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54876
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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 (C) 1996-2019 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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49234
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54876
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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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49234
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54876
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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(), FT_MulFix(), FT_DivFix(), FT_RoundFix(), FT_CeilFix(),
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* and FT_FloorFix() are declared in freetype.h.
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*
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*/
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#include <ft2build.h>
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#include FT_GLYPH_H
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#include FT_TRIGONOMETRY_H
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#include FT_INTERNAL_CALC_H
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#include FT_INTERNAL_DEBUG_H
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#include FT_INTERNAL_OBJECTS_H
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#ifdef FT_MULFIX_ASSEMBLER
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#undef FT_MulFix
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#endif
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/* we need to emulate a 64-bit data type if a real one isn't available */
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#ifndef FT_LONG64
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typedef struct FT_Int64_
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{
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FT_UInt32 lo;
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FT_UInt32 hi;
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} FT_Int64;
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#endif /* !FT_LONG64 */
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54876
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/**************************************************************************
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*
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* The macro FT_COMPONENT is used in trace mode. It is an implicit
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* parameter of the FT_TRACE() and FT_ERROR() macros, used to print/log
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* messages during execution.
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*/
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#undef FT_COMPONENT
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54876
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#define FT_COMPONENT calc
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49234
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/* transfer sign, leaving a positive number; */
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/* we need an unsigned value to safely negate INT_MIN (or LONG_MIN) */
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#define FT_MOVE_SIGN( x, x_unsigned, s ) \
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FT_BEGIN_STMNT \
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if ( x < 0 ) \
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{ \
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x_unsigned = 0U - (x_unsigned); \
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s = -s; \
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} \
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FT_END_STMNT
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/* The following three functions are available regardless of whether */
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/* FT_LONG64 is defined. */
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/* documentation is in freetype.h */
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FT_EXPORT_DEF( FT_Fixed )
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FT_RoundFix( FT_Fixed a )
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{
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return ( ADD_LONG( a, 0x8000L - ( a < 0 ) ) ) & ~0xFFFFL;
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}
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/* documentation is in freetype.h */
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FT_EXPORT_DEF( FT_Fixed )
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FT_CeilFix( FT_Fixed a )
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{
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return ( ADD_LONG( a, 0xFFFFL ) ) & ~0xFFFFL;
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}
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/* documentation is in freetype.h */
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FT_EXPORT_DEF( FT_Fixed )
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FT_FloorFix( FT_Fixed a )
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{
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return a & ~0xFFFFL;
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}
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#ifndef FT_MSB
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FT_BASE_DEF ( FT_Int )
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FT_MSB( FT_UInt32 z )
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{
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FT_Int shift = 0;
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/* determine msb bit index in `shift' */
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if ( z & 0xFFFF0000UL )
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{
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z >>= 16;
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shift += 16;
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}
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if ( z & 0x0000FF00UL )
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{
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z >>= 8;
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shift += 8;
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}
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if ( z & 0x000000F0UL )
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{
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z >>= 4;
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shift += 4;
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}
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if ( z & 0x0000000CUL )
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{
