506 lines
20 KiB
C
506 lines
20 KiB
C
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/***************************************************************************/
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/* */
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/* ftcalc.c */
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/* */
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/* Arithmetic computations (body). */
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/* */
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/* Copyright 1996-1999 by */
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/* David Turner, Robert Wilhelm, and Werner Lemberg. */
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/* */
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/* This file is part of the FreeType project, and may only be used */
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/* modified and distributed under the terms of the FreeType project */
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/* license, LICENSE.TXT. By continuing to use, modify, or distribute */
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/* this file you indicate that you have read the license and */
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/* understand and accept it fully. */
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/* */
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/***************************************************************************/
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/*************************************************************************/
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/* */
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/* Support for 1-complement arithmetic has been totally dropped in this */
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/* release. You can still write your own code if you need it. */
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/* */
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/*************************************************************************/
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/*************************************************************************/
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/* */
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/* Implementing basic computation routines. */
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/* */
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/* FT_MulDiv() and FT_MulFix() are declared in freetype.h. */
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/* */
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/*************************************************************************/
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#include <ftcalc.h>
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#include <ftdebug.h>
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#include <ftobjs.h> /* for ABS() */
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BASE_FUNC
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FT_Int32 FT_Sqrt32( FT_Int32 x )
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{
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FT_ULong val, root, newroot, mask;
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root = 0;
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mask = 0x40000000;
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val = (FT_ULong)x;
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do
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{
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newroot = root+mask;
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if (newroot <= val)
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{
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val -= newroot;
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root = newroot+mask;
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}
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root >>= 1;
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mask >>= 2;
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}
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while (mask != 0);
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return root;
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}
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#ifdef LONG64
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_MulDiv */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation `(A*B)/C' */
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/* with maximum accuracy (it uses a 64-bit intermediate integer */
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/* whenever necessary). */
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/* */
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/* This function isn't necessarily as fast as some processor specific */
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/* operations, but is at least completely portable. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. */
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/* c :: The divisor. */
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/* */
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/* <Return> */
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/* The result of `(a*b)/c'. This function never traps when trying to */
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/* divide by zero, it simply returns `MaxInt' or `MinInt' depending */
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/* on the signs of `a' and `b'. */
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/* */
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EXPORT_FUNC
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FT_Long FT_MulDiv( FT_Long a,
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FT_Long b,
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FT_Long c )
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{
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FT_Int s;
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s = 1;
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if ( a < 0 ) { a = -a; s = -s; }
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if ( b < 0 ) { b = -b; s = -s; }
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if ( c < 0 ) { c = -c; s = -s; }
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return s*( ((FT_Int64)a * b + (c >> 1) )/c);
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}
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_MulFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(A*B)/0x10000' with maximum accuracy. Most of the time, this is */
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/* used to multiply a given value by a 16.16 fixed float factor. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. Use a 16.16 factor here whenever */
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/* possible (see note below). */
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/* */
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/* <Return> */
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/* The result of `(a*b)/0x10000'. */
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/* */
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/* <Note> */
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/* This function has been optimized for the case where the absolute */
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/* value of `a' is less than 2048, and `b' is a 16.16 scaling factor. */
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/* As this happens mainly when scaling from notional units to */
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/* fractional pixels in FreeType, it resulted in noticeable speed */
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/* improvements between versions 2.0 and 1.x. */
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/* */
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/* As a conclusion, always try to place a 16.16 factor as the */
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/* _second_ argument of this function; this can make a great */
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/* difference. */
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/* */
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EXPORT_FUNC
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FT_Long FT_MulFix( FT_Long a,
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FT_Long b )
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{
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FT_Int s;
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s = 1;
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if ( a < 0 ) { a = -a; s = -s; }
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if ( b < 0 ) { b = -b; s = -s; }
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return s*(FT_Long)((FT_Int64)a * b + 0x8000) >> 16);
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}
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_DivFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(A*0x10000)/B' with maximum accuracy. Most of the time, this is */
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/* used to divide a given value by a 16.16 fixed float factor. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. Use a 16.16 factor here whenever */
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/* possible (see note below). */
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/* */
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/* <Return> */
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/* The result of `(a*0x10000)/b'. */
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/* */
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/* <Note> */
