE; } #if defined(__x86_64__) || defined(__i386__) float CDECL sse2_sqrtf(float); __ASM_GLOBAL_FUNC( sse2_sqrtf, "sqrtss %xmm0, %xmm0\n\t" "ret" ) #endif /********************************************************************* * sqrtf (MSVCRT.@) * * Copied from musl: src/math/sqrtf.c */ float CDECL sqrtf( float x ) { #ifdef __x86_64__ if (!sqrtf_validate(&x)) return x; return sse2_sqrtf(x); #else static const float tiny = 1.0e-30; float z; int ix,s,q,m,t,i; unsigned int r; ix = *(int*)&x; if (!sqrtf_validate(&x)) return x; /* normalize x */ m = ix >> 23; if (m == 0) { /* subnormal x */ for (i = 0; (ix & 0x00800000) == 0; i++) ix <<= 1; m -= i - 1; } m -= 127; /* unbias exponent */ ix = (ix & 0x007fffff) | 0x00800000; if (m & 1) /* odd m, double x to make it even */ ix += ix; m >>= 1; /* m = [m/2] */ /* generate sqrt(x) bit by bit */ ix += ix; q = s = 0; /* q = sqrt(x) */ r = 0x01000000; /* r = moving bit from right to left */ while (r != 0) { t = s + r; if (t <= ix) { s = t + r; ix -= t; q += r; } ix += ix; r >>= 1; } /* use floating add to find out rounding direction */ if (ix != 0) { z = 1.0f - tiny; /* raise inexact flag */ if (z >= 1.0f) { z = 1.0f + tiny; if (z > 1.0f) q += 2; else q += q & 1; } } ix = (q >> 1) + 0x3f000000; r = ix + ((unsigned int)m << 23); z = *(float*)&r; return z; #endif } /* Copied from musl: src/math/__tandf.c */ static float __tandf(double x, int odd) { static const double T[] = { 0x15554d3418c99f.0p-54, 0x1112fd38999f72.0p-55, 0x1b54c91d865afe.0p-57, 0x191df3908c33ce.0p-58, 0x185dadfcecf44e.0p-61, 0x1362b9bf971bcd.0p-59, }; double z, r, w, s, t, u; z = x * x; r = T[4] + z * T[5]; t = T[2] + z * T[3]; w = z * z; s = z * x; u = T[0] + z * T[1]; r = (x + s * u) + (s * w) * (t + w * r); return odd ? -1.0 / r : r; } /********************************************************************* * tanf (MSVCRT.@) * * Copied from musl: src/math/tanf.c */ float CDECL tanf( float x ) { static const double t1pio2 = 1*M_PI_2, t2pio2 = 2*M_PI_2, t3pio2 = 3*M_PI_2, t4pio2 = 4*M_PI_2; double y; UINT32 ix; unsigned n, sign; ix = *(UINT32*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix <= 0x3f490fda) { /* |x| ~<= pi/4 */ if (ix < 0x39800000) { /* |x| < 2**-12 */ /* raise inexact if x!=0 and underflow if subnormal */ fp_barrierf(ix < 0x00800000 ? x / 0x1p120f : x + 0x1p120f); return x; } return __tandf(x, 0); } if (ix <= 0x407b53d1) { /* |x| ~<= 5*pi/4 */ if (ix <= 0x4016cbe3) /* |x| ~<= 3pi/4 */ return __tandf((sign ? x + t1pio2 : x - t1pio2), 1); else return __tandf((sign ? x + t2pio2 : x - t2pio2), 0); } if (ix <= 0x40e231d5) { /* |x| ~<= 9*pi/4 */ if (ix <= 0x40afeddf) /* |x| ~<= 7*pi/4 */ return __tandf((sign ? x + t3pio2 : x - t3pio2), 1); else return __tandf((sign ? x + t4pio2 : x - t4pio2), 0); } /* tan(Inf or NaN) is NaN */ if (isinf(x)) return math_error(_DOMAIN, "tanf", x, 0, x - x); if (ix >= 0x7f800000) return x - x; /* argument reduction */ n = __rem_pio2f(x, &y); return __tandf(y, n & 1); } /********************************************************************* * tanhf (MSVCRT.@) */ float CDECL tanhf( float x ) { UINT32 ui = *(UINT32*)&x; UINT32 sign = ui & 0x80000000; float t; /* x = |x| */ ui &= 0x7fffffff; x = *(float*)&ui; if (ui > 0x3f0c9f54) { /* |x| > log(3)/2 ~= 0.5493 or nan */ if (ui > 0x41200000) { if (ui > 0x7f800000) { *(UINT32*)&x = ui | sign | 0x400000; #if _MSVCR_VER < 140 return math_error(_DOMAIN, "tanhf", x, 0, x); #else return x; #endif } /* |x| > 10 */ fp_barrierf(x + 0x1p120f); t = 1 + 0 / x; } else { t = __expm1f(2 * x); t = 1 - 2 / (t + 2); } } else if (ui > 0x3e82c578) { /* |x| > log(5/3)/2 ~= 0.2554 */ t = __expm1f(2 * x); t = t / (t + 2); } else if (ui >= 0x00800000) { /* |x| >= 0x1p-126 */ t = __expm1f(-2 * x); t = -t / (t + 2); } else { /* |x| is subnormal */ fp_barrierf(x * x); t = x; } return sign ? -t : t; } /********************************************************************* * ceilf (MSVCRT.@) * * Copied from musl: src/math/ceilf.c */ float CDECL ceilf( float x ) { union {float f; UINT32 i;} u = {x}; int e = (int)(u.i >> 23 & 0xff) - 0x7f; UINT32 m; if (e >= 23) return x; if (e >= 0) { m = 0x007fffff >> e; if ((u.i & m) == 0) return x; if (u.i >> 31 == 0) u.i += m; u.i &= ~m; } else { if (u.i >> 31) return -0.0; else if (u.i << 1) return 1.0; } return u.f; } /********************************************************************* * floorf (MSVCRT.@) * * Copied from musl: src/math/floorf.c */ float CDECL floorf( float x ) { union {float f; UINT32 i;} u = {x}; int e = (int)(u.i >> 23 & 0xff) - 0x7f; UINT32 m; if (e >= 23) return x; if (e >= 0) { m = 0x007fffff >> e; if ((u.i & m) == 0) return x; if (u.i >> 31) u.i += m; u.i &= ~m; } else { if (u.i >> 31 == 0) return 0; else if (u.i << 1) return -1; } return u.f; } /********************************************************************* * frexpf (MSVCRT.@) * * Copied from musl: src/math/frexpf.c */ float CDECL frexpf( float x, int *e ) { UINT32 ux = *(UINT32*)&x; int ee = ux >> 23 & 0xff; if (!ee) { if (x) { x = frexpf(x * 0x1p64, e); *e -= 64; } else *e = 0; return x; } else if (ee == 0xff) { return x; } *e = ee - 0x7e; ux &= 0x807ffffful; ux |= 0x3f000000ul; return *(float*)&ux; } /********************************************************************* * modff (MSVCRT.@) * * Copied from musl: src/math/modff.c */ float CDECL modff( float x, float *iptr ) { union {float f; UINT32 i;} u = {x}; UINT32 mask; int e = (u.i >> 23 & 0xff) - 0x7f; /* no fractional part */ if (e >= 23) { *iptr = x; if (e == 0x80 && u.i << 9 != 0) { /* nan */ return x; } u.i &= 0x80000000; return u.f; } /* no integral part */ if (e < 0) { u.i &= 0x80000000; *iptr = u.f; return x; } mask = 0x007fffff >> e; if ((u.i & mask) == 0) { *iptr = x; u.i &= 0x80000000; return u.f; } u.i &= ~mask; *iptr = u.f; return x - u.f; } #endif #if !defined(__i386__) && !defined(__x86_64__) && (_MSVCR_VER == 0 || _MSVCR_VER >= 110) /********************************************************************* * fabsf (MSVCRT.@) * * Copied from musl: src/math/fabsf.c */ float CDECL fabsf( float x ) { union { float f; UINT32 i; } u = { x }; u.i &= 0x7fffffff; return u.f; } #endif /********************************************************************* * acos (MSVCRT.@) * * Copied from musl: src/math/acos.c */ static double acos_R(double z) { static const double pS0 = 1.66666666666666657415e-01, pS1 = -3.25565818622400915405e-01, pS2 = 2.01212532134862925881e-01, pS3 = -4.00555345006794114027e-02, pS4 = 7.91534994289814532176e-04, pS5 = 3.47933107596021167570e-05, qS1 = -2.40339491173441421878e+00, qS2 = 2.02094576023350569471e+00, qS3 = -6.88283971605453293030e-01, qS4 = 7.70381505559019352791e-02; double p, q; p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); return p/q; } double CDECL acos( double x ) { static const double pio2_hi = 1.57079632679489655800e+00, pio2_lo = 6.12323399573676603587e-17; double z, w, s, c, df; unsigned int hx, ix; ULONGLONG llx; hx = *(ULONGLONG*)&x >> 32; ix = hx & 0x7fffffff; /* |x| >= 1 or nan */ if (ix >= 0x3ff00000) { unsigned int lx; lx = *(ULONGLONG*)&x; if (((ix - 0x3ff00000) | lx) == 0) { /* acos(1)=0, acos(-1)=pi */ if (hx >> 31) return 2 * pio2_hi + 7.5231638452626401e-37; return 0; } if (isnan(x)) return x; return math_error(_DOMAIN, "acos", x, 0, 0 / (x - x)); } /* |x| < 0.5 */ if (ix < 0x3fe00000) { if (ix <= 0x3c600000) /* |x| < 2**-57 */ return pio2_hi + 7.5231638452626401e-37; return pio2_hi - (x - (pio2_lo - x * acos_R(x * x))); } /* x < -0.5 */ if (hx >> 31) { z = (1.0 + x) * 0.5; s = sqrt(z); w = acos_R(z) * s - pio2_lo; return 2 * (pio2_hi - (s + w)); } /* x > 0.5 */ z = (1.0 - x) * 0.5; s = sqrt(z); df = s; llx = (*(ULONGLONG*)&df >> 32) << 32; df = *(double*)&llx; c = (z - df * df) / (s + df); w = acos_R(z) * s + c; return 2 * (df + w); } /********************************************************************* * asin (MSVCRT.@) * * Copied from musl: src/math/asin.c */ static double asin_R(double z) { /* coefficients for R(x^2) */ static const double pS0 = 1.66666666666666657415e-01, pS1 = -3.25565818622400915405e-01, pS2 = 2.01212532134862925881e-01, pS3 = -4.00555345006794114027e-02, pS4 = 7.91534994289814532176e-04, pS5 = 3.47933107596021167570e-05, qS1 = -2.40339491173441421878e+00, qS2 = 2.02094576023350569471e+00, qS3 = -6.88283971605453293030e-01, qS4 = 7.70381505559019352791e-02; double p, q; p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5))))); q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4))); return p / q; } #ifdef __i386__ double CDECL x87_asin(double); __ASM_GLOBAL_FUNC( x87_asin, "fldl 4(%esp)\n\t" SET_X87_CW(~0x37f) "fld %st\n\t" "fld1\n\t" "fsubp\n\t" "fld1\n\t" "fadd %st(2)\n\t" "fmulp\n\t" "fsqrt\n\t" "fpatan\n\t" RESET_X87_CW "ret" ) #endif double CDECL asin( double x ) { static const double pio2_hi = 1.57079632679489655800e+00, pio2_lo = 6.12323399573676603587e-17; double z, r, s; unsigned int hx, ix; ULONGLONG llx; #ifdef __i386__ unsigned int x87_cw, sse2_cw; #endif hx = *(ULONGLONG*)&x >> 32; ix = hx & 0x7fffffff; /* |x| >= 1 or nan */ if (ix >= 0x3ff00000) { unsigned int lx; lx = *(ULONGLONG*)&x; if (((ix - 0x3ff00000) | lx) == 0) /* asin(1) = +-pi/2 with inexact */ return x * pio2_hi + 7.5231638452626401e-37; if (isnan(x)) { #ifdef __i386__ return math_error(_DOMAIN, "asin", x, 0, x); #else return x; #endif } return math_error(_DOMAIN, "asin", x, 0, 0 / (x - x)); } #ifdef __i386__ __control87_2(0, 0, &x87_cw, &sse2_cw); if (!sse2_enabled || (x87_cw & _MCW_EM) != _MCW_EM || (sse2_cw & (_MCW_EM | _MCW_RC)) != _MCW_EM) return x87_asin(x); #endif /* |x| < 0.5 */ if (ix < 0x3fe00000) { /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ if (ix < 0x3e500000 && ix >= 0x00100000) return x; return x + x * asin_R(x * x); } /* 1 > |x| >= 0.5 */ z = (1 - fabs(x)) * 0.5; s = sqrt(z); r = asin_R(z); if (ix >= 0x3fef3333) { /* if |x| > 0.975 */ x = pio2_hi - (2 * (s + s * r) - pio2_lo); } else { double f, c; /* f+c = sqrt(z) */ f = s; llx = (*(ULONGLONG*)&f >> 32) << 32; f = *(double*)&llx; c = (z - f * f) / (s + f); x = 0.5 * pio2_hi - (2 * s * r - (pio2_lo - 2 * c) - (0.5 * pio2_hi - 2 * f)); } if (hx >> 31) return -x; return x; } /********************************************************************* * atan (MSVCRT.@) * * Copied from musl: src/math/atan.c */ double CDECL atan( double x ) { static const double atanhi[] = { 4.63647609000806093515e-01, 7.85398163397448278999e-01, 9.82793723247329054082e-01, 1.57079632679489655800e+00, }; static const double atanlo[] = { 2.26987774529616870924e-17, 3.06161699786838301793e-17, 1.39033110312309984516e-17, 6.12323399573676603587e-17, }; static const double aT[] = { 3.33333333333329318027e-01, -1.99999999998764832476e-01, 1.42857142725034663711e-01, -1.11111104054623557880e-01, 9.09088713343650656196e-02, -7.69187620504482999495e-02, 6.66107313738753120669e-02, -5.83357013379057348645e-02, 4.97687799461593236017e-02, -3.65315727442169155270e-02, 1.62858201153657823623e-02, }; double w, s1, s2, z; unsigned int ix, sign; int id; #if _MSVCR_VER == 0 if (isnan(x)) return math_error(_DOMAIN, "atan", x, 0, x); #endif ix = *(ULONGLONG*)&x >> 32; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x44100000) { /* if |x| >= 2^66 */ if (isnan(x)) return x; z = atanhi[3] + 7.5231638452626401e-37; return sign ? -z : z; } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ if (ix < 0x3e400000) { /* |x| < 2^-27 */ if (ix < 0x00100000) /* raise underflow for subnormal x */ fp_barrierf((float)x); return x; } id = -1; } else { x = fabs(x); if (ix < 0x3ff30000) { /* |x| < 1.1875 */ if (ix < 0x3fe60000) { /* 7/16 <= |x| < 11/16 */ id = 0; x = (2.0 * x - 1.0) / (2.0 + x); } else { /* 11/16 <= |x| < 19/16 */ id = 1; x = (x - 1.0) / (x + 1.0); } } else { if (ix < 0x40038000) { /* |x| < 2.4375 */ id = 2; x = (x - 1.5) / (1.0 + 1.5 * x); } else { /* 2.4375 <= |x| < 2^66 */ id = 3; x = -1.0 / x; } } } /* end of argument reduction */ z = x * x; w = z * z; /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ s1 = z * (aT[0] + w * (aT[2] + w * (aT[4] + w * (aT[6] + w * (aT[8] + w * aT[10]))))); s2 = w * (aT[1] + w * (aT[3] + w * (aT[5] + w * (aT[7] + w * aT[9])))); if (id < 0) return x - x * (s1 + s2); z = atanhi[id] - (x * (s1 + s2) - atanlo[id] - x); return sign ? -z : z; } /********************************************************************* * atan2 (MSVCRT.@) * * Copied from musl: src/math/atan2.c */ double CDECL atan2( double y, double x ) { static const double pi = 3.1415926535897931160E+00, pi_lo = 1.2246467991473531772E-16; double z; unsigned int m, lx, ly, ix, iy; if (isnan(x) || isnan(y)) return x+y; ix = *(ULONGLONG*)&x >> 32; lx = *(ULONGLONG*)&x; iy = *(ULONGLONG*)&y >> 32; ly = *(ULONGLONG*)&y; if (((ix - 0x3ff00000) | lx) == 0) /* x = 1.0 */ return atan(y); m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */ ix = ix & 0x7fffffff; iy = iy & 0x7fffffff; /* when y = 0 */ if ((iy | ly) == 0) { switch(m) { case 0: case 1: return y; /* atan(+-0,+anything)=+-0 */ case 2: return pi; /* atan(+0,-anything) = pi */ case 3: return -pi; /* atan(-0,-anything) =-pi */ } } /* when x = 0 */ if ((ix | lx) == 0) return m & 1 ? -pi / 2 : pi / 2; /* when x is INF */ if (ix == 0x7ff00000) { if (iy == 0x7ff00000) { switch(m) { case 0: return pi / 4; /* atan(+INF,+INF) */ case 1: return -pi / 4; /* atan(-INF,+INF) */ case 2: return 3 * pi / 4; /* atan(+INF,-INF) */ case 3: return -3 * pi / 4; /* atan(-INF,-INF) */ } } else { switch(m) { case 0: return 0.0; /* atan(+...,+INF) */ case 1: return -0.0; /* atan(-...,+INF) */ case 2: return pi; /* atan(+...,-INF) */ case 3: return -pi; /* atan(-...,-INF) */ } } } /* |y/x| > 0x1p64 */ if (ix + (64 << 20) < iy || iy == 0x7ff00000) return m & 1 ? -pi / 2 : pi / 2; /* z = atan(|y/x|) without spurious underflow */ if ((m & 2) && iy + (64 << 20) < ix) /* |y/x| < 0x1p-64, x<0 */ z = 0; else z = atan(fabs(y / x)); switch (m) { case 0: return z; /* atan(+,+) */ case 1: return -z; /* atan(-,+) */ case 2: return pi - (z - pi_lo); /* atan(+,-) */ default: /* case 3 */ return (z - pi_lo) - pi; /* atan(-,-) */ } } /* Copied from musl: src/math/rint.c */ static double __rint(double x) { static const double toint = 1 / DBL_EPSILON; ULONGLONG llx = *(ULONGLONG*)&x; int e = llx >> 52 & 0x7ff; int s = llx >> 63; unsigned cw; double y; if (e >= 0x3ff+52) return x; cw = _controlfp(0, 0); if ((cw & _MCW_PC) != _PC_53) _controlfp(_PC_53, _MCW_PC); if (s) y = fp_barrier(x - toint) + toint; else y = fp_barrier(x + toint) - toint; if ((cw & _MCW_PC) != _PC_53) _controlfp(cw, _MCW_PC); if (y == 0) return s ? -0.0 : 0; return y; } /* Copied from musl: src/math/__rem_pio2.c */ static int __rem_pio2(double x, double *y) { static const double pio4 = 0x1.921fb54442d18p-1, invpio2 = 6.36619772367581382433e-01, pio2_1 = 1.57079632673412561417e+00, pio2_1t = 6.07710050650619224932e-11, pio2_2 = 6.07710050630396597660e-11, pio2_2t = 2.02226624879595063154e-21, pio2_3 = 2.02226624871116645580e-21, pio2_3t = 8.47842766036889956997e-32; union {double f; UINT64 i;} u = {x}; double z, w, t, r, fn, tx[3], ty[2]; UINT32 ix; int sign, n, ex, ey, i; sign = u.i >> 63; ix = u.i >> 32 & 0x7fffffff; if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ goto medium; /* cancellation -- use medium case */ if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ if (!sign) { z = x - pio2_1; /* one round good to 85 bits */ y[0] = z - pio2_1t; y[1] = (z - y[0]) - pio2_1t; return 1; } else { z = x + pio2_1; y[0] = z + pio2_1t; y[1] = (z - y[0]) + pio2_1t; return -1; } } else { if (!sign) { z = x - 2 * pio2_1; y[0] = z - 2 * pio2_1t; y[1] = (z - y[0]) - 2 * pio2_1t; return 2; } else { z = x + 2 * pio2_1; y[0] = z + 2 * pio2_1t; y[1] = (z - y[0]) + 2 * pio2_1t; return -2; } } } if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ goto medium; if (!sign) { z = x - 3 * pio2_1; y[0] = z - 3 * pio2_1t; y[1] = (z - y[0]) - 3 * pio2_1t; return 3; } else { z = x + 3 * pio2_1; y[0] = z + 3 * pio2_1t; y[1] = (z - y[0]) + 3 * pio2_1t; return -3; } } else { if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ goto medium; if (!sign) { z = x - 4 * pio2_1; y[0] = z - 4 * pio2_1t; y[1] = (z - y[0]) - 4 * pio2_1t; return 4; } else { z = x + 4 * pio2_1; y[0] = z + 4 * pio2_1t; y[1] = (z - y[0]) + 4 * pio2_1t; return -4; } } } if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ medium: fn = __rint(x * invpio2); n = (INT32)fn; r = x - fn * pio2_1; w = fn * pio2_1t; /* 1st round, good to 85 bits */ /* Matters with directed rounding. */ if (r - w < -pio4) { n--; fn--; r = x - fn * pio2_1; w = fn * pio2_1t; } else if (r - w > pio4) { n++; fn++; r = x - fn * pio2_1; w = fn * pio2_1t; } y[0] = r - w; u.f = y[0]; ey = u.i >> 52 & 0x7ff; ex = ix >> 20; if (ex - ey > 16) { /* 2nd round, good to 118 bits */ t = r; w = fn * pio2_2; r = t - w; w = fn * pio2_2t - ((t - r) - w); y[0] = r - w; u.f = y[0]; ey = u.i >> 52 & 0x7ff; if (ex - ey > 49) { /* 3rd round, good to 151 bits, covers all cases */ t = r; w = fn * pio2_3; r = t - w; w = fn * pio2_3t - ((t - r) - w); y[0] = r - w; } } y[1] = (r - y[0]) - w; return n; } /* * all other (large) arguments */ if (ix >= 0x7ff00000) { /* x is inf or NaN */ y[0] = y[1] = x - x; return 0; } /* set z = scalbn(|x|,-ilogb(x)+23) */ u.f = x; u.i &= (UINT64)-1 >> 12; u.i |= (UINT64)(0x3ff + 23) << 52; z = u.f; for (i = 0; i < 2; i++) { tx[i] = (double)(INT32)z; z = (z - tx[i]) * 0x1p24; } tx[i] = z; /* skip zero terms, first term is non-zero */ while (tx[i] == 0.0) i--; n = __rem_pio2_large(tx, ty, (int)(ix >> 20) - (0x3ff + 23), i + 1, 1); if (sign) { y[0] = -ty[0]; y[1] = -ty[1]; return -n; } y[0] = ty[0]; y[1] = ty[1]; return n; } /* Copied from musl: src/math/__sin.c */ static double __sin(double x, double y, int iy) { static const double S1 = -1.66666666666666324348e-01, S2 = 8.33333333332248946124e-03, S3 = -1.98412698298579493134e-04, S4 = 2.75573137070700676789e-06, S5 = -2.50507602534068634195e-08, S6 = 1.58969099521155010221e-10; double z, r, v, w; z = x * x; w = z * z; r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6); v = z * x; if (iy == 0) return x + v * (S1 + z * r); else return x - ((z * (0.5 * y - v * r) - y) - v * S1); } /* Copied from musl: src/math/__cos.c */ static double __cos(double x, double y) { static const double C1 = 4.16666666666666019037e-02, C2 = -1.38888888888741095749e-03, C3 = 2.48015872894767294178e-05, C4 = -2.75573143513906633035e-07, C5 = 2.08757232129817482790e-09, C6 = -1.13596475577881948265e-11; double hz, z, r, w; z = x * x; w = z * z; r = z * (C1 + z * (C2 + z * C3)) + w * w * (C4 + z * (C5 + z * C6)); hz = 0.5 * z; w = 1.0 - hz; return w + (((1.0 - w) - hz) + (z * r - x * y)); } /********************************************************************* * cos (MSVCRT.@) * * Copied from musl: src/math/cos.c */ double CDECL cos( double x ) { double y[2]; UINT32 ix; unsigned n; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; /* |x| ~< pi/4 */ if (ix <= 0x3fe921fb) { if (ix < 0x3e46a09e) { /* |x| < 2**-27 * sqrt(2) */ /* raise inexact if x!=0 */ fp_barrier(x + 0x1p120f); return 1.0; } return __cos(x, 0); } /* cos(Inf or NaN) is NaN */ if (isinf(x)) return math_error(_DOMAIN, "cos", x, 0, x - x); if (ix >= 0x7ff00000) return x - x; /* argument reduction */ n = __rem_pio2(x, y); switch (n & 3) { case 0: return __cos(y[0], y[1]); case 1: return -__sin(y[0], y[1], 1); case 2: return -__cos(y[0], y[1]); default: return __sin(y[0], y[1], 1); } } /* Copied from musl: src/math/expm1.c */ static double __expm1(double x) { static const double o_threshold = 7.09782712893383973096e+02, ln2_hi = 6.93147180369123816490e-01, ln2_lo = 1.90821492927058770002e-10, invln2 = 1.44269504088896338700e+00, Q1 = -3.33333333333331316428e-02, Q2 = 1.58730158725481460165e-03, Q3 = -7.93650757867487942473e-05, Q4 = 4.00821782732936239552e-06, Q5 = -2.01099218183624371326e-07; double y, hi, lo, c, t, e, hxs, hfx, r1, twopk; union {double f; UINT64 i;} u = {x}; UINT32 hx = u.i >> 32 & 0x7fffffff; int k, sign = u.i >> 63; /* filter out huge and non-finite argument */ if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ if (isnan(x)) return x; if (isinf(x)) return sign ? -1 : x; if (sign) return math_error(_UNDERFLOW, "exp", x, 0, -1); if (x > o_threshold) return math_error(_OVERFLOW, "exp", x, 0, x * 0x1p1023); } /* argument reduction */ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ if (!sign) { hi = x - ln2_hi; lo = ln2_lo; k = 1; } else { hi = x + ln2_hi; lo = -ln2_lo; k = -1; } } else { k = invln2 * x + (sign ? -0.5 : 0.5); t = k; hi = x - t * ln2_hi; /* t*ln2_hi is exact here */ lo = t * ln2_lo; } x = hi - lo; c = (hi - x) - lo; } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */ fp_barrier(x + 0x1p120f); if (hx < 0x00100000) fp_barrier((float)x); return x; } else k = 0; /* x is now in primary range */ hfx = 0.5 * x; hxs = x * hfx; r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5)))); t = 3.0 - r1 * hfx; e = hxs * ((r1 - t) / (6.0 - x * t)); if (k == 0) /* c is 0 */ return x - (x * e - hxs); e = x * (e - c) - c; e -= hxs; /* exp(x) ~ 2^k (x_reduced - e + 1) */ if (k == -1) return 0.5 * (x - e) - 0.5; if (k == 1) { if (x < -0.25) return -2.0 * (e - (x + 0.5)); return 1.0 + 2.0 * (x - e); } u.i = (UINT64)(0x3ff + k) << 52; /* 2^k */ twopk = u.f; if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ y = x - e + 1.0; if (k == 1024) y = y * 2.0 * 0x1p1023; else y = y * twopk; return y - 1.0; } u.i = (UINT64)(0x3ff - k) << 52; /* 2^-k */ if (k < 20) y = (x - e + (1 - u.f)) * twopk; else y = (x - (e + u.f) + 1) * twopk; return y; } static double __expo2(double x, double sign) { static const int k = 2043; static const double kln2 = 0x1.62066151add8bp+10; double scale; *(UINT64*)&scale = (UINT64)(0x3ff + k / 2) << 52; return exp(x - kln2) * (sign * scale) * scale; } /********************************************************************* * cosh (MSVCRT.@) * * Copied from musl: src/math/cosh.c */ double CDECL cosh( double x ) { UINT64 ux = *(UINT64*)&x; UINT64 sign = ux & 0x8000000000000000ULL; UINT32 w; double t; /* |x| */ ux &= (uint64_t)-1 / 2; x = *(double*)&ux; w = ux >> 32; /* |x| < log(2) */ if (w < 0x3fe62e42) { if (w < 0x3ff00000 - (26 << 20)) { fp_barrier(x + 0x1p120f); return 1; } t = __expm1(x); return 1 + t * t / (2 * (1 + t)); } /* |x| < log(DBL_MAX) */ if (w < 0x40862e42) { t = exp(x); /* note: if x>log(0x1p26) then the 1/t is not needed */ return 0.5 * (t + 1 / t); } /* |x| > log(DBL_MAX) or nan */ /* note: the result is stored to handle overflow */ if (ux > 0x7ff0000000000000ULL) *(UINT64*)&t = ux | sign | 0x0008000000000000ULL; else t = __expo2(x, 1.0); return t; } /* Copied from musl: src/math/exp_data.c */ static const UINT64 exp_T[] = { 0x0ULL, 0x3ff0000000000000ULL, 0x3c9b3b4f1a88bf6eULL, 0x3feff63da9fb3335ULL, 0xbc7160139cd8dc5dULL, 0x3fefec9a3e778061ULL, 0xbc905e7a108766d1ULL, 0x3fefe315e86e7f85ULL, 0x3c8cd2523567f613ULL, 0x3fefd9b0d3158574ULL, 0xbc8bce8023f98efaULL, 0x3fefd06b29ddf6deULL, 0x3c60f74e61e6c861ULL, 0x3fefc74518759bc8ULL, 0x3c90a3e45b33d399ULL, 0x3fefbe3ecac6f383ULL, 0x3c979aa65d837b6dULL, 0x3fefb5586cf9890fULL, 0x3c8eb51a92fdeffcULL, 0x3fefac922b7247f7ULL, 0x3c3ebe3d702f9cd1ULL, 0x3fefa3ec32d3d1a2ULL, 0xbc6a033489906e0bULL, 0x3fef9b66affed31bULL, 0xbc9556522a2fbd0eULL, 0x3fef9301d0125b51ULL, 0xbc5080ef8c4eea55ULL, 0x3fef8abdc06c31ccULL, 0xbc91c923b9d5f416ULL, 0x3fef829aaea92de0ULL, 0x3c80d3e3e95c55afULL, 0x3fef7a98c8a58e51ULL, 0xbc801b15eaa59348ULL, 0x3fef72b83c7d517bULL, 0xbc8f1ff055de323dULL, 0x3fef6af9388c8deaULL, 0x3c8b898c3f1353bfULL, 0x3fef635beb6fcb75ULL, 0xbc96d99c7611eb26ULL, 0x3fef5be084045cd4ULL, 0x3c9aecf73e3a2f60ULL, 0x3fef54873168b9aaULL, 0xbc8fe782cb86389dULL, 0x3fef4d5022fcd91dULL, 0x3c8a6f4144a6c38dULL, 0x3fef463b88628cd6ULL, 0x3c807a05b0e4047dULL, 0x3fef3f49917ddc96ULL, 0x3c968efde3a8a894ULL, 0x3fef387a6e756238ULL, 0x3c875e18f274487dULL, 0x3fef31ce4fb2a63fULL, 0x3c80472b981fe7f2ULL, 0x3fef2b4565e27cddULL, 0xbc96b87b3f71085eULL, 0x3fef24dfe1f56381ULL, 0x3c82f7e16d09ab31ULL, 0x3fef1e9df51fdee1ULL, 0xbc3d219b1a6fbffaULL, 0x3fef187fd0dad990ULL, 0x3c8b3782720c0ab4ULL, 0x3fef1285a6e4030bULL, 0x3c6e149289cecb8fULL, 0x3fef0cafa93e2f56ULL, 0x3c834d754db0abb6ULL, 0x3fef06fe0a31b715ULL, 0x3c864201e2ac744cULL, 0x3fef0170fc4cd831ULL, 0x3c8fdd395dd3f84aULL, 0x3feefc08b26416ffULL, 0xbc86a3803b8e5b04ULL, 0x3feef6c55f929ff1ULL, 0xbc924aedcc4b5068ULL, 0x3feef1a7373aa9cbULL, 0xbc9907f81b512d8eULL, 0x3feeecae6d05d866ULL, 0xbc71d1e83e9436d2ULL, 0x3feee7db34e59ff7ULL, 0xbc991919b3ce1b15ULL, 0x3feee32dc313a8e5ULL, 0x3c859f48a72a4c6dULL, 0x3feedea64c123422ULL, 0xbc9312607a28698aULL, 0x3feeda4504ac801cULL, 0xbc58a78f4817895bULL, 0x3feed60a21f72e2aULL, 0xbc7c2c9b67499a1bULL, 0x3feed1f5d950a897ULL, 0x3c4363ed60c2ac11ULL, 0x3feece086061892dULL, 0x3c9666093b0664efULL, 0x3feeca41ed1d0057ULL, 0x3c6ecce1daa10379ULL, 0x3feec6a2b5c13cd0ULL, 0x3c93ff8e3f0f1230ULL, 0x3feec32af0d7d3deULL, 0x3c7690cebb7aafb0ULL, 0x3feebfdad5362a27ULL, 0x3c931dbdeb54e077ULL, 0x3feebcb299fddd0dULL, 0xbc8f94340071a38eULL, 0x3feeb9b2769d2ca7ULL, 0xbc87deccdc93a349ULL, 0x3feeb6daa2cf6642ULL, 0xbc78dec6bd0f385fULL, 0x3feeb42b569d4f82ULL, 0xbc861246ec7b5cf6ULL, 0x3feeb1a4ca5d920fULL, 0x3c93350518fdd78eULL, 0x3feeaf4736b527daULL, 0x3c7b98b72f8a9b05ULL, 0x3feead12d497c7fdULL, 0x3c9063e1e21c5409ULL, 0x3feeab07dd485429ULL, 0x3c34c7855019c6eaULL, 0x3feea9268a5946b7ULL, 0x3c9432e62b64c035ULL, 0x3feea76f15ad2148ULL, 0xbc8ce44a6199769fULL, 0x3feea5e1b976dc09ULL, 0xbc8c33c53bef4da8ULL, 0x3feea47eb03a5585ULL, 0xbc845378892be9aeULL, 0x3feea34634ccc320ULL, 0xbc93cedd78565858ULL, 0x3feea23882552225ULL, 0x3c5710aa807e1964ULL, 0x3feea155d44ca973ULL, 0xbc93b3efbf5e2228ULL, 0x3feea09e667f3bcdULL, 0xbc6a12ad8734b982ULL, 0x3feea012750bdabfULL, 0xbc6367efb86da9eeULL, 0x3fee9fb23c651a2fULL, 0xbc80dc3d54e08851ULL, 0x3fee9f7df9519484ULL, 0xbc781f647e5a3ecfULL, 0x3fee9f75e8ec5f74ULL, 0xbc86ee4ac08b7db0ULL, 0x3fee9f9a48a58174ULL, 0xbc8619321e55e68aULL, 0x3fee9feb564267c9ULL, 0x3c909ccb5e09d4d3ULL, 0x3feea0694fde5d3fULL, 0xbc7b32dcb94da51dULL, 0x3feea11473eb0187ULL, 0x3c94ecfd5467c06bULL, 0x3feea1ed0130c132ULL, 0x3c65ebe1abd66c55ULL, 0x3feea2f336cf4e62ULL, 0xbc88a1c52fb3cf42ULL, 0x3feea427543e1a12ULL, 0xbc9369b6f13b3734ULL, 0x3feea589994cce13ULL, 0xbc805e843a19ff1eULL, 0x3feea71a4623c7adULL, 0xbc94d450d872576eULL, 0x3feea8d99b4492edULL, 0x3c90ad675b0e8a00ULL, 0x3feeaac7d98a6699ULL, 0x3c8db72fc1f0eab4ULL, 0x3feeace5422aa0dbULL, 0xbc65b6609cc5e7ffULL, 0x3feeaf3216b5448cULL, 0x3c7bf68359f35f44ULL, 0x3feeb1ae99157736ULL, 0xbc93091fa71e3d83ULL, 0x3feeb45b0b91ffc6ULL, 0xbc5da9b88b6c1e29ULL, 0x3feeb737b0cdc5e5ULL, 0xbc6c23f97c90b959ULL, 0x3feeba44cbc8520fULL, 0xbc92434322f4f9aaULL, 0x3feebd829fde4e50ULL, 0xbc85ca6cd7668e4bULL, 0x3feec0f170ca07baULL, 0x3c71affc2b91ce27ULL, 0x3feec49182a3f090ULL, 0x3c6dd235e10a73bbULL, 0x3feec86319e32323ULL, 0xbc87c50422622263ULL, 0x3feecc667b5de565ULL, 0x3c8b1c86e3e231d5ULL, 0x3feed09bec4a2d33ULL, 0xbc91bbd1d3bcbb15ULL, 0x3feed503b23e255dULL, 0x3c90cc319cee31d2ULL, 0x3feed99e1330b358ULL, 0x3c8469846e735ab3ULL, 0x3feede6b5579fdbfULL, 0xbc82dfcd978e9db4ULL, 0x3feee36bbfd3f37aULL, 0x3c8c1a7792cb3387ULL, 0x3feee89f995ad3adULL, 0xbc907b8f4ad1d9faULL, 0x3feeee07298db666ULL, 0xbc55c3d956dcaebaULL, 0x3feef3a2b84f15fbULL, 0xbc90a40e3da6f640ULL, 0x3feef9728de5593aULL, 0xbc68d6f438ad9334ULL, 0x3feeff76f2fb5e47ULL, 0xbc91eee26b588a35ULL, 0x3fef05b030a1064aULL, 0x3c74ffd70a5fddcdULL, 0x3fef0c1e904bc1d2ULL, 0xbc91bdfbfa9298acULL, 0x3fef12c25bd71e09ULL, 0x3c736eae30af0cb3ULL, 0x3fef199bdd85529cULL, 0x3c8ee3325c9ffd94ULL, 0x3fef20ab5fffd07aULL, 0x3c84e08fd10959acULL, 0x3fef27f12e57d14bULL, 0x3c63cdaf384e1a67ULL, 0x3fef2f6d9406e7b5ULL, 0x3c676b2c6c921968ULL, 0x3fef3720dcef9069ULL, 0xbc808a1883ccb5d2ULL, 0x3fef3f0b555dc3faULL, 0xbc8fad5d3ffffa6fULL, 0x3fef472d4a07897cULL, 0xbc900dae3875a949ULL, 0x3fef4f87080d89f2ULL, 0x3c74a385a63d07a7ULL, 0x3fef5818dcfba487ULL, 0xbc82919e2040220fULL, 0x3fef60e316c98398ULL, 0x3c8e5a50d5c192acULL, 0x3fef69e603db3285ULL, 0x3c843a59ac016b4bULL, 0x3fef7321f301b460ULL, 0xbc82d52107b43e1fULL, 0x3fef7c97337b9b5fULL, 0xbc892ab93b470dc9ULL, 0x3fef864614f5a129ULL, 0x3c74b604603a88d3ULL, 0x3fef902ee78b3ff6ULL, 0x3c83c5ec519d7271ULL, 0x3fef9a51fbc74c83ULL, 0xbc8ff7128fd391f0ULL, 0x3fefa4afa2a490daULL, 0xbc8dae98e223747dULL, 0x3fefaf482d8e67f1ULL, 0x3c8ec3bc41aa2008ULL, 0x3fefba1bee615a27ULL, 0x3c842b94c3a9eb32ULL, 0x3fefc52b376bba97ULL, 0x3c8a64a931d185eeULL, 0x3fefd0765b6e4540ULL, 0xbc8e37bae43be3edULL, 0x3fefdbfdad9cbe14ULL, 0x3c77893b4d91cd9dULL, 0x3fefe7c1819e90d8ULL, 0x3c5305c14160cc89ULL, 0x3feff3c22b8f71f1ULL }; /********************************************************************* * exp (MSVCRT.