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z >>= 2;
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shift += 2;
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}
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if ( z & 0x00000002UL )
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{
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/* z >>= 1; */
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shift += 1;
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}
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return shift;
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}
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#endif /* !FT_MSB */
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/* documentation is in ftcalc.h */
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FT_BASE_DEF( FT_Fixed )
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FT_Hypot( FT_Fixed x,
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FT_Fixed y )
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{
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FT_Vector v;
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v.x = x;
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v.y = y;
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return FT_Vector_Length( &v );
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}
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#ifdef FT_LONG64
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/* documentation is in freetype.h */
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FT_EXPORT_DEF( FT_Long )
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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 = 1;
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FT_UInt64 a, b, c, d;
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FT_Long d_;
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a = (FT_UInt64)a_;
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b = (FT_UInt64)b_;
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c = (FT_UInt64)c_;
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186 |
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FT_MOVE_SIGN( a_, a, s );
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FT_MOVE_SIGN( b_, b, s );
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FT_MOVE_SIGN( c_, c, s );
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d = c > 0 ? ( a * b + ( c >> 1 ) ) / c
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: 0x7FFFFFFFUL;
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d_ = (FT_Long)d;
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return s < 0 ? NEG_LONG( d_ ) : d_;
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}
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198 |
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199 |
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/* documentation is in ftcalc.h */
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201 |
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FT_BASE_DEF( FT_Long )
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FT_MulDiv_No_Round( 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 = 1;
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FT_UInt64 a, b, c, d;
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FT_Long d_;
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210 |
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211 |
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a = (FT_UInt64)a_;
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b = (FT_UInt64)b_;
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c = (FT_UInt64)c_;
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215 |
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FT_MOVE_SIGN( a_, a, s );
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FT_MOVE_SIGN( b_, b, s );
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FT_MOVE_SIGN( c_, c, s );
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219 |
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d = c > 0 ? a * b / c
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: 0x7FFFFFFFUL;
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d_ = (FT_Long)d;
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224 |
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return s < 0 ? NEG_LONG( d_ ) : d_;
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}
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227 |
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228 |
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/* documentation is in freetype.h */
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230 |
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FT_EXPORT_DEF( FT_Long )
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FT_MulFix( FT_Long a_,
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FT_Long b_ )
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{
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#ifdef FT_MULFIX_ASSEMBLER
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236 |
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return FT_MULFIX_ASSEMBLER( (FT_Int32)a_, (FT_Int32)b_ );
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238 |
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#else
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240 |
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FT_Int64 ab = (FT_Int64)a_ * (FT_Int64)b_;
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/* this requires arithmetic right shift of signed numbers */
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return (FT_Long)( ( ab + 0x8000L - ( ab < 0 ) ) >> 16 );
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#endif /* FT_MULFIX_ASSEMBLER */
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}
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248 |
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249 |
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250 |
/* documentation is in freetype.h */
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251 |
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FT_EXPORT_DEF( FT_Long )
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FT_DivFix( FT_Long a_,
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FT_Long b_ )
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{
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FT_Int s = 1;
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257 |
FT_UInt64 a, b, q;
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FT_Long q_;
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259 |
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260 |
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a = (FT_UInt64)a_;
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262 |
b = (FT_UInt64)b_;
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263 |