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/* The optimisation for FT_DivFix() is simple : if (a << 16) fits */
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/* in 32 bits, then the division is computed directly. Otherwise, */
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/* we use a specialised version of the old FT_MulDiv64 */
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/* */
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EXPORT_FUNC
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FT_Int32 FT_DivFix( FT_Long a,
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FT_Long b )
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{
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FT_Int32 s;
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FT_Word32 q;
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s = a; a = ABS(a);
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s ^= b; b = ABS(b);
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if ( b == 0 )
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/* check for divide by 0 */
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q = 0x7FFFFFFF;
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else
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/* compute result directly */
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q = ((FT_Int64)a << 16) / b;
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return (FT_Int32)( s < 0 ? -q : q );
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}
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#else /* LONG64 */
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_MulDiv */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation `(A*B)/C' */
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/* with maximum accuracy (it uses a 64-bit intermediate integer */
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/* whenever necessary). */
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/* */
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/* This function isn't necessarily as fast as some processor specific */
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/* operations, but is at least completely portable. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. */
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/* c :: The divisor. */
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/* */
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/* <Return> */
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/* The result of `(a*b)/c'. This function never traps when trying to */
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/* divide by zero, it simply returns `MaxInt' or `MinInt' depending */
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/* on the signs of `a' and `b'. */
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/* */
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/* <Note> */
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/* The FT_MulDiv() function has been optimized thanks to ideas from */
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/* Graham Asher. The trick is to optimize computation if everything */
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/* fits within 32 bits (a rather common case). */
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/* */
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/* We compute `a*b+c/2', then divide it by `c'. (positive values) */
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/* */
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/* 46340 is FLOOR(SQRT(2^31-1)). */
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/* */
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/* if ( a <= 46340 && b <= 46340 ) then ( a*b <= 0x7FFEA810 ) */
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/* */
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/* 0x7FFFFFFF - 0x7FFEA810 = 0x157F0 */
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/* */
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/* if ( c < 0x157F0*2 ) then ( a*b+c/2 <= 0x7FFFFFFF ) */
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/* */
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/* and 2*0x157F0 = 176096 */
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/* */
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EXPORT_FUNC
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FT_Long FT_MulDiv( FT_Long a,
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FT_Long b,
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FT_Long c )
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{
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long s;
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if ( a == 0 || b == c )
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return a;
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s = a; a = ABS( a );
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s ^= b; b = ABS( b );
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s ^= c; c = ABS( c );
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if ( a <= 46340 && b <= 46340 && c <= 176095L )
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{
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a = ( a*b + (c >> 1) ) / c;
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}
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else
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{
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FT_Int64 temp, temp2;
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FT_MulTo64( a, b, &temp );
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temp2.hi = (FT_Int32)(c >> 31);
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temp2.lo = (FT_Word32)(c / 2);
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FT_Add64( &temp, &temp2, &temp );
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a = FT_Div64by32( &temp, c );
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}
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return ( s < 0 ) ? -a : a;
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}
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_MulFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(A*B)/0x10000' with maximum accuracy. Most of the time, this is */
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/* used to multiply a given value by a 16.16 fixed float factor. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. Use a 16.16 factor here whenever */
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/* possible (see note below). */
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/* */
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/* <Return> */
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/* The result of `(a*b)/0x10000'. */
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/* */
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/* <Note> */
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/* The optimisation for FT_MulFix() is different. We could simply be */
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/* happy by applying the same principles as with FT_MulDiv(), because */
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/* */
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/* c = 0x10000 < 176096 */
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/* */
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/* However, in most cases, we have a `b' with a value around 0x10000 */
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/* which is greater than 46340. */
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/* */
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/* According to some testing, most cases have `a' < 2048, so a good */
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/* idea is to use bounds like 2048 and 1048576 (=floor((2^31-1)/2048) */
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/* for `a' and `b' respectively. */
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/* */
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EXPORT_FUNC
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FT_Long FT_MulFix( FT_Long a,
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FT_Long b )
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{
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FT_Long s;
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if ( a == 0 || b == 0x10000L )
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return a;
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s = a; a = ABS(a);
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s ^= b; b = ABS(b);
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if ( a <= 2048 && b <= 1048576L )
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{
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a = ( a*b + 0x8000 ) >> 16;
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}
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else
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{
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FT_Long al = a & 0xFFFF;
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a = (a >> 16)*b + al*(b >> 16) + ( al*(b & 0xFFFF) >> 16 );
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}
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return ( s < 0 ? -a : a );
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}
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/*************************************************************************/
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/* */
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/* <Function> */
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/* FT_DivFix */
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/* */
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/* <Description> */