@) * * Copied from musl: src/math/exp.c */ double CDECL exp( double x ) { static const double C[] = { 0x1.ffffffffffdbdp-2, 0x1.555555555543cp-3, 0x1.55555cf172b91p-5, 0x1.1111167a4d017p-7 }; static const double invln2N = 0x1.71547652b82fep0 * (1 << 7), negln2hiN = -0x1.62e42fefa0000p-8, negln2loN = -0x1.cf79abc9e3b3ap-47; UINT32 abstop; UINT64 ki, idx, top, sbits; double kd, z, r, r2, scale, tail, tmp; abstop = (*(UINT64*)&x >> 52) & 0x7ff; if (abstop - 0x3c9 >= 0x408 - 0x3c9) { if (abstop - 0x3c9 >= 0x80000000) /* Avoid spurious underflow for tiny x. */ /* Note: 0 is common input. */ return 1.0 + x; if (abstop >= 0x409) { if (*(UINT64*)&x == 0xfff0000000000000ULL) return 0.0; #if _MSVCR_VER == 0 if (*(UINT64*)&x > 0x7ff0000000000000ULL) return math_error(_DOMAIN, "exp", x, 0, 1.0 + x); #endif if (abstop >= 0x7ff) return 1.0 + x; if (*(UINT64*)&x >> 63) return math_error(_UNDERFLOW, "exp", x, 0, fp_barrier(DBL_MIN) * DBL_MIN); else return math_error(_OVERFLOW, "exp", x, 0, fp_barrier(DBL_MAX) * DBL_MAX); } /* Large x is special cased below. */ abstop = 0; } /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ z = invln2N * x; kd = __round(z); ki = (INT64)kd; r = x + kd * negln2hiN + kd * negln2loN; /* 2^(k/N) ~= scale * (1 + tail). */ idx = 2 * (ki % (1 << 7)); top = ki << (52 - 7); tail = *(double*)&exp_T[idx]; /* This is only a valid scale when -1023*N < k < 1024*N. */ sbits = exp_T[idx + 1] + top; /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ /* Evaluation is optimized assuming superscalar pipelined execution. */ r2 = r * r; /* Without fma the worst case error is 0.25/N ulp larger. */ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ tmp = tail + r + r2 * (C[0] + r * C[1]) + r2 * r2 * (C[2] + r * C[3]); if (abstop == 0) { /* Handle cases that may overflow or underflow when computing the result that is scale*(1+TMP) without intermediate rounding. The bit representation of scale is in SBITS, however it has a computed exponent that may have overflown into the sign bit so that needs to be adjusted before using it as a double. (int32_t)KI is the k used in the argument reduction and exponent adjustment of scale, positive k here means the result may overflow and negative k means the result may underflow. */ double scale, y; if ((ki & 0x80000000) == 0) { /* k > 0, the exponent of scale might have overflowed by <= 460. */ sbits -= 1009ull << 52; scale = *(double*)&sbits; y = 0x1p1009 * (scale + scale * tmp); if (isinf(y)) return math_error(_OVERFLOW, "exp", x, 0, y); return y; } /* k < 0, need special care in the subnormal range. */ sbits += 1022ull << 52; scale = *(double*)&sbits; y = scale + scale * tmp; if (y < 1.0) { /* Round y to the right precision before scaling it into the subnormal range to avoid double rounding that can cause 0.5+E/2 ulp error where E is the worst-case ulp error outside the subnormal range. So this is only useful if the goal is better than 1 ulp worst-case error. */ double hi, lo; lo = scale - y + scale * tmp; hi = 1.0 + y; lo = 1.0 - hi + y + lo; y = hi + lo - 1.0; /* Avoid -0.0 with downward rounding. */ if (y == 0.0) y = 0.0; /* The underflow exception needs to be signaled explicitly. */ fp_barrier(fp_barrier(0x1p-1022) * 0x1p-1022); y = 0x1p-1022 * y; return math_error(_UNDERFLOW, "exp", x, 0, y); } y = 0x1p-1022 * y; return y; } scale = *(double*)&sbits; /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there is no spurious underflow here even without fma. */ return scale + scale * tmp; } /********************************************************************* * fmod (MSVCRT.@) * * Copied from musl: src/math/fmod.c */ double CDECL fmod( double x, double y ) { UINT64 xi = *(UINT64*)&x; UINT64 yi = *(UINT64*)&y; int ex = xi >> 52 & 0x7ff; int ey = yi >> 52 & 0x7ff; int sx = xi >> 63; UINT64 i; if (isinf(x)) return math_error(_DOMAIN, "fmod", x, y, (x * y) / (x * y)); if (yi << 1 == 0 || isnan(y) || ex == 0x7ff) return (x * y) / (x * y); if (xi << 1 <= yi << 1) { if (xi << 1 == yi << 1) return 0 * x; return x; } /* normalize x and y */ if (!ex) { for (i = xi << 12; i >> 63 == 0; ex--, i <<= 1); xi <<= -ex + 1; } else { xi &= -1ULL >> 12; xi |= 1ULL << 52; } if (!ey) { for (i = yi << 12; i >> 63 == 0; ey--, i <<= 1); yi <<= -ey + 1; } else { yi &= -1ULL >> 12; yi |= 1ULL << 52; } /* x mod y */ for (; ex > ey; ex--) { i = xi - yi; if (i >> 63 == 0) { if (i == 0) return 0 * x; xi = i; } xi <<= 1; } i = xi - yi; if (i >> 63 == 0) { if (i == 0) return 0 * x; xi = i; } for (; xi >> 52 == 0; xi <<= 1, ex--); /* scale result */ if (ex > 0) { xi -= 1ULL << 52; xi |= (UINT64)ex << 52; } else { xi >>= -ex + 1; } xi |= (UINT64)sx << 63; return *(double*)ξ } /********************************************************************* * log (MSVCRT.@) * * Copied from musl: src/math/log.c src/math/log_data.c */ double CDECL log( double x ) { static const double Ln2hi = 0x1.62e42fefa3800p-1, Ln2lo = 0x1.ef35793c76730p-45; static const double A[] = { -0x1.0000000000001p-1, 0x1.555555551305bp-2, -0x1.fffffffeb459p-3, 0x1.999b324f10111p-3, -0x1.55575e506c89fp-3 }; static const double B[] = { -0x1p-1, 0x1.5555555555577p-2, -0x1.ffffffffffdcbp-3, 0x1.999999995dd0cp-3, -0x1.55555556745a7p-3, 0x1.24924a344de3p-3, -0x1.fffffa4423d65p-4, 0x1.c7184282ad6cap-4, -0x1.999eb43b068ffp-4, 0x1.78182f7afd085p-4, -0x1.5521375d145cdp-4 }; static const struct { double invc, logc; } T[] = { {0x1.734f0c3e0de9fp+0, -0x1.7cc7f79e69000p-2}, {0x1.713786a2ce91fp+0, -0x1.76feec20d0000p-2}, {0x1.6f26008fab5a0p+0, -0x1.713e31351e000p-2}, {0x1.6d1a61f138c7dp+0, -0x1.6b85b38287800p-2}, {0x1.6b1490bc5b4d1p+0, -0x1.65d5590807800p-2}, {0x1.69147332f0cbap+0, -0x1.602d076180000p-2}, {0x1.6719f18224223p+0, -0x1.5a8ca86909000p-2}, {0x1.6524f99a51ed9p+0, -0x1.54f4356035000p-2}, {0x1.63356aa8f24c4p+0, -0x1.4f637c36b4000p-2}, {0x1.614b36b9ddc14p+0, -0x1.49da7fda85000p-2}, {0x1.5f66452c65c4cp+0, -0x1.445923989a800p-2}, {0x1.5d867b5912c4fp+0, -0x1.3edf439b0b800p-2}, {0x1.5babccb5b90dep+0, -0x1.396ce448f7000p-2}, {0x1.59d61f2d91a78p+0, -0x1.3401e17bda000p-2}, {0x1.5805612465687p+0, -0x1.2e9e2ef468000p-2}, {0x1.56397cee76bd3p+0, -0x1.2941b3830e000p-2}, {0x1.54725e2a77f93p+0, -0x1.23ec58cda8800p-2}, {0x1.52aff42064583p+0, -0x1.1e9e129279000p-2}, {0x1.50f22dbb2bddfp+0, -0x1.1956d2b48f800p-2}, {0x1.4f38f4734ded7p+0, -0x1.141679ab9f800p-2}, {0x1.4d843cfde2840p+0, -0x1.0edd094ef9800p-2}, {0x1.4bd3ec078a3c8p+0, -0x1.09aa518db1000p-2}, {0x1.4a27fc3e0258ap+0, -0x1.047e65263b800p-2}, {0x1.4880524d48434p+0, -0x1.feb224586f000p-3}, {0x1.46dce1b192d0bp+0, -0x1.f474a7517b000p-3}, {0x1.453d9d3391854p+0, -0x1.ea4443d103000p-3}, {0x1.43a2744b4845ap+0, -0x1.e020d44e9b000p-3}, {0x1.420b54115f8fbp+0, -0x1.d60a22977f000p-3}, {0x1.40782da3ef4b1p+0, -0x1.cc00104959000p-3}, {0x1.3ee8f5d57fe8fp+0, -0x1.c202956891000p-3}, {0x1.3d5d9a00b4ce9p+0, -0x1.b81178d811000p-3}, {0x1.3bd60c010c12bp+0, -0x1.ae2c9ccd3d000p-3}, {0x1.3a5242b75dab8p+0, -0x1.a45402e129000p-3}, {0x1.38d22cd9fd002p+0, -0x1.9a877681df000p-3}, {0x1.3755bc5847a1cp+0, -0x1.90c6d69483000p-3}, {0x1.35dce49ad36e2p+0, -0x1.87120a645c000p-3}, {0x1.34679984dd440p+0, -0x1.7d68fb4143000p-3}, {0x1.32f5cceffcb24p+0, -0x1.73cb83c627000p-3}, {0x1.3187775a10d49p+0, -0x1.6a39a9b376000p-3}, {0x1.301c8373e3990p+0, -0x1.60b3154b7a000p-3}, {0x1.2eb4ebb95f841p+0, -0x1.5737d76243000p-3}, {0x1.2d50a0219a9d1p+0, -0x1.4dc7b8fc23000p-3}, {0x1.2bef9a8b7fd2ap+0, -0x1.4462c51d20000p-3}, {0x1.2a91c7a0c1babp+0, -0x1.3b08abc830000p-3}, {0x1.293726014b530p+0, -0x1.31b996b490000p-3}, {0x1.27dfa5757a1f5p+0, -0x1.2875490a44000p-3}, {0x1.268b39b1d3bbfp+0, -0x1.1f3b9f879a000p-3}, {0x1.2539d838ff5bdp+0, -0x1.160c8252ca000p-3}, {0x1.23eb7aac9083bp+0, -0x1.0ce7f57f72000p-3}, {0x1.22a012ba940b6p+0, -0x1.03cdc49fea000p-3}, {0x1.2157996cc4132p+0, -0x1.f57bdbc4b8000p-4}, {0x1.201201dd2fc9bp+0, -0x1.e370896404000p-4}, {0x1.1ecf4494d480bp+0, -0x1.d17983ef94000p-4}, {0x1.1d8f5528f6569p+0, -0x1.bf9674ed8a000p-4}, {0x1.1c52311577e7cp+0, -0x1.adc79202f6000p-4}, {0x1.1b17c74cb26e9p+0, -0x1.9c0c3e7288000p-4}, {0x1.19e010c2c1ab6p+0, -0x1.8a646b372c000p-4}, {0x1.18ab07bb670bdp+0, -0x1.78d01b3ac0000p-4}, {0x1.1778a25efbcb6p+0, -0x1.674f145380000p-4}, {0x1.1648d354c31dap+0, -0x1.55e0e6d878000p-4}, {0x1.151b990275fddp+0, -0x1.4485cdea1e000p-4}, {0x1.13f0ea432d24cp+0, -0x1.333d94d6aa000p-4}, {0x1.12c8b7210f9dap+0, -0x1.22079f8c56000p-4}, {0x1.11a3028ecb531p+0, -0x1.10e4698622000p-4}, {0x1.107fbda8434afp+0, -0x1.ffa6c6ad20000p-5}, {0x1.0f5ee0f4e6bb3p+0, -0x1.dda8d4a774000p-5}, {0x1.0e4065d2a9fcep+0, -0x1.bbcece4850000p-5}, {0x1.0d244632ca521p+0, -0x1.9a1894012c000p-5}, {0x1.0c0a77ce2981ap+0, -0x1.788583302c000p-5}, {0x1.0af2f83c636d1p+0, -0x1.5715e67d68000p-5}, {0x1.09ddb98a01339p+0, -0x1.35c8a49658000p-5}, {0x1.08cabaf52e7dfp+0, -0x1.149e364154000p-5}, {0x1.07b9f2f4e28fbp+0, -0x1.e72c082eb8000p-6}, {0x1.06ab58c358f19p+0, -0x1.a55f152528000p-6}, {0x1.059eea5ecf92cp+0, -0x1.63d62cf818000p-6}, {0x1.04949cdd12c90p+0, -0x1.228fb8caa0000p-6}, {0x1.038c6c6f0ada9p+0, -0x1.c317b20f90000p-7}, {0x1.02865137932a9p+0, -0x1.419355daa0000p-7}, {0x1.0182427ea7348p+0, -0x1.81203c2ec0000p-8}, {0x1.008040614b195p+0, -0x1.0040979240000p-9}, {0x1.fe01ff726fa1ap-1, 0x1.feff384900000p-9}, {0x1.fa11cc261ea74p-1, 0x1.7dc41353d0000p-7}, {0x1.f6310b081992ep-1, 0x1.3cea3c4c28000p-6}, {0x1.f25f63ceeadcdp-1, 0x1.b9fc114890000p-6}, {0x1.ee9c8039113e7p-1, 0x1.1b0d8ce110000p-5}, {0x1.eae8078cbb1abp-1, 0x1.58a5bd001c000p-5}, {0x1.e741aa29d0c9bp-1, 0x1.95c8340d88000p-5}, {0x1.e3a91830a99b5p-1, 0x1.d276aef578000p-5}, {0x1.e01e009609a56p-1, 0x1.07598e598c000p-4}, {0x1.dca01e577bb98p-1, 0x1.253f5e30d2000p-4}, {0x1.d92f20b7c9103p-1, 0x1.42edd8b380000p-4}, {0x1.d5cac66fb5ccep-1, 0x1.606598757c000p-4}, {0x1.d272caa5ede9dp-1, 0x1.7da76356a0000p-4}, {0x1.cf26e3e6b2ccdp-1, 0x1.9ab434e1c6000p-4}, {0x1.cbe6da2a77902p-1, 0x1.b78c7bb0d6000p-4}, {0x1.c8b266d37086dp-1, 0x1.d431332e72000p-4}, {0x1.c5894bd5d5804p-1, 0x1.f0a3171de6000p-4}, {0x1.c26b533bb9f8cp-1, 0x1.067152b914000p-3}, {0x1.bf583eeece73fp-1, 0x1.147858292b000p-3}, {0x1.bc4fd75db96c1p-1, 0x1.2266ecdca3000p-3}, {0x1.b951e0c864a28p-1, 0x1.303d7a6c55000p-3}, {0x1.b65e2c5ef3e2cp-1, 0x1.3dfc33c331000p-3}, {0x1.b374867c9888bp-1, 0x1.4ba366b7a8000p-3}, {0x1.b094b211d304ap-1, 0x1.5933928d1f000p-3}, {0x1.adbe885f2ef7ep-1, 0x1.66acd2418f000p-3}, {0x1.aaf1d31603da2p-1, 0x1.740f8ec669000p-3}, {0x1.a82e63fd358a7p-1, 0x1.815c0f51af000p-3}, {0x1.a5740ef09738bp-1, 0x1.8e92954f68000p-3}, {0x1.a2c2a90ab4b27p-1, 0x1.9bb3602f84000p-3}, {0x1.a01a01393f2d1p-1, 0x1.a8bed1c2c0000p-3}, {0x1.9d79f24db3c1bp-1, 0x1.b5b515c01d000p-3}, {0x1.9ae2505c7b190p-1, 0x1.c2967ccbcc000p-3}, {0x1.9852ef297ce2fp-1, 0x1.cf635d5486000p-3}, {0x1.95cbaeea44b75p-1, 0x1.dc1bd3446c000p-3}, {0x1.934c69de74838p-1, 0x1.e8c01b8cfe000p-3}, {0x1.90d4f2f6752e6p-1, 0x1.f5509c0179000p-3}, {0x1.8e6528effd79dp-1, 0x1.00e6c121fb800p-2}, {0x1.8bfce9fcc007cp-1, 0x1.071b80e93d000p-2}, {0x1.899c0dabec30ep-1, 0x1.0d46b9e867000p-2}, {0x1.87427aa2317fbp-1, 0x1.13687334bd000p-2}, {0x1.84f00acb39a08p-1, 0x1.1980d67234800p-2}, {0x1.82a49e8653e55p-1, 0x1.1f8ffe0cc8000p-2}, {0x1.8060195f40260p-1, 0x1.2595fd7636800p-2}, {0x1.7e22563e0a329p-1, 0x1.2b9300914a800p-2}, {0x1.7beb377dcb5adp-1, 0x1.3187210436000p-2}, {0x1.79baa679725c2p-1, 0x1.377266dec1800p-2}, {0x1.77907f2170657p-1, 0x1.3d54ffbaf3000p-2}, {0x1.756cadbd6130cp-1, 0x1.432eee32fe000p-2} }; static const struct { double chi, clo; } T2[] = { {0x1.61000014fb66bp-1, 0x1.e026c91425b3cp-56}, {0x1.63000034db495p-1, 0x1.dbfea48005d41p-55}, {0x1.650000d94d478p-1, 0x1.e7fa786d6a5b7p-55}, {0x1.67000074e6fadp-1, 0x1.1fcea6b54254cp-57}, {0x1.68ffffedf0faep-1, -0x1.c7e274c590efdp-56}, {0x1.6b0000763c5bcp-1, -0x1.ac16848dcda01p-55}, {0x1.6d0001e5cc1f6p-1, 0x1.33f1c9d499311p-55}, {0x1.6efffeb05f63ep-1, -0x1.e80041ae22d53p-56}, {0x1.710000e86978p-1, 0x1.bff6671097952p-56}, {0x1.72ffffc67e912p-1, 0x1.c00e226bd8724p-55}, {0x1.74fffdf81116ap-1, -0x1.e02916ef101d2p-57}, {0x1.770000f679c9p-1, -0x1.7fc71cd549c74p-57}, {0x1.78ffffa7ec835p-1, 0x1.1bec19ef50483p-55}, {0x1.7affffe20c2e6p-1, -0x1.07e1729cc6465p-56}, {0x1.7cfffed3fc9p-1, -0x1.08072087b8b1cp-55}, {0x1.7efffe9261a76p-1, 0x1.dc0286d9df9aep-55}, {0x1.81000049ca3e8p-1, 0x1.97fd251e54c33p-55}, {0x1.8300017932c8fp-1, -0x1.afee9b630f381p-55}, {0x1.850000633739cp-1, 0x1.9bfbf6b6535bcp-55}, {0x1.87000204289c6p-1, -0x1.bbf65f3117b75p-55}, {0x1.88fffebf57904p-1, -0x1.9006ea23dcb57p-55}, {0x1.8b00022bc04dfp-1, -0x1.d00df38e04b0ap-56}, {0x1.8cfffe50c1b8ap-1, -0x1.8007146ff9f05p-55}, {0x1.8effffc918e43p-1, 0x1.3817bd07a7038p-55}, {0x1.910001efa5fc7p-1, 0x1.93e9176dfb403p-55}, {0x1.9300013467bb9p-1, 0x1.f804e4b980276p-56}, {0x1.94fffe6ee076fp-1, -0x1.f7ef0d9ff622ep-55}, {0x1.96fffde3c12d1p-1, -0x1.082aa962638bap-56}, {0x1.98ffff4458a0dp-1, -0x1.7801b9164a8efp-55}, {0x1.9afffdd982e3ep-1, -0x1.740e08a5a9337p-55}, {0x1.9cfffed49fb66p-1, 0x1.fce08c19bep-60}, {0x1.9f00020f19c51p-1, -0x1.a3faa27885b0ap-55}, {0x1.a10001145b006p-1, 0x1.4ff489958da56p-56}, {0x1.a300007bbf6fap-1, 0x1.cbeab8a2b6d18p-55}, {0x1.a500010971d79p-1, 0x1.8fecadd78793p-55}, {0x1.a70001df52e48p-1, -0x1.f41763dd8abdbp-55}, {0x1.a90001c593352p-1, -0x1.ebf0284c27612p-55}, {0x1.ab0002a4f3e4bp-1, -0x1.9fd043cff3f5fp-57}, {0x1.acfffd7ae1ed1p-1, -0x1.23ee7129070b4p-55}, {0x1.aefffee510478p-1, 0x1.a063ee00edea3p-57}, {0x1.b0fffdb650d5bp-1, 0x1.a06c8381f0ab9p-58}, {0x1.b2ffffeaaca57p-1, -0x1.9011e74233c1dp-56}, {0x1.b4fffd995badcp-1, -0x1.9ff1068862a9fp-56}, {0x1.b7000249e659cp-1, 0x1.aff45d0864f3ep-55}, {0x1.b8ffff987164p-1, 0x1.cfe7796c2c3f9p-56}, {0x1.bafffd204cb4fp-1, -0x1.3ff27eef22bc4p-57}, {0x1.bcfffd2415c45p-1, -0x1.cffb7ee3bea21p-57}, {0x1.beffff86309dfp-1, -0x1.14103972e0b5cp-55}, {0x1.c0fffe1b57653p-1, 0x1.bc16494b76a19p-55}, {0x1.c2ffff1fa57e3p-1, -0x1.4feef8d30c6edp-57}, {0x1.c4fffdcbfe424p-1, -0x1.43f68bcec4775p-55}, {0x1.c6fffed54b9f7p-1, 0x1.47ea3f053e0ecp-55}, {0x1.c8fffeb998fd5p-1, 0x1.383068df992f1p-56}, {0x1.cb0002125219ap-1, -0x1.8fd8e64180e04p-57}, {0x1.ccfffdd94469cp-1, 0x1.e7ebe1cc7ea72p-55}, {0x1.cefffeafdc476p-1, 0x1.ebe39ad9f88fep-55}, {0x1.d1000169af82bp-1, 0x1.57d91a8b95a71p-56}, {0x1.d30000d0ff71dp-1, 0x1.9c1906970c7dap-55}, {0x1.d4fffea790fc4p-1, -0x1.80e37c558fe0cp-58}, {0x1.d70002edc87e5p-1, -0x1.f80d64dc10f44p-56}, {0x1.d900021dc82aap-1, -0x1.47c8f94fd5c5cp-56}, {0x1.dafffd86b0283p-1, 0x1.c7f1dc521617ep-55}, {0x1.dd000296c4739p-1, 0x1.8019eb2ffb153p-55}, {0x1.defffe54490f5p-1, 0x1.e00d2c652cc89p-57}, {0x1.e0fffcdabf694p-1, -0x1.f8340202d69d2p-56}, {0x1.e2fffdb52c8ddp-1, 0x1.b00c1ca1b0864p-56}, {0x1.e4ffff24216efp-1, 0x1.2ffa8b094ab51p-56}, {0x1.e6fffe88a5e11p-1, -0x1.7f673b1efbe59p-58}, {0x1.e9000119eff0dp-1, -0x1.4808d5e0bc801p-55}, {0x1.eafffdfa51744p-1, 0x1.80006d54320b5p-56}, {0x1.ed0001a127fa1p-1, -0x1.002f860565c92p-58}, {0x1.ef00007babcc4p-1, -0x1.540445d35e611p-55}, {0x1.f0ffff57a8d02p-1, -0x1.ffb3139ef9105p-59}, {0x1.f30001ee58ac7p-1, 0x1.a81acf2731155p-55}, {0x1.f4ffff5823494p-1, 0x1.a3f41d4d7c743p-55}, {0x1.f6ffffca94c6bp-1, -0x1.202f41c987875p-57}, {0x1.f8fffe1f9c441p-1, 0x1.77dd1f477e74bp-56}, {0x1.fafffd2e0e37ep-1, -0x1.f01199a7ca331p-57}, {0x1.fd0001c77e49ep-1, 0x1.181ee4bceacb1p-56}, {0x1.feffff7e0c331p-1, -0x1.e05370170875ap-57}, {0x1.00ffff465606ep+0, -0x1.a7ead491c0adap-55}, {0x1.02ffff3867a58p+0, -0x1.77f69c3fcb2ep-54}, {0x1.04ffffdfc0d17p+0, 0x1.7bffe34cb945bp-54}, {0x1.0700003cd4d82p+0, 0x1.20083c0e456cbp-55}, {0x1.08ffff9f2cbe8p+0, -0x1.dffdfbe37751ap-57}, {0x1.0b000010cda65p+0, -0x1.13f7faee626ebp-54}, {0x1.0d00001a4d338p+0, 0x1.07dfa79489ff7p-55}, {0x1.0effffadafdfdp+0, -0x1.7040570d66bcp-56}, {0x1.110000bbafd96p+0, 0x1.e80d4846d0b62p-55}, {0x1.12ffffae5f45dp+0, 0x1.dbffa64fd36efp-54}, {0x1.150000dd59ad9p+0, 0x1.a0077701250aep-54}, {0x1.170000f21559ap+0, 0x1.dfdf9e2e3deeep-55}, {0x1.18ffffc275426p+0, 0x1.10030dc3b7273p-54}, {0x1.1b000123d3c59p+0, 0x1.97f7980030188p-54}, {0x1.1cffff8299eb7p+0, -0x1.5f932ab9f8c67p-57}, {0x1.1effff48ad4p+0, 0x1.37fbf9da75bebp-54}, {0x1.210000c8b86a4p+0, 0x1.f806b91fd5b22p-54}, {0x1.2300003854303p+0, 0x1.3ffc2eb9fbf33p-54}, {0x1.24fffffbcf684p+0, 0x1.601e77e2e2e72p-56}, {0x1.26ffff52921d9p+0, 0x1.ffcbb767f0c61p-56}, {0x1.2900014933a3cp+0, -0x1.202ca3c02412bp-56}, {0x1.2b00014556313p+0, -0x1.2808233f21f02p-54}, {0x1.2cfffebfe523bp+0, -0x1.8ff7e384fdcf2p-55}, {0x1.2f0000bb8ad96p+0, -0x1.5ff51503041c5p-55}, {0x1.30ffffb7ae2afp+0, -0x1.10071885e289dp-55}, {0x1.32ffffeac5f7fp+0, -0x1.1ff5d3fb7b715p-54}, {0x1.350000ca66756p+0, 0x1.57f82228b82bdp-54}, {0x1.3700011fbf721p+0, 0x1.000bac40dd5ccp-55}, {0x1.38ffff9592fb9p+0, -0x1.43f9d2db2a751p-54}, {0x1.3b00004ddd242p+0, 0x1.57f6b707638e1p-55}, {0x1.3cffff5b2c957p+0, 0x1.a023a10bf1231p-56}, {0x1.3efffeab0b418p+0, 0x1.87f6d66b152bp-54}, {0x1.410001532aff4p+0, 0x1.7f8375f198524p-57}, {0x1.4300017478b29p+0, 0x1.301e672dc5143p-55}, {0x1.44fffe795b463p+0, 0x1.9ff69b8b2895ap-55}, {0x1.46fffe80475ep+0, -0x1.5c0b19bc2f254p-54}, {0x1.48fffef6fc1e7p+0, 0x1.b4009f23a2a72p-54}, {0x1.4afffe5bea704p+0, -0x1.4ffb7bf0d7d45p-54}, {0x1.4d000171027dep+0, -0x1.9c06471dc6a3dp-54}, {0x1.4f0000ff03ee2p+0, 0x1.77f890b85531cp-54}, {0x1.5100012dc4bd1p+0, 0x1.004657166a436p-57}, {0x1.530001605277ap+0, -0x1.6bfcece233209p-54}, {0x1.54fffecdb704cp+0, -0x1.902720505a1d7p-55}, {0x1.56fffef5f54a9p+0, 0x1.bbfe60ec96412p-54}, {0x1.5900017e61012p+0, 0x1.87ec581afef9p-55}, {0x1.5b00003c93e92p+0, -0x1.f41080abf0ccp-54}, {0x1.5d0001d4919bcp+0, -0x1.8812afb254729p-54}, {0x1.5efffe7b87a89p+0, -0x1.47eb780ed6904p-54} }; double w, z, r, r2, r3, y, invc, logc, kd, hi, lo; UINT64 ix, iz, tmp; UINT32 top; int k, i; ix = *(UINT64*)&x; top = ix >> 48; if (ix - 0x3fee000000000000ULL < 0x3090000000000ULL) { double rhi, rlo; /* Handle close to 1.0 inputs separately. */ /* Fix sign of zero with downward rounding when x==1. */ if (ix == 0x3ff0000000000000ULL) return 0; r = x - 1.0; r2 = r * r; r3 = r * r2; y = r3 * (B[1] + r * B[2] + r2 * B[3] + r3 * (B[4] + r * B[5] + r2 * B[6] + r3 * (B[7] + r * B[8] + r2 * B[9] + r3 * B[10]))); /* Worst-case error is around 0.507 ULP. */ w = r * 0x1p27; rhi = r + w - w; rlo = r - rhi; w = rhi * rhi * B[0]; /* B[0] == -0.5. */ hi = r + w; lo = r - hi + w; lo += B[0] * rlo * (rhi + r); y += lo; y += hi; return y; } if (top - 0x0010 >= 0x7ff0 - 0x0010) { /* x < 0x1p-1022 or inf or nan. */ if (ix * 2 == 0) return math_error(_SING, "log", x, 0, (top & 0x8000 ? 1.0 : -1.0) / x); if (ix == 0x7ff0000000000000ULL) /* log(inf) == inf. */ return x; if ((top & 0x7ff0) == 0x7ff0 && (ix & 0xfffffffffffffULL)) return x; if (top & 0x8000) return math_error(_DOMAIN, "log", x, 0, (x - x) / (x - x)); /* x is subnormal, normalize it. */ x *= 0x1p52; ix = *(UINT64*)&x; ix -= 52ULL << 52; } /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3fe6000000000000ULL; i = (tmp >> (52 - 7)) % (1 << 7); k = (INT64)tmp >> 52; /* arithmetic shift */ iz = ix - (tmp & 0xfffULL << 52); invc = T[i].invc; logc = T[i].logc; z = *(double*)&iz; /* log(x) = log1p(z/c-1) + log(c) + k*Ln2. */ /* r ~= z/c - 1, |r| < 1/(2*N). */ r = (z - T2[i].chi - T2[i].clo) * invc; kd = (double)k; /* hi + lo = r + log(c) + k*Ln2. */ w = kd * Ln2hi + logc; hi = w + r; lo = w - hi + r + kd * Ln2lo; /* log(x) = lo + (log1p(r) - r) + hi. */ r2 = r * r; /* rounding error: 0x1p-54/N^2. */ /* Worst case error if |y| > 0x1p-5: 0.5 + 4.13/N + abs-poly-error*2^57 ULP (+ 0.002 ULP without fma) Worst case error if |y| > 0x1p-4: 0.5 + 2.06/N + abs-poly-error*2^56 ULP (+ 0.001 ULP without fma). */ y = lo + r2 * A[0] + r * r2 * (A[1] + r * A[2] + r2 * (A[3] + r * A[4])) + hi; return y; } /********************************************************************* * log10 (MSVCRT.@) */ double CDECL log10( double x ) { static const double ivln10hi = 4.34294481878168880939e-01, ivln10lo = 2.50829467116452752298e-11, log10_2hi = 3.01029995663611771306e-01, log10_2lo = 3.69423907715893078616e-13, Lg1 = 6.666666666666735130e-01, Lg2 = 3.999999999940941908e-01, Lg3 = 2.857142874366239149e-01, Lg4 = 2.222219843214978396e-01, Lg5 = 1.818357216161805012e-01, Lg6 = 1.531383769920937332e-01, Lg7 = 1.479819860511658591e-01; union {double f; UINT64 i;} u = {x}; double hfsq, f, s, z, R, w, t1, t2, dk, y, hi, lo, val_hi, val_lo; UINT32 hx; int k; hx = u.i >> 32; k = 0; if (hx < 0x00100000 || hx >> 31) { if (u.i << 1 == 0) return math_error(_SING, "log10", x, 0, -1 / (x * x)); if ((u.i & ~(1ULL << 63)) > 0x7ff0000000000000ULL) return x; if (hx >> 31) return math_error(_DOMAIN, "log10", x, 0, (x - x) / (x - x)); /* subnormal number, scale x up */ k -= 54; x *= 0x1p54; u.f = x; hx = u.i >> 32; } else if (hx >= 0x7ff00000) { return x; } else if (hx == 0x3ff00000 && u.i<<32 == 0) return 0; /* reduce x into [sqrt(2)/2, sqrt(2)] */ hx += 0x3ff00000 - 0x3fe6a09e; k += (int)(hx >> 20) - 0x3ff; hx = (hx & 0x000fffff) + 0x3fe6a09e; u.i = (UINT64)hx << 32 | (u.i & 0xffffffff); x = u.f; f = x - 1.0; hfsq = 0.5 * f * f; s = f / (2.0 + f); z = s * s; w = z * z; t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); R = t2 + t1; /* hi+lo = f - hfsq + s*(hfsq+R) ~ log(1+f) */ hi = f - hfsq; u.f = hi; u.i &= (UINT64)-1 << 32; hi = u.f; lo = f - hi - hfsq + s * (hfsq + R); /* val_hi+val_lo ~ log10(1+f) + k*log10(2) */ val_hi = hi * ivln10hi; dk = k; y = dk * log10_2hi; val_lo = dk * log10_2lo + (lo + hi) * ivln10lo + lo * ivln10hi; /* * Extra precision in for adding y is not strictly needed * since there is no very large cancellation near x = sqrt(2) or * x = 1/sqrt(2), but we do it anyway since it costs little on CPUs * with some parallelism and it reduces the error for many args. */ w = y + val_hi; val_lo += (y - w) + val_hi; val_hi = w; return val_lo + val_hi; } /* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about additional 15 bits precision. IX is the bit representation of x, but normalized in the subnormal range using the sign bit for the exponent. */ static double pow_log(UINT64 ix, double *tail) { static const struct { double invc, logc, logctail; } T[] = { {0x1.6a00000000000p+0, -0x1.62c82f2b9c800p-2, 0x1.ab42428375680p-48}, {0x1.6800000000000p+0, -0x1.5d1bdbf580800p-2, -0x1.ca508d8e0f720p-46}, {0x1.6600000000000p+0, -0x1.5767717455800p-2, -0x1.362a4d5b6506dp-45}, {0x1.6400000000000p+0, -0x1.51aad872df800p-2, -0x1.684e49eb067d5p-49}, {0x1.6200000000000p+0, -0x1.4be5f95777800p-2, -0x1.41b6993293ee0p-47}, {0x1.6000000000000p+0, -0x1.4618bc21c6000p-2, 0x1.3d82f484c84ccp-46}, {0x1.5e00000000000p+0, -0x1.404308686a800p-2, 0x1.c42f3ed820b3ap-50}, {0x1.5c00000000000p+0, -0x1.3a64c55694800p-2, 0x1.0b1c686519460p-45}, {0x1.5a00000000000p+0, -0x1.347dd9a988000p-2, 0x1.5594dd4c58092p-45}, {0x1.5800000000000p+0, -0x1.2e8e2bae12000p-2, 0x1.67b1e99b72bd8p-45}, {0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46}, {0x1.5600000000000p+0, -0x1.2895a13de8800p-2, 0x1.5ca14b6cfb03fp-46}, {0x1.5400000000000p+0, -0x1.22941fbcf7800p-2, -0x1.65a242853da76p-46}, {0x1.5200000000000p+0, -0x1.1c898c1699800p-2, -0x1.fafbc68e75404p-46}, {0x1.5000000000000p+0, -0x1.1675cababa800p-2, 0x1.f1fc63382a8f0p-46}, {0x1.4e00000000000p+0, -0x1.1058bf9ae4800p-2, -0x1.6a8c4fd055a66p-45}, {0x1.4c00000000000p+0, -0x1.0a324e2739000p-2, -0x1.c6bee7ef4030ep-47}, {0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48}, {0x1.4a00000000000p+0, -0x1.0402594b4d000p-2, -0x1.036b89ef42d7fp-48}, {0x1.4800000000000p+0, -0x1.fb9186d5e4000p-3, 0x1.d572aab993c87p-47}, {0x1.4600000000000p+0, -0x1.ef0adcbdc6000p-3, 0x1.b26b79c86af24p-45}, {0x1.4400000000000p+0, -0x1.e27076e2af000p-3, -0x1.72f4f543fff10p-46}, {0x1.4200000000000p+0, -0x1.d5c216b4fc000p-3, 0x1.1ba91bbca681bp-45}, {0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45}, {0x1.4000000000000p+0, -0x1.c8ff7c79aa000p-3, 0x1.7794f689f8434p-45}, {0x1.3e00000000000p+0, -0x1.bc286742d9000p-3, 