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FT_MOVE_SIGN( a_, a, s );
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265 |
FT_MOVE_SIGN( b_, b, s );
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266 |
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267 |
q = b > 0 ? ( ( a << 16 ) + ( b >> 1 ) ) / b
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: 0x7FFFFFFFUL;
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269 |
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270 |
q_ = (FT_Long)q;
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271 |
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272 |
return s < 0 ? NEG_LONG( q_ ) : q_;
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273 |
}
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274 |
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275 |
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276 |
#else /* !FT_LONG64 */
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277 |
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278 |
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279 |
static void
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280 |
ft_multo64( FT_UInt32 x,
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281 |
FT_UInt32 y,
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282 |
FT_Int64 *z )
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283 |
{
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284 |
FT_UInt32 lo1, hi1, lo2, hi2, lo, hi, i1, i2;
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285 |
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286 |
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287 |
lo1 = x & 0x0000FFFFU; hi1 = x >> 16;
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288 |
lo2 = y & 0x0000FFFFU; hi2 = y >> 16;
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289 |
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290 |
lo = lo1 * lo2;
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291 |
i1 = lo1 * hi2;
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292 |
i2 = lo2 * hi1;
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293 |
hi = hi1 * hi2;
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294 |
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295 |
/* Check carry overflow of i1 + i2 */
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296 |
i1 += i2;
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297 |
hi += (FT_UInt32)( i1 < i2 ) << 16;
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298 |
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299 |
hi += i1 >> 16;
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300 |
i1 = i1 << 16;
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301 |
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302 |
/* Check carry overflow of i1 + lo */
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303 |
lo += i1;
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304 |
hi += ( lo < i1 );
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305 |
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306 |
z->lo = lo;
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307 |
z->hi = hi;
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308 |
}
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309 |
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310 |
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311 |
static FT_UInt32
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312 |
ft_div64by32( FT_UInt32 hi,
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313 |
FT_UInt32 lo,
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314 |
FT_UInt32 y )
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315 |
{
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316 |
FT_UInt32 r, q;
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317 |
FT_Int i;
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318 |
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319 |
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320 |
if ( hi >= y )
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321 |
return (FT_UInt32)0x7FFFFFFFL;
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322 |
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323 |
/* We shift as many bits as we can into the high register, perform */
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324 |
/* 32-bit division with modulo there, then work through the remaining */
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325 |
/* bits with long division. This optimization is especially noticeable */
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326 |
/* for smaller dividends that barely use the high register. */
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327 |
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328 |
i = 31 - FT_MSB( hi );
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329 |
r = ( hi << i ) | ( lo >> ( 32 - i ) ); lo <<= i; /* left 64-bit shift */
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330 |
q = r / y;
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331 |
r -= q * y; /* remainder */
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332 |
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333 |
i = 32 - i; /* bits remaining in low register */
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334 |
do
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335 |
{
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336 |
q <<= 1;
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337 |
r = ( r << 1 ) | ( lo >> 31 ); lo <<= 1;
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338 |
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339 |
if ( r >= y )
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340 |
{
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341 |
r -= y;
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342 |
q |= 1;
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343 |
}
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344 |
} while ( --i );
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345 |
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346 |
return q;
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347 |
}
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348 |
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349 |
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350 |
static void
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351 |
FT_Add64( FT_Int64* x,
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352 |
FT_Int64* y,
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353 |
FT_Int64 *z )
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354 |
{
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355 |
FT_UInt32 lo, hi;
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356 |
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357 |