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/* A very simple function used to perform the computation */
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/* `(A*0x10000)/B' with maximum accuracy. Most of the time, this is */
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/* used to divide a given value by a 16.16 fixed float factor. */
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/* */
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/* <Input> */
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/* a :: The first multiplier. */
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/* b :: The second multiplier. Use a 16.16 factor here whenever */
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/* possible (see note below). */
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/* */
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/* <Return> */
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/* The result of `(a*0x10000)/b'. */
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/* */
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/* <Note> */
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/* The optimisation for FT_DivFix() is simple : if (a << 16) fits */
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/* in 32 bits, then the division is computed directly. Otherwise, */
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/* we use a specialised version of the old FT_MulDiv64 */
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/* */
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EXPORT_FUNC
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FT_Long FT_DivFix( FT_Long a,
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FT_Long b )
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{
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FT_Int32 s;
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FT_Word32 q;
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s = a; a = ABS(a);
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s ^= b; b = ABS(b);
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if ( b == 0 )
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/* check for divide by 0 */
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q = 0x7FFFFFFF;
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else if ( (a >> 16) == 0 )
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{
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/* compute result directly */
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q = (FT_Word32)(a << 16) / (FT_Word32)b;
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}
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else
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{
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/* we need more bits, we'll have to do it by hand */
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FT_Word32 c;
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q = (a/b) << 16;
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c = a%b;
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/* we must compute C*0x10000/B, we simply shift C and B so */
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/* C becomes smaller than 16 bits */
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while (c >> 16)
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{
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c >>= 1;
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b <<= 1;
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}
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q += (c << 16)/b;
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}
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return ( s < 0 ? -(FT_Int32)q : (FT_Int32)q );
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}
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BASE_FUNC
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void FT_Add64( FT_Int64* x,
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FT_Int64* y,
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FT_Int64* z )
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{
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register FT_Word32 lo, hi;
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lo = x->lo + y->lo;
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hi = x->hi + y->hi + ( lo < x->lo );
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z->lo = lo;
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z->hi = hi;
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}
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BASE_FUNC
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void FT_MulTo64( FT_Int32 x,
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FT_Int32 y,
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FT_Int64* z )
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{
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FT_Int32 s;
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s = x; x = ABS( x );
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s ^= y; y = ABS( y );
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{
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FT_Word32 lo1, hi1, lo2, hi2, lo, hi, i1, i2;
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lo1 = x & 0x0000FFFF; hi1 = x >> 16;
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lo2 = y & 0x0000FFFF; hi2 = y >> 16;
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lo = lo1 * lo2;
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i1 = lo1 * hi2;
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i2 = lo2 * hi1;
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hi = hi1 * hi2;
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/* Check carry overflow of i1 + i2 */
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i1 += i2;
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if ( i1 < i2 )
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hi += 1L << 16;
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hi += (i1 >> 16);
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i1 = i1 << 16;
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/* Check carry overflow of i1 + lo */
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lo += i1;
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hi += (lo < i1);
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z->lo = lo;
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z->hi = hi;
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}
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if ( s < 0 )
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{
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z->lo = (FT_Word32)-(FT_Int32)z->lo;
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z->hi = ~z->hi + !(z->lo);
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}
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}
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BASE_FUNC
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FT_Int32 FT_Div64by32( FT_Int64* x,
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FT_Int32 y )
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{
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FT_Int32 s;
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FT_Word32 q, r, i, lo;
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s = x->hi;
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if ( s < 0 )
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{
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x->lo = (FT_Word32)-(FT_Int32)x->lo;
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x->hi = ~x->hi + !(x->lo);
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}
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s ^= y; y = ABS( y );
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/* Shortcut */
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if ( x->hi == 0 )
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{
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q = x->lo / y;
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return ( s < 0 ) ? -(FT_Int32)q : (FT_Int32)q;
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}
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r = x->hi;
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lo = x->lo;
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if ( r >= (FT_Word32)y ) /* we know y is to be treated as unsigned here */
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return ( s < 0 ) ? 0x80000001L : 0x7FFFFFFFL;
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/* Return Max/Min Int32 if divide overflow. */
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/* This includes division by zero! */
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q = 0;
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for ( i = 0; i < 32; i++ )
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{
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r <<= 1;
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q <<= 1;
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r |= lo >> 31;
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if ( r >= (FT_Word32)y )
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{
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r -= y;
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q |= 1;
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}
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lo <<= 1;
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}
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return ( s < 0 ) ? -(FT_Int32)q : (FT_Int32)q;
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}
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#endif /* LONG64 */
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/* END */
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