0x1.94eb0318bb78fp-46}, {0x1.3c00000000000p+0, -0x1.af3c94e80c000p-3, 0x1.a4e633fcd9066p-52}, {0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45}, {0x1.3a00000000000p+0, -0x1.a23bc1fe2b000p-3, -0x1.58c64dc46c1eap-45}, {0x1.3800000000000p+0, -0x1.9525a9cf45000p-3, -0x1.ad1d904c1d4e3p-45}, {0x1.3600000000000p+0, -0x1.87fa06520d000p-3, 0x1.bbdbf7fdbfa09p-45}, {0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45}, {0x1.3400000000000p+0, -0x1.7ab890210e000p-3, 0x1.bdb9072534a58p-45}, {0x1.3200000000000p+0, -0x1.6d60fe719d000p-3, -0x1.0e46aa3b2e266p-46}, {0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46}, {0x1.3000000000000p+0, -0x1.5ff3070a79000p-3, -0x1.e9e439f105039p-46}, {0x1.2e00000000000p+0, -0x1.526e5e3a1b000p-3, -0x1.0de8b90075b8fp-45}, {0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46}, {0x1.2c00000000000p+0, -0x1.44d2b6ccb8000p-3, 0x1.70cc16135783cp-46}, {0x1.2a00000000000p+0, -0x1.371fc201e9000p-3, 0x1.178864d27543ap-48}, {0x1.2800000000000p+0, -0x1.29552f81ff000p-3, -0x1.48d301771c408p-45}, {0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45}, {0x1.2600000000000p+0, -0x1.1b72ad52f6000p-3, -0x1.e80a41811a396p-45}, {0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47}, {0x1.2400000000000p+0, -0x1.0d77e7cd09000p-3, 0x1.a699688e85bf4p-47}, {0x1.2200000000000p+0, -0x1.fec9131dbe000p-4, -0x1.575545ca333f2p-45}, {0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45}, {0x1.2000000000000p+0, -0x1.e27076e2b0000p-4, 0x1.a342c2af0003cp-45}, {0x1.1e00000000000p+0, -0x1.c5e548f5bc000p-4, -0x1.d0c57585fbe06p-46}, {0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45}, {0x1.1c00000000000p+0, -0x1.a926d3a4ae000p-4, 0x1.53935e85baac8p-45}, {0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46}, {0x1.1a00000000000p+0, -0x1.8c345d631a000p-4, 0x1.37c294d2f5668p-46}, {0x1.1800000000000p+0, -0x1.6f0d28ae56000p-4, -0x1.69737c93373dap-45}, {0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46}, {0x1.1600000000000p+0, -0x1.51b073f062000p-4, 0x1.f025b61c65e57p-46}, {0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45}, {0x1.1400000000000p+0, -0x1.341d7961be000p-4, 0x1.c5edaccf913dfp-45}, {0x1.1200000000000p+0, -0x1.16536eea38000p-4, 0x1.47c5e768fa309p-46}, {0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45}, {0x1.1000000000000p+0, -0x1.f0a30c0118000p-5, 0x1.d599e83368e91p-45}, {0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46}, {0x1.0e00000000000p+0, -0x1.b42dd71198000p-5, 0x1.c827ae5d6704cp-46}, {0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45}, {0x1.0c00000000000p+0, -0x1.77458f632c000p-5, -0x1.cfc4634f2a1eep-45}, {0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48}, {0x1.0a00000000000p+0, -0x1.39e87b9fec000p-5, 0x1.502b7f526feaap-48}, {0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45}, {0x1.0800000000000p+0, -0x1.f829b0e780000p-6, -0x1.980267c7e09e4p-45}, {0x1.0600000000000p+0, -0x1.7b91b07d58000p-6, -0x1.88d5493faa639p-45}, {0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50}, {0x1.0400000000000p+0, -0x1.fc0a8b0fc0000p-7, -0x1.f1e7cf6d3a69cp-50}, {0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46}, {0x1.0200000000000p+0, -0x1.fe02a6b100000p-8, -0x1.9e23f0dda40e4p-46}, {0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0}, {0x1.0000000000000p+0, 0x0.0000000000000p+0, 0x0.0000000000000p+0}, {0x1.fc00000000000p-1, 0x1.0101575890000p-7, -0x1.0c76b999d2be8p-46}, {0x1.f800000000000p-1, 0x1.0205658938000p-6, -0x1.3dc5b06e2f7d2p-45}, {0x1.f400000000000p-1, 0x1.8492528c90000p-6, -0x1.aa0ba325a0c34p-45}, {0x1.f000000000000p-1, 0x1.0415d89e74000p-5, 0x1.111c05cf1d753p-47}, {0x1.ec00000000000p-1, 0x1.466aed42e0000p-5, -0x1.c167375bdfd28p-45}, {0x1.e800000000000p-1, 0x1.894aa149fc000p-5, -0x1.97995d05a267dp-46}, {0x1.e400000000000p-1, 0x1.ccb73cdddc000p-5, -0x1.a68f247d82807p-46}, {0x1.e200000000000p-1, 0x1.eea31c006c000p-5, -0x1.e113e4fc93b7bp-47}, {0x1.de00000000000p-1, 0x1.1973bd1466000p-4, -0x1.5325d560d9e9bp-45}, {0x1.da00000000000p-1, 0x1.3bdf5a7d1e000p-4, 0x1.cc85ea5db4ed7p-45}, {0x1.d600000000000p-1, 0x1.5e95a4d97a000p-4, -0x1.c69063c5d1d1ep-45}, {0x1.d400000000000p-1, 0x1.700d30aeac000p-4, 0x1.c1e8da99ded32p-49}, {0x1.d000000000000p-1, 0x1.9335e5d594000p-4, 0x1.3115c3abd47dap-45}, {0x1.cc00000000000p-1, 0x1.b6ac88dad6000p-4, -0x1.390802bf768e5p-46}, {0x1.ca00000000000p-1, 0x1.c885801bc4000p-4, 0x1.646d1c65aacd3p-45}, {0x1.c600000000000p-1, 0x1.ec739830a2000p-4, -0x1.dc068afe645e0p-45}, {0x1.c400000000000p-1, 0x1.fe89139dbe000p-4, -0x1.534d64fa10afdp-45}, {0x1.c000000000000p-1, 0x1.1178e8227e000p-3, 0x1.1ef78ce2d07f2p-45}, {0x1.be00000000000p-1, 0x1.1aa2b7e23f000p-3, 0x1.ca78e44389934p-45}, {0x1.ba00000000000p-1, 0x1.2d1610c868000p-3, 0x1.39d6ccb81b4a1p-47}, {0x1.b800000000000p-1, 0x1.365fcb0159000p-3, 0x1.62fa8234b7289p-51}, {0x1.b400000000000p-1, 0x1.4913d8333b000p-3, 0x1.5837954fdb678p-45}, {0x1.b200000000000p-1, 0x1.527e5e4a1b000p-3, 0x1.633e8e5697dc7p-45}, {0x1.ae00000000000p-1, 0x1.6574ebe8c1000p-3, 0x1.9cf8b2c3c2e78p-46}, {0x1.ac00000000000p-1, 0x1.6f0128b757000p-3, -0x1.5118de59c21e1p-45}, {0x1.aa00000000000p-1, 0x1.7898d85445000p-3, -0x1.c661070914305p-46}, {0x1.a600000000000p-1, 0x1.8beafeb390000p-3, -0x1.73d54aae92cd1p-47}, {0x1.a400000000000p-1, 0x1.95a5adcf70000p-3, 0x1.7f22858a0ff6fp-47}, {0x1.a000000000000p-1, 0x1.a93ed3c8ae000p-3, -0x1.8724350562169p-45}, {0x1.9e00000000000p-1, 0x1.b31d8575bd000p-3, -0x1.c358d4eace1aap-47}, {0x1.9c00000000000p-1, 0x1.bd087383be000p-3, -0x1.d4bc4595412b6p-45}, {0x1.9a00000000000p-1, 0x1.c6ffbc6f01000p-3, -0x1.1ec72c5962bd2p-48}, {0x1.9600000000000p-1, 0x1.db13db0d49000p-3, -0x1.aff2af715b035p-45}, {0x1.9400000000000p-1, 0x1.e530effe71000p-3, 0x1.212276041f430p-51}, {0x1.9200000000000p-1, 0x1.ef5ade4dd0000p-3, -0x1.a211565bb8e11p-51}, {0x1.9000000000000p-1, 0x1.f991c6cb3b000p-3, 0x1.bcbecca0cdf30p-46}, {0x1.8c00000000000p-1, 0x1.07138604d5800p-2, 0x1.89cdb16ed4e91p-48}, {0x1.8a00000000000p-1, 0x1.0c42d67616000p-2, 0x1.7188b163ceae9p-45}, {0x1.8800000000000p-1, 0x1.1178e8227e800p-2, -0x1.c210e63a5f01cp-45}, {0x1.8600000000000p-1, 0x1.16b5ccbacf800p-2, 0x1.b9acdf7a51681p-45}, {0x1.8400000000000p-1, 0x1.1bf99635a6800p-2, 0x1.ca6ed5147bdb7p-45}, {0x1.8200000000000p-1, 0x1.214456d0eb800p-2, 0x1.a87deba46baeap-47}, {0x1.7e00000000000p-1, 0x1.2bef07cdc9000p-2, 0x1.a9cfa4a5004f4p-45}, {0x1.7c00000000000p-1, 0x1.314f1e1d36000p-2, -0x1.8e27ad3213cb8p-45}, {0x1.7a00000000000p-1, 0x1.36b6776be1000p-2, 0x1.16ecdb0f177c8p-46}, {0x1.7800000000000p-1, 0x1.3c25277333000p-2, 0x1.83b54b606bd5cp-46}, {0x1.7600000000000p-1, 0x1.419b423d5e800p-2, 0x1.8e436ec90e09dp-47}, {0x1.7400000000000p-1, 0x1.4718dc271c800p-2, -0x1.f27ce0967d675p-45}, {0x1.7200000000000p-1, 0x1.4c9e09e173000p-2, -0x1.e20891b0ad8a4p-45}, {0x1.7000000000000p-1, 0x1.522ae0738a000p-2, 0x1.ebe708164c759p-45}, {0x1.6e00000000000p-1, 0x1.57bf753c8d000p-2, 0x1.fadedee5d40efp-46}, {0x1.6c00000000000p-1, 0x1.5d5bddf596000p-2, -0x1.a0b2a08a465dcp-47}, }; static const double A[] = { -0x1p-1, 0x1.555555555556p-2 * -2, -0x1.0000000000006p-2 * -2, 0x1.999999959554ep-3 * 4, -0x1.555555529a47ap-3 * 4, 0x1.2495b9b4845e9p-3 * -8, -0x1.0002b8b263fc3p-3 * -8 }; static const double ln2hi = 0x1.62e42fefa3800p-1, ln2lo = 0x1.ef35793c76730p-45; double z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p; double zhi, zlo, rhi, rlo, ar, ar2, ar3, lo3, lo4, arhi, arhi2; UINT64 iz, tmp; int k, i; /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3fe6955500000000ULL; i = (tmp >> (52 - 7)) % (1 << 7); k = (INT64)tmp >> 52; /* arithmetic shift */ iz = ix - (tmp & 0xfffULL << 52); z = *(double*)&iz; kd = k; /* log(x) = k*Ln2 + log(c) + log1p(z/c-1). */ invc = T[i].invc; logc = T[i].logc; logctail = T[i].logctail; /* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible. */ /* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|. */ iz = (iz + (1ULL << 31)) & (-1ULL << 32); zhi = *(double*)&iz; zlo = z - zhi; rhi = zhi * invc - 1.0; rlo = zlo * invc; r = rhi + rlo; /* k*Ln2 + log(c) + r. */ t1 = kd * ln2hi + logc; t2 = t1 + r; lo1 = kd * ln2lo + logctail; lo2 = t1 - t2 + r; /* Evaluation is optimized assuming superscalar pipelined execution. */ ar = A[0] * r; /* A[0] = -0.5. */ ar2 = r * ar; ar3 = r * ar2; /* k*Ln2 + log(c) + r + A[0]*r*r. */ arhi = A[0] * rhi; arhi2 = rhi * arhi; hi = t2 + arhi2; lo3 = rlo * (ar + arhi); lo4 = t2 - hi + arhi2; /* p = log1p(r) - r - A[0]*r*r. */ p = (ar3 * (A[1] + r * A[2] + ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * A[6])))); lo = lo1 + lo2 + lo3 + lo4 + p; y = hi + lo; *tail = hi - y + lo; return y; } /* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|. The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1. */ static double pow_exp(double argx, double argy, double x, double xtail, UINT32 sign_bias) { static const double C[] = { 0x1.ffffffffffdbdp-2, 0x1.555555555543cp-3, 0x1.55555cf172b91p-5, 0x1.1111167a4d017p-7 }; static const double invln2N = 0x1.71547652b82fep0 * (1 << 7), negln2hiN = -0x1.62e42fefa0000p-8, negln2loN = -0x1.cf79abc9e3b3ap-47; UINT32 abstop; UINT64 ki, idx, top, sbits; double kd, z, r, r2, scale, tail, tmp; abstop = (*(UINT64*)&x >> 52) & 0x7ff; if (abstop - 0x3c9 >= 0x408 - 0x3c9) { if (abstop - 0x3c9 >= 0x80000000) { /* Avoid spurious underflow for tiny x. */ /* Note: 0 is common input. */ double one = 1.0 + x; return sign_bias ? -one : one; } if (abstop >= 0x409) { /* Note: inf and nan are already handled. */ if (*(UINT64*)&x >> 63) return math_error(_UNDERFLOW, "pow", argx, argy, (sign_bias ? -DBL_MIN : DBL_MIN) * DBL_MIN); return math_error(_OVERFLOW, "pow", argx, argy, (sign_bias ? -DBL_MAX : DBL_MAX) * DBL_MAX); } /* Large x is special cased below. */ abstop = 0; } /* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)]. */ /* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N]. */ z = invln2N * x; kd = __round(z); ki = (INT64)kd; r = x + kd * negln2hiN + kd * negln2loN; /* The code assumes 2^-200 < |xtail| < 2^-8/N. */ r += xtail; /* 2^(k/N) ~= scale * (1 + tail). */ idx = 2 * (ki % (1 << 7)); top = (ki + sign_bias) << (52 - 7); tail = *(double*)&exp_T[idx]; /* This is only a valid scale when -1023*N < k < 1024*N. */ sbits = exp_T[idx + 1] + top; /* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1). */ /* Evaluation is optimized assuming superscalar pipelined execution. */ r2 = r * r; /* Without fma the worst case error is 0.25/N ulp larger. */ /* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp. */ tmp = tail + r + r2 * (C[0] + r * C[1]) + r2 * r2 * (C[2] + r * C[3]); if (abstop == 0) { /* Handle cases that may overflow or underflow when computing the result that is scale*(1+TMP) without intermediate rounding. The bit representation of scale is in SBITS, however it has a computed exponent that may have overflown into the sign bit so that needs to be adjusted before using it as a double. (int32_t)KI is the k used in the argument reduction and exponent adjustment of scale, positive k here means the result may overflow and negative k means the result may underflow. */ double scale, y; if ((ki & 0x80000000) == 0) { /* k > 0, the exponent of scale might have overflowed by <= 460. */ sbits -= 1009ull << 52; scale = *(double*)&sbits; y = 0x1p1009 * (scale + scale * tmp); if (isinf(y)) return math_error(_OVERFLOW, "pow", argx, argy, y); return y; } /* k < 0, need special care in the subnormal range. */ sbits += 1022ull << 52; /* Note: sbits is signed scale. */ scale = *(double*)&sbits; y = scale + scale * tmp; if (fabs(y) < 1.0) { /* Round y to the right precision before scaling it into the subnormal range to avoid double rounding that can cause 0.5+E/2 ulp error where E is the worst-case ulp error outside the subnormal range. So this is only useful if the goal is better than 1 ulp worst-case error. */ double hi, lo, one = 1.0; if (y < 0.0) one = -1.0; lo = scale - y + scale * tmp; hi = one + y; lo = one - hi + y + lo; y = hi + lo - one; /* Fix the sign of 0. */ if (y == 0.0) { sbits &= 0x8000000000000000ULL; y = *(double*)&sbits; } /* The underflow exception needs to be signaled explicitly. */ fp_barrier(fp_barrier(0x1p-1022) * 0x1p-1022); y = 0x1p-1022 * y; return math_error(_UNDERFLOW, "pow", argx, argy, y); } y = 0x1p-1022 * y; return y; } scale = *(double*)&sbits; /* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there is no spurious underflow here even without fma. */ return scale + scale * tmp; } /* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is the bit representation of a non-zero finite floating-point value. */ static inline int pow_checkint(UINT64 iy) { int e = iy >> 52 & 0x7ff; if (e < 0x3ff) return 0; if (e > 0x3ff + 52) return 2; if (iy & ((1ULL << (0x3ff + 52 - e)) - 1)) return 0; if (iy & (1ULL << (0x3ff + 52 - e))) return 1; return 2; } /********************************************************************* * pow (MSVCRT.@) * * Copied from musl: src/math/pow.c */ double CDECL pow( double x, double y ) { UINT32 sign_bias = 0; UINT64 ix, iy; UINT32 topx, topy; double lo, hi, ehi, elo, yhi, ylo, lhi, llo; ix = *(UINT64*)&x; iy = *(UINT64*)&y; topx = ix >> 52; topy = iy >> 52; if (topx - 0x001 >= 0x7ff - 0x001 || (topy & 0x7ff) - 0x3be >= 0x43e - 0x3be) { /* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0 and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1. */ /* Special cases: (x < 0x1p-126 or inf or nan) or (|y| < 0x1p-65 or |y| >= 0x1p63 or nan). */ if (2 * iy - 1 >= 2 * 0x7ff0000000000000ULL - 1) { if (2 * iy == 0) return 1.0; if (ix == 0x3ff0000000000000ULL) return 1.0; if (2 * ix > 2 * 0x7ff0000000000000ULL || 2 * iy > 2 * 0x7ff0000000000000ULL) return x + y; if (2 * ix == 2 * 0x3ff0000000000000ULL) return 1.0; if ((2 * ix < 2 * 0x3ff0000000000000ULL) == !(iy >> 63)) return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf. */ return y * y; } if (2 * ix - 1 >= 2 * 0x7ff0000000000000ULL - 1) { double x2 = x * x; if (ix >> 63 && pow_checkint(iy) == 1) x2 = -x2; if (iy & 0x8000000000000000ULL && x2 == 0.0) return math_error(_SING, "pow", x, y, 1 / x2); /* Without the barrier some versions of clang hoist the 1/x2 and thus division by zero exception can be signaled spuriously. */ return iy >> 63 ? fp_barrier(1 / x2) : x2; } /* Here x and y are non-zero finite. */ if (ix >> 63) { /* Finite x < 0. */ int yint = pow_checkint(iy); if (yint == 0) return math_error(_DOMAIN, "pow", x, y, 0 / (x - x)); if (yint == 1) sign_bias = 0x800 << 7; ix &= 0x7fffffffffffffff; topx &= 0x7ff; } if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be) { /* Note: sign_bias == 0 here because y is not odd. */ if (ix == 0x3ff0000000000000ULL) return 1.0; if ((topy & 0x7ff) < 0x3be) { /* |y| < 2^-65, x^y ~= 1 + y*log(x). */ return ix > 0x3ff0000000000000ULL ? 1.0 + y : 1.0 - y; } if ((ix > 0x3ff0000000000000ULL) == (topy < 0x800)) return math_error(_OVERFLOW, "pow", x, y, fp_barrier(DBL_MAX) * DBL_MAX); return math_error(_UNDERFLOW, "pow", x, y, fp_barrier(DBL_MIN) * DBL_MIN); } if (topx == 0) { /* Normalize subnormal x so exponent becomes negative. */ x *= 0x1p52; ix = *(UINT64*)&x; ix &= 0x7fffffffffffffff; ix -= 52ULL << 52; } } hi = pow_log(ix, &lo); iy &= -1ULL << 27; yhi = *(double*)&iy; ylo = y - yhi; *(UINT64*)&lhi = *(UINT64*)&hi & -1ULL << 27; llo = fp_barrier(hi - lhi + lo); ehi = yhi * lhi; elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25. */ return pow_exp(x, y, ehi, elo, sign_bias); } /********************************************************************* * sin (MSVCRT.@) * * Copied from musl: src/math/sin.c */ double CDECL sin( double x ) { double y[2]; UINT32 ix; unsigned n; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; /* |x| ~< pi/4 */ if (ix <= 0x3fe921fb) { if (ix < 0x3e500000) { /* |x| < 2**-26 */ /* raise inexact if x != 0 and underflow if subnormal*/ fp_barrier(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f); return x; } return __sin(x, 0.0, 0); } /* sin(Inf or NaN) is NaN */ if (isinf(x)) return math_error(_DOMAIN, "sin", x, 0, x - x); if (ix >= 0x7ff00000) return x - x; /* argument reduction needed */ n = __rem_pio2(x, y); switch (n&3) { case 0: return __sin(y[0], y[1], 1); case 1: return __cos(y[0], y[1]); case 2: return -__sin(y[0], y[1], 1); default: return -__cos(y[0], y[1]); } } /********************************************************************* * sinh (MSVCRT.@) */ double CDECL sinh( double x ) { UINT64 ux = *(UINT64*)&x; UINT64 sign = ux & 0x8000000000000000ULL; UINT32 w; double t, h, absx; h = 0.5; if (ux >> 63) h = -h; /* |x| */ ux &= (UINT64)-1 / 2; absx = *(double*)&ux; w = ux >> 32; /* |x| < log(DBL_MAX) */ if (w < 0x40862e42) { t = __expm1(absx); if (w < 0x3ff00000) { if (w < 0x3ff00000 - (26 << 20)) return x; return h * (2 * t - t * t / (t + 1)); } return h * (t + t / (t + 1)); } /* |x| > log(DBL_MAX) or nan */ /* note: the result is stored to handle overflow */ if (ux > 0x7ff0000000000000ULL) *(UINT64*)&t = ux | sign | 0x0008000000000000ULL; else t = __expo2(absx, 2 * h); return t; } static BOOL sqrt_validate( double *x, BOOL update_sw ) { short c = _dclass(*x); if (c == FP_ZERO) return FALSE; if (c == FP_NAN) { #ifdef __i386__ if (update_sw) *x = math_error(_DOMAIN, "sqrt", *x, 0, *x); #else /* set signaling bit */ *(ULONGLONG*)x |= 0x8000000000000ULL; #endif return FALSE; } if (signbit(*x)) { *x = math_error(_DOMAIN, "sqrt", *x, 0, ret_nan(update_sw)); return FALSE; } if (c == FP_INFINITE) return FALSE; return TRUE; } #if defined(__x86_64__) || defined(__i386__) double CDECL sse2_sqrt(double); __ASM_GLOBAL_FUNC( sse2_sqrt, "sqrtsd %xmm0, %xmm0\n\t" "ret" ) #endif #ifdef __i386__ double CDECL x87_sqrt(double); __ASM_GLOBAL_FUNC( x87_sqrt, "fldl 4(%esp)\n\t" SET_X87_CW(0xc00) "fsqrt\n\t" RESET_X87_CW "ret" ) #endif /********************************************************************* * sqrt (MSVCRT.@) * * Copied from musl: src/math/sqrt.c */ double CDECL sqrt( double x ) { #ifdef __x86_64__ if (!sqrt_validate(&x, TRUE)) return x; return sse2_sqrt(x); #elif defined( __i386__ ) if (!sqrt_validate(&x, TRUE)) return x; return x87_sqrt(x); #else static const double tiny = 1.0e-300; double z; int sign = 0x80000000; int ix0,s0,q,m,t,i; unsigned int r,t1,s1,ix1,q1; ULONGLONG ix; if (!sqrt_validate(&x, TRUE)) return x; ix = *(ULONGLONG*)&x; ix0 = ix >> 32; ix1 = ix; /* normalize x */ m = ix0 >> 20; if (m == 0) { /* subnormal x */ while (ix0 == 0) { m -= 21; ix0 |= (ix1 >> 11); ix1 <<= 21; } for (i=0; (ix0 & 0x00100000) == 0; i++) ix0 <<= 1; m -= i - 1; ix0 |= ix1 >> (32 - i); ix1 <<= i; } m -= 1023; /* unbias exponent */ ix0 = (ix0 & 0x000fffff) | 0x00100000; if (m & 1) { /* odd m, double x to make it even */ ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; } m >>= 1; /* m = [m/2] */ /* generate sqrt(x) bit by bit */ ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ r = 0x00200000; /* r = moving bit from right to left */ while (r != 0) { t = s0 + r; if (t <= ix0) { s0 = t + r; ix0 -= t; q += r; } ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; r >>= 1; } r = sign; while (r != 0) { t1 = s1 + r; t = s0; if (t < ix0 || (t == ix0 && t1 <= ix1)) { s1 = t1 + r; if ((t1&sign) == sign && (s1 & sign) == 0) s0++; ix0 -= t; if (ix1 < t1) ix0--; ix1 -= t1; q1 += r; } ix0 += ix0 + ((ix1 & sign) >> 31); ix1 += ix1; r >>= 1; } /* use floating add to find out rounding direction */ if ((ix0 | ix1) != 0) { z = 1.0 - tiny; /* raise inexact flag */ if (z >= 1.0) { z = 1.0 + tiny; if (q1 == (unsigned int)0xffffffff) { q1 = 0; q++; } else if (z > 1.0) { if (q1 == (unsigned int)0xfffffffe) q++; q1 += 2; } else q1 += q1 & 1; } } ix0 = (q >> 1) + 0x3fe00000; ix1 = q1 >> 1; if (q & 1) ix1 |= sign; ix = ix0 + ((unsigned int)m << 20); ix <<= 32; ix |= ix1; return *(double*)&ix; #endif } /* Copied from musl: src/math/__tan.c */ static double __tan(double x, double y, int odd) { static const double T[] = { 3.33333333333334091986e-01, 1.33333333333201242699e-01, 5.39682539762260521377e-02, 2.18694882948595424599e-02, 8.86323982359930005737e-03, 3.59207910759131235356e-03, 1.45620945432529025516e-03, 5.88041240820264096874e-04, 2.46463134818469906812e-04, 7.81794442939557092300e-05, 7.14072491382608190305e-05, -1.85586374855275456654e-05, 2.59073051863633712884e-05, }; static const double pio4 = 7.85398163397448278999e-01; static const double pio4lo = 3.06161699786838301793e-17; double z, r, v, w, s, a, w0, a0; UINT32 hx; int big, sign; hx = *(ULONGLONG*)&x >> 32; big = (hx & 0x7fffffff) >= 0x3FE59428; /* |x| >= 0.6744 */ if (big) { sign = hx >> 31; if (sign) { x = -x; y = -y; } x = (pio4 - x) + (pio4lo - y); y = 0.0; } z = x * x; w = z * z; r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + w * T[11])))); v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + w * T[12]))))); s = z * x; r = y + z * (s * (r + v) + y) + s * T[0]; w = x + r; if (big) { s = 1 - 2 * odd; v = s - 2.0 * (x + (r - w * w / (w + s))); return sign ? -v : v; } if (!odd) return w; /* -1.0/(x+r) has up to 2ulp error, so compute it accurately */ w0 = w; *(LONGLONG*)&w0 = *(LONGLONG*)&w0 & 0xffffffff00000000ULL; v = r - (w0 - x); /* w0+v = r+x */ a0 = a = -1.0 / w; *(LONGLONG*)&a0 = *(LONGLONG*)&a0 & 0xffffffff00000000ULL; return a0 + a * (1.0 + a0 * w0 + a0 * v); } /********************************************************************* * tan (MSVCRT.@) * * Copied from musl: src/math/tan.c */ double CDECL tan( double x ) { double y[2]; UINT32 ix; unsigned n; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; if (ix <= 0x3fe921fb) { /* |x| ~< pi/4 */ if (ix < 0x3e400000) { /* |x| < 2**-27 */ /* raise inexact if x!=0 and underflow if subnormal */ fp_barrier(ix < 0x00100000 ? x / 0x1p120f : x + 0x1p120f); return x; } return __tan(x, 0.0, 0); } if (isinf(x)) return math_error(_DOMAIN, "tan", x, 0, x - x); if (ix >= 0x7ff00000) return x - x; n = __rem_pio2(x, y); return __tan(y[0], y[1], n & 1); } /********************************************************************* * tanh (MSVCRT.@) */ double CDECL tanh( double x ) { UINT64 ui = *(UINT64*)&x; UINT64 sign = ui & 0x8000000000000000ULL; UINT32 w; double t; /* x = |x| */ ui &= (UINT64)-1 / 2; x = *(double*)&ui; w = ui >> 32; if (w > 0x3fe193ea) { /* |x| > log(3)/2 ~= 0.5493 or nan */ if (w > 0x40340000) { if (ui > 0x7ff0000000000000ULL) { *(UINT64*)&x = ui | sign | 0x0008000000000000ULL; #if _MSVCR_VER < 140 return math_error(_DOMAIN, "tanh", x, 0, x); #else return x; #endif } /* |x| > 20 */ /* note: this branch avoids raising overflow */ fp_barrier(x + 0x1p120f); t = 1 - 0 / x; } else { t = __expm1(2 * x); t = 1 - 2 / (t + 2); } } else if (w > 0x3fd058ae) { /* |x| > log(5/3)/2 ~= 0.2554 */ t = __expm1(2 * x); t = t / (t + 2); } else if (w >= 0x00100000) { /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */ t = __expm1(-2 * x); t = -t / (t + 2); } else { /* |x| is subnormal */ /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */ fp_barrier((float)x); t = x; } return sign ? -t : t; } #if (defined(__GNUC__) || defined(__clang__)) && defined(__i386__) #define CREATE_FPU_FUNC1(name, call) \ __ASM_GLOBAL_FUNC(name, \ "pushl %ebp\n\t" \ __ASM_CFI(".cfi_adjust_cfa_offset 4\n\t") \ __ASM_CFI(".cfi_rel_offset %ebp,0\n\t") \ "movl %esp, %ebp\n\t" \ __ASM_CFI(".cfi_def_cfa_register %ebp\n\t") \ "subl $68, %esp\n\t" /* sizeof(double)*8 + sizeof(int) */ \ "fstpl (%esp)\n\t" /* store function argument */ \ "fwait\n\t" \ "movl $1, %ecx\n\t" /* empty FPU stack */ \ "1:\n\t" \ "fxam\n\t" \ "fstsw %ax\n\t" \ "and $0x4500, %ax\n\t" \ "cmp $0x4100, %ax\n\t" \ "je 2f\n\t" \ "fstpl (%esp,%ecx,8)\n\t" \ "fwait\n\t" \ "incl %ecx\n\t" \ "jmp 1b\n\t" \ "2:\n\t" \ "movl %ecx, -4(%ebp)\n\t" \ "call " __ASM_NAME( #call ) "\n\t" \ "movl -4(%ebp), %ecx\n\t" \ "fstpl (%esp)\n\t" /* save result */ \ "3:\n\t" /* restore FPU stack */ \ "decl %ecx\n\t" \ "fldl (%esp,%ecx,8)\n\t" \ "cmpl $0, %ecx\n\t" \ "jne 3b\n\t" \ "leave\n\t" \ __ASM_CFI(".cfi_def_cfa %esp,4\n\t") \ __ASM_CFI(".cfi_same_value %ebp\n\t") \ "ret") #define CREATE_FPU_FUNC2(name, call) \ __ASM_GLOBAL_FUNC(name, \ "pushl %ebp\n\t" \ __ASM_CFI(".cfi_adjust_cfa_offset 4\n\t") \ __ASM_CFI(".cfi_rel_offset %ebp,0\n\t") \ "movl %esp, %ebp\n\t" \ __ASM_CFI(".cfi_def_cfa_register %ebp\n\t") \ "subl $68, %esp\n\t" /* sizeof(double)*8 + sizeof(int) */ \ "fstpl 8(%esp)\n\t" /* store function argument */ \ "fwait\n\t" \ "fstpl (%esp)\n\t" \ "fwait\n\t" \ "movl $2, %ecx\n\t" /* empty FPU stack */ \ "1:\n\t" \ "fxam\n\t" \ "fstsw %ax\n\t" \ "and $0x4500, %ax\n\t" \ "cmp $0x4100, %ax\n\t" \ "je 2f\n\t" \ "fstpl (%esp,%ecx,8)\n\t" \ "fwait\n\t" \ "incl %ecx\n\t" \ "jmp 1b\n\t" \ "2:\n\t" \ "movl %ecx, -4(%ebp)\n\t" \ "call " __ASM_NAME( #call ) "\n\t" \ "movl -4(%ebp), %ecx\n\t" \ "fstpl 8(%esp)\n\t" /* save result */ \ "3:\n\t" /* restore FPU stack */ \ "decl %ecx\n\t" \ "fldl (%esp,%ecx,8)\n\t" \ "cmpl $1, %ecx\n\t" \ "jne 3b\n\t" \ "leave\n\t" \ __ASM_CFI(".cfi_def_cfa %esp,4\n\t") \ __ASM_CFI(".cfi_same_value %ebp\n\t") \ "ret") CREATE_FPU_FUNC1(_CIacos, acos) CREATE_FPU_FUNC1(_CIasin, asin) CREATE_FPU_FUNC1(_CIatan, atan) CREATE_FPU_FUNC2(_CIatan2, atan2) CREATE_FPU_FUNC1(_CIcos, cos) CREATE_FPU_FUNC1(_CIcosh, cosh) CREATE_FPU_FUNC1(_CIexp, exp) CREATE_FPU_FUNC2(_CIfmod, fmod) CREATE_FPU_FUNC1(_CIlog, log) CREATE_FPU_FUNC1(_CIlog10, log10) CREATE_FPU_FUNC2(_CIpow, pow) CREATE_FPU_FUNC1(_CIsin, sin) CREATE_FPU_FUNC1(_CIsinh, sinh) CREATE_FPU_FUNC1(_CIsqrt, sqrt) CREATE_FPU_FUNC1(_CItan, tan) CREATE_FPU_FUNC1(_CItanh, tanh) __ASM_GLOBAL_FUNC(_ftol, "pushl %ebp\n\t" __ASM_CFI(".cfi_adjust_cfa_offset 4\n\t") __ASM_CFI(".cfi_rel_offset %ebp,0\n\t") "movl %esp, %ebp\n\t" __ASM_CFI(".cfi_def_cfa_register %ebp\n\t") "subl $12, %esp\n\t" /* sizeof(LONGLONG) + 2*sizeof(WORD) */ "fnstcw (%esp)\n\t" "mov (%esp), %ax\n\t" "or $0xc00, %ax\n\t" "mov %ax, 2(%esp)\n\t" "fldcw 2(%esp)\n\t" "fistpq 4(%esp)\n\t" "fldcw (%esp)\n\t" "movl 4(%esp), %eax\n\t" "movl 8(%esp), %edx\n\t" "leave\n\t" __ASM_CFI(".cfi_def_cfa %esp,4\n\t") __ASM_CFI(".cfi_same_value %ebp\n\t") "ret") #endif /* (defined(__GNUC__) || defined(__clang__)) && defined(__i386__) */ /********************************************************************* * _fpclass (MSVCRT.