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358 |
lo = x->lo + y->lo;
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359 |
hi = x->hi + y->hi + ( lo < x->lo );
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360 |
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361 |
z->lo = lo;
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|
362 |
z->hi = hi;
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363 |
}
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364 |
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365 |
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|
366 |
/* The FT_MulDiv function has been optimized thanks to ideas from */
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|
367 |
/* Graham Asher and Alexei Podtelezhnikov. The trick is to optimize */
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|
368 |
/* a rather common case when everything fits within 32-bits. */
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369 |
/* */
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370 |
/* We compute 'a*b+c/2', then divide it by 'c' (all positive values). */
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371 |
/* */
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372 |
/* The product of two positive numbers never exceeds the square of */
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373 |
/* its mean values. Therefore, we always avoid the overflow by */
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374 |
/* imposing */
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375 |
/* */
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|
376 |
/* (a + b) / 2 <= sqrt(X - c/2) , */
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|
377 |
/* */
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|
378 |
/* where X = 2^32 - 1, the maximum unsigned 32-bit value, and using */
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|
379 |
/* unsigned arithmetic. Now we replace `sqrt' with a linear function */
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|
380 |
/* that is smaller or equal for all values of c in the interval */
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|
381 |
/* [0;X/2]; it should be equal to sqrt(X) and sqrt(3X/4) at the */
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|
382 |
/* endpoints. Substituting the linear solution and explicit numbers */
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|
383 |
/* we get */
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|
384 |
/* */
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|
385 |
/* a + b <= 131071.99 - c / 122291.84 . */
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|
386 |
/* */
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|
387 |
/* In practice, we should use a faster and even stronger inequality */
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|
388 |
/* */
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|
389 |
/* a + b <= 131071 - (c >> 16) */
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|
390 |
/* */
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391 |
/* or, alternatively, */
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|
392 |
/* */
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393 |
/* a + b <= 129894 - (c >> 17) . */
|
|
|
394 |
/* */
|
|
|
395 |
/* FT_MulFix, on the other hand, is optimized for a small value of */
|
|
|
396 |
/* the first argument, when the second argument can be much larger. */
|
|
|
397 |
/* This can be achieved by scaling the second argument and the limit */
|
|
|
398 |
/* in the above inequalities. For example, */
|
|
|
399 |
/* */
|
|
|
400 |
/* a + (b >> 8) <= (131071 >> 4) */
|
|
|
401 |
/* */
|
|
|
402 |
/* covers the practical range of use. The actual test below is a bit */
|
|
|
403 |
/* tighter to avoid the border case overflows. */
|
|
|
404 |
/* */
|
|
|
405 |
/* In the case of FT_DivFix, the exact overflow check */
|
|
|
406 |
/* */
|
|
|
407 |
/* a << 16 <= X - c/2 */
|
|
|
408 |
/* */
|
|
|
409 |
/* is scaled down by 2^16 and we use */
|
|
|
410 |
/* */
|
|
|
411 |
/* a <= 65535 - (c >> 17) . */
|
|
|
412 |
|
|
|
413 |
/* documentation is in freetype.h */
|
|
|
414 |
|
|
|
415 |
FT_EXPORT_DEF( FT_Long )
|
|
|
416 |
FT_MulDiv( FT_Long a_,
|
|
|
417 |
FT_Long b_,
|
|
|
418 |
FT_Long c_ )
|
|
|
419 |
{
|
|
|
420 |
FT_Int s = 1;
|
|
|
421 |
FT_UInt32 a, b, c;
|
|
|
422 |
|
|
|
423 |
|
|
|
424 |
/* XXX: this function does not allow 64-bit arguments */
|
|
|
425 |
|
|
|
426 |
a = (FT_UInt32)a_;
|
|
|
427 |
b = (FT_UInt32)b_;
|
|
|
428 |
c = (FT_UInt32)c_;
|
|
|
429 |
|
|
|
430 |
FT_MOVE_SIGN( a_, a, s );
|
|
|
431 |
FT_MOVE_SIGN( b_, b, s );
|
|
|
432 |
FT_MOVE_SIGN( c_, c, s );
|
|
|
433 |
|
|
|
434 |
if ( c == 0 )
|
|
|
435 |
a = 0x7FFFFFFFUL;
|
|
|
436 |
|
|
|
437 |
else if ( a + b <= 129894UL - ( c >> 17 ) )
|
|
|
438 |
a = ( a * b + ( c >> 1 ) ) / c;
|
|
|
439 |
|
|
|
440 |
else
|
|
|
441 |
{
|
|
|
442 |
FT_Int64 temp, temp2;
|
|
|
443 |
|
|
|
444 |
|
|
|
445 |
ft_multo64( a, b, &temp );
|
|
|
446 |
|
|
|
447 |
temp2.hi = 0;
|
|
|
448 |
temp2.lo = c >> 1;
|
|
|
449 |
|
|
|
450 |
FT_Add64( &temp, &temp2, &temp );
|
|
|
451 |
|
|
|
452 |
/* last attempt to ditch long division */
|
|
|
453 |
a = ( temp.hi == 0 ) ? temp.lo / c
|
|
|
454 |
: ft_div64by32( temp.hi, temp.lo, c );
|
|
|
455 |
}
|
|
|
456 |
|
|
|
457 |
a_ = (FT_Long)a;
|
|
|
458 |
|
|
|
459 |
return s < 0 ? NEG_LONG( a_ ) : a_;
|
|
|
460 |
}
|
|
|
461 |
|
|
|
462 |
|
|
|
463 |
FT_BASE_DEF( FT_Long )
|
|
|
464 |
FT_MulDiv_No_Round( FT_Long a_,
|
|
|
465 |
FT_Long b_,
|
|
|
466 |
FT_Long c_ )
|
|
|
467 |
{
|
|
|
468 |
FT_Int s = 1;
|
|
|
469 |
FT_UInt32 a, b, c;
|
|
|
470 |
|
|
|
471 |
|
|
|
472 |
/* XXX: this function does not allow 64-bit arguments */
|
|
|
473 |
|
|
|
474 |
a = (FT_UInt32)a_;
|
|
|
475 |
b = (FT_UInt32)b_;
|
|
|
476 |
c = (FT_UInt32)c_;
|
|
|
477 |
|
|
|
478 |
FT_MOVE_SIGN( a_, a, s );
|
|
|
479 |
FT_MOVE_SIGN( b_, b, s );
|
|
|
480 |
FT_MOVE_SIGN( c_, c, s );
|
|
|
481 |
|
|
|
482 |
if ( c == 0 )
|
|
|
483 |
a = 0x7FFFFFFFUL;
|
|
|
484 |
|
|
|
485 |
else if ( a + b <= 131071UL )
|
|
|
486 |
a = a * b / c;
|
|
|
487 |
|
|
|
488 |
else
|
|
|
489 |
{
|
|
|
490 |
FT_Int64 temp;
|
|
|
491 |
|
|
|
492 |
|
|
|
493 |
ft_multo64( a, b, &temp );
|
|
|
494 |
|
|
|
495 |
/* last attempt to ditch long division */
|
|
|
496 |
a = ( temp.hi == 0 ) ? temp.lo / c
|
|
|
497 |
: ft_div64by32( temp.hi, temp.lo, c );
|
|
|
498 |
}
|
|
|
499 |
|
|
|
500 |
a_ = (FT_Long)a;
|
|
|
501 |
|
|
|
502 |
return s < 0 ? NEG_LONG( a_ ) : a_;
|
|
|
503 |
}
|
|
|
504 |
|
|
|
505 |
|
|
|
506 |
/* documentation is in freetype.h */
|
|
|
507 |
|
|
|
508 |
FT_EXPORT_DEF( FT_Long )
|
|
|
509 |
FT_MulFix( FT_Long a_,
|
|
|
510 |
FT_Long b_ )
|
|
|
511 |
{
|
|
|
512 |
#ifdef FT_MULFIX_ASSEMBLER
|
|
|
513 |
|
|
|
514 |
return FT_MULFIX_ASSEMBLER( a_, b_ );
|
|
|
515 |
|
|
|
516 |
#elif 0
|
|
|
517 |
|
|
|
518 |
/*
|
|
54876
|
519 |
* This code is nonportable. See comment below.
|
|
49234
|
520 |
*
|
|
54876
|
521 |
* However, on a platform where right-shift of a signed quantity fills
|
|
|
522 |
* the leftmost bits by copying the sign bit, it might be faster.
|
|
49234
|
523 |
*/
|
|
|
524 |
|
|
|
525 |
FT_Long sa, sb;
|
|
|
526 |
FT_UInt32 a, b;
|
|
|
527 |
|
|
|
528 |
|
|
|
529 |
/*
|
|
54876
|
530 |
* This is a clever way of converting a signed number `a' into its
|
|
|
531 |
* absolute value (stored back into `a') and its sign. The sign is
|
|
|
532 |
* stored in `sa'; 0 means `a' was positive or zero, and -1 means `a'
|
|
|
533 |
* was negative. (Similarly for `b' and `sb').
|
|
49234
|
534 |
*
|
|
54876
|
535 |
* Unfortunately, it doesn't work (at least not portably).
|
|
49234
|
536 |
*
|
|
54876
|
537 |
* It makes the assumption that right-shift on a negative signed value
|
|
|
538 |
* fills the leftmost bits by copying the sign bit. This is wrong.
|
|
|
539 |
* According to K&R 2nd ed, section `A7.8 Shift Operators' on page 206,
|
|
|
540 |
* the result of right-shift of a negative signed value is
|
|
|
541 |
* implementation-defined. At least one implementation fills the
|
|
|
542 |
* leftmost bits with 0s (i.e., it is exactly the same as an unsigned
|
|
|
543 |
* right shift). This means that when `a' is negative, `sa' ends up
|
|
|
544 |
* with the value 1 rather than -1. After that, everything else goes
|
|
|
545 |
* wrong.
|
|
49234
|
546 |
*/
|
|
|
547 |
sa = ( a_ >> ( sizeof ( a_ ) * 8 - 1 ) );
|
|
|
548 |
a = ( a_ ^ sa ) - sa;
|
|
|
549 |
sb = ( b_ >> ( sizeof ( b_ ) * 8 - 1 ) );
|
|
|
550 |
b = ( b_ ^ sb ) - sb;
|
|
|
551 |
|
|
|
552 |
a = (FT_UInt32)a_;
|
|
|
553 |
b = (FT_UInt32)b_;
|
|
|
554 |
|
|
|
555 |
if ( a + ( b >> 8 ) <= 8190UL )
|
|
|
556 |
a = ( a * b + 0x8000U ) >> 16;
|
|
|
557 |
else
|
|
|
558 |
{
|
|
|
559 |
FT_UInt32 al = a & 0xFFFFUL;
|
|
|
560 |
|
|
|
561 |
|
|
|
562 |
a = ( a >> 16 ) * b + al * ( b >> 16 ) +
|
|
|
563 |
( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 );
|
|
|
564 |
}
|
|
|
565 |
|
|
|
566 |
sa ^= sb;
|
|
|
567 |
a = ( a ^ sa ) - sa;
|
|
|
568 |
|
|
|
569 |
return (FT_Long)a;
|
|
|
570 |
|
|
|
571 |
#else /* 0 */
|
|
|
572 |
|
|
|
573 |
FT_Int s = 1;
|
|
|
574 |
FT_UInt32 a, b;
|
|
|
575 |
|
|
|
576 |
|
|
|
577 |
/* XXX: this function does not allow 64-bit arguments */
|
|
|
578 |
|
|
|
579 |
a = (FT_UInt32)a_;
|
|
|
580 |
b = (FT_UInt32)b_;
|
|
|
581 |
|
|
|
582 |