@) */ int CDECL _fpclass(double num) { union { double f; UINT64 i; } u = { num }; int e = u.i >> 52 & 0x7ff; int s = u.i >> 63; switch (e) { case 0: if (u.i << 1) return s ? _FPCLASS_ND : _FPCLASS_PD; return s ? _FPCLASS_NZ : _FPCLASS_PZ; case 0x7ff: if (u.i << 12) return ((u.i >> 51) & 1) ? _FPCLASS_QNAN : _FPCLASS_SNAN; return s ? _FPCLASS_NINF : _FPCLASS_PINF; default: return s ? _FPCLASS_NN : _FPCLASS_PN; } } /********************************************************************* * _rotl (MSVCRT.@) */ unsigned int CDECL MSVCRT__rotl(unsigned int num, int shift) { shift &= 31; return (num << shift) | (num >> (32-shift)); } /********************************************************************* * _lrotl (MSVCRT.@) */ __msvcrt_ulong CDECL MSVCRT__lrotl(__msvcrt_ulong num, int shift) { shift &= 0x1f; return (num << shift) | (num >> (32-shift)); } /********************************************************************* * _lrotr (MSVCRT.@) */ __msvcrt_ulong CDECL MSVCRT__lrotr(__msvcrt_ulong num, int shift) { shift &= 0x1f; return (num >> shift) | (num << (32-shift)); } /********************************************************************* * _rotr (MSVCRT.@) */ unsigned int CDECL MSVCRT__rotr(unsigned int num, int shift) { shift &= 0x1f; return (num >> shift) | (num << (32-shift)); } /********************************************************************* * _rotl64 (MSVCRT.@) */ unsigned __int64 CDECL MSVCRT__rotl64(unsigned __int64 num, int shift) { shift &= 63; return (num << shift) | (num >> (64-shift)); } /********************************************************************* * _rotr64 (MSVCRT.@) */ unsigned __int64 CDECL MSVCRT__rotr64(unsigned __int64 num, int shift) { shift &= 63; return (num >> shift) | (num << (64-shift)); } /********************************************************************* * abs (MSVCRT.@) */ int CDECL abs( int n ) { return n >= 0 ? n : -n; } /********************************************************************* * labs (MSVCRT.@) */ __msvcrt_long CDECL labs( __msvcrt_long n ) { return n >= 0 ? n : -n; } #if _MSVCR_VER>=100 /********************************************************************* * llabs (MSVCR100.@) */ __int64 CDECL llabs( __int64 n ) { return n >= 0 ? n : -n; } #endif #if _MSVCR_VER>=120 /********************************************************************* * imaxabs (MSVCR120.@) */ intmax_t CDECL imaxabs( intmax_t n ) { return n >= 0 ? n : -n; } #endif /********************************************************************* * _abs64 (MSVCRT.@) */ __int64 CDECL _abs64( __int64 n ) { return n >= 0 ? n : -n; } /* Copied from musl: src/math/ilogb.c */ static int __ilogb(double x) { union { double f; UINT64 i; } u = { x }; int e = u.i >> 52 & 0x7ff; if (!e) { u.i <<= 12; if (u.i == 0) return FP_ILOGB0; /* subnormal x */ for (e = -0x3ff; u.i >> 63 == 0; e--, u.i <<= 1); return e; } if (e == 0x7ff) return u.i << 12 ? FP_ILOGBNAN : INT_MAX; return e - 0x3ff; } /********************************************************************* * _logb (MSVCRT.@) * * Copied from musl: src/math/logb.c */ double CDECL _logb(double x) { if (!isfinite(x)) return x * x; if (x == 0) return math_error(_SING, "_logb", x, 0, -1 / (x * x)); return __ilogb(x); } static void sq(double *hi, double *lo, double x) { double xh, xl, xc; xc = x * (0x1p27 + 1); xh = x - xc + xc; xl = x - xh; *hi = x * x; *lo = xh * xh - *hi + 2 * xh * xl + xl * xl; } /********************************************************************* * _hypot (MSVCRT.@) * * Copied from musl: src/math/hypot.c */ double CDECL _hypot(double x, double y) { UINT64 ux = *(UINT64*)&x, uy = *(UINT64*)&y, ut; double hx, lx, hy, ly, z; int ex, ey; /* arrange |x| >= |y| */ ux &= -1ULL >> 1; uy &= -1ULL >> 1; if (ux < uy) { ut = ux; ux = uy; uy = ut; } /* special cases */ ex = ux >> 52; ey = uy >> 52; x = *(double*)&ux; y = *(double*)&uy; /* note: hypot(inf,nan) == inf */ if (ey == 0x7ff) return y; if (ex == 0x7ff || uy == 0) return x; /* note: hypot(x,y) ~= x + y*y/x/2 with inexact for small y/x */ /* 64 difference is enough for ld80 double_t */ if (ex - ey > 64) return x + y; /* precise sqrt argument in nearest rounding mode without overflow */ /* xh*xh must not overflow and xl*xl must not underflow in sq */ z = 1; if (ex > 0x3ff + 510) { z = 0x1p700; x *= 0x1p-700; y *= 0x1p-700; } else if (ey < 0x3ff - 450) { z = 0x1p-700; x *= 0x1p700; y *= 0x1p700; } sq(&hx, &lx, x); sq(&hy, &ly, y); return z * sqrt(ly + lx + hy + hx); } /********************************************************************* * _hypotf (MSVCRT.@) * * Copied from musl: src/math/hypotf.c */ float CDECL _hypotf(float x, float y) { UINT32 ux = *(UINT32*)&x, uy = *(UINT32*)&y, ut; float z; ux &= -1U >> 1; uy &= -1U >> 1; if (ux < uy) { ut = ux; ux = uy; uy = ut; } x = *(float*)&ux; y = *(float*)&uy; if (uy == 0xff << 23) return y; if (ux >= 0xff << 23 || uy == 0 || ux - uy >= 25 << 23) return x + y; z = 1; if (ux >= (0x7f + 60) << 23) { z = 0x1p90f; x *= 0x1p-90f; y *= 0x1p-90f; } else if (uy < (0x7f - 60) << 23) { z = 0x1p-90f; x *= 0x1p90f; y *= 0x1p90f; } return z * sqrtf((double)x * x + (double)y * y); } /********************************************************************* * ceil (MSVCRT.@) * * Based on musl: src/math/ceilf.c */ double CDECL ceil( double x ) { union {double f; UINT64 i;} u = {x}; int e = (u.i >> 52 & 0x7ff) - 0x3ff; UINT64 m; if (e >= 52) return x; if (e >= 0) { m = 0x000fffffffffffffULL >> e; if ((u.i & m) == 0) return x; if (u.i >> 63 == 0) u.i += m; u.i &= ~m; } else { if (u.i >> 63) return -0.0; else if (u.i << 1) return 1.0; } return u.f; } /********************************************************************* * floor (MSVCRT.@) * * Based on musl: src/math/floorf.c */ double CDECL floor( double x ) { union {double f; UINT64 i;} u = {x}; int e = (int)(u.i >> 52 & 0x7ff) - 0x3ff; UINT64 m; if (e >= 52) return x; if (e >= 0) { m = 0x000fffffffffffffULL >> e; if ((u.i & m) == 0) return x; if (u.i >> 63) u.i += m; u.i &= ~m; } else { if (u.i >> 63 == 0) return 0; else if (u.i << 1) return -1; } return u.f; } /********************************************************************* * fma (MSVCRT.@) * * Copied from musl: src/math/fma.c */ struct fma_num { UINT64 m; int e; int sign; }; static struct fma_num normalize(double x) { UINT64 ix = *(UINT64*)&x; int e = ix >> 52; int sign = e & 0x800; struct fma_num ret; e &= 0x7ff; if (!e) { x *= 0x1p63; ix = *(UINT64*)&x; e = ix >> 52 & 0x7ff; e = e ? e - 63 : 0x800; } ix &= (1ull << 52) - 1; ix |= 1ull << 52; ix <<= 1; e -= 0x3ff + 52 + 1; ret.m = ix; ret.e = e; ret.sign = sign; return ret; } static void mul(UINT64 *hi, UINT64 *lo, UINT64 x, UINT64 y) { UINT64 t1, t2, t3; UINT64 xlo = (UINT32)x, xhi = x >> 32; UINT64 ylo = (UINT32)y, yhi = y >> 32; t1 = xlo * ylo; t2 = xlo * yhi + xhi * ylo; t3 = xhi * yhi; *lo = t1 + (t2 << 32); *hi = t3 + (t2 >> 32) + (t1 > *lo); } double CDECL fma( double x, double y, double z ) { int e, d, sign, samesign, nonzero; UINT64 rhi, rlo, zhi, zlo; struct fma_num nx, ny, nz; double r; INT64 i; /* normalize so top 10bits and last bit are 0 */ nx = normalize(x); ny = normalize(y); nz = normalize(z); if (nx.e >= 0x7ff - 0x3ff - 52 - 1 || ny.e >= 0x7ff - 0x3ff - 52 - 1) { r = x * y + z; if (!isnan(x) && !isnan(y) && !isnan(z) && isnan(r)) *_errno() = EDOM; return r; } if (nz.e >= 0x7ff - 0x3ff - 52 - 1) { if (nz.e > 0x7ff - 0x3ff - 52 - 1) {/* z==0 */ r = x * y + z; if (!isnan(x) && !isnan(y) && isnan(r)) *_errno() = EDOM; return r; } return z; } /* mul: r = x*y */ mul(&rhi, &rlo, nx.m, ny.m); /* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */ /* align exponents */ e = nx.e + ny.e; d = nz.e - e; /* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */ if (d > 0) { if (d < 64) { zlo = nz.m << d; zhi = nz.m >> (64 - d); } else { zlo = 0; zhi = nz.m; e = nz.e - 64; d -= 64; if (d < 64 && d) { rlo = rhi << (64 - d) | rlo >> d | !!(rlo << (64 - d)); rhi = rhi >> d; } else if (d) { rlo = 1; rhi = 0; } } } else { zhi = 0; d = -d; if (d == 0) { zlo = nz.m; } else if (d < 64) { zlo = nz.m >> d | !!(nz.m << (64 - d)); } else { zlo = 1; } } /* add */ sign = nx.sign ^ ny.sign; samesign = !(sign ^ nz.sign); nonzero = 1; if (samesign) { /* r += z */ rlo += zlo; rhi += zhi + (rlo < zlo); } else { /* r -= z */ UINT64 t = rlo; rlo -= zlo; rhi = rhi - zhi - (t < rlo); if (rhi >> 63) { rlo = -rlo; rhi = -rhi - !!rlo; sign = !sign; } nonzero = !!rhi; } /* set rhi to top 63bit of the result (last bit is sticky) */ if (nonzero) { e += 64; if (rhi >> 32) { BitScanReverse((DWORD*)&d, rhi >> 32); d = 31 - d - 1; } else { BitScanReverse((DWORD*)&d, rhi); d = 63 - d - 1; } /* note: d > 0 */ rhi = rhi << d | rlo >> (64 - d) | !!(rlo << d); } else if (rlo) { if (rlo >> 32) { BitScanReverse((DWORD*)&d, rlo >> 32); d = 31 - d - 1; } else { BitScanReverse((DWORD*)&d, rlo); d = 63 - d - 1; } if (d < 0) rhi = rlo >> 1 | (rlo & 1); else rhi = rlo << d; } else { /* exact +-0 */ return x * y + z; } e -= d; /* convert to double */ i = rhi; /* i is in [1<<62,(1<<63)-1] */ if (sign) i = -i; r = i; /* |r| is in [0x1p62,0x1p63] */ if (e < -1022 - 62) { /* result is subnormal before rounding */ if (e == -1022 - 63) { double c = 0x1p63; if (sign) c = -c; if (r == c) { /* min normal after rounding, underflow depends on arch behaviour which can be imitated by a double to float conversion */ float fltmin = 0x0.ffffff8p-63 * FLT_MIN * r; return DBL_MIN / FLT_MIN * fltmin; } /* one bit is lost when scaled, add another top bit to only round once at conversion if it is inexact */ if (rhi << 53) { double tiny; i = rhi >> 1 | (rhi & 1) | 1ull << 62; if (sign) i = -i; r = i; r = 2 * r - c; /* remove top bit */ /* raise underflow portably, such that it cannot be optimized away */ tiny = DBL_MIN / FLT_MIN * r; r += (double)(tiny * tiny) * (r - r); } } else { /* only round once when scaled */ d = 10; i = (rhi >> d | !!(rhi << (64 - d))) << d; if (sign) i = -i; r = i; } } return __scalbn(r, e); } /********************************************************************* * fmaf (MSVCRT.@) * * Copied from musl: src/math/fmaf.c */ float CDECL fmaf( float x, float y, float z ) { union { double f; UINT64 i; } u; double xy, adjust; int e; xy = (double)x * y; u.f = xy + z; e = u.i>>52 & 0x7ff; /* Common case: The double precision result is fine. */ if ((u.i & 0x1fffffff) != 0x10000000 || /* not a halfway case */ e == 0x7ff || /* NaN */ (u.f - xy == z && u.f - z == xy) || /* exact */ (_controlfp(0, 0) & _MCW_RC) != _RC_NEAR) /* not round-to-nearest */ { if (!isnan(x) && !isnan(y) && !isnan(z) && isnan(u.f)) *_errno() = EDOM; /* underflow may not be raised correctly, example: fmaf(0x1p-120f, 0x1p-120f, 0x1p-149f) */ if (e < 0x3ff-126 && e >= 0x3ff-149 && _statusfp() & _SW_INEXACT) fp_barrierf((float)u.f * (float)u.f); return u.f; } /* * If result is inexact, and exactly halfway between two float values, * we need to adjust the low-order bit in the direction of the error. */ _controlfp(_RC_CHOP, _MCW_RC); adjust = fp_barrier(xy + z); _controlfp(_RC_NEAR, _MCW_RC); if (u.f == adjust) u.i++; return u.f; } /********************************************************************* * fabs (MSVCRT.@) * * Copied from musl: src/math/fabsf.c */ double CDECL fabs( double x ) { union { double f; UINT64 i; } u = { x }; u.i &= ~0ull >> 1; return u.f; } /********************************************************************* * frexp (MSVCRT.@) * * Copied from musl: src/math/frexp.c */ double CDECL frexp( double x, int *e ) { UINT64 ux = *(UINT64*)&x; int ee = ux >> 52 & 0x7ff; if (!ee) { if (x) { x = frexp(x * 0x1p64, e); *e -= 64; } else *e = 0; return x; } else if (ee == 0x7ff) { return x; } *e = ee - 0x3fe; ux &= 0x800fffffffffffffull; ux |= 0x3fe0000000000000ull; return *(double*)&ux; } /********************************************************************* * modf (MSVCRT.@) * * Copied from musl: src/math/modf.c */ double CDECL modf( double x, double *iptr ) { union {double f; UINT64 i;} u = {x}; UINT64 mask; int e = (u.i >> 52 & 0x7ff) - 0x3ff; /* no fractional part */ if (e >= 52) { *iptr = x; if (e == 0x400 && u.i << 12 != 0) /* nan */ return x; u.i &= 1ULL << 63; return u.f; } /* no integral part*/ if (e < 0) { u.i &= 1ULL << 63; *iptr = u.f; return x; } mask = -1ULL >> 12 >> e; if ((u.i & mask) == 0) { *iptr = x; u.i &= 1ULL << 63; return u.f; } u.i &= ~mask; *iptr = u.f; return x - u.f; } #if defined(__i386__) || defined(__x86_64__) static void _setfp_sse( unsigned int *cw, unsigned int cw_mask, unsigned int *sw, unsigned int sw_mask ) { #if defined(__GNUC__) || defined(__clang__) unsigned long old_fpword, fpword; unsigned int flags; __asm__ __volatile__( "stmxcsr %0" : "=m" (fpword) ); old_fpword = fpword; cw_mask &= _MCW_EM | _MCW_RC | _MCW_DN; sw_mask &= _MCW_EM; if (sw) { flags = 0; if (fpword & 0x1) flags |= _SW_INVALID; if (fpword & 0x2) flags |= _SW_DENORMAL; if (fpword & 0x4) flags |= _SW_ZERODIVIDE; if (fpword & 0x8) flags |= _SW_OVERFLOW; if (fpword & 0x10) flags |= _SW_UNDERFLOW; if (fpword & 0x20) flags |= _SW_INEXACT; *sw = (flags & ~sw_mask) | (*sw & sw_mask); TRACE("sse2 update sw %08x to %08x\n", flags, *sw); fpword &= ~0x3f; if (*sw & _SW_INVALID) fpword |= 0x1; if (*sw & _SW_DENORMAL) fpword |= 0x2; if (*sw & _SW_ZERODIVIDE) fpword |= 0x4; if (*sw & _SW_OVERFLOW) fpword |= 0x8; if (*sw & _SW_UNDERFLOW) fpword |= 0x10; if (*sw & _SW_INEXACT) fpword |= 0x20; *sw = flags; } if (cw) { flags = 0; if (fpword & 0x80) flags |= _EM_INVALID; if (fpword & 0x100) flags |= _EM_DENORMAL; if (fpword & 0x200) flags |= _EM_ZERODIVIDE; if (fpword & 0x400) flags |= _EM_OVERFLOW; if (fpword & 0x800) flags |= _EM_UNDERFLOW; if (fpword & 0x1000) flags |= _EM_INEXACT; switch (fpword & 0x6000) { case 0x6000: flags |= _RC_UP|_RC_DOWN; break; case 0x4000: flags |= _RC_UP; break; case 0x2000: flags |= _RC_DOWN; break; } switch (fpword & 0x8040) { case 0x0040: flags |= _DN_FLUSH_OPERANDS_SAVE_RESULTS; break; case 0x8000: flags |= _DN_SAVE_OPERANDS_FLUSH_RESULTS; break; case 0x8040: flags |= _DN_FLUSH; break; } *cw = (flags & ~cw_mask) | (*cw & cw_mask); TRACE("sse2 update cw %08x to %08x\n", flags, *cw); fpword &= ~0xffc0; if (*cw & _EM_INVALID) fpword |= 0x80; if (*cw & _EM_DENORMAL) fpword |= 0x100; if (*cw & _EM_ZERODIVIDE) fpword |= 0x200; if (*cw & _EM_OVERFLOW) fpword |= 0x400; if (*cw & _EM_UNDERFLOW) fpword |= 0x800; if (*cw & _EM_INEXACT) fpword |= 0x1000; switch (*cw & _MCW_RC) { case _RC_UP|_RC_DOWN: fpword |= 0x6000; break; case _RC_UP: fpword |= 0x4000; break; case _RC_DOWN: fpword |= 0x2000; break; } switch (*cw & _MCW_DN) { case _DN_FLUSH_OPERANDS_SAVE_RESULTS: fpword |= 0x0040; break; case _DN_SAVE_OPERANDS_FLUSH_RESULTS: fpword |= 0x8000; break; case _DN_FLUSH: fpword |= 0x8040; break; } /* clear status word if anything changes */ if (fpword != old_fpword && !sw) { TRACE("sse2 clear status word\n"); fpword &= ~0x3f; } } if (fpword != old_fpword) __asm__ __volatile__( "ldmxcsr %0" : : "m" (fpword) ); #else FIXME("not implemented\n"); if (cw) *cw = 0; if (sw) *sw = 0; #endif } #endif static void _setfp( unsigned int *cw, unsigned int cw_mask, unsigned int *sw, unsigned int sw_mask ) { #if (defined(__GNUC__) || defined(__clang__)) && defined(__i386__) unsigned long oldcw = 0, newcw = 0; unsigned long oldsw = 0, newsw = 0; unsigned int flags; cw_mask &= _MCW_EM | _MCW_IC | _MCW_RC | _MCW_PC; sw_mask &= _MCW_EM; if (sw) { __asm__ __volatile__( "fstsw %0" : "=m" (newsw) ); oldsw = newsw; flags = 0; if (newsw & 0x1) flags |= _SW_INVALID; if (newsw & 0x2) flags |= _SW_DENORMAL; if (newsw & 0x4) flags |= _SW_ZERODIVIDE; if (newsw & 0x8) flags |= _SW_OVERFLOW; if (newsw & 0x10) flags |= _SW_UNDERFLOW; if (newsw & 0x20) flags |= _SW_INEXACT; *sw = (flags & ~sw_mask) | (*sw & sw_mask); TRACE("x86 update sw %08x to %08x\n", flags, *sw); newsw &= ~0x3f; if (*sw & _SW_INVALID) newsw |= 0x1; if (*sw & _SW_DENORMAL) newsw |= 0x2; if (*sw & _SW_ZERODIVIDE) newsw |= 0x4; if (*sw & _SW_OVERFLOW) newsw |= 0x8; if (*sw & _SW_UNDERFLOW) newsw |= 0x10; if (*sw & _SW_INEXACT) newsw |= 0x20; *sw = flags; } if (cw) { __asm__ __volatile__( "fstcw %0" : "=m" (newcw) ); oldcw = newcw; flags = 0; if (newcw & 0x1) flags |= _EM_INVALID; if (newcw & 0x2) flags |= _EM_DENORMAL; if (newcw & 0x4) flags |= _EM_ZERODIVIDE; if (newcw & 0x8) flags |= _EM_OVERFLOW; if (newcw & 0x10) flags |= _EM_UNDERFLOW; if (newcw & 0x20) flags |= _EM_INEXACT; switch (newcw & 0xc00) { case 0xc00: flags |= _RC_UP|_RC_DOWN; break; case 0x800: flags |= _RC_UP; break; case 0x400: flags |= _RC_DOWN; break; } switch (newcw & 0x300) { case 0x0: flags |= _PC_24; break; case 0x200: flags |= _PC_53; break; case 0x300: flags |= _PC_64; break; } if (newcw & 0x1000) flags |= _IC_AFFINE; *cw = (flags & ~cw_mask) | (*cw & cw_mask); TRACE("x86 update cw %08x to %08x\n", flags, *cw); newcw &= ~0x1f3f; if (*cw & _EM_INVALID) newcw |= 0x1; if (*cw & _EM_DENORMAL) newcw |= 0x2; if (*cw & _EM_ZERODIVIDE) newcw |= 0x4; if (*cw & _EM_OVERFLOW) newcw |= 0x8; if (*cw & _EM_UNDERFLOW) newcw |= 0x10; if (*cw & _EM_INEXACT) newcw |= 0x20; switch (*cw & _MCW_RC) { case _RC_UP|_RC_DOWN: newcw |= 0xc00; break; case _RC_UP: newcw |= 0x800; break; case _RC_DOWN: newcw |= 0x400; break; } switch (*cw & _MCW_PC) { case _PC_64: newcw |= 0x300; break; case _PC_53: newcw |= 0x200; break; case _PC_24: newcw |= 0x0; break; } if (*cw & _IC_AFFINE) newcw |= 0x1000; } if (oldsw != newsw && (newsw & 0x3f)) { struct { WORD control_word; WORD unused1; WORD status_word; WORD unused2; WORD tag_word; WORD unused3; DWORD instruction_pointer; WORD code_segment; WORD unused4; DWORD operand_addr; WORD data_segment; WORD unused5; } fenv; assert(cw); __asm__ __volatile__( "fnstenv %0" : "=m" (fenv) ); fenv.control_word = newcw; fenv.status_word = newsw; __asm__ __volatile__( "fldenv %0" : : "m" (fenv) : "st", "st(1)", "st(2)", "st(3)", "st(4)", "st(5)", "st(6)", "st(7)" ); return; } if (oldsw != newsw) __asm__ __volatile__( "fnclex" ); if (oldcw != newcw) __asm__ __volatile__( "fldcw %0" : : "m" (newcw) ); #elif defined(__x86_64__) _setfp_sse(cw, cw_mask, sw, sw_mask); #elif defined(__aarch64__) ULONG_PTR old_fpsr = 0, fpsr = 0, old_fpcr = 0, fpcr = 0; unsigned int flags; cw_mask &= _MCW_EM | _MCW_RC; sw_mask &= _MCW_EM; if (sw) { __asm__ __volatile__( "mrs %0, fpsr" : "=r" (fpsr) ); old_fpsr = fpsr; flags = 0; if (fpsr & 0x1) flags |= _SW_INVALID; if (fpsr & 0x2) flags |= _SW_ZERODIVIDE; if (fpsr & 0x4) flags |= _SW_OVERFLOW; if (fpsr & 0x8) flags |= _SW_UNDERFLOW; if (fpsr & 0x10) flags |= _SW_INEXACT; if (fpsr & 0x80) flags |= _SW_DENORMAL; *sw = (flags & ~sw_mask) | (*sw & sw_mask); TRACE("aarch64 update sw %08x to %08x\n", flags, *sw); fpsr &= ~0x9f; if (*sw & _SW_INVALID) fpsr |= 0x1; if (*sw & _SW_ZERODIVIDE) fpsr |= 0x2; if (*sw & _SW_OVERFLOW) fpsr |= 0x4; if (*sw & _SW_UNDERFLOW) fpsr |= 0x8; if (*sw & _SW_INEXACT) fpsr |= 0x10; if (*sw & _SW_DENORMAL) fpsr |= 0x80; *sw = flags; } if (cw) { __asm__ __volatile__( "mrs %0, fpcr" : "=r" (fpcr) ); old_fpcr = fpcr; flags = 0; if (!(fpcr & 0x100)) flags |= _EM_INVALID; if (!(fpcr & 0x200)) flags |= _EM_ZERODIVIDE; if (!(fpcr & 0x400)) flags |= _EM_OVERFLOW; if (!(fpcr & 0x800)) flags |= _EM_UNDERFLOW; if (!(fpcr & 0x1000)) flags |= _EM_INEXACT; if (!(fpcr & 0x8000)) flags |= _EM_DENORMAL; switch (fpcr & 0xc00000) { case 0x400000: flags |= _RC_UP; break; case 0x800000: flags |= _RC_DOWN; break; case 0xc00000: flags |= _RC_CHOP; break; } *cw = (flags & ~cw_mask) | (*cw & cw_mask); TRACE("aarch64 update cw %08x to %08x\n", flags, *cw); fpcr &= ~0xc09f00ul; if (!(*cw & _EM_INVALID)) fpcr |= 0x100; if (!(*cw & _EM_ZERODIVIDE)) fpcr |= 0x200; if (!(*cw & _EM_OVERFLOW)) fpcr |= 0x400; if (!(*cw & _EM_UNDERFLOW)) fpcr |= 0x800; if (!(*cw & _EM_INEXACT)) fpcr |= 0x1000; if (!(*cw & _EM_DENORMAL)) fpcr |= 0x8000; switch (*cw & _MCW_RC) { case _RC_CHOP: fpcr |= 0xc00000; break; case _RC_UP: fpcr |= 0x400000; break; case _RC_DOWN: fpcr |= 0x800000; break; } } /* mask exceptions if needed */ if (old_fpcr != fpcr && ~(old_fpcr >> 8) & fpsr & 0x9f != fpsr & 0x9f) { ULONG_PTR mask = fpcr & ~0x9f00; __asm__ __volatile__( "msr fpcr, %0" :: "r" (mask) ); } if (old_fpsr != fpsr) __asm__ __volatile__( "msr fpsr, %0" :: "r" (fpsr) ); if (old_fpcr != fpcr) __asm__ __volatile__( "msr fpcr, %0" :: "r" (fpcr) ); #elif defined(__arm__) && !defined(__SOFTFP__) DWORD old_fpscr, fpscr; unsigned int flags; __asm__ __volatile__( "vmrs %0, fpscr" : "=r" (fpscr) ); old_fpscr = fpscr; cw_mask &= _MCW_EM | _MCW_RC; sw_mask &= _MCW_EM; if (sw) { flags = 0; if (fpscr & 0x1) flags |= _SW_INVALID; if (fpscr & 0x2) flags |= _SW_ZERODIVIDE; if (fpscr & 0x4) flags |= _SW_OVERFLOW; if (fpscr & 0x8) flags |= _SW_UNDERFLOW; if (fpscr & 0x10) flags |= _SW_INEXACT; if (fpscr & 0x80) flags |= _SW_DENORMAL; *sw = (flags & ~sw_mask) | (*sw & sw_mask); TRACE("arm update sw %08x to %08x\n", flags, *sw); fpscr &= ~0x9f; if (*sw & _SW_INVALID) fpscr |= 0x1; if (*sw & _SW_ZERODIVIDE) fpscr |= 0x2; if (*sw & _SW_OVERFLOW) fpscr |= 0x4; if (*sw & _SW_UNDERFLOW) fpscr |= 0x8; if (*sw & _SW_INEXACT) fpscr |= 0x10; if (*sw & _SW_DENORMAL) fpscr |= 0x80; *sw = flags; } if (cw) { flags = 0; if (!(fpscr & 0x100)) flags |= _EM_INVALID; if (!(fpscr & 0x200)) flags |= _EM_ZERODIVIDE; if (!(fpscr & 0x400)) flags |= _EM_OVERFLOW; if (!(fpscr & 0x800)) flags |= _EM_UNDERFLOW; if (!(fpscr & 0x1000)) flags |= _EM_INEXACT; if (!(fpscr & 0x8000)) flags |= _EM_DENORMAL; switch (fpscr & 0xc00000) { case 0x400000: flags |= _RC_UP; break; case 0x800000: flags |= _RC_DOWN; break; case 0xc00000: flags |= _RC_CHOP; break; } *cw = (flags & ~cw_mask) | (*cw & cw_mask); TRACE("arm update cw %08x to %08x\n", flags, *cw); fpscr &= ~0xc09f00ul; if (!(*cw & _EM_INVALID)) fpscr |= 0x100; if (!(*cw & _EM_ZERODIVIDE)) fpscr |= 0x200; if (!(*cw & _EM_OVERFLOW)) fpscr |= 0x400; if (!(*cw & _EM_UNDERFLOW)) fpscr |= 0x800; if (!(*cw & _EM_INEXACT)) fpscr |= 0x1000; if (!(*cw & _EM_DENORMAL)) fpscr |= 0x8000; switch (*cw & _MCW_RC) { case _RC_CHOP: fpscr |= 0xc00000; break; case _RC_UP: fpscr |= 0x400000; break; case _RC_DOWN: fpscr |= 0x800000; break; } } if (old_fpscr != fpscr) __asm__ __volatile__( "vmsr fpscr, %0" :: "r" (fpscr) ); #else FIXME("not implemented\n"); if (cw) *cw = 0; if (sw) *sw = 0; #endif } /********************************************************************** * _statusfp2 (MSVCR80.@) */ #if defined(__i386__) void CDECL _statusfp2( unsigned int *x86_sw, unsigned int *sse2_sw ) { if (x86_sw) _setfp(NULL, 0, x86_sw, 0); if (!sse2_sw) return; if (sse2_supported) _setfp_sse(NULL, 0, sse2_sw, 0); else *sse2_sw = 0; } #endif /********************************************************************** * _statusfp (MSVCRT.@) */ unsigned int CDECL _statusfp(void) { unsigned int flags = 0; #if defined(__i386__) unsigned int x86_sw, sse2_sw; _statusfp2( &x86_sw, &sse2_sw ); /* FIXME: there's no definition for ambiguous status, just return all status bits for now */ flags = x86_sw | sse2_sw; #else _setfp(NULL, 0, &flags, 0); #endif return flags; } /********************************************************************* * _clearfp (MSVCRT.@) */ unsigned int CDECL _clearfp(void) { unsigned int flags = 0; #ifdef __i386__ _setfp(NULL, 0, &flags, _MCW_EM); if (sse2_supported) { unsigned int sse_sw = 0; _setfp_sse(NULL, 0, &sse_sw, _MCW_EM); flags |= sse_sw; } #else _setfp(NULL, 0, &flags, _MCW_EM); #endif return flags; } /********************************************************************* * __fpecode (MSVCRT.@) */ int * CDECL __fpecode(void) { return &msvcrt_get_thread_data()->fpecode; } /********************************************************************* * ldexp (MSVCRT.@) */ double CDECL ldexp(double num, int exp) { double z = __scalbn(num, exp); if (isfinite(num) && !isfinite(z)) return math_error(_OVERFLOW, "ldexp", num, exp, z); if (num && isfinite(num) && !z) return math_error(_UNDERFLOW, "ldexp", num, exp, z); return z; } /********************************************************************* * _cabs (MSVCRT.@) */ double CDECL _cabs(struct _complex num) { return sqrt(num.x * num.x + num.y * num.y); } /********************************************************************* * _chgsign (MSVCRT.@) */ double CDECL _chgsign(double num) { union { double f; UINT64 i; } u = { num }; u.i ^= 1ull << 63; return u.f; } /********************************************************************* * __control87_2 (MSVCR80.@) * * Not exported by native msvcrt, added in msvcr80. */ #ifdef __i386__ int CDECL __control87_2( unsigned int newval, unsigned int mask, unsigned int *x86_cw, unsigned int *sse2_cw ) { if (x86_cw) { *x86_cw = newval; _setfp(x86_cw, mask, NULL, 0); } if (!sse2_cw) return 1; if (sse2_supported) { *sse2_cw = newval; _setfp_sse(sse2_cw, mask, NULL, 0); } else *sse2_cw = 0; return 1; } #endif /********************************************************************* * _control87 (MSVCRT.@) */ unsigned int CDECL _control87(unsigned int newval, unsigned int mask) { unsigned int flags = 0; #ifdef __i386__ unsigned int sse2_cw; __control87_2( newval, mask, &flags, &sse2_cw ); if (sse2_supported) { if ((flags ^ sse2_cw) & (_MCW_EM | _MCW_RC)) flags |= _EM_AMBIGUOUS; flags |= sse2_cw; } #else flags = newval; _setfp(&flags, mask, NULL, 0); #endif return flags; } /********************************************************************* * _controlfp (MSVCRT.@) */ unsigned int CDECL _controlfp(unsigned int newval, unsigned int mask) { return _control87( newval, mask & ~_EM_DENORMAL ); } /********************************************************************* * _set_controlfp (MSVCRT.@) */ void CDECL _set_controlfp( unsigned int newval, unsigned int mask ) { _controlfp( newval, mask ); } /********************************************************************* * _controlfp_s (MSVCRT.@) */ int CDECL _controlfp_s(unsigned int *cur, unsigned int newval, unsigned int mask) { static const unsigned int all_flags = (_MCW_EM | _MCW_IC | _MCW_RC | _MCW_PC | _MCW_DN); unsigned int val; if (!MSVCRT_CHECK_PMT( !