FT_MOVE_SIGN( a_, a, s );
|
|
|
583 |
FT_MOVE_SIGN( b_, b, s );
|
|
|
584 |
|
|
|
585 |
if ( a + ( b >> 8 ) <= 8190UL )
|
|
|
586 |
a = ( a * b + 0x8000UL ) >> 16;
|
|
|
587 |
else
|
|
|
588 |
{
|
|
|
589 |
FT_UInt32 al = a & 0xFFFFUL;
|
|
|
590 |
|
|
|
591 |
|
|
|
592 |
a = ( a >> 16 ) * b + al * ( b >> 16 ) +
|
|
|
593 |
( ( al * ( b & 0xFFFFUL ) + 0x8000UL ) >> 16 );
|
|
|
594 |
}
|
|
|
595 |
|
|
|
596 |
a_ = (FT_Long)a;
|
|
|
597 |
|
|
|
598 |
return s < 0 ? NEG_LONG( a_ ) : a_;
|
|
|
599 |
|
|
|
600 |
#endif /* 0 */
|
|
|
601 |
|
|
|
602 |
}
|
|
|
603 |
|
|
|
604 |
|
|
|
605 |
/* documentation is in freetype.h */
|
|
|
606 |
|
|
|
607 |
FT_EXPORT_DEF( FT_Long )
|
|
|
608 |
FT_DivFix( FT_Long a_,
|
|
|
609 |
FT_Long b_ )
|
|
|
610 |
{
|
|
|
611 |
FT_Int s = 1;
|
|
|
612 |
FT_UInt32 a, b, q;
|
|
|
613 |
FT_Long q_;
|
|
|
614 |
|
|
|
615 |
|
|
|
616 |
/* XXX: this function does not allow 64-bit arguments */
|
|
|
617 |
|
|
|
618 |
a = (FT_UInt32)a_;
|
|
|
619 |
b = (FT_UInt32)b_;
|
|
|
620 |
|
|
|
621 |
FT_MOVE_SIGN( a_, a, s );
|
|
|
622 |
FT_MOVE_SIGN( b_, b, s );
|
|
|
623 |
|
|
|
624 |
if ( b == 0 )
|
|
|
625 |
{
|
|
|
626 |
/* check for division by 0 */
|
|
|
627 |
q = 0x7FFFFFFFUL;
|
|
|
628 |
}
|
|
|
629 |
else if ( a <= 65535UL - ( b >> 17 ) )
|
|
|
630 |
{
|
|
|
631 |
/* compute result directly */
|
|
|
632 |
q = ( ( a << 16 ) + ( b >> 1 ) ) / b;
|
|
|
633 |
}
|
|
|
634 |
else
|
|
|
635 |
{
|
|
|
636 |
/* we need more bits; we have to do it by hand */
|
|
|
637 |
FT_Int64 temp, temp2;
|
|
|
638 |
|
|
|
639 |
|
|
|
640 |
temp.hi = a >> 16;
|
|
|
641 |
temp.lo = a << 16;
|
|
|
642 |
temp2.hi = 0;
|
|
|
643 |
temp2.lo = b >> 1;
|
|
|
644 |
|
|
|
645 |
FT_Add64( &temp, &temp2, &temp );
|
|
|
646 |
q = ft_div64by32( temp.hi, temp.lo, b );
|
|
|
647 |
}
|
|
|
648 |
|
|
|
649 |
q_ = (FT_Long)q;
|
|
|
650 |
|
|
|
651 |
return s < 0 ? NEG_LONG( q_ ) : q_;
|
|
|
652 |
}
|
|
|
653 |
|
|
|
654 |
|
|
|
655 |
#endif /* !FT_LONG64 */
|
|
|
656 |
|
|
|
657 |
|
|
|
658 |
/* documentation is in ftglyph.h */
|
|
|
659 |
|
|
|
660 |
FT_EXPORT_DEF( void )
|
|
|
661 |
FT_Matrix_Multiply( const FT_Matrix* a,
|
|
|
662 |
FT_Matrix *b )
|
|
|
663 |
{
|
|
|
664 |
FT_Fixed xx, xy, yx, yy;
|
|
|
665 |
|
|
|
666 |
|
|
|
667 |
if ( !a || !b )
|
|
|
668 |
return;
|
|
|
669 |
|
|
|
670 |
xx = ADD_LONG( FT_MulFix( a->xx, b->xx ),
|
|
|
671 |
FT_MulFix( a->xy, b->yx ) );
|
|
|
672 |