(newval & mask & ~all_flags) )) { if (cur) *cur = _controlfp( 0, 0 ); /* retrieve it anyway */ return EINVAL; } val = _controlfp( newval, mask ); if (cur) *cur = val; return 0; } #if _MSVCR_VER >= 140 && (defined(__i386__) || defined(__x86_64__)) enum fenv_masks { FENV_X_INVALID = 0x00100010, FENV_X_DENORMAL = 0x00200020, FENV_X_ZERODIVIDE = 0x00080008, FENV_X_OVERFLOW = 0x00040004, FENV_X_UNDERFLOW = 0x00020002, FENV_X_INEXACT = 0x00010001, FENV_X_AFFINE = 0x00004000, FENV_X_UP = 0x00800200, FENV_X_DOWN = 0x00400100, FENV_X_24 = 0x00002000, FENV_X_53 = 0x00001000, FENV_Y_INVALID = 0x10000010, FENV_Y_DENORMAL = 0x20000020, FENV_Y_ZERODIVIDE = 0x08000008, FENV_Y_OVERFLOW = 0x04000004, FENV_Y_UNDERFLOW = 0x02000002, FENV_Y_INEXACT = 0x01000001, FENV_Y_UP = 0x80000200, FENV_Y_DOWN = 0x40000100, FENV_Y_FLUSH = 0x00000400, FENV_Y_FLUSH_SAVE = 0x00000800 }; /* encodes x87/sse control/status word in ulong */ static __msvcrt_ulong fenv_encode(unsigned int x, unsigned int y) { __msvcrt_ulong ret = 0; #ifdef __i386__ if (x & _EM_INVALID) ret |= FENV_X_INVALID; if (x & _EM_DENORMAL) ret |= FENV_X_DENORMAL; if (x & _EM_ZERODIVIDE) ret |= FENV_X_ZERODIVIDE; if (x & _EM_OVERFLOW) ret |= FENV_X_OVERFLOW; if (x & _EM_UNDERFLOW) ret |= FENV_X_UNDERFLOW; if (x & _EM_INEXACT) ret |= FENV_X_INEXACT; if (x & _IC_AFFINE) ret |= FENV_X_AFFINE; if (x & _RC_UP) ret |= FENV_X_UP; if (x & _RC_DOWN) ret |= FENV_X_DOWN; if (x & _PC_24) ret |= FENV_X_24; if (x & _PC_53) ret |= FENV_X_53; #endif x &= ~(_MCW_EM | _MCW_IC | _MCW_RC | _MCW_PC); if (y & _EM_INVALID) ret |= FENV_Y_INVALID; if (y & _EM_DENORMAL) ret |= FENV_Y_DENORMAL; if (y & _EM_ZERODIVIDE) ret |= FENV_Y_ZERODIVIDE; if (y & _EM_OVERFLOW) ret |= FENV_Y_OVERFLOW; if (y & _EM_UNDERFLOW) ret |= FENV_Y_UNDERFLOW; if (y & _EM_INEXACT) ret |= FENV_Y_INEXACT; if (y & _RC_UP) ret |= FENV_Y_UP; if (y & _RC_DOWN) ret |= FENV_Y_DOWN; if (y & _DN_FLUSH) ret |= FENV_Y_FLUSH; if (y & _DN_FLUSH_OPERANDS_SAVE_RESULTS) ret |= FENV_Y_FLUSH_SAVE; y &= ~(_MCW_EM | _MCW_IC | _MCW_RC | _MCW_DN); if(x || y) FIXME("unsupported flags: %x, %x\n", x, y); return ret; } /* decodes x87/sse control/status word, returns FALSE on error */ static BOOL fenv_decode(__msvcrt_ulong enc, unsigned int *x, unsigned int *y) { *x = *y = 0; if ((enc & FENV_X_INVALID) == FENV_X_INVALID) *x |= _EM_INVALID; if ((enc & FENV_X_DENORMAL) == FENV_X_DENORMAL) *x |= _EM_DENORMAL; if ((enc & FENV_X_ZERODIVIDE) == FENV_X_ZERODIVIDE) *x |= _EM_ZERODIVIDE; if ((enc & FENV_X_OVERFLOW) == FENV_X_OVERFLOW) *x |= _EM_OVERFLOW; if ((enc & FENV_X_UNDERFLOW) == FENV_X_UNDERFLOW) *x |= _EM_UNDERFLOW; if ((enc & FENV_X_INEXACT) == FENV_X_INEXACT) *x |= _EM_INEXACT; if ((enc & FENV_X_AFFINE) == FENV_X_AFFINE) *x |= _IC_AFFINE; if ((enc & FENV_X_UP) == FENV_X_UP) *x |= _RC_UP; if ((enc & FENV_X_DOWN) == FENV_X_DOWN) *x |= _RC_DOWN; if ((enc & FENV_X_24) == FENV_X_24) *x |= _PC_24; if ((enc & FENV_X_53) == FENV_X_53) *x |= _PC_53; if ((enc & FENV_Y_INVALID) == FENV_Y_INVALID) *y |= _EM_INVALID; if ((enc & FENV_Y_DENORMAL) == FENV_Y_DENORMAL) *y |= _EM_DENORMAL; if ((enc & FENV_Y_ZERODIVIDE) == FENV_Y_ZERODIVIDE) *y |= _EM_ZERODIVIDE; if ((enc & FENV_Y_OVERFLOW) == FENV_Y_OVERFLOW) *y |= _EM_OVERFLOW; if ((enc & FENV_Y_UNDERFLOW) == FENV_Y_UNDERFLOW) *y |= _EM_UNDERFLOW; if ((enc & FENV_Y_INEXACT) == FENV_Y_INEXACT) *y |= _EM_INEXACT; if ((enc & FENV_Y_UP) == FENV_Y_UP) *y |= _RC_UP; if ((enc & FENV_Y_DOWN) == FENV_Y_DOWN) *y |= _RC_DOWN; if ((enc & FENV_Y_FLUSH) == FENV_Y_FLUSH) *y |= _DN_FLUSH; if ((enc & FENV_Y_FLUSH_SAVE) == FENV_Y_FLUSH_SAVE) *y |= _DN_FLUSH_OPERANDS_SAVE_RESULTS; if (fenv_encode(*x, *y) != enc) { WARN("can't decode: %lx\n", enc); return FALSE; } return TRUE; } #elif _MSVCR_VER >= 120 static __msvcrt_ulong fenv_encode(unsigned int x, unsigned int y) { if (y & _EM_DENORMAL) y = (y & ~_EM_DENORMAL) | 0x20; return x | y; } static BOOL fenv_decode(__msvcrt_ulong enc, unsigned int *x, unsigned int *y) { if (enc & 0x20) enc = (enc & ~0x20) | _EM_DENORMAL; *x = *y = enc; return TRUE; } #endif #if _MSVCR_VER>=120 /********************************************************************* * fegetenv (MSVCR120.@) */ int CDECL fegetenv(fenv_t *env) { #if _MSVCR_VER>=140 && defined(__i386__) unsigned int x87, sse; __control87_2(0, 0, &x87, &sse); env->_Fe_ctl = fenv_encode(x87, sse); _statusfp2(&x87, &sse); env->_Fe_stat = fenv_encode(x87, sse); #elif _MSVCR_VER>=140 env->_Fe_ctl = fenv_encode(0, _control87(0, 0)); env->_Fe_stat = fenv_encode(0, _statusfp()); #else env->_Fe_ctl = _controlfp(0, 0) & (_EM_INEXACT | _EM_UNDERFLOW | _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID | _MCW_RC); env->_Fe_stat = _statusfp(); #endif return 0; } /********************************************************************* * feupdateenv (MSVCR120.@) */ int CDECL feupdateenv(const fenv_t *env) { fenv_t set; fegetenv(&set); set._Fe_ctl = env->_Fe_ctl; set._Fe_stat |= env->_Fe_stat; return fesetenv(&set); } /********************************************************************* * fetestexcept (MSVCR120.@) */ int CDECL fetestexcept(int flags) { return _statusfp() & flags; } /********************************************************************* * fesetexceptflag (MSVCR120.@) */ int CDECL fesetexceptflag(const fexcept_t *status, int excepts) { fenv_t env; excepts &= FE_ALL_EXCEPT; if(!excepts) return 0; fegetenv(&env); env._Fe_stat &= ~fenv_encode(excepts, excepts); env._Fe_stat |= *status & fenv_encode(excepts, excepts); return fesetenv(&env); } /********************************************************************* * feraiseexcept (MSVCR120.@) */ int CDECL feraiseexcept(int flags) { fenv_t env; flags &= FE_ALL_EXCEPT; fegetenv(&env); env._Fe_stat |= fenv_encode(flags, flags); return fesetenv(&env); } /********************************************************************* * feclearexcept (MSVCR120.@) */ int CDECL feclearexcept(int flags) { fenv_t env; fegetenv(&env); flags &= FE_ALL_EXCEPT; env._Fe_stat &= ~fenv_encode(flags, flags); return fesetenv(&env); } /********************************************************************* * fegetexceptflag (MSVCR120.@) */ int CDECL fegetexceptflag(fexcept_t *status, int excepts) { #if _MSVCR_VER>=140 && defined(__i386__) unsigned int x87, sse; _statusfp2(&x87, &sse); *status = fenv_encode(x87 & excepts, sse & excepts); #else *status = fenv_encode(0, _statusfp() & excepts); #endif return 0; } #endif #if _MSVCR_VER>=140 /********************************************************************* * __fpe_flt_rounds (UCRTBASE.@) */ int CDECL __fpe_flt_rounds(void) { unsigned int fpc = _controlfp(0, 0) & _RC_CHOP; TRACE("()\n"); switch(fpc) { case _RC_CHOP: return 0; case _RC_NEAR: return 1; case _RC_UP: return 2; default: return 3; } } #endif #if _MSVCR_VER>=120 /********************************************************************* * fegetround (MSVCR120.@) */ int CDECL fegetround(void) { return _controlfp(0, 0) & _MCW_RC; } /********************************************************************* * fesetround (MSVCR120.@) */ int CDECL fesetround(int round_mode) { if (round_mode & (~_MCW_RC)) return 1; _controlfp(round_mode, _MCW_RC); return 0; } #endif /* _MSVCR_VER>=120 */ /********************************************************************* * _copysign (MSVCRT.@) * * Copied from musl: src/math/copysign.c */ double CDECL _copysign( double x, double y ) { union { double f; UINT64 i; } ux = { x }, uy = { y }; ux.i &= ~0ull >> 1; ux.i |= uy.i & 1ull << 63; return ux.f; } /********************************************************************* * _finite (MSVCRT.@) */ int CDECL _finite(double num) { union { double f; UINT64 i; } u = { num }; return (u.i & ~0ull >> 1) < 0x7ffull << 52; } /********************************************************************* * _fpreset (MSVCRT.@) */ void CDECL _fpreset(void) { #if (defined(__GNUC__) || defined(__clang__)) && defined(__i386__) const unsigned int x86_cw = 0x27f; __asm__ __volatile__( "fninit; fldcw %0" : : "m" (x86_cw) ); if (sse2_supported) { unsigned int cw = _MCW_EM, sw = 0; _setfp_sse(&cw, ~0, &sw, ~0); } #else unsigned int cw = _MCW_EM, sw = 0; _setfp(&cw, ~0, &sw, ~0); #endif } #if _MSVCR_VER>=120 /********************************************************************* * fesetenv (MSVCR120.@) */ int CDECL fesetenv(const fenv_t *env) { unsigned int x87_cw, cw, x87_stat, stat; unsigned int mask; TRACE( "(%p)\n", env ); if (!env->_Fe_ctl && !env->_Fe_stat) { _fpreset(); return 0; } if (!fenv_decode(env->_Fe_ctl, &x87_cw, &cw)) return 1; if (!fenv_decode(env->_Fe_stat, &x87_stat, &stat)) return 1; #if _MSVCR_VER >= 140 mask = ~0; #else mask = _EM_INEXACT | _EM_UNDERFLOW | _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID | _MCW_RC; #endif #ifdef __i386__ _setfp(&x87_cw, mask, &x87_stat, ~0); if (sse2_supported) _setfp_sse(&cw, mask, &stat, ~0); return 0; #else _setfp(&cw, mask, &stat, ~0); return 0; #endif } #endif /********************************************************************* * _isnan (MSVCRT.@) */ int CDECL _isnan(double num) { union { double f; UINT64 i; } u = { num }; return (u.i & ~0ull >> 1) > 0x7ffull << 52; } static double pzero(double x) { static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 0.00000000000000000000e+00, -7.03124999999900357484e-02, -8.08167041275349795626e+00, -2.57063105679704847262e+02, -2.48521641009428822144e+03, -5.25304380490729545272e+03, }, pS8[5] = { 1.16534364619668181717e+02, 3.83374475364121826715e+03, 4.05978572648472545552e+04, 1.16752972564375915681e+05, 4.76277284146730962675e+04, }, pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -1.14125464691894502584e-11, -7.03124940873599280078e-02, -4.15961064470587782438e+00, -6.76747652265167261021e+01, -3.31231299649172967747e+02, -3.46433388365604912451e+02, }, pS5[5] = { 6.07539382692300335975e+01, 1.05125230595704579173e+03, 5.97897094333855784498e+03, 9.62544514357774460223e+03, 2.40605815922939109441e+03, }, pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ -2.54704601771951915620e-09, -7.03119616381481654654e-02, -2.40903221549529611423e+00, -2.19659774734883086467e+01, -5.80791704701737572236e+01, -3.14479470594888503854e+01, }, pS3[5] = { 3.58560338055209726349e+01, 3.61513983050303863820e+02, 1.19360783792111533330e+03, 1.12799679856907414432e+03, 1.73580930813335754692e+02, }, pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ -8.87534333032526411254e-08, -7.03030995483624743247e-02, -1.45073846780952986357e+00, -7.63569613823527770791e+00, -1.11931668860356747786e+01, -3.23364579351335335033e+00, }, pS2[5] = { 2.22202997532088808441e+01, 1.36206794218215208048e+02, 2.70470278658083486789e+02, 1.53875394208320329881e+02, 1.46576176948256193810e+01, }; const double *p, *q; double z, r, s; UINT32 ix; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; if (ix >= 0x40200000) { p = pR8; q = pS8; } else if (ix >= 0x40122E8B) { p = pR5; q = pS5; } else if (ix >= 0x4006DB6D) { p = pR3; q = pS3; } else /*ix >= 0x40000000*/ { p = pR2; q = pS2; } z = 1.0 / (x * x); r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); return 1.0 + r / s; } static double qzero(double x) { static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 0.00000000000000000000e+00, 7.32421874999935051953e-02, 1.17682064682252693899e+01, 5.57673380256401856059e+02, 8.85919720756468632317e+03, 3.70146267776887834771e+04, }, qS8[6] = { 1.63776026895689824414e+02, 8.09834494656449805916e+03, 1.42538291419120476348e+05, 8.03309257119514397345e+05, 8.40501579819060512818e+05, -3.43899293537866615225e+05, }, qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 1.84085963594515531381e-11, 7.32421766612684765896e-02, 5.83563508962056953777e+00, 1.35111577286449829671e+02, 1.02724376596164097464e+03, 1.98997785864605384631e+03, }, qS5[6] = { 8.27766102236537761883e+01, 2.07781416421392987104e+03, 1.88472887785718085070e+04, 5.67511122894947329769e+04, 3.59767538425114471465e+04, -5.35434275601944773371e+03, }, qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ 4.37741014089738620906e-09, 7.32411180042911447163e-02, 3.34423137516170720929e+00, 4.26218440745412650017e+01, 1.70808091340565596283e+02, 1.66733948696651168575e+02, }, qS3[6] = { 4.87588729724587182091e+01, 7.09689221056606015736e+02, 3.70414822620111362994e+03, 6.46042516752568917582e+03, 2.51633368920368957333e+03, -1.49247451836156386662e+02, }, qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ 1.50444444886983272379e-07, 7.32234265963079278272e-02, 1.99819174093815998816e+00, 1.44956029347885735348e+01, 3.16662317504781540833e+01, 1.62527075710929267416e+01, }, qS2[6] = { 3.03655848355219184498e+01, 2.69348118608049844624e+02, 8.44783757595320139444e+02, 8.82935845112488550512e+02, 2.12666388511798828631e+02, -5.31095493882666946917e+00, }; const double *p, *q; double s, r, z; unsigned int ix; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; if (ix >= 0x40200000) { p = qR8; q = qS8; } else if (ix >= 0x40122E8B) { p = qR5; q = qS5; } else if (ix >= 0x4006DB6D) { p = qR3; q = qS3; } else /*ix >= 0x40000000*/ { p = qR2; q = qS2; } z = 1.0 / (x * x); r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); return (-0.125 + r / s) / x; } /* j0 and y0 approximation for |x|>=2 */ static double j0_y0_approx(unsigned int ix, double x, BOOL y0) { static const double invsqrtpi = 5.64189583547756279280e-01; double s, c, ss, cc, z; s = sin(x); c = cos(x); if (y0) c = -c; cc = s + c; /* avoid overflow in 2*x, big ulp error when x>=0x1p1023 */ if (ix < 0x7fe00000) { ss = s - c; z = -cos(2 * x); if (s * c < 0) cc = z / ss; else ss = z / cc; if (ix < 0x48000000) { if (y0) ss = -ss; cc = pzero(x) * cc - qzero(x) * ss; } } return invsqrtpi * cc / sqrt(x); } /********************************************************************* * _j0 (MSVCRT.@) * * Copied from musl: src/math/j0.c */ double CDECL _j0(double x) { static const double R02 = 1.56249999999999947958e-02, R03 = -1.89979294238854721751e-04, R04 = 1.82954049532700665670e-06, R05 = -4.61832688532103189199e-09, S01 = 1.56191029464890010492e-02, S02 = 1.16926784663337450260e-04, S03 = 5.13546550207318111446e-07, S04 = 1.16614003333790000205e-09; double z, r, s; unsigned int ix; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; /* j0(+-inf)=0, j0(nan)=nan */ if (ix >= 0x7ff00000) return math_error(_DOMAIN, "_j0", x, 0, 1 / (x * x)); x = fabs(x); if (ix >= 0x40000000) { /* |x| >= 2 */ /* large ulp error near zeros: 2.4, 5.52, 8.6537,.. */ return j0_y0_approx(ix, x, FALSE); } if (ix >= 0x3f200000) { /* |x| >= 2**-13 */ /* up to 4ulp error close to 2 */ z = x * x; r = z * (R02 + z * (R03 + z * (R04 + z * R05))); s = 1 + z * (S01 + z * (S02 + z * (S03 + z * S04))); return (1 + x / 2) * (1 - x / 2) + z * (r / s); } /* 1 - x*x/4 */ /* prevent underflow */ /* inexact should be raised when x!=0, this is not done correctly */ if (ix >= 0x38000000) /* |x| >= 2**-127 */ x = 0.25 * x * x; return 1 - x; } static double pone(double x) { static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 0.00000000000000000000e+00, 1.17187499999988647970e-01, 1.32394806593073575129e+01, 4.12051854307378562225e+02, 3.87474538913960532227e+03, 7.91447954031891731574e+03, }, ps8[5] = { 1.14207370375678408436e+02, 3.65093083420853463394e+03, 3.69562060269033463555e+04, 9.76027935934950801311e+04, 3.08042720627888811578e+04, }, pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ 1.31990519556243522749e-11, 1.17187493190614097638e-01, 6.80275127868432871736e+00, 1.08308182990189109773e+02, 5.17636139533199752805e+02, 5.28715201363337541807e+02, }, ps5[5] = { 5.92805987221131331921e+01, 9.91401418733614377743e+02, 5.35326695291487976647e+03, 7.84469031749551231769e+03, 1.50404688810361062679e+03, }, pr3[6] = { 3.02503916137373618024e-09, 1.17186865567253592491e-01, 3.93297750033315640650e+00, 3.51194035591636932736e+01, 9.10550110750781271918e+01, 4.85590685197364919645e+01, }, ps3[5] = { 3.47913095001251519989e+01, 3.36762458747825746741e+02, 1.04687139975775130551e+03, 8.90811346398256432622e+02, 1.03787932439639277504e+02, }, pr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ 1.07710830106873743082e-07, 1.17176219462683348094e-01, 2.36851496667608785174e+00, 1.22426109148261232917e+01, 1.76939711271687727390e+01, 5.07352312588818499250e+00, }, ps2[5] = { 2.14364859363821409488e+01, 1.25290227168402751090e+02, 2.32276469057162813669e+02, 1.17679373287147100768e+02, 8.36463893371618283368e+00, }; const double *p, *q; double z, r, s; unsigned int ix; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; if (ix >= 0x40200000) { p = pr8; q = ps8; } else if (ix >= 0x40122E8B) { p = pr5; q = ps5; } else if (ix >= 0x4006DB6D) { p = pr3; q = ps3; } else /*ix >= 0x40000000*/ { p = pr2; q = ps2; } z = 1.0 / (x * x); r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4])))); return 1.0 + r / s; } static double qone(double x) { static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ 0.00000000000000000000e+00, -1.02539062499992714161e-01, -1.62717534544589987888e+01, -7.59601722513950107896e+02, -1.18498066702429587167e+04, -4.84385124285750353010e+04, }, qs8[6] = { 1.61395369700722909556e+02, 7.82538599923348465381e+03, 1.33875336287249578163e+05, 7.19657723683240939863e+05, 6.66601232617776375264e+05, -2.94490264303834643215e+05, }, qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ -2.08979931141764104297e-11, -1.02539050241375426231e-01, -8.05644828123936029840e+00, -1.83669607474888380239e+02, -1.37319376065508163265e+03, -2.61244440453215656817e+03, }, qs5[6] = { 8.12765501384335777857e+01, 1.99179873460485964642e+03, 1.74684851924908907677e+04, 4.98514270910352279316e+04, 2.79480751638918118260e+04, -4.71918354795128470869e+03, }, qr3[6] = { -5.07831226461766561369e-09, -1.02537829820837089745e-01, -4.61011581139473403113e+00, -5.78472216562783643212e+01, -2.28244540737631695038e+02, -2.19210128478909325622e+02, }, qs3[6] = { 4.76651550323729509273e+01, 6.73865112676699709482e+02, 3.38015286679526343505e+03, 5.54772909720722782367e+03, 1.90311919338810798763e+03, -1.35201191444307340817e+02, }, qr2[6] = { /* for x in [2.8570,2]=1/[0.3499,0.5] */ -1.78381727510958865572e-07, -1.02517042607985553460e-01, -2.75220568278187460720e+00, -1.96636162643703720221e+01, -4.23253133372830490089e+01, -2.13719211703704061733e+01, }, qs2[6] = { 2.95333629060523854548e+01, 2.52981549982190529136e+02, 7.57502834868645436472e+02, 7.39393205320467245656e+02, 1.55949003336666123687e+02, -4.95949898822628210127e+00, }; const double *p, *q; double s, r, z; unsigned int ix; ix = *(ULONGLONG*)&x >> 32; ix &= 0x7fffffff; if (ix >= 0x40200000) { p = qr8; q = qs8; } else if (ix >= 0x40122E8B) { p = qr5; q = qs5; } else if (ix >= 0x4006DB6D) { p = qr3; q = qs3; } else /*ix >= 0x40000000*/ { p = qr2; q = qs2; } z = 1.0 / (x * x); r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5])))); s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5]))))); return (0.375 + r / s) / x; } static double j1_y1_approx(unsigned int ix, double x, BOOL y1, int sign) { static const double invsqrtpi = 5.64189583547756279280e-01; double z, s, c, ss, cc; s = sin(x); if (y1) s = -s; c = cos(x); cc = s - c; if (ix < 0x7fe00000) { ss = -s - c; z = cos(2 * x); if (s * c > 0) cc = z / ss; else ss = z / cc; if (ix < 0x48000000) { if (y1) ss = -ss; cc = pone(x) * cc - qone(x) * ss; } } if (sign) cc = -cc; return invsqrtpi * cc / sqrt(x); } /********************************************************************* * _j1 (MSVCRT.@) * * Copied from musl: src/math/j1.c */ double CDECL _j1(double x) { static const double r00 = -6.25000000000000000000e-02, r01 = 1.40705666955189706048e-03, r02 = -1.59955631084035597520e-05, r03 = 4.96727999609584448412e-08, s01 = 1.91537599538363460805e-02, s02 = 1.85946785588630915560e-04, s03 = 1.17718464042623683263e-06, s04 = 5.04636257076217042715e-09, s05 = 1.23542274426137913908e-11; double z, r, s; unsigned int ix; int sign; ix = *(ULONGLONG*)&x >> 32; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x7ff00000) return math_error(isnan(x) ? 0 : _DOMAIN, "_j1", x, 0, 1 / (x * x)); if (ix >= 0x40000000) /* |x| >= 2 */ return j1_y1_approx(ix, fabs(x), FALSE, sign); if (ix >= 0x38000000) { /* |x| >= 2**-127 */ z = x * x; r = z * (r00 + z * (r01 + z * (r02 + z * r03))); s = 1 + z * (s01 + z * (s02 + z * (s03 + z * (s04 + z * s05)))); z = r / s; } else { /* avoid underflow, raise inexact if x!=0 */ z = x; } return (0.5 + z) * x; } /********************************************************************* * _jn (MSVCRT.@) * * Copied from musl: src/math/jn.c */ double CDECL _jn(int n, double x) { static const double invsqrtpi = 5.64189583547756279280e-01; unsigned int ix, lx; int nm1, i, sign; double a, b, temp; ix = *(ULONGLONG*)&x >> 32; lx = *(ULONGLONG*)&x; sign = ix >> 31; ix &= 0x7fffffff; if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */ return x; if (n == 0) return _j0(x); if (n < 0) { nm1 = -(n + 1); x = -x; sign ^= 1; } else { nm1 = n-1; } if (nm1 == 0) return j1(x); sign &= n; /* even n: 0, odd n: signbit(x) */ x = fabs(x); if ((ix | lx) == 0 || ix == 0x7ff00000) /* if x is 0 or inf */ b = 0.0; else if (nm1 < x) { if (ix >= 0x52d00000) { /* x > 2**302 */ switch(nm1 & 3) { case 0: temp = -cos(x) + sin(x); break; case 1: temp = -cos(x) - sin(x); break; case 2: temp = cos(x) - sin(x); break; default: temp = cos(x) + sin(x); break; } b = invsqrtpi * temp / sqrt(x); } else { a = _j0(x); b = _j1(x); for (i = 0; i < nm1; ) { i++; temp = b; b = b * (2.0 * i / x) - a; /* avoid underflow */ a = temp; } } } else { if (ix < 0x3e100000) { /* x < 2**-29 */ if (nm1 > 32) /* underflow */ b = 0.0; else { temp = x * 0.5; b = temp; a = 1.0; for (i = 2; i <= nm1 + 1; i++) { a *= (double)i; /* a = n! */ b *= temp; /* b = (x/2)^n */ } b = b / a; } } else { double t, q0, q1, w, h, z, tmp, nf; int k; nf = nm1 + 1.0; w = 2 * nf / x; h = 2 / x; z = w + h; q0 = w; q1 = w * z - 1.0; k = 1; while (q1 < 1.0e9) { k += 1; z += h; tmp = z * q1 - q0; q0 = q1; q1 = tmp; } for (t = 0.0, i = k; i >= 0; i--) t = 1 / (2 * (i + nf) / x - t); a = t; b = 1.0; tmp = nf * log(fabs(w)); if (tmp < 7.09782712893383973096e+02) { for (i = nm1; i > 0; i--) { temp = b; b = b * (2.0 * i) / x - a; a = temp; } } else { for (i = nm1; i > 0; i--) { temp = b; b = b * (2.0 * i) / x - a; a = temp; /* scale b to avoid spurious overflow */ if (b > 0x1p500) { a /= b; t /= b; b = 1.0; } } } z = j0(x); w = j1(x); if (fabs(z) >= fabs(w)) b = t * z / b; else b = t * w / a; } } return sign ? -b : b; } /********************************************************************* * _y0 (MSVCRT.@) */ double CDECL _y0(double x) { static const double tpi = 6.36619772367581382433e-01, u00 = -7.38042951086872317523e-02, u01 = 1.76666452509181115538e-01, u02 = -1.38185671945596898896e-02, u03 = 3.47453432093683650238e-04, u04 = -3.81407053724364161125e-06, u05 = 1.95590137035022920206e-08, u06 = -3.98205194132103398453e-11, v01 = 1.27304834834123699328e-02, v02 = 7.60068627350353253702e-05, v03 = 2.59150851840457805467e-07, v04 = 4.41110311332675467403e-10; double z, u, v; unsigned int ix, lx; ix = *(ULONGLONG*)&x >> 32; lx = *(ULONGLONG*)&x; /* y0(nan)=nan, y0(<0)=nan, y0(0)=-inf, y0(inf)=0 */ if ((ix << 1 | lx) == 0) return math_error(_OVERFLOW, "_y0", x, 0, -INFINITY); if (isnan(x)) return x; if (ix >> 31) return math_error(_DOMAIN, "_y0", x, 0, 0 / (x - x)); if (ix >= 0x7ff00000) return 1 / x; if (ix >= 0x40000000) { /* x >= 2 */ /* large ulp errors near zeros: 3.958, 7.086,.. */ return j0_y0_approx(ix, x, TRUE); } if (ix >= 0x3e400000) { /* x >= 2**-27 */ /* large ulp error near the first zero, x ~= 0.89 */ z = x * x; u = u00 + z * (u01 + z * (u02 + z * (u03 + z * (u04 + z * (u05 + z * u06))))); v = 1.0 + z * (v01 + z * (v02 + z * (v03 + z * v04))); return u / v + tpi * (j0(x) * log(x)); } return u00 + tpi * log(x); } /********************************************************************* * _y1 (MSVCRT.@) */ double CDECL _y1(double x) { static const double tpi = 6.36619772367581382433e-01, u00 = -1.96057090646238940668e-01, u01 = 5.04438716639811282616e-02, u02 = -1.91256895875763547298e-03, u03 = 2.35252600561610495928e-05, u04 = -9.19099158039878874504e-08, v00 = 1.99167318236649903973e-02, v01 = 2.02552581025135171496e-04, v02 = 1.35608801097516229404e-06, v03 = 6.22741452364621501295e-09, v04 = 1.66559246207992079114e-11; double z, u, v; unsigned int ix, lx; ix = *(ULONGLONG*)&x >> 32; lx = *(ULONGLONG*)&x; /* y1(nan)=nan, y1(<0)=nan, y1(0)=-inf, y1(inf)=0 */ if ((ix << 1 | lx) == 0) return math_error(_OVERFLOW, "_y1", x, 0, -INFINITY); if (isnan(x)) return x; if (ix >> 31) return math_error(_DOMAIN, "_y1", x, 0, 0 / (x - x)); if (ix >= 0x7ff00000) return 1 / x; if (ix >= 0x40000000) /* x >= 2 */ return j1_y1_approx(ix, x, TRUE, 0); if (ix < 0x3c900000) /* x < 2**-54 */ return -tpi / x; z = x * x; u = u00 + z * (u01 + z * (u02 + z * (u03 + z * u04))); v = 1 + z * (v00 + z * (v01 + z * (v02 + z * (v03 + z * v04)))); return x * (u / v) + tpi * (j1(x) * log(x) - 1 / x); } /********************************************************************* * _yn (MSVCRT.@) * * Copied from musl: src/math/jn.c */ double CDECL _yn(int n, double x) { static const double invsqrtpi = 5.64189583547756279280e-01; unsigned int ix, lx, ib; int nm1, sign, i; double a, b, temp; ix = *(ULONGLONG*)&x >> 32; lx = *(ULONGLONG*)&x; sign = ix >> 31; ix &= 0x7fffffff; if ((ix | (lx | -lx) >> 31) > 0x7ff00000) /* nan */ return x; if (sign && (ix | lx) != 0) /* x < 0 */ return math_error(_DOMAIN, "_y1", x, 0, 0 / (x - x)); if (ix == 0x7ff00000) return 0.0; if (n == 0) return y0(x); if (n < 0) { nm1 = -(n + 1); sign = n & 1; } else { nm1 = n - 1; sign = 0; } if (nm1 == 0) return sign ? -y1(x) : y1(x); if (ix >= 0x52d00000) { /* x > 2**302 */ switch(nm1 & 3) { case 0: temp = -sin(x) - cos(x); break; case 1: temp = -sin(x) + cos(x); break; case 2: temp = sin(x) + cos(x); break; default: temp = sin(x) - cos(x); break; } b = invsqrtpi * temp / sqrt(x); } else { a = y0(x); b = y1(x); /* quit if b is -inf */ ib = *(ULONGLONG*)&b >> 32; for (i = 0; i < nm1 && ib != 0xfff00000;) { i++; temp = b; b = (2.0 * i / x) * b - a; ib = *(ULONGLONG*)&b >> 32; a = temp; } } return sign ? -b : b; } #if _MSVCR_VER>=120 /********************************************************************* * _nearbyint (MSVCR120.@) * * Based on musl: src/math/nearbyteint.c */ double CDECL nearbyint(double x) { fenv_t env; fegetenv(&env); _control87(_MCW_EM, _MCW_EM); x = rint(x); feclearexcept(FE_INEXACT); feupdateenv(&env); return x; } /********************************************************************* * _nearbyintf (MSVCR120.@) * * Based on musl: src/math/nearbyteintf.c */ float CDECL nearbyintf(float x) { fenv_t env; fegetenv(&env); _control87(_MCW_EM, _MCW_EM); x = rintf(x); feclearexcept(FE_INEXACT); feupdateenv(&env); return x; } /********************************************************************* * nexttoward (MSVCR120.@) */ double CDECL MSVCRT_nexttoward(double num, double next) { return _nextafter(num, next); } /********************************************************************* * nexttowardf (MSVCR120.@) * * Copied from musl: src/math/nexttowardf.c */ float CDECL MSVCRT_nexttowardf(float x, double y) { unsigned int ix = *(unsigned int*)&x; unsigned int e; float ret; if (isnan(x) || isnan(y)) return x + y; if (x == y) return y; if (x == 0) { ix = 1; if (signbit(y)) ix |= 0x80000000; } else if (x < y) { if (signbit(x)) ix--; else ix++; } else { if (signbit(x)) ix++; else ix--; } e = ix & 0x7f800000; /* raise overflow if ix is infinite and x is finite */ if (e == 0x7f800000) { fp_barrierf(x + x); *_errno() = ERANGE; } ret = *(float*)&ix; /* raise underflow if ret is subnormal or zero */ if (e == 0) { fp_barrierf(x * x + ret * ret); *_errno() = ERANGE; } return ret; } #endif /* _MSVCR_VER>=120 */ /********************************************************************* * _nextafter (MSVCRT.@) * * Copied from musl: src/math/nextafter.c */ double CDECL _nextafter(double x, double y) { ULONGLONG llx = *(ULONGLONG*)&x; ULONGLONG lly = *(ULONGLONG*)&y; ULONGLONG ax, ay; int e; if (isnan(x) || isnan(y)) return x + y; if (llx == lly) { if (_fpclass(y) & (_FPCLASS_ND | _FPCLASS_PD | _FPCLASS_NZ | _FPCLASS_PZ )) *_errno() = ERANGE; return y; } ax = llx & -1ULL / 2; ay = lly & -1ULL / 2; if (ax == 0) { if (ay == 0) return y; llx = (lly & 1ULL << 63) | 1; } else if (ax > ay || ((llx ^ lly) & 1ULL << 63)) llx--; else llx++; e = llx >> 52 & 0x7ff; /* raise overflow if llx is infinite and x is finite */ if (e == 0x7ff) { fp_barrier(x + x); *_errno() = ERANGE; } /* raise underflow if llx is subnormal or zero */ y = *(double*)&llx; if (e == 0) { fp_barrier(x * x + y * y); *_errno() = ERANGE; } return y; } /********************************************************************* * _ecvt (MSVCRT.@) */ char * CDECL _ecvt( double number, int ndigits, int *decpt, int *sign ) { int prec, len; thread_data_t *data = msvcrt_get_thread_data(); /* FIXME: check better for overflow (native supports over 300 chars) */ ndigits = min( ndigits, 80 - 8); /* 8 : space for sign, dec point, "e", * 4 for exponent and one for * terminating '\0' */ if (!data->efcvt_buffer) data->efcvt_buffer = malloc( 80 ); /* ought to be enough */ /* handle cases with zero ndigits or less */ prec = ndigits; if( prec < 1) prec = 2; len = _snprintf(data->efcvt_buffer, 80, "%.*le", prec - 1, number); if (data->efcvt_buffer[0] == '-') { memmove( data->efcvt_buffer, data->efcvt_buffer + 1, len-- ); *sign = 1; } else *sign = 0; /* take the decimal "point away */ if( prec != 1) memmove( data->efcvt_buffer + 1, data->efcvt_buffer + 2, len - 1 ); /* take the exponential "e" out */ data->efcvt_buffer[ prec] = '\0'; /* read the exponent */ sscanf( data->efcvt_buffer + prec + 1, "%d", decpt); (*decpt)++; /* adjust for some border cases */ if( data->efcvt_buffer[0] == '0')/* value is zero */ *decpt = 0; /* handle cases with zero ndigits or less */ if( ndigits < 1){ if( data->efcvt_buffer[ 0] >= '5') (*decpt)++; data->efcvt_buffer[ 0] = '\0'; } TRACE("out=\"%s\"\n",data->efcvt_buffer); return data->efcvt_buffer; } /********************************************************************* * _ecvt_s (MSVCRT.@) */ int CDECL _ecvt_s( char *buffer, size_t length, double number, int ndigits, int *decpt, int *sign ) { int prec, len; char *result; if (!MSVCRT_CHECK_PMT(buffer != NULL)) return EINVAL; if (!MSVCRT_CHECK_PMT(decpt != NULL)) return EINVAL; if (!MSVCRT_CHECK_PMT(sign != NULL)) return EINVAL; if (!MSVCRT_CHECK_PMT_ERR( length > 2, ERANGE )) return ERANGE; if (!MSVCRT_CHECK_PMT_ERR(ndigits < (int)length - 1, ERANGE )) return ERANGE; /* handle cases with zero ndigits or less */ prec = ndigits; if( prec < 1) prec = 2; result = malloc(prec + 8); len = _snprintf(result, prec + 8, "%.*le", prec - 1, number); if (result[0] == '-') { memmove( result, result + 1, len-- ); *sign = 1; } else *sign = 0; /* take the decimal "point away */ if( prec != 1) memmove( result + 1, result + 2, len - 1 ); /* take the exponential "e" out */ result[ prec] = '\0'; /* read the exponent */ sscanf( result + prec + 1, "%d", decpt); (*decpt)++; /* adjust for some border cases */ if( result[0] == '0')/* value is zero */ *decpt = 0; /* handle cases with zero ndigits or less */ if( ndigits < 1){ if( result[ 0] >= '5') (*decpt)++; result[ 0] = '\0'; } memcpy( buffer, result, max(ndigits + 1, 1) ); free( result ); return 0; } /*********************************************************************** * _fcvt (MSVCRT.@) */ char * CDECL _fcvt( double number, int ndigits, int *decpt, int *sign ) { thread_data_t *data = msvcrt_get_thread_data(); int stop, dec1, dec2; char *ptr1, *ptr2, *first; char buf[80]; /* ought to be enough */ char decimal_separator = get_locinfo()->lconv->decimal_point[0]; if (!data->efcvt_buffer) data->efcvt_buffer = malloc( 80 ); /* ought to be enough */ stop = _snprintf(buf, 80, "%.*f", ndigits < 0 ? 0 : ndigits, number); ptr1 = buf; ptr2 = data->efcvt_buffer; first = NULL; dec1 = 0; dec2 = 0; if (*ptr1 == '-') { *sign = 1; ptr1++; } else *sign = 0; /* For numbers below the requested resolution, work out where the decimal point will be rather than finding it in the string */ if (number < 1.0 && number > 0.0) { dec2 = log10(number + 1e-10); if (-dec2 <= ndigits) dec2 = 0; } /* If requested digits is zero or less, we will need to truncate * the returned string */ if (ndigits < 1) { stop += ndigits; } while (*ptr1 == '0') ptr1++; /* Skip leading zeroes */ while (*ptr1 != '\0' && *ptr1 != decimal_separator) { if (!first) first = ptr2; if ((ptr1 - buf) < stop) { *ptr2++ = *ptr1++; } else { ptr1++; } dec1++; } if (ndigits > 0) { ptr1++; if (!first) { while (*ptr1 == '0') { /* Process leading zeroes */ *ptr2++ = *ptr1++; dec1--; } } while (*ptr1 != '\0') { if (!first) first = ptr2; *ptr2++ = *ptr1++; } } *ptr2 = '\0'; /* We never found a non-zero digit, then our number is either * smaller than the requested precision, or 0.0 */ if (!first) { if (number > 0.0) { first = ptr2; } else { first = data->efcvt_buffer; dec1 = 0; } } *decpt = dec2 ? dec2 : dec1; return first; } /*********************************************************************** * _fcvt_s (MSVCRT.@) */ int CDECL _fcvt_s(char* outbuffer, size_t size, double number, int ndigits, int *decpt, int *sign) { int stop, dec1, dec2; char *ptr1, *ptr2, *first; char buf[80]; /* ought to be enough */ char decimal_separator = get_locinfo()->lconv->decimal_point[0]; if (!outbuffer || !decpt || !sign || size == 0) { *_errno() = EINVAL; return EINVAL; } stop = _snprintf(buf, 80, "%.*f", ndigits < 0 ? 0 : ndigits, number); ptr1 = buf; ptr2 = outbuffer; first = NULL; dec1 = 0; dec2 = 0; if (*ptr1 == '-') { *sign = 1; ptr1++; } else *sign = 0; /* For numbers below the requested resolution, work out where the decimal point will be rather than finding it in the string */ if (number < 1.0 && number > 0.0) { dec2 = log10(number + 1e-10); if (-dec2 <= ndigits) dec2 = 0; } /* If requested digits is zero or less, we will need to truncate * the returned string */ if (ndigits < 1) { stop += ndigits; } while (*ptr1 == '0') ptr1++; /* Skip leading zeroes */ while (*ptr1 != '\0' && *ptr1 != decimal_separator) { if (!first) first = ptr2; if ((ptr1 - buf) < stop) { if (size > 1) { *ptr2++ = *ptr1++; size--; } } else { ptr1++; } dec1++; } if (ndigits > 0) { ptr1++; if (!first) { while (*ptr1 == '0') { /* Process leading zeroes */ if (number == 0.0 && size > 1) { *ptr2++ = '0'; size--; } ptr1++; dec1--; } } while (*ptr1 != '\0') { if (!first) first = ptr2; if (size > 1) { *ptr2++ = *ptr1++; size--; } } } *ptr2 = '\0'; /* We never found a non-zero digit, then our number is either * smaller than the requested precision, or 0.0 */ if (!first && (number <= 0.0)) dec1 = 0; *decpt = dec2 ? dec2 : dec1; return 0; } /*********************************************************************** * _gcvt (MSVCRT.@) */ char * CDECL _gcvt( double number, int ndigit, char *buff ) { if(!buff) { *_errno() = EINVAL; return NULL; } if(ndigit < 0) { *_errno() = ERANGE; return NULL; } sprintf(buff, "%.*g", ndigit, number); return buff; } /*********************************************************************** * _gcvt_s (MSVCRT.@) */ int CDECL _gcvt_s(char *buff, size_t size, double number, int digits) { int len; if(!buff) { *_errno() = EINVAL; return EINVAL; } if( digits<0 || digits>=size) { if(size) buff[0] = '\0'; *_errno() = ERANGE; return ERANGE; } len = _scprintf("%.*g", digits, number); if(len > size) { buff[0] = '\0'; *_errno() = ERANGE; return ERANGE; } sprintf(buff, "%.*g", digits, number); return 0; } #include /* div_t, ldiv_t */ /********************************************************************* * div (MSVCRT.@) * VERSION * [i386] Windows binary compatible - returns the struct in eax/edx. */ #ifdef __i386__ unsigned __int64 CDECL div(int num, int denom) { union { div_t div; unsigned __int64 uint64; } ret; ret.div.quot = num / denom; ret.div.rem = num % denom; return ret.uint64; } #else /********************************************************************* * div (MSVCRT.@) * VERSION * [!i386] Non-x86 can't run win32 apps so we don't need binary compatibility */ div_t CDECL div(int num, int denom) { div_t ret; ret.quot = num / denom; ret.rem = num % denom; return ret; } #endif /* ifdef __i386__ */ /********************************************************************* * ldiv (MSVCRT.@) * VERSION * [i386] Windows binary compatible - returns the struct in eax/edx. */ #ifdef __i386__ unsigned __int64 CDECL ldiv(__msvcrt_long num, __msvcrt_long denom) { union { ldiv_t ldiv; unsigned __int64 uint64; } ret; ret.ldiv.quot = num / denom; ret.ldiv.rem = num % denom; return ret.uint64; } #else /********************************************************************* * ldiv (MSVCRT.@) * VERSION * [!i386] Non-x86 can't run win32 apps so we don't need binary compatibility */ ldiv_t CDECL ldiv(__msvcrt_long num, __msvcrt_long denom) { ldiv_t ret; ret.quot = num / denom; ret.rem = num % denom; return ret; } #endif /* ifdef __i386__ */ #if _MSVCR_VER>=100 /********************************************************************* * lldiv (MSVCR100.@) */ lldiv_t CDECL lldiv(__int64 num, __int64 denom) { lldiv_t ret; ret.quot = num / denom; ret.rem = num % denom; return ret; } #endif #ifdef __i386__ /********************************************************************* * _adjust_fdiv (MSVCRT.@) * Used by the MSVC compiler to work around the Pentium FDIV bug. */ int MSVCRT__adjust_fdiv = 0; /*********************************************************************** * _adj_fdiv_m16i (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdiv_m16i( short arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdiv_m32 (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdiv_m32( unsigned int arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdiv_m32i (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdiv_m32i( int arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdiv_m64 (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdiv_m64( unsigned __int64 arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdiv_r (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _adj_fdiv_r(void) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdivr_m16i (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdivr_m16i( short arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdivr_m32 (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdivr_m32( unsigned int arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdivr_m32i (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdivr_m32i( int arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fdivr_m64 (MSVCRT.@) * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void __stdcall _adj_fdivr_m64( unsigned __int64 arg ) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fpatan (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _adj_fpatan(void) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fprem (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _adj_fprem(void) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fprem1 (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _adj_fprem1(void) { TRACE("(): stub\n"); } /*********************************************************************** * _adj_fptan (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _adj_fptan(void) { TRACE("(): stub\n"); } /*********************************************************************** * _safe_fdiv (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _safe_fdiv(void) { TRACE("(): stub\n"); } /*********************************************************************** * _safe_fdivr (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _safe_fdivr(void) { TRACE("(): stub\n"); } /*********************************************************************** * _safe_fprem (MSVCRT.@) * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _safe_fprem(void) { TRACE("(): stub\n"); } /*********************************************************************** * _safe_fprem1 (MSVCRT.@) * * FIXME * This function is likely to have the wrong number of arguments. * * NOTE * I _think_ this function is intended to work around the Pentium * fdiv bug. */ void _safe_fprem1(void) { TRACE("(): stub\n"); } /*********************************************************************** * __libm_sse2_acos (MSVCRT.@) */ void __cdecl __libm_sse2_acos(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = acos( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_acosf (MSVCRT.@) */ void __cdecl __libm_sse2_acosf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = acosf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_asin (MSVCRT.@) */ void __cdecl __libm_sse2_asin(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = asin( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_asinf (MSVCRT.@) */ void __cdecl __libm_sse2_asinf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = asinf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_atan (MSVCRT.@) */ void __cdecl __libm_sse2_atan(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = atan( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_atan2 (MSVCRT.@) */ void __cdecl __libm_sse2_atan2(void) { double d1, d2; __asm__ __volatile__( "movq %%xmm0,%0; movq %%xmm1,%1 " : "=m" (d1), "=m" (d2) ); d1 = atan2( d1, d2 ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d1) ); } /*********************************************************************** * __libm_sse2_atanf (MSVCRT.@) */ void __cdecl __libm_sse2_atanf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = atanf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_cos (MSVCRT.@) */ void __cdecl __libm_sse2_cos(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = cos( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_cosf (MSVCRT.@) */ void __cdecl __libm_sse2_cosf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = cosf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_exp (MSVCRT.@) */ void __cdecl __libm_sse2_exp(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = exp( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_expf (MSVCRT.@) */ void __cdecl __libm_sse2_expf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = expf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_log (MSVCRT.@) */ void __cdecl __libm_sse2_log(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = log( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_log10 (MSVCRT.@) */ void __cdecl __libm_sse2_log10(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = log10( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_log10f (MSVCRT.@) */ void __cdecl __libm_sse2_log10f(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = log10f( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_logf (MSVCRT.@) */ void __cdecl __libm_sse2_logf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = logf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_pow (MSVCRT.@) */ void __cdecl __libm_sse2_pow(void) { double d1, d2; __asm__ __volatile__( "movq %%xmm0,%0; movq %%xmm1,%1 " : "=m" (d1), "=m" (d2) ); d1 = pow( d1, d2 ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d1) ); } /*********************************************************************** * __libm_sse2_powf (MSVCRT.@) */ void __cdecl __libm_sse2_powf(void) { float f1, f2; __asm__ __volatile__( "movd %%xmm0,%0; movd %%xmm1,%1" : "=g" (f1), "=g" (f2) ); f1 = powf( f1, f2 ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f1) ); } /*********************************************************************** * __libm_sse2_sin (MSVCRT.@) */ void __cdecl __libm_sse2_sin(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = sin( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_sinf (MSVCRT.@) */ void __cdecl __libm_sse2_sinf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = sinf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_tan (MSVCRT.@) */ void __cdecl __libm_sse2_tan(void) { double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); d = tan( d ); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); } /*********************************************************************** * __libm_sse2_tanf (MSVCRT.@) */ void __cdecl __libm_sse2_tanf(void) { float f; __asm__ __volatile__( "movd %%xmm0,%0" : "=g" (f) ); f = tanf( f ); __asm__ __volatile__( "movd %0,%%xmm0" : : "g" (f) ); } /*********************************************************************** * __libm_sse2_sqrt_precise (MSVCR110.@) */ void __cdecl __libm_sse2_sqrt_precise(void) { unsigned int cw; double d; __asm__ __volatile__( "movq %%xmm0,%0" : "=m" (d) ); __control87_2(0, 0, NULL, &cw); if (cw & _MCW_RC) { d = sqrt(d); __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); return; } if (!sqrt_validate(&d, FALSE)) { __asm__ __volatile__( "movq %0,%%xmm0" : : "m" (d) ); return; } __asm__ __volatile__( "call " __ASM_NAME( "sse2_sqrt" ) ); } #endif /* __i386__ */ #if _MSVCR_VER>=120 /********************************************************************* * cbrt (MSVCR120.@) * * Copied from musl: src/math/cbrt.c */ double CDECL cbrt(double x) { static const UINT32 B1 = 715094163, B2 = 696219795; static const double P0 = 1.87595182427177009643, P1 = -1.88497979543377169875, P2 = 1.621429720105354466140, P3 = -0.758397934778766047437, P4 = 0.145996192886612446982; union {double f; UINT64 i;} u = {x}; double r,s,t,w; UINT32 hx = u.i >> 32 & 0x7fffffff; if (hx >= 0x7ff00000) /* cbrt(NaN,INF) is itself */ return x + x; if (hx < 0x00100000) { /* zero or subnormal? */ u.f = x * 0x1p54; hx = u.i>>32 & 0x7fffffff; if (hx == 0) return x; hx = hx / 3 + B2; } else hx = hx / 3 + B1; u.i &= 1ULL << 63; u.i |= (UINT64)hx << 32; t = u.f; r = (t * t) * (t / x); t = t * ((P0 + r * (P1 + r * P2)) + ((r * r) * r) * (P3 + r * P4)); u.f = t; u.i = (u.i + 0x80000000) & 0xffffffffc0000000ULL; t = u.f; s = t * t; r = x / s; w = t + t; r = (r - t) / (w + r); t = t + t * r; return t; } /********************************************************************* * cbrtf (MSVCR120.@) * * Copied from musl: src/math/cbrtf.c */ float CDECL cbrtf(float x) { static const unsigned B1 = 709958130, B2 = 642849266; double r,T; union {float f; UINT32 i;} u = {x}; UINT32 hx = u.i & 0x7fffffff; if (hx >= 0x7f800000) return x + x; if (hx < 0x00800000) { /* zero or subnormal? */ if (hx == 0) return x; u.f = x * 0x1p24f; hx = u.i & 0x7fffffff; hx = hx / 3 + B2; } else hx = hx / 3 + B1; u.i &= 0x80000000; u.i |= hx; T = u.f; r = T * T * T; T = T * (x + x + r) / (x + r + r); r = T * T * T; T = T * (x + x + r) / (x + r + r); return T; } /********************************************************************* * exp2 (MSVCR120.@) * * Copied from musl: src/math/exp2.c */ double CDECL exp2(double x) { static const double C[] = { 0x1.62e42fefa39efp-1, 0x1.ebfbdff82c424p-3, 0x1.c6b08d70cf4b5p-5, 0x1.3b2abd24650ccp-7, 0x1.5d7e09b4e3a84p-10 }; UINT32 abstop; UINT64 ki, idx, top, sbits; double kd, r, r2, scale, tail, tmp; abstop = (*(UINT64*)&x >> 52) & 0x7ff; if (abstop - 0x3c9 >= 0x408 - 0x3c9) { if (abstop - 0x3c9 >= 0x80000000) { /* Avoid spurious underflow for tiny x. */ /* Note: 0 is common input. */ return 1.0 + x; } if (abstop >= 409) { if (*(UINT64*)&x == 0xfff0000000000000ull) return 0.0; if (abstop >= 0x7ff) return 1.0 + x; if (!(*(UINT64*)&x >> 63)) { *_errno() = ERANGE; return fp_barrier(DBL_MAX) * DBL_MAX; } else if (x <= -2147483648.0) { fp_barrier(x + 0x1p120f); return 0; } else if (*(UINT64*)&x >= 0xc090cc0000000000ull) { *_errno() = ERANGE; fp_barrier(x + 0x1p120f); return 0; } } if (2 * *(UINT64*)&x > 2 * 0x408d000000000000ull) /* Large x is special cased below. */ abstop = 0; } /* exp2(x) = 2^(k/N) * 2^r, with 2^r in [2^(-1/2N),2^(1/2N)]. */ /* x = k/N + r, with int k and r in [-1/2N, 1/2N]. */ kd = fp_barrier(x + 0x1.8p52 / (1 << 7)); ki = *(UINT64*)&kd; /* k. */ kd -= 0x1.8p52 / (1 << 7); /* k/N for int k. */ r = x - kd; /* 2^(k/N) ~= scale * (1 + tail). */ idx = 2 * (ki % (1 << 7)); top = ki << (52 - 7); tail = *(double*)&exp_T[idx]; /* This is only a valid scale when -1023*N < k < 1024*N. */ sbits = exp_T[idx + 1] + top; /* exp2(x) = 2^(k/N) * 2^r ~= scale + scale * (tail + 2^r - 1). */ /* Evaluation is optimized assuming superscalar pipelined execution. */ r2 = r * r; /* Without fma the worst case error is 0.5/N ulp larger. */ /* Worst case error is less than 0.5+0.86/N+(abs poly error * 2^53) ulp. */ tmp = tail + r * C[0] + r2 * (C[1] + r * C[2]) + r2 * r2 * (C[3] + r * C[4]); if (abstop == 0) { /* Handle cases that may overflow or underflow when computing the result that is scale*(1+TMP) without intermediate rounding. The bit representation of scale is in SBITS, however it has a computed exponent that may have overflown into the sign bit so that needs to be adjusted before using it as a double. (int32_t)KI is the k used in the argument reduction and exponent adjustment of scale, positive k here means the result may overflow and negative k means the result may underflow. */ double scale, y; if ((ki & 0x80000000) == 0) { /* k > 0, the exponent of scale might have overflowed by 1. */ sbits -= 1ull << 52; scale = *(double*)&sbits; y = 2 * (scale + scale * tmp); return y; } /* k < 0, need special care in the subnormal range. */ sbits += 1022ull << 52; scale = *(double*)&sbits; y = scale + scale * tmp; if (y < 1.0) { /* Round y to the right precision before scaling it into the subnormal range to avoid double rounding that can cause 0.5+E/2 ulp error where E is the worst-case ulp error outside the subnormal range. So this is only useful if the goal is better than 1 ulp worst-case error. */ double hi, lo; lo = scale - y + scale * tmp; hi = 1.0 + y; lo = 1.0 - hi + y + lo; y = hi + lo - 1.0; /* Avoid -0.0 with downward rounding. */ if (y == 0.0) y = 0.0; /* The underflow exception needs to be signaled explicitly. */ fp_barrier(fp_barrier(0x1p-1022) * 0x1p-1022); } y = 0x1p-1022 * y; return y; } scale = *(double*)&sbits; /* Note: tmp == 0 or |tmp| > 2^-65 and scale > 2^-928, so there is no spurious underflow here even without fma. */ return scale + scale * tmp; } /********************************************************************* * exp2f (MSVCR120.@) * * Copied from musl: src/math/exp2f.c */ float CDECL exp2f(float x) { static const double C[] = { 0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1 }; static const double shift = 0x1.8p+52 / (1 << 5); double kd, xd, z, r, r2, y, s; UINT32 abstop; UINT64 ki, t; xd = x; abstop = (*(UINT32*)&x >> 20) & 0x7ff; if (abstop >= 0x430) { /* |x| >= 128 or x is nan. */ if (*(UINT32*)&x == 0xff800000) return 0.0f; if (abstop >= 0x7f8) return x + x; if (x > 0.0f) { *_errno() = ERANGE; return fp_barrierf(x * FLT_MAX); } if (x <= -150.0f) { fp_barrierf(x - 0x1p120); return 0; } } /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k, N = 1 << 5. */ kd = xd + shift; ki = *(UINT64*)&kd; kd -= shift; /* k/(1<<5) for int k. */ r = xd - kd; /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ t = exp2f_T[ki % (1 << 5)]; t += ki << (52 - 5); s = *(double*)&t; z = C[0] * r + C[1]; r2 = r * r; y = C[2] * r + 1; y = z * r2 + y; y = y * s; return y; } /********************************************************************* * expm1 (MSVCR120.@) */ double CDECL expm1(double x) { return __expm1(x); } /********************************************************************* * expm1f (MSVCR120.@) */ float CDECL expm1f(float x) { return __expm1f(x); } /********************************************************************* * log1p (MSVCR120.@) * * Copied from musl: src/math/log1p.c */ double CDECL log1p(double x) { static const double ln2_hi = 6.93147180369123816490e-01, ln2_lo = 1.90821492927058770002e-10, Lg1 = 6.666666666666735130e-01, Lg2 = 3.999999999940941908e-01, Lg3 = 2.857142874366239149e-01, Lg4 = 2.222219843214978396e-01, Lg5 = 1.818357216161805012e-01, Lg6 = 1.531383769920937332e-01, Lg7 = 1.479819860511658591e-01; union {double f; UINT64 i;} u = {x}; double hfsq, f, c, s, z, R, w, t1, t2, dk; UINT32 hx, hu; int k; hx = u.i >> 32; k = 1; if (hx < 0x3fda827a || hx >> 31) { /* 1+x < sqrt(2)+ */ if (hx >= 0xbff00000) { /* x <= -1.0 */ if (x == -1) { *_errno() = ERANGE; return x / 0.0; /* og1p(-1) = -inf */ } *_errno() = EDOM; return (x-x) / 0.0; /* log1p(x<-1) = NaN */ } if (hx << 1 < 0x3ca00000 << 1) { /* |x| < 2**-53 */ fp_barrier(x + 0x1p120f); /* underflow if subnormal */ if ((hx & 0x7ff00000) == 0) fp_barrierf(x); return x; } if (hx <= 0xbfd2bec4) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ k = 0; c = 0; f = x; } } else if (hx >= 0x7ff00000) return x; if (k) { u.f = 1 + x; hu = u.i >> 32; hu += 0x3ff00000 - 0x3fe6a09e; k = (int)(hu >> 20) - 0x3ff; /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ if (k < 54) { c = k >= 2 ? 