xy = ADD_LONG( FT_MulFix( a->xx, b->xy ),
|
|
|
673 |
FT_MulFix( a->xy, b->yy ) );
|
|
|
674 |
yx = ADD_LONG( FT_MulFix( a->yx, b->xx ),
|
|
|
675 |
FT_MulFix( a->yy, b->yx ) );
|
|
|
676 |
yy = ADD_LONG( FT_MulFix( a->yx, b->xy ),
|
|
|
677 |
FT_MulFix( a->yy, b->yy ) );
|
|
|
678 |
|
|
|
679 |
b->xx = xx;
|
|
|
680 |
b->xy = xy;
|
|
|
681 |
b->yx = yx;
|
|
|
682 |
b->yy = yy;
|
|
|
683 |
}
|
|
|
684 |
|
|
|
685 |
|
|
|
686 |
/* documentation is in ftglyph.h */
|
|
|
687 |
|
|
|
688 |
FT_EXPORT_DEF( FT_Error )
|
|
|
689 |
FT_Matrix_Invert( FT_Matrix* matrix )
|
|
|
690 |
{
|
|
|
691 |
FT_Pos delta, xx, yy;
|
|
|
692 |
|
|
|
693 |
|
|
|
694 |
if ( !matrix )
|
|
|
695 |
return FT_THROW( Invalid_Argument );
|
|
|
696 |
|
|
|
697 |
/* compute discriminant */
|
|
|
698 |
delta = FT_MulFix( matrix->xx, matrix->yy ) -
|
|
|
699 |
FT_MulFix( matrix->xy, matrix->yx );
|
|
|
700 |
|
|
|
701 |
if ( !delta )
|
|
|
702 |
return FT_THROW( Invalid_Argument ); /* matrix can't be inverted */
|
|
|
703 |
|
|
54876
|
704 |
matrix->xy = -FT_DivFix( matrix->xy, delta );
|
|
|
705 |
matrix->yx = -FT_DivFix( matrix->yx, delta );
|
|
49234
|
706 |
|
|
|
707 |
xx = matrix->xx;
|
|
|
708 |
yy = matrix->yy;
|
|
|
709 |
|
|
|
710 |
matrix->xx = FT_DivFix( yy, delta );
|
|
|
711 |
matrix->yy = FT_DivFix( xx, delta );
|
|
|
712 |
|
|
|
713 |
return FT_Err_Ok;
|
|
|
714 |
}
|
|
|
715 |
|
|
|
716 |
|
|
|
717 |
/* documentation is in ftcalc.h */
|
|
|
718 |
|
|
|
719 |
FT_BASE_DEF( void )
|
|
|
720 |
FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
|
|
|
721 |
FT_Matrix *b,
|
|
|
722 |
FT_Long scaling )
|
|
|
723 |
{
|
|
|
724 |
FT_Fixed xx, xy, yx, yy;
|
|
|
725 |
|
|
|
726 |
FT_Long val = 0x10000L * scaling;
|
|
|
727 |
|
|
|
728 |
|
|
|
729 |
if ( !a || !b )
|
|
|
730 |
return;
|
|
|
731 |
|
|
|
732 |
xx = ADD_LONG( FT_MulDiv( a->xx, b->xx, val ),
|
|
|
733 |
FT_MulDiv( a->xy, b->yx, val ) );
|
|
|
734 |
xy = ADD_LONG( FT_MulDiv( a->xx, b->xy, val ),
|
|
|
735 |
FT_MulDiv( a->xy, b->yy, val ) );
|
|
|
736 |
yx = ADD_LONG( FT_MulDiv( a->yx, b->xx, val ),
|
|
|
737 |
FT_MulDiv( a->yy, b->yx, val ) );
|
|
|
738 |
yy = ADD_LONG( FT_MulDiv( a->yx, b->xy, val ),
|
|
|
739 |
FT_MulDiv( a->yy, b->yy, val ) );
|
|
|
740 |
|
|
|
741 |
b->xx = xx;
|
|
|
742 |
b->xy = xy;
|
|
|
743 |
b->yx = yx;
|
|
|
744 |
b->yy = yy;
|
|
|
745 |
}
|
|
|
746 |
|
|
|
747 |
|
|
|
748 |
/* documentation is in ftcalc.h */