1 - (u.f - x) : x - (u.f - 1); c /= u.f; } else c = 0; /* reduce u into [sqrt(2)/2, sqrt(2)] */ hu = (hu & 0x000fffff) + 0x3fe6a09e; u.i = (UINT64)hu << 32 | (u.i & 0xffffffff); f = u.f - 1; } hfsq = 0.5 * f * f; s = f / (2.0 + f); z = s * s; w = z * z; t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); R = t2 + t1; dk = k; return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi; } /********************************************************************* * log1pf (MSVCR120.@) * * Copied from musl: src/math/log1pf.c */ float CDECL log1pf(float x) { static const float ln2_hi = 6.9313812256e-01, ln2_lo = 9.0580006145e-06, Lg1 = 0xaaaaaa.0p-24, Lg2 = 0xccce13.0p-25, Lg3 = 0x91e9ee.0p-25, Lg4 = 0xf89e26.0p-26; union {float f; UINT32 i;} u = {x}; float hfsq, f, c, s, z, R, w, t1, t2, dk; UINT32 ix, iu; int k; ix = u.i; k = 1; if (ix < 0x3ed413d0 || ix >> 31) { /* 1+x < sqrt(2)+ */ if (ix >= 0xbf800000) { /* x <= -1.0 */ if (x == -1) { *_errno() = ERANGE; return x / 0.0f; /* log1p(-1)=+inf */ } *_errno() = EDOM; return (x - x) / 0.0f; /* log1p(x<-1)=NaN */ } if (ix<<1 < 0x33800000<<1) { /* |x| < 2**-24 */ /* underflow if subnormal */ if ((ix & 0x7f800000) == 0) fp_barrierf(x * x); return x; } if (ix <= 0xbe95f619) { /* sqrt(2)/2- <= 1+x < sqrt(2)+ */ k = 0; c = 0; f = x; } } else if (ix >= 0x7f800000) return x; if (k) { u.f = 1 + x; iu = u.i; iu += 0x3f800000 - 0x3f3504f3; k = (int)(iu >> 23) - 0x7f; /* correction term ~ log(1+x)-log(u), avoid underflow in c/u */ if (k < 25) { c = k >= 2 ? 1 - (u.f - x) : x - (u.f - 1); c /= u.f; } else c = 0; /* reduce u into [sqrt(2)/2, sqrt(2)] */ iu = (iu & 0x007fffff) + 0x3f3504f3; u.i = iu; f = u.f - 1; } s = f / (2.0f + f); z = s * s; w = z * z; t1= w * (Lg2 + w * Lg4); t2= z * (Lg1 + w * Lg3); R = t2 + t1; hfsq = 0.5f * f * f; dk = k; return s * (hfsq + R) + (dk * ln2_lo + c) - hfsq + f + dk * ln2_hi; } /********************************************************************* * log2 (MSVCR120.@) * * Copied from musl: src/math/log2.c */ double CDECL log2(double x) { static const double invln2hi = 0x1.7154765200000p+0, invln2lo = 0x1.705fc2eefa200p-33; static const double A[] = { -0x1.71547652b8339p-1, 0x1.ec709dc3a04bep-2, -0x1.7154764702ffbp-2, 0x1.2776c50034c48p-2, -0x1.ec7b328ea92bcp-3, 0x1.a6225e117f92ep-3 }; static const double B[] = { -0x1.71547652b82fep-1, 0x1.ec709dc3a03f7p-2, -0x1.71547652b7c3fp-2, 0x1.2776c50f05be4p-2, -0x1.ec709dd768fe5p-3, 0x1.a61761ec4e736p-3, -0x1.7153fbc64a79bp-3, 0x1.484d154f01b4ap-3, -0x1.289e4a72c383cp-3, 0x1.0b32f285aee66p-3 }; static const struct { double invc, logc; } T[] = { {0x1.724286bb1acf8p+0, -0x1.1095feecdb000p-1}, {0x1.6e1f766d2cca1p+0, -0x1.08494bd76d000p-1}, {0x1.6a13d0e30d48ap+0, -0x1.00143aee8f800p-1}, {0x1.661ec32d06c85p+0, -0x1.efec5360b4000p-2}, {0x1.623fa951198f8p+0, -0x1.dfdd91ab7e000p-2}, {0x1.5e75ba4cf026cp+0, -0x1.cffae0cc79000p-2}, {0x1.5ac055a214fb8p+0, -0x1.c043811fda000p-2}, {0x1.571ed0f166e1ep+0, -0x1.b0b67323ae000p-2}, {0x1.53909590bf835p+0, -0x1.a152f5a2db000p-2}, {0x1.5014fed61adddp+0, -0x1.9217f5af86000p-2}, {0x1.4cab88e487bd0p+0, -0x1.8304db0719000p-2}, {0x1.49539b4334feep+0, -0x1.74189f9a9e000p-2}, {0x1.460cbdfafd569p+0, -0x1.6552bb5199000p-2}, {0x1.42d664ee4b953p+0, -0x1.56b23a29b1000p-2}, {0x1.3fb01111dd8a6p+0, -0x1.483650f5fa000p-2}, {0x1.3c995b70c5836p+0, -0x1.39de937f6a000p-2}, {0x1.3991c4ab6fd4ap+0, -0x1.2baa1538d6000p-2}, {0x1.3698e0ce099b5p+0, -0x1.1d98340ca4000p-2}, {0x1.33ae48213e7b2p+0, -0x1.0fa853a40e000p-2}, {0x1.30d191985bdb1p+0, -0x1.01d9c32e73000p-2}, {0x1.2e025cab271d7p+0, -0x1.e857da2fa6000p-3}, {0x1.2b404cf13cd82p+0, -0x1.cd3c8633d8000p-3}, {0x1.288b02c7ccb50p+0, -0x1.b26034c14a000p-3}, {0x1.25e2263944de5p+0, -0x1.97c1c2f4fe000p-3}, {0x1.234563d8615b1p+0, -0x1.7d6023f800000p-3}, {0x1.20b46e33eaf38p+0, -0x1.633a71a05e000p-3}, {0x1.1e2eefdcda3ddp+0, -0x1.494f5e9570000p-3}, {0x1.1bb4a580b3930p+0, -0x1.2f9e424e0a000p-3}, {0x1.19453847f2200p+0, -0x1.162595afdc000p-3}, {0x1.16e06c0d5d73cp+0, -0x1.f9c9a75bd8000p-4}, {0x1.1485f47b7e4c2p+0, -0x1.c7b575bf9c000p-4}, {0x1.12358ad0085d1p+0, -0x1.960c60ff48000p-4}, {0x1.0fef00f532227p+0, -0x1.64ce247b60000p-4}, {0x1.0db2077d03a8fp+0, -0x1.33f78b2014000p-4}, {0x1.0b7e6d65980d9p+0, -0x1.0387d1a42c000p-4}, {0x1.0953efe7b408dp+0, -0x1.a6f9208b50000p-5}, {0x1.07325cac53b83p+0, -0x1.47a954f770000p-5}, {0x1.05197e40d1b5cp+0, -0x1.d23a8c50c0000p-6}, {0x1.03091c1208ea2p+0, -0x1.16a2629780000p-6}, {0x1.0101025b37e21p+0, -0x1.720f8d8e80000p-8}, {0x1.fc07ef9caa76bp-1, 0x1.6fe53b1500000p-7}, {0x1.f4465d3f6f184p-1, 0x1.11ccce10f8000p-5}, {0x1.ecc079f84107fp-1, 0x1.c4dfc8c8b8000p-5}, {0x1.e573a99975ae8p-1, 0x1.3aa321e574000p-4}, {0x1.de5d6f0bd3de6p-1, 0x1.918a0d08b8000p-4}, {0x1.d77b681ff38b3p-1, 0x1.e72e9da044000p-4}, {0x1.d0cb5724de943p-1, 0x1.1dcd2507f6000p-3}, {0x1.ca4b2dc0e7563p-1, 0x1.476ab03dea000p-3}, {0x1.c3f8ee8d6cb51p-1, 0x1.7074377e22000p-3}, {0x1.bdd2b4f020c4cp-1, 0x1.98ede8ba94000p-3}, {0x1.b7d6c006015cap-1, 0x1.c0db86ad2e000p-3}, {0x1.b20366e2e338fp-1, 0x1.e840aafcee000p-3}, {0x1.ac57026295039p-1, 0x1.0790ab4678000p-2}, {0x1.a6d01bc2731ddp-1, 0x1.1ac056801c000p-2}, {0x1.a16d3bc3ff18bp-1, 0x1.2db11d4fee000p-2}, {0x1.9c2d14967feadp-1, 0x1.406464ec58000p-2}, {0x1.970e4f47c9902p-1, 0x1.52dbe093af000p-2}, {0x1.920fb3982bcf2p-1, 0x1.651902050d000p-2}, {0x1.8d30187f759f1p-1, 0x1.771d2cdeaf000p-2}, {0x1.886e5ebb9f66dp-1, 0x1.88e9c857d9000p-2}, {0x1.83c97b658b994p-1, 0x1.9a80155e16000p-2}, {0x1.7f405ffc61022p-1, 0x1.abe186ed3d000p-2}, {0x1.7ad22181415cap-1, 0x1.bd0f2aea0e000p-2}, {0x1.767dcf99eff8cp-1, 0x1.ce0a43dbf4000p-2} }; static const struct { double chi, clo; } T2[] = { {0x1.6200012b90a8ep-1, 0x1.904ab0644b605p-55}, {0x1.66000045734a6p-1, 0x1.1ff9bea62f7a9p-57}, {0x1.69fffc325f2c5p-1, 0x1.27ecfcb3c90bap-55}, {0x1.6e00038b95a04p-1, 0x1.8ff8856739326p-55}, {0x1.71fffe09994e3p-1, 0x1.afd40275f82b1p-55}, {0x1.7600015590e1p-1, -0x1.2fd75b4238341p-56}, {0x1.7a00012655bd5p-1, 0x1.808e67c242b76p-56}, {0x1.7e0003259e9a6p-1, -0x1.208e426f622b7p-57}, {0x1.81fffedb4b2d2p-1, -0x1.402461ea5c92fp-55}, {0x1.860002dfafcc3p-1, 0x1.df7f4a2f29a1fp-57}, {0x1.89ffff78c6b5p-1, -0x1.e0453094995fdp-55}, {0x1.8e00039671566p-1, -0x1.a04f3bec77b45p-55}, {0x1.91fffe2bf1745p-1, -0x1.7fa34400e203cp-56}, {0x1.95fffcc5c9fd1p-1, -0x1.6ff8005a0695dp-56}, {0x1.9a0003bba4767p-1, 0x1.0f8c4c4ec7e03p-56}, {0x1.9dfffe7b92da5p-1, 0x1.e7fd9478c4602p-55}, {0x1.a1fffd72efdafp-1, -0x1.a0c554dcdae7ep-57}, {0x1.a5fffde04ff95p-1, 0x1.67da98ce9b26bp-55}, {0x1.a9fffca5e8d2bp-1, -0x1.284c9b54c13dep-55}, {0x1.adfffddad03eap-1, 0x1.812c8ea602e3cp-58}, {0x1.b1ffff10d3d4dp-1, -0x1.efaddad27789cp-55}, {0x1.b5fffce21165ap-1, 0x1.3cb1719c61237p-58}, {0x1.b9fffd950e674p-1, 0x1.3f7d94194cep-56}, {0x1.be000139ca8afp-1, 0x1.50ac4215d9bcp-56}, {0x1.c20005b46df99p-1, 0x1.beea653e9c1c9p-57}, {0x1.c600040b9f7aep-1, -0x1.c079f274a70d6p-56}, {0x1.ca0006255fd8ap-1, -0x1.a0b4076e84c1fp-56}, {0x1.cdfffd94c095dp-1, 0x1.8f933f99ab5d7p-55}, {0x1.d1ffff975d6cfp-1, -0x1.82c08665fe1bep-58}, {0x1.d5fffa2561c93p-1, -0x1.b04289bd295f3p-56}, {0x1.d9fff9d228b0cp-1, 0x1.70251340fa236p-55}, {0x1.de00065bc7e16p-1, -0x1.5011e16a4d80cp-56}, {0x1.e200002f64791p-1, 0x1.9802f09ef62ep-55}, {0x1.e600057d7a6d8p-1, -0x1.e0b75580cf7fap-56}, {0x1.ea00027edc00cp-1, -0x1.c848309459811p-55}, {0x1.ee0006cf5cb7cp-1, -0x1.f8027951576f4p-55}, {0x1.f2000782b7dccp-1, -0x1.f81d97274538fp-55}, {0x1.f6000260c450ap-1, -0x1.071002727ffdcp-59}, {0x1.f9fffe88cd533p-1, -0x1.81bdce1fda8bp-58}, {0x1.fdfffd50f8689p-1, 0x1.7f91acb918e6ep-55}, {0x1.0200004292367p+0, 0x1.b7ff365324681p-54}, {0x1.05fffe3e3d668p+0, 0x1.6fa08ddae957bp-55}, {0x1.0a0000a85a757p+0, -0x1.7e2de80d3fb91p-58}, {0x1.0e0001a5f3fccp+0, -0x1.1823305c5f014p-54}, {0x1.11ffff8afbaf5p+0, -0x1.bfabb6680bac2p-55}, {0x1.15fffe54d91adp+0, -0x1.d7f121737e7efp-54}, {0x1.1a00011ac36e1p+0, 0x1.c000a0516f5ffp-54}, {0x1.1e00019c84248p+0, -0x1.082fbe4da5dap-54}, {0x1.220000ffe5e6ep+0, -0x1.8fdd04c9cfb43p-55}, {0x1.26000269fd891p+0, 0x1.cfe2a7994d182p-55}, {0x1.2a00029a6e6dap+0, -0x1.00273715e8bc5p-56}, {0x1.2dfffe0293e39p+0, 0x1.b7c39dab2a6f9p-54}, {0x1.31ffff7dcf082p+0, 0x1.df1336edc5254p-56}, {0x1.35ffff05a8b6p+0, -0x1.e03564ccd31ebp-54}, {0x1.3a0002e0eaeccp+0, 0x1.5f0e74bd3a477p-56}, {0x1.3e000043bb236p+0, 0x1.c7dcb149d8833p-54}, {0x1.4200002d187ffp+0, 0x1.e08afcf2d3d28p-56}, {0x1.460000d387cb1p+0, 0x1.20837856599a6p-55}, {0x1.4a00004569f89p+0, -0x1.9fa5c904fbcd2p-55}, {0x1.4e000043543f3p+0, -0x1.81125ed175329p-56}, {0x1.51fffcc027f0fp+0, 0x1.883d8847754dcp-54}, {0x1.55ffffd87b36fp+0, -0x1.709e731d02807p-55}, {0x1.59ffff21df7bap+0, 0x1.7f79f68727b02p-55}, {0x1.5dfffebfc3481p+0, -0x1.180902e30e93ep-54} }; double z, r, r2, r4, y, invc, logc, kd, hi, lo, t1, t2, t3, p, rhi, rlo; UINT64 ix, iz, tmp; UINT32 top; int k, i; ix = *(UINT64*)&x; top = ix >> 48; if (ix - 0x3feea4af00000000ULL < 0x210aa00000000ULL) { /* Handle close to 1.0 inputs separately. */ /* Fix sign of zero with downward rounding when x==1. */ if (ix == 0x3ff0000000000000ULL) return 0; r = x - 1.0; *(UINT64*)&rhi = *(UINT64*)&r & -1ULL << 32; rlo = r - rhi; hi = rhi * invln2hi; lo = rlo * invln2hi + r * invln2lo; r2 = r * r; /* rounding error: 0x1p-62. */ r4 = r2 * r2; /* Worst-case error is less than 0.54 ULP (0.55 ULP without fma). */ p = r2 * (B[0] + r * B[1]); y = hi + p; lo += hi - y + p; lo += r4 * (B[2] + r * B[3] + r2 * (B[4] + r * B[5]) + r4 * (B[6] + r * B[7] + r2 * (B[8] + r * B[9]))); y += lo; return y; } if (top - 0x0010 >= 0x7ff0 - 0x0010) { /* x < 0x1p-1022 or inf or nan. */ if (ix * 2 == 0) { *_errno() = ERANGE; return -1.0 / x; } if (ix == 0x7ff0000000000000ULL) /* log(inf) == inf. */ return x; if ((top & 0x7ff0) == 0x7ff0 && (ix & 0xfffffffffffffULL)) return x; if (top & 0x8000) { *_errno() = EDOM; return (x - x) / (x - x); } /* x is subnormal, normalize it. */ x *= 0x1p52; ix = *(UINT64*)&x; ix -= 52ULL << 52; } /* x = 2^k z; where z is in range [OFF,2*OFF) and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3fe6000000000000ULL; i = (tmp >> (52 - 6)) % (1 << 6); k = (INT64)tmp >> 52; /* arithmetic shift */ iz = ix - (tmp & 0xfffULL << 52); invc = T[i].invc; logc = T[i].logc; z = *(double*)&iz; kd = k; /* log2(x) = log2(z/c) + log2(c) + k. */ /* r ~= z/c - 1, |r| < 1/(2*N). */ /* rounding error: 0x1p-55/N + 0x1p-65. */ r = (z - T2[i].chi - T2[i].clo) * invc; *(UINT64*)&rhi = *(UINT64*)&r & -1ULL << 32; rlo = r - rhi; t1 = rhi * invln2hi; t2 = rlo * invln2hi + r * invln2lo; /* hi + lo = r/ln2 + log2(c) + k. */ t3 = kd + logc; hi = t3 + t1; lo = t3 - hi + t1 + t2; /* log2(r+1) = r/ln2 + r^2*poly(r). */ /* Evaluation is optimized assuming superscalar pipelined execution. */ r2 = r * r; /* rounding error: 0x1p-54/N^2. */ r4 = r2 * r2; /* Worst-case error if |y| > 0x1p-4: 0.547 ULP (0.550 ULP without fma). ~ 0.5 + 2/N/ln2 + abs-poly-error*0x1p56 ULP (+ 0.003 ULP without fma). */ p = A[0] + r * A[1] + r2 * (A[2] + r * A[3]) + r4 * (A[4] + r * A[5]); y = lo + r2 * p + hi; return y; } /********************************************************************* * log2f (MSVCR120.@) * * Copied from musl: src/math/log2f.c */ float CDECL log2f(float x) { static const double A[] = { -0x1.712b6f70a7e4dp-2, 0x1.ecabf496832ep-2, -0x1.715479ffae3dep-1, 0x1.715475f35c8b8p0 }; static const struct { double invc, logc; } T[] = { { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 }, { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 }, { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 }, { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 }, { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 }, { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 }, { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 }, { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 }, { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 }, { 0x1p+0, 0x0p+0 }, { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 }, { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 }, { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 }, { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 }, { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 }, { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 } }; double z, r, r2, p, y, y0, invc, logc; UINT32 ix, iz, top, tmp; int k, i; ix = *(UINT32*)&x; /* Fix sign of zero with downward rounding when x==1. */ if (ix == 0x3f800000) return 0; if (ix - 0x00800000 >= 0x7f800000 - 0x00800000) { /* x < 0x1p-126 or inf or nan. */ if (ix * 2 == 0) { *_errno() = ERANGE; return -1.0f / x; } if (ix == 0x7f800000) /* log2(inf) == inf. */ return x; if (ix * 2 > 0xff000000) return x; if (ix & 0x80000000) { *_errno() = EDOM; return (x - x) / (x - x); } /* x is subnormal, normalize it. */ x *= 0x1p23f; ix = *(UINT32*)&x; ix -= 23 << 23; } /* x = 2^k z; where z is in range [OFF,2*OFF] and exact. The range is split into N subintervals. The ith subinterval contains z and c is near its center. */ tmp = ix - 0x3f330000; i = (tmp >> (23 - 4)) % (1 << 4); top = tmp & 0xff800000; iz = ix - top; k = (INT32)tmp >> 23; /* arithmetic shift */ invc = T[i].invc; logc = T[i].logc; z = *(float*)&iz; /* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */ r = z * invc - 1; y0 = logc + (double)k; /* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */ r2 = r * r; y = A[1] * r + A[2]; y = A[0] * r2 + y; p = A[3] * r + y0; y = y * r2 + p; return y; } /********************************************************************* * rint (MSVCR120.@) */ double CDECL rint(double x) { return __rint(x); } /********************************************************************* * rintf (MSVCR120.@) * * Copied from musl: src/math/rintf.c */ float CDECL rintf(float x) { static const float toint = 1 / FLT_EPSILON; unsigned int ix = *(unsigned int*)&x; int e = ix >> 23 & 0xff; int s = ix >> 31; float y; if (e >= 0x7f + 23) return x; if (s) y = fp_barrierf(x - toint) + toint; else y = fp_barrierf(x + toint) - toint; if (y == 0) return s ? -0.0f : 0.0f; return y; } /********************************************************************* * lrint (MSVCR120.@) */ __msvcrt_long CDECL lrint(double x) { double d; d = rint(x); if ((d < 0 && d != (double)(__msvcrt_long)d) || (d >= 0 && d != (double)(__msvcrt_ulong)d)) { *_errno() = EDOM; return 0; } return d; } /********************************************************************* * lrintf (MSVCR120.@) */ __msvcrt_long CDECL lrintf(float x) { float f; f = rintf(x); if ((f < 0 && f != (float)(__msvcrt_long)f) || (f >= 0 && f != (float)(__msvcrt_ulong)f)) { *_errno() = EDOM; return 0; } return f; } /********************************************************************* * llrint (MSVCR120.@) */ __int64 CDECL llrint(double x) { double d; d = rint(x); if ((d < 0 && d != (double)(__int64)d) || (d >= 0 && d != (double)(unsigned __int64)d)) { *_errno() = EDOM; return 0; } return d; } /********************************************************************* * llrintf (MSVCR120.@) */ __int64 CDECL llrintf(float x) { float f; f = rintf(x); if ((f < 0 && f != (float)(__int64)f) || (f >= 0 && f != (float)(unsigned __int64)f)) { *_errno() = EDOM; return 0; } return f; } /********************************************************************* * round (MSVCR120.@) */ double CDECL round(double x) { return __round(x); } /********************************************************************* * roundf (MSVCR120.@) * * Copied from musl: src/math/roundf.c */ float CDECL roundf(float x) { static const float toint = 1 / FLT_EPSILON; unsigned int ix = *(unsigned int*)&x; int e = ix >> 23 & 0xff; float y; if (e >= 0x7f + 23) return x; if (ix >> 31) x = -x; if (e < 0x7f - 1) return 0 * *(float*)&ix; y = fp_barrierf(x + toint) - toint - x; if (y > 0.5f) y = y + x - 1; else if (y <= -0.5f) y = y + x + 1; else y = y + x; if (ix >> 31) y = -y; return y; } /********************************************************************* * lround (MSVCR120.@) * * Copied from musl: src/math/lround.c */ __msvcrt_long CDECL lround(double x) { double d = round(x); if (d != (double)(__msvcrt_long)d) { *_errno() = EDOM; return 0; } return d; } /********************************************************************* * lroundf (MSVCR120.@) * * Copied from musl: src/math/lroundf.c */ __msvcrt_long CDECL lroundf(float x) { float f = roundf(x); if (f != (float)(__msvcrt_long)f) { *_errno() = EDOM; return 0; } return f; } /********************************************************************* * llround (MSVCR120.@) * * Copied from musl: src/math/llround.c */ __int64 CDECL llround(double x) { double d = round(x); if (d != (double)(__int64)d) { *_errno() = EDOM; return 0; } return d; } /********************************************************************* * llroundf (MSVCR120.@) * * Copied from musl: src/math/llroundf.c */ __int64 CDECL llroundf(float x) { float f = roundf(x); if (f != (float)(__int64)f) { *_errno() = EDOM; return 0; } return f; } /********************************************************************* * trunc (MSVCR120.@) * * Copied from musl: src/math/trunc.c */ double CDECL trunc(double x) { union {double f; UINT64 i;} u = {x}; int e = (u.i >> 52 & 0x7ff) - 0x3ff + 12; UINT64 m; if (e >= 52 + 12) return x; if (e < 12) e = 1; m = -1ULL >> e; if ((u.i & m) == 0) return x; u.i &= ~m; return u.f; } /********************************************************************* * truncf (MSVCR120.@) * * Copied from musl: src/math/truncf.c */ float CDECL truncf(float x) { union {float f; UINT32 i;} u = {x}; int e = (u.i >> 23 & 0xff) - 0x7f + 9; UINT32 m; if (e >= 23 + 9) return x; if (e < 9) e = 1; m = -1U >> e; if ((u.i & m) == 0) return x; u.i &= ~m; return u.f; } /********************************************************************* * _dtest (MSVCR120.@) */ short CDECL _dtest(double *x) { return _dclass(*x); } /********************************************************************* * _fdtest (MSVCR120.@) */ short CDECL _fdtest(float *x) { return _fdclass(*x); } static double erfc1(double x) { static const double erx = 8.45062911510467529297e-01, pa0 = -2.36211856075265944077e-03, pa1 = 4.14856118683748331666e-01, pa2 = -3.72207876035701323847e-01, pa3 = 3.18346619901161753674e-01, pa4 = -1.10894694282396677476e-01, pa5 = 3.54783043256182359371e-02, pa6 = -2.16637559486879084300e-03, qa1 = 1.06420880400844228286e-01, qa2 = 5.40397917702171048937e-01, qa3 = 7.18286544141962662868e-02, qa4 = 1.26171219808761642112e-01, qa5 = 1.36370839120290507362e-02, qa6 = 1.19844998467991074170e-02; double s, P, Q; s = fabs(x) - 1; P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6))))); Q = 1 + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6))))); return 1 - erx - P / Q; } static double erfc2(UINT32 ix, double x) { static const double ra0 = -9.86494403484714822705e-03, ra1 = -6.93858572707181764372e-01, ra2 = -1.05586262253232909814e+01, ra3 = -6.23753324503260060396e+01, ra4 = -1.62396669462573470355e+02, ra5 = -1.84605092906711035994e+02, ra6 = -8.12874355063065934246e+01, ra7 = -9.81432934416914548592e+00, sa1 = 1.96512716674392571292e+01, sa2 = 1.37657754143519042600e+02, sa3 = 4.34565877475229228821e+02, sa4 = 6.45387271733267880336e+02, sa5 = 4.29008140027567833386e+02, sa6 = 1.08635005541779435134e+02, sa7 = 6.57024977031928170135e+00, sa8 = -6.04244152148580987438e-02, rb0 = -9.86494292470009928597e-03, rb1 = -7.99283237680523006574e-01, rb2 = -1.77579549177547519889e+01, rb3 = -1.60636384855821916062e+02, rb4 = -6.37566443368389627722e+02, rb5 = -1.02509513161107724954e+03, rb6 = -4.83519191608651397019e+02, sb1 = 3.03380607434824582924e+01, sb2 = 3.25792512996573918826e+02, sb3 = 1.53672958608443695994e+03, sb4 = 3.19985821950859553908e+03, sb5 = 2.55305040643316442583e+03, sb6 = 4.74528541206955367215e+02, sb7 = -2.24409524465858183362e+01; double s, R, S, z; UINT64 iz; if (ix < 0x3ff40000) /* |x| < 1.25 */ return erfc1(x); x = fabs(x); s = 1 / (x * x); if (ix < 0x4006db6d) { /* |x| < 1/.35 ~ 2.85714 */ R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + s * (ra5 + s * (ra6 + s * ra7)))))); S = 1.0 + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + s * (sa5 + s * (sa6 + s * (sa7 + s * sa8))))))); } else { /* |x| > 1/.35 */ R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6))))); S = 1.0 + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + s * (sb5 + s * (sb6 + s * sb7)))))); } z = x; iz = *(ULONGLONG*)&z; iz &= 0xffffffff00000000ULL; z = *(double*)&iz; return exp(-z * z - 0.5625) * exp((z - x) * (z + x) + R / S) / x; } /********************************************************************* * erf (MSVCR120.@) */ double CDECL erf(double x) { static const double efx8 = 1.02703333676410069053e+00, pp0 = 1.28379167095512558561e-01, pp1 = -3.25042107247001499370e-01, pp2 = -2.84817495755985104766e-02, pp3 = -5.77027029648944159157e-03, pp4 = -2.37630166566501626084e-05, qq1 = 3.97917223959155352819e-01, qq2 = 6.50222499887672944485e-02, qq3 = 5.08130628187576562776e-03, qq4 = 1.32494738004321644526e-04, qq5 = -3.96022827877536812320e-06; double r, s, z, y; UINT32 ix; int sign; ix = *(UINT64*)&x >> 32; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x7ff00000) { /* erf(nan)=nan, erf(+-inf)=+-1 */ return 1 - 2 * sign + 1 / x; } if (ix < 0x3feb0000) { /* |x| < 0.84375 */ if (ix < 0x3e300000) { /* |x| < 2**-28 */ /* avoid underflow */ return 0.125 * (8 * x + efx8 * x); } z = x * x; r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); s = 1.0 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); y = r / s; return x + x * y; } if (ix < 0x40180000) /* 0.84375 <= |x| < 6 */ y = 1 - erfc2(ix, x); else y = 1 - DBL_MIN; return sign ? -y : y; } static float erfc1f(float x) { static const float erx = 8.4506291151e-01, pa0 = -2.3621185683e-03, pa1 = 4.1485610604e-01, pa2 = -3.7220788002e-01, pa3 = 3.1834661961e-01, pa4 = -1.1089469492e-01, pa5 = 3.5478305072e-02, pa6 = -2.1663755178e-03, qa1 = 1.0642088205e-01, qa2 = 5.4039794207e-01, qa3 = 7.1828655899e-02, qa4 = 1.2617121637e-01, qa5 = 1.3637083583e-02, qa6 = 1.1984500103e-02; float s, P, Q; s = fabsf(x) - 1; P = pa0 + s * (pa1 + s * (pa2 + s * (pa3 + s * (pa4 + s * (pa5 + s * pa6))))); Q = 1 + s * (qa1 + s * (qa2 + s * (qa3 + s * (qa4 + s * (qa5 + s * qa6))))); return 1 - erx - P / Q; } static float erfc2f(UINT32 ix, float x) { static const float ra0 = -9.8649440333e-03, ra1 = -6.9385856390e-01, ra2 = -1.0558626175e+01, ra3 = -6.2375331879e+01, ra4 = -1.6239666748e+02, ra5 = -1.8460508728e+02, ra6 = -8.1287437439e+01, ra7 = -9.8143291473e+00, sa1 = 1.9651271820e+01, sa2 = 1.3765776062e+02, sa3 = 4.3456588745e+02, sa4 = 6.4538726807e+02, sa5 = 4.2900814819e+02, sa6 = 1.0863500214e+02, sa7 = 6.5702495575e+00, sa8 = -6.0424413532e-02, rb0 = -9.8649431020e-03, rb1 = -7.9928326607e-01, rb2 = -1.7757955551e+01, rb3 = -1.6063638306e+02, rb4 = -6.3756646729e+02, rb5 = -1.0250950928e+03, rb6 = -4.8351919556e+02, sb1 = 3.0338060379e+01, sb2 = 3.2579251099e+02, sb3 = 1.5367296143e+03, sb4 = 3.1998581543e+03, sb5 = 2.5530502930e+03, sb6 = 4.7452853394e+02, sb7 = -2.2440952301e+01; float s, R, S, z; if (ix < 0x3fa00000) /* |x| < 1.25 */ return erfc1f(x); x = fabsf(x); s = 1 / (x * x); if (ix < 0x4036db6d) { /* |x| < 1/0.35 */ R = ra0 + s * (ra1 + s * (ra2 + s * (ra3 + s * (ra4 + s * (ra5 + s * (ra6 + s * ra7)))))); S = 1.0f + s * (sa1 + s * (sa2 + s * (sa3 + s * (sa4 + s * (sa5 + s * (sa6 + s * (sa7 + s * sa8))))))); } else { /* |x| >= 1/0.35 */ R = rb0 + s * (rb1 + s * (rb2 + s * (rb3 + s * (rb4 + s * (rb5 + s * rb6))))); S = 1.0f + s * (sb1 + s * (sb2 + s * (sb3 + s * (sb4 + s * (sb5 + s * (sb6 + s * sb7)))))); } ix = *(UINT32*)&x & 0xffffe000; z = *(float*)&ix; return expf(-z * z - 0.5625f) * expf((z - x) * (z + x) + R / S) / x; } /********************************************************************* * erff (MSVCR120.@) * * Copied from musl: src/math/erff.c */ float CDECL erff(float x) { static const float efx8 = 1.0270333290e+00, pp0 = 1.2837916613e-01, pp1 = -3.2504209876e-01, pp2 = -2.8481749818e-02, pp3 = -5.7702702470e-03, pp4 = -2.3763017452e-05, qq1 = 3.9791721106e-01, qq2 = 6.5022252500e-02, qq3 = 5.0813062117e-03, qq4 = 1.3249473704e-04, qq5 = -3.9602282413e-06; float r, s, z, y; UINT32 ix; int sign; ix = *(UINT32*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x7f800000) { /* erf(nan)=nan, erf(+-inf)=+-1 */ return 1 - 2 * sign + 1 / x; } if (ix < 0x3f580000) { /* |x| < 0.84375 */ if (ix < 0x31800000) { /* |x| < 2**-28 */ /*avoid underflow */ return 0.125f * (8 * x + efx8 * x); } z = x * x; r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); s = 1 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); y = r / s; return x + x * y; } if (ix < 0x40c00000) /* |x| < 6 */ y = 1 - erfc2f(ix, x); else y = 1 - FLT_MIN; return sign ? -y : y; } /********************************************************************* * erfc (MSVCR120.@) * * Copied from musl: src/math/erf.c */ double CDECL erfc(double x) { static const double pp0 = 1.28379167095512558561e-01, pp1 = -3.25042107247001499370e-01, pp2 = -2.84817495755985104766e-02, pp3 = -5.77027029648944159157e-03, pp4 = -2.37630166566501626084e-05, qq1 = 3.97917223959155352819e-01, qq2 = 6.50222499887672944485e-02, qq3 = 5.08130628187576562776e-03, qq4 = 1.32494738004321644526e-04, qq5 = -3.96022827877536812320e-06; double r, s, z, y; UINT32 ix; int sign; ix = *(ULONGLONG*)&x >> 32; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x7ff00000) { /* erfc(nan)=nan, erfc(+-inf)=0,2 */ return 2 * sign + 1 / x; } if (ix < 0x3feb0000) { /* |x| < 0.84375 */ if (ix < 0x3c700000) /* |x| < 2**-56 */ return 1.0 - x; z = x * x; r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); s = 1.0 + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); y = r / s; if (sign || ix < 0x3fd00000) { /* x < 1/4 */ return 1.0 - (x + x * y); } return 0.5 - (x - 0.5 + x * y); } if (ix < 0x403c0000) { /* 0.84375 <= |x| < 28 */ return sign ? 2 - erfc2(ix, x) : erfc2(ix, x); } if (sign) return 2 - DBL_MIN; *_errno() = ERANGE; return fp_barrier(DBL_MIN) * DBL_MIN; } /********************************************************************* * erfcf (MSVCR120.@) * * Copied from musl: src/math/erff.c */ float CDECL erfcf(float x) { static const float pp0 = 1.2837916613e-01, pp1 = -3.2504209876e-01, pp2 = -2.8481749818e-02, pp3 = -5.7702702470e-03, pp4 = -2.3763017452e-05, qq1 = 3.9791721106e-01, qq2 = 6.5022252500e-02, qq3 = 5.0813062117e-03, qq4 = 1.3249473704e-04, qq5 = -3.9602282413e-06; float r, s, z, y; UINT32 ix; int sign; ix = *(UINT32*)&x; sign = ix >> 31; ix &= 0x7fffffff; if (ix >= 0x7f800000) { /* erfc(nan)=nan, erfc(+-inf)=0,2 */ return 2 * sign + 1 / x; } if (ix < 0x3f580000) { /* |x| < 0.84375 */ if (ix < 0x23800000) /* |x| < 2**-56 */ return 1.0f - x; z = x * x; r = pp0 + z * (pp1 + z * (pp2 + z * (pp3 + z * pp4))); s = 1.0f + z * (qq1 + z * (qq2 + z * (qq3 + z * (qq4 + z * qq5)))); y = r / s; if (sign || ix < 0x3e800000) /* x < 1/4 */ return 1.0f - (x + x * y); return 0.5f - (x - 0.5f + x * y); } if (ix < 0x41e00000) { /* |x| < 28 */ return sign ? 2 - erfc2f(ix, x) : erfc2f(ix, x); } if (sign) return 2 - FLT_MIN; *_errno() = ERANGE; return FLT_MIN * FLT_MIN; } /********************************************************************* * fmaxf (MSVCR120.@) */ float CDECL fmaxf(float x, float y) { if(isnan(x)) return y; if(isnan(y)) return x; if(x==0 && y==0) return signbit(x) ? y : x; return xy ? x-y : 0; } /********************************************************************* * fdim (MSVCR120.@) */ double CDECL fdim(double x, double y) { if(isnan(x)) return x; if(isnan(y)) return y; return x>y ? x-y : 0; } /********************************************************************* * _fdsign (MSVCR120.@) */ int CDECL _fdsign(float x) { union { float f; UINT32 i; } u = { x }; return (u.i >> 16) & 0x8000; } /********************************************************************* * _dsign (MSVCR120.@) */ int CDECL _dsign(double x) { union { double f; UINT64 i; } u = { x }; return (u.i >> 48) & 0x8000; } /********************************************************************* * _dpcomp (MSVCR120.@) */ int CDECL _dpcomp(double x, double y) { if(isnan(x) || isnan(y)) return 0; if(x == y) return 2; return x < y ? 1 : 4; } /********************************************************************* * _fdpcomp (MSVCR120.@) */ int CDECL _fdpcomp(float x, float y) { return _dpcomp(x, y); } /********************************************************************* * fminf (MSVCR120.@) */ float CDECL fminf(float x, float y) { if(isnan(x)) return y; if(isnan(y)) return x; if(x==0 && y==0) return signbit(x) ? x : y; return x> 52 & 0x7ff; int s = ux >> 63; /* |x| */ ux &= (UINT64)-1 / 2; x = *(double*)&ux; if (e >= 0x3ff + 26) /* |x| >= 0x1p26 or inf or nan */ x = log(x) + 0.693147180559945309417232121458176568; else if (e >= 0x3ff + 1) /* |x| >= 2 */ x = log(2 * x + 1 / (sqrt(x * x + 1) + x)); else if (e >= 0x3ff - 26) /* |x| >= 0x1p-26 */ x = log1p(x + x * x / (sqrt(x * x + 1) + 1)); else /* |x| < 0x1p-26, raise inexact if x != 0 */ fp_barrier(x + 0x1p120f); return s ? -x : x; } /********************************************************************* * asinhf (MSVCR120.@) * * Copied from musl: src/math/asinhf.c */ float CDECL asinhf(float x) { UINT32 ux = *(UINT32*)&x; UINT32 i = ux & 0x7fffffff; int s = ux >> 31; /* |x| */ x = *(float*)&i; if (i >= 0x3f800000 + (12 << 23))/* |x| >= 0x1p12 or inf or nan */ x = logf(x) + 0.693147180559945309417232121458176568f; else if (i >= 0x3f800000 + (1 << 23)) /* |x| >= 2 */ x = logf(2 * x + 1 / (sqrtf(x * x + 1) + x)); else if (i >= 0x3f800000 - (12 << 23)) /* |x| >= 0x1p-12 */ x = log1pf(x + x * x / (sqrtf(x * x + 1) + 1)); else /* |x| < 0x1p-12, raise inexact if x!=0 */ fp_barrierf(x + 0x1p120f); return s ? -x : x; } /********************************************************************* * acosh (MSVCR120.@) * * Copied from musl: src/math/acosh.c */ double CDECL acosh(double x) { int e = *(UINT64*)&x >> 52 & 0x7ff; if (x < 1) { *_errno() = EDOM; feraiseexcept(FE_INVALID); return NAN; } if (e < 0x3ff + 1) /* |x| < 2, up to 2ulp error in [1,1.125] */ return log1p(x - 1 + sqrt((x - 1) * (x - 1) + 2 * (x - 1))); if (e < 0x3ff + 26) /* |x| < 0x1p26 */ return log(2 * x - 1 / (x + sqrt(x * x - 1))); /* |x| >= 0x1p26 or nan */ return log(x) + 0.693147180559945309417232121458176568; } /********************************************************************* * acoshf (MSVCR120.@) * * Copied from musl: src/math/acoshf.c */ float CDECL acoshf(float x) { UINT32 a = *(UINT32*)&x & 0x7fffffff; if (x < 1) { *_errno() = EDOM; feraiseexcept(FE_INVALID); return NAN; } if (a < 0x3f800000 + (1 << 23)) /* |x| < 2, up to 2ulp error in [1,1.125] */ return log1pf(x - 1 + sqrtf((x - 1) * (x - 1) + 2 * (x - 1))); if (*(UINT32*)&x < 0x3f800000 + (12 << 23)) /* 2 <= x < 0x1p12 */ return logf(2 * x - 1 / (x + sqrtf(x * x - 1))); /* x >= 0x1p12 or x <= -2 or nan */ return logf(x) + 0.693147180559945309417232121458176568f; } /********************************************************************* * atanh (MSVCR120.@) * * Copied from musl: src/math/atanh.c */ double CDECL atanh(double x) { UINT64 ux = *(UINT64*)&x; int e = ux >> 52 & 0x7ff; int s = ux >> 63; /* |x| */ ux &= (UINT64)-1 / 2; x = *(double*)&ux; if (x > 1) { *_errno() = EDOM; feraiseexcept(FE_INVALID); return NAN; } if (e < 0x3ff - 1) { if (e < 0x3ff - 32) { fp_barrier(x + 0x1p120f); if (e == 0) /* handle underflow */ fp_barrier(x * x); } else { /* |x| < 0.5, up to 1.7ulp error */ x = 0.5 * log1p(2 * x + 2 * x * x / (1 - x)); } } else { /* avoid overflow */ x = 0.5 * log1p(2 * (x / (1 - x))); if (isinf(x)) *_errno() = ERANGE; } return s ? -x : x; } /********************************************************************* * atanhf (MSVCR120.@) * * Copied from musl: src/math/atanhf.c */ float CDECL atanhf(float x) { UINT32 ux = *(UINT32*)&x; int s = ux >> 31; /* |x| */ ux &= 0x7fffffff; x = *(float*)&ux; if (x > 1) { *_errno() = EDOM; feraiseexcept(FE_INVALID); return NAN; } if (ux < 0x3f800000 - (1 << 23)) { if (ux < 0x3f800000 - (32 << 23)) { fp_barrierf(x + 0x1p120f); if (ux < (1 << 23)) /* handle underflow */ fp_barrierf(x * x); } else { /* |x| < 0.5, up to 1.7ulp error */ x = 0.5f * log1pf(2 * x + 2 * x * x / (1 - x)); } } else { /* avoid overflow */ x = 0.5f * log1pf(2 * (x / (1 - x))); if (isinf(x)) *_errno() = ERANGE; } return s ? -x : x; } #endif /* _MSVCR_VER>=120 */ /********************************************************************* * _scalb (MSVCRT.@) * scalbn (MSVCR120.@) * scalbln (MSVCR120.@) */ double CDECL _scalb(double num, __msvcrt_long power) { return ldexp(num, power); } /********************************************************************* * _scalbf (MSVCRT.@) * scalbnf (MSVCR120.@) * scalblnf (MSVCR120.@) */ float CDECL _scalbf(float num, __msvcrt_long power) { return ldexp(num, power); } #if _MSVCR_VER>=120 /********************************************************************* * remainder (MSVCR120.@) * * Copied from musl: src/math/remainder.c */ double CDECL remainder(double x, double y) { int q; #if _MSVCR_VER == 120 && defined(__x86_64__) if (isnan(x) || isnan(y)) *_errno() = EDOM; #endif return remquo(x, y, &q); } /********************************************************************* * remainderf (MSVCR120.@) * * Copied from musl: src/math/remainderf.c */ float CDECL remainderf(float x, float y) { int q; #if _MSVCR_VER == 120 && defined(__x86_64__) if (isnan(x) || isnan(y)) *_errno() = EDOM; #endif return remquof(x, y, &q); } /********************************************************************* * remquo (MSVCR120.@) * * Copied from musl: src/math/remquo.c */ double CDECL remquo(double x, double y, int *quo) { UINT64 uxi = *(UINT64*)&x; UINT64 uyi = *(UINT64*)&y; int ex = uxi >> 52 & 0x7ff; int ey = uyi >> 52 & 0x7ff; int sx = uxi >> 63; int sy = uyi >> 63; UINT32 q; UINT64 i; *quo = 0; if (y == 0 || isinf(x)) *_errno() = EDOM; if (uyi << 1 == 0 || isnan(y) || ex == 0x7ff) return (x * y) / (x * y); if (uxi << 1 == 0) return x; /* normalize x and y */ if (!ex) { for (i = uxi << 12; i >> 63 == 0; ex--, i <<= 1); uxi <<= -ex + 1; } else { uxi &= -1ULL >> 12; uxi |= 1ULL << 52; } if (!ey) { for (i = uyi << 12; i >> 63 == 0; ey--, i <<= 1); uyi <<= -ey + 1; } else { uyi &= -1ULL >> 12; uyi |= 1ULL << 52; } q = 0; if (ex < ey) { if (ex+1 == ey) goto end; return x; } /* x mod y */ for (; ex > ey; ex--) { i = uxi - uyi; if (i >> 63 == 0) { uxi = i; q++; } uxi <<= 1; q <<= 1; } i = uxi - uyi; if (i >> 63 == 0) { uxi = i; q++; } if (uxi == 0) ex = -60; else for (; uxi >> 52 == 0; uxi <<= 1, ex--); end: /* scale result and decide between |x| and |x|-|y| */ if (ex > 0) { uxi -= 1ULL << 52; uxi |= (UINT64)ex << 52; } else { uxi >>= -ex + 1; } x = *(double*)&uxi; if (sy) y = -y; if (ex == ey || (ex + 1 == ey && (2 * x > y || (2 * x == y && q % 2)))) { x -= y; q++; } q &= 0x7fffffff; *quo = sx ^ sy ? -(int)q : (int)q; return sx ? -x : x; } /********************************************************************* * remquof (MSVCR120.@) * * Copied from musl: src/math/remquof.c */ float CDECL remquof(float x, float y, int *quo) { UINT32 uxi = *(UINT32*)&x; UINT32 uyi = *(UINT32*)&y; int ex = uxi >> 23 & 0xff; int ey = uyi >> 23 & 0xff; int sx = uxi >> 31; int sy = uyi>> 31; UINT32 q, i; *quo = 0; if (y == 0 || isinf(x)) *_errno() = EDOM; if (uyi << 1 == 0 || isnan(y) || ex == 0xff) return (x * y) / (x * y); if (uxi << 1 == 0) return x; /* normalize x and y */ if (!ex) { for (i = uxi << 9; i >> 31 == 0; ex--, i <<= 1); uxi <<= -ex + 1; } else { uxi &= -1U >> 9; uxi |= 1U << 23; } if (!ey) { for (i = uyi << 9; i >> 31 == 0; ey--, i <<= 1); uyi <<= -ey + 1; } else { uyi &= -1U >> 9; uyi |= 1U << 23; } q = 0; if (ex < ey) { if (ex + 1 == ey) goto end; return x; } /* x mod y */ for (; ex > ey; ex--) { i = uxi - uyi; if (i >> 31 == 0) { uxi = i; q++; } uxi <<= 1; q <<= 1; } i = uxi - uyi; if (i >> 31 == 0) { uxi = i; q++; } if (uxi == 0) ex = -30; else for (; uxi >> 23 == 0; uxi <<= 1, ex--); end: /* scale result and decide between |x| and |x|-|y| */ if (ex > 0) { uxi -= 1U << 23; uxi |= (UINT32)ex << 23; } else { uxi >>= -ex + 1; } x = *(float*)&uxi; if (sy) y = -y; if (ex == ey || (ex + 1 == ey && (2 * x > y || (2 * x == y && q % 2)))) { x -= y; q++; } q &= 0x7fffffff; *quo = sx ^ sy ? -(int)q : (int)q; return sx ? -x : x; } /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ static double sin_pi(double x) { int n; /* spurious inexact if odd int */ x = 2.0 * (x * 0.5 - floor(x * 0.5)); /* x mod 2.0 */ n = x * 4.0; n = (n + 1) / 2; x -= n * 0.5f; x *= M_PI; switch (n) { default: /* case 4: */ case 0: return __sin(x, 0.0, 0); case 1: return __cos(x, 0.0); case 2: return __sin(-x, 0.0, 0); case 3: return -__cos(x, 0.0); } } /********************************************************************* * lgamma (MSVCR120.@) * * Copied from musl: src/math/lgamma_r.c */ double CDECL lgamma(double x) { static const double pi = 3.14159265358979311600e+00, a0 = 7.72156649015328655494e-02, a1 = 3.22467033424113591611e-01, a2 = 6.73523010531292681824e-02, a3 = 2.05808084325167332806e-02, a4 = 7.38555086081402883957e-03, a5 = 2.89051383673415629091e-03, a6 = 1.19270763183362067845e-03, a7 = 5.10069792153511336608e-04, a8 = 2.20862790713908385557e-04, a9 = 1.08011567247583939954e-04, a10 = 2.52144565451257326939e-05, a11 = 4.48640949618915160150e-05, tc = 1.46163214496836224576e+00, tf = -1.21486290535849611461e-01, tt = -3.63867699703950536541e-18, t0 = 4.83836122723810047042e-01, t1 = -1.47587722994593911752e-01, t2 = 6.46249402391333854778e-02, t3 = -3.27885410759859649565e-02, t4 = 1.79706750811820387126e-02, t5 = -1.03142241298341437450e-02, t6 = 6.10053870246291332635e-03, t7 = -3.68452016781138256760e-03, t8 = 2.25964780900612472250e-03, t9 = -1.40346469989232843813e-03, t10 = 8.81081882437654011382e-04, t11 = -5.38595305356740546715e-04, t12 = 3.15632070903625950361e-04, t13 = -3.12754168375120860518e-04, t14 = 3.35529192635519073543e-04, u0 = -7.72156649015328655494e-02, u1 = 6.32827064025093366517e-01, u2 = 1.45492250137234768737e+00, u3 = 9.77717527963372745603e-01, u4 = 2.28963728064692451092e-01, u5 = 1.33810918536787660377e-02, v1 = 2.45597793713041134822e+00, v2 = 2.12848976379893395361e+00, v3 = 7.69285150456672783825e-01, v4 = 1.04222645593369134254e-01, v5 = 3.21709242282423911810e-03, s0 = -7.72156649015328655494e-02, s1 = 2.14982415960608852501e-01, s2 = 3.25778796408930981787e-01, s3 = 1.46350472652464452805e-01, s4 = 2.66422703033638609560e-02, s5 = 1.84028451407337715652e-03, s6 = 3.19475326584100867617e-05, r1 = 1.39200533467621045958e+00, r2 = 7.21935547567138069525e-01, r3 = 1.71933865632803078993e-01, r4 = 1.86459191715652901344e-02, r5 = 7.77942496381893596434e-04, r6 = 7.32668430744625636189e-06, w0 = 4.18938533204672725052e-01, w1 = 8.33333333333329678849e-02, w2 = -2.77777777728775536470e-03, w3 = 7.93650558643019558500e-04, w4 = -5.95187557450339963135e-04, w5 = 8.36339918996282139126e-04, w6 = -1.63092934096575273989e-03; union {double f; UINT64 i;} u = {x}; double t, y, z, nadj, p, p1, p2, p3, q, r, w; UINT32 ix; int sign,i; /* purge off +-inf, NaN, +-0, tiny and negative arguments */ sign = u.i >> 63; ix = u.i >> 32 & 0x7fffffff; if (ix >= 0x7ff00000) return x * x; if (ix < (0x3ff - 70) << 20) { /* |x|<2**-70, return -log(|x|) */ if(sign) x = -x; return -log(x); } if (sign) { x = -x; t = sin_pi(x); if (t == 0.0) { /* -integer */ *_errno() = ERANGE; return 1.0 / (x - x); } if (t <= 0.0) t = -t; nadj = log(pi / (t * x)); } /* purge off 1 and 2 */ if ((ix == 0x3ff00000 || ix == 0x40000000) && (UINT32)u.i == 0) r = 0; /* for x < 2.0 */ else if (ix < 0x40000000) { if (ix <= 0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */ r = -log(x); if (ix >= 0x3FE76944) { y = 1.0 - x; i = 0; } else if (ix >= 0x3FCDA661) { y = x - (tc - 1.0); i = 1; } else { y = x; i = 2; } } else { r = 0.0; if (ix >= 0x3FFBB4C3) { /* [1.7316,2] */ y = 2.0 - x; i = 0; } else if(ix >= 0x3FF3B4C4) { /* [1.23,1.73] */ y = x - tc; i = 1; } else { y = x - 1.0; i = 2; } } switch (i) { case 0: z = y * y; p1 = a0 + z * (a2 + z * (a4 + z * (a6 + z * (a8 + z * a10)))); p2 = z * (a1 + z * (a3 + z * (a5 + z * (a7 + z * (a9 + z * a11))))); p = y * p1 + p2; r += (p - 0.5 * y); break; case 1: z = y * y; w = z * y; p1 = t0 + w * (t3 + w * (t6 + w * (t9 + w * t12))); /* parallel comp */ p2 = t1 + w * (t4 + w * (t7 + w * (t10 + w * t13))); p3 = t2 + w * (t5 + w * (t8 + w * (t11 + w * t14))); p = z * p1 - (tt - w * (p2 + y * p3)); r += tf + p; break; case 2: p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * u5))))); p2 = 1.0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5)))); r += -0.5 * y + p1 / p2; } } else if (ix < 0x40200000) { /* x < 8.0 */ i = (int)x; y = x - (double)i; p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); q = 1.0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6))))); r = 0.5 * y + p / q; z = 1.0; /* lgamma(1+s) = log(s) + lgamma(s) */ switch (i) { case 7: z *= y + 6.0; /* fall through */ case 6: z *= y + 5.0; /* fall through */ case 5: z *= y + 4.0; /* fall through */ case 4: z *= y + 3.0; /* fall through */ case 3: z *= y + 2.0; r += log(z); break; } } else if (ix < 0x43900000) { /* 8.0 <= x < 2**58 */ t = log(x); z = 1.0 / x; y = z * z; w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6))))); r = (x - 0.5) * (t - 1.0) + w; } else /* 2**58 <= x <= inf */ r = x * (log(x) - 1.0); if (sign) r = nadj - r; return r; } /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */ static float sinf_pi(float x) { double y; int n; /* spurious inexact if odd int */ x = 2 * (x * 0.5f - floorf(x * 0.5f)); /* x mod 2.0 */ n = (int)(x * 4); n = (n + 1) / 2; y = x - n * 0.5f; y *= M_PI; switch (n) { default: /* case 4: */ case 0: return __sindf(y); case 1: return __cosdf(y); case 2: return __sindf(-y); case 3: return -__cosdf(y); } } /********************************************************************* * lgammaf (MSVCR120.@) * * Copied from musl: src/math/lgammaf_r.c */ float CDECL lgammaf(float x) { static const float pi = 3.1415927410e+00, a0 = 7.7215664089e-02, a1 = 3.2246702909e-01, a2 = 6.7352302372e-02, a3 = 2.0580807701e-02, a4 = 7.3855509982e-03, a5 = 2.8905137442e-03, a6 = 1.1927076848e-03, a7 = 5.1006977446e-04, a8 = 2.2086278477e-04, a9 = 1.0801156895e-04, a10 = 2.5214456400e-05, a11 = 4.4864096708e-05, tc = 1.4616321325e+00, tf = -1.2148628384e-01, tt = 6.6971006518e-09, t0 = 4.8383611441e-01, t1 = -1.4758771658e-01, t2 = 6.4624942839e-02, t3 = -3.2788541168e-02, t4 = 1.7970675603e-02, t5 = -1.0314224288e-02, t6 = 6.1005386524e-03, t7 = -3.6845202558e-03, t8 = 2.2596477065e-03, t9 = -1.4034647029e-03, t10 = 8.8108185446e-04, t11 = -5.3859531181e-04, t12 = 3.1563205994e-04, t13 = -3.1275415677e-04, t14 = 3.3552918467e-04, u0 = -7.7215664089e-02, u1 = 6.3282704353e-01, u2 = 1.4549225569e+00, u3 = 9.7771751881e-01, u4 = 2.2896373272e-01, u5 = 1.3381091878e-02, v1 = 2.4559779167e+00, v2 = 2.1284897327e+00, v3 = 7.6928514242e-01, v4 = 1.0422264785e-01, v5 = 3.2170924824e-03, s0 = -7.7215664089e-02, s1 = 2.1498242021e-01, s2 = 3.2577878237e-01, s3 = 1.4635047317e-01, s4 = 2.6642270386e-02, s5 = 1.8402845599e-03, s6 = 3.1947532989e-05, r1 = 1.3920053244e+00, r2 = 7.2193557024e-01, r3 = 1.7193385959e-01, r4 = 1.8645919859e-02, r5 = 7.7794247773e-04, r6 = 7.3266842264e-06, w0 = 4.1893854737e-01, w1 = 8.3333335817e-02, w2 = -2.7777778450e-03, w3 = 7.9365057172e-04, w4 = -5.9518753551e-04, w5 = 8.3633989561e-04, w6 = -1.6309292987e-03; union {float f; UINT32 i;} u = {x}; float t, y, z, nadj, p, p1, p2, p3, q, r, w; UINT32 ix; int i, sign; /* purge off +-inf, NaN, +-0, tiny and negative arguments */ sign = u.i >> 31; ix = u.i & 0x7fffffff; if (ix >= 0x7f800000) return x * x; if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */ if (sign) x = -x; return -logf(x); } if (sign) { x = -x; t = sinf_pi(x); if (t == 0.0f) { /* -integer */ *_errno() = ERANGE; return 1.0f / (x - x); } if (t <= 0.0f) t = -t; nadj = logf(pi / (t * x)); } /* purge off 1 and 2 */ if (ix == 0x3f800000 || ix == 0x40000000) r = 0; /* for x < 2.0 */ else if (ix < 0x40000000) { if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */ r = -logf(x); if (ix >= 0x3f3b4a20) { y = 1.0f - x; i = 0; } else if (ix >= 0x3e6d3308) { y = x - (tc - 1.0f); i = 1; } else { y = x; i = 2; } } else { r = 0.0f; if (ix >= 0x3fdda618) { /* [1.7316,2] */ y = 2.0f - x; i = 0; } else if (ix >= 0x3F9da620) { /* [1.23,1.73] */ y = x - tc; i = 1; } else { y = x - 1.0f; i = 2; } } switch(i) { case 0: z = y * y; p1 = a0 + z * (a2 + z * (a4 + z * (a6 + z * (a8 + z * a10)))); p2 = z * (a1 + z * (a3 + z * (a5 + z * (a7 + z * (a9 + z * a11))))); p = y * p1 + p2; r += p - 0.5f * y; break; case 1: z = y * y; w = z * y; p1 = t0 + w * (t3 + w * (t6 + w * (t9 + w * t12))); /* parallel comp */ p2 = t1 + w * (t4 + w * (t7 + w * (t10 + w * t13))); p3 = t2 + w * (t5 + w * (t8 + w * (t11 + w * t14))); p = z * p1 - (tt - w * (p2 + y * p3)); r += (tf + p); break; case 2: p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * u5))))); p2 = 1.0f + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * v5)))); r += -0.5f * y + p1 / p2; } } else if (ix < 0x41000000) { /* x < 8.0 */ i = (int)x; y = x - (float)i; p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); q = 1.0f + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * r6))))); r = 0.5f * y + p / q; z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */ switch (i) { case 7: z *= y + 6.0f; /* fall through */ case 6: z *= y + 5.0f; /* fall through */ case 5: z *= y + 4.0f; /* fall through */ case 4: z *= y + 3.0f; /* fall through */ case 3: z *= y + 2.0f; r += logf(z); break; } } else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */ t = logf(x); z = 1.0f / x; y = z * z; w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * w6))))); r = (x - 0.5f) * (t - 1.0f) + w; } else /* 2**58 <= x <= inf */ r = x * (logf(x) - 1.0f); if (sign) r = nadj - r; return r; } static double tgamma_S(double x) { static const double Snum[] = { 23531376880.410759688572007674451636754734846804940, 42919803642.649098768957899047001988850926355848959, 35711959237.355668049440185451547166705960488635843, 17921034426.037209699919755754458931112671403265390, 6039542586.3520280050642916443072979210699388420708, 1439720407.3117216736632230727949123939715485786772, 248874557.86205415651146038641322942321632125127801, 31426415.585400194380614231628318205362874684987640, 2876370.6289353724412254090516208496135991145378768, 186056.26539522349504029498971604569928220784236328, 8071.6720023658162106380029022722506138218516325024, 210.82427775157934587250973392071336271166969580291, 2.5066282746310002701649081771338373386264310793408, }; static const double Sden[] = { 0, 39916800, 120543840, 150917976, 105258076, 45995730, 13339535, 2637558, 357423, 32670, 1925, 66, 1, }; double num = 0, den = 0; int i; /* to avoid overflow handle large x differently */ if (x < 8) for (i = ARRAY_SIZE(Snum) - 1; i >= 0; i--) { num = num * x + Snum[i]; den = den * x + Sden[i]; } else for (i = 0; i < ARRAY_SIZE(Snum); i++) { num = num / x + Snum[i]; den = den / x + Sden[i]; } return num / den; } /********************************************************************* * tgamma (MSVCR120.@) * * Copied from musl: src/math/tgamma.c */ double CDECL tgamma(double x) { static const double gmhalf = 5.524680040776729583740234375; static const double fact[] = { 1, 1, 2, 6, 24, 120, 720, 5040.0, 40320.0, 362880.0, 3628800.0, 39916800.0, 479001600.0, 6227020800.0, 87178291200.0, 1307674368000.0, 20922789888000.0, 355687428096000.0, 6402373705728000.0, 121645100408832000.0, 2432902008176640000.0, 51090942171709440000.0, 1124000727777607680000.0, }; union {double f; UINT64 i;} u = {x}; double absx, y, dy, z, r; UINT32 ix = u.i >> 32 & 0x7fffffff; int sign = u.i >> 63; /* special cases */ if (ix >= 0x7ff00000) { /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */ if (u.i == 0xfff0000000000000ULL) *_errno() = EDOM; return x + INFINITY; } if (ix < (0x3ff - 54) << 20) { /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */ if (x == 0.0) *_errno() = ERANGE; return 1 / x; } /* integer arguments */ /* raise inexact when non-integer */ if (x == floor(x)) { if (sign) { *_errno() = EDOM; return 0 / (x - x); } if (x <= ARRAY_SIZE(fact)) return fact[(int)x - 1]; } /* x >= 172: tgamma(x)=inf with overflow */ /* x =< -184: tgamma(x)=+-0 with underflow */ if (ix >= 0x40670000) { /* |x| >= 184 */ *_errno() = ERANGE; if (sign) { fp_barrierf(0x1p-126 / x); return 0; } x *= 0x1p1023; return x; } absx = sign ? -x : x; /* handle the error of x + g - 0.5 */ y = absx + gmhalf; if (absx > gmhalf) { dy = y - absx; dy -= gmhalf; } else { dy = y - gmhalf; dy -= absx; } z = absx - 0.5; r = tgamma_S(absx) * exp(-y); if (x < 0) { /* reflection formula for negative x */ /* sinpi(absx) is not 0, integers are already handled */ r = -M_PI / (sin_pi(absx) * absx * r); dy = -dy; z = -z; } r += dy * (gmhalf + 0.5) * r / y; z = pow(y, 0.5 * z); y = r * z * z; return y; } /********************************************************************* * tgammaf (MSVCR120.@) * * Copied from musl: src/math/tgammaf.c */ float CDECL tgammaf(float x) { return tgamma(x); } /********************************************************************* * nan (MSVCR120.@) */ double CDECL nan(const char *tagp) { /* Windows ignores input (MSDN) */ return NAN; } /********************************************************************* * nanf (MSVCR120.@) */ float CDECL nanf(const char *tagp) { return NAN; } /********************************************************************* * _except1 (MSVCR120.@) * TODO: * - find meaning of ignored cw and operation bits * - unk parameter */ double CDECL _except1(DWORD fpe, _FP_OPERATION_CODE op, double arg, double res, DWORD cw, void *unk) { ULONG_PTR exception_arg; DWORD exception = 0; DWORD fpword = 0; WORD operation; int raise = 0; TRACE("(%x %x %lf %lf %x %p)\n", fpe, op, arg, res, cw, unk); #ifdef _WIN64 cw = ((cw >> 7) & 0x3f) | ((cw >> 3) & 0xc00); #endif operation = op << 5; exception_arg = (ULONG_PTR)&operation; if (fpe & 0x1) { /* overflow */ if ((fpe == 0x1 && (cw & 0x8)) || (fpe==0x11 && (cw & 0x28))) { /* 32-bit version also sets SW_INEXACT here */ raise |= FE_OVERFLOW; if (fpe & 0x10) raise |= FE_INEXACT; res = signbit(res) ? -INFINITY : INFINITY; } else { exception = EXCEPTION_FLT_OVERFLOW; } } else if (fpe & 0x2) { /* underflow */ if ((fpe == 0x2 && (cw & 0x10)) || (fpe==0x12 && (cw & 0x30))) { raise |= FE_UNDERFLOW; if (fpe & 0x10) raise |= FE_INEXACT; res = signbit(res) ? -0.0 : 0.0; } else { exception = EXCEPTION_FLT_UNDERFLOW; } } else if (fpe & 0x4) { /* zerodivide */ if ((fpe == 0x4 && (cw & 0x4)) || (fpe==0x14 && (cw & 0x24))) { raise |= FE_DIVBYZERO; if (fpe & 0x10) raise |= FE_INEXACT; } else { exception = EXCEPTION_FLT_DIVIDE_BY_ZERO; } } else if (fpe & 0x8) { /* invalid */ if (fpe == 0x8 && (cw & 0x1)) { raise |= FE_INVALID; } else { exception = EXCEPTION_FLT_INVALID_OPERATION; } } else if (fpe & 0x10) { /* inexact */ if (fpe == 0x10 && (cw & 0x20)) { raise |= FE_INEXACT; } else { exception = EXCEPTION_FLT_INEXACT_RESULT; } } if (exception) raise = 0; feraiseexcept(raise); if (exception) RaiseException(exception, 0, 1, &exception_arg); if (cw & 0x1) fpword |= _EM_INVALID; if (cw & 0x2) fpword |= _EM_DENORMAL; if (cw & 0x4) fpword |= _EM_ZERODIVIDE; if (cw & 0x8) fpword |= _EM_OVERFLOW; if (cw & 0x10) fpword |= _EM_UNDERFLOW; if (cw & 0x20) fpword |= _EM_INEXACT; switch (cw & 0xc00) { case 0xc00: fpword |= _RC_UP|_RC_DOWN; break; case 0x800: fpword |= _RC_UP; break; case 0x400: fpword |= _RC_DOWN; break; } switch (cw & 0x300) { case 0x0: fpword |= _PC_24; break; case 0x200: fpword |= _PC_53; break; case 0x300: fpword |= _PC_64; break; } if (cw & 0x1000) fpword |= _IC_AFFINE; _control87(fpword, 0xffffffff); return res; } _Dcomplex* CDECL _Cbuild(_Dcomplex *ret, double r, double i) { ret->_Val[0] = r; ret->_Val[1] = i; return ret; } double CDECL MSVCR120_creal(_Dcomplex z) { return z._Val[0]; } /********************************************************************* * ilogb (MSVCR120.@) */ int CDECL ilogb(double x) { return __ilogb(x); } /********************************************************************* * ilogbf (MSVCR120.@) */ int CDECL ilogbf(float x) { return __ilogbf(x); } #endif /* _MSVCR_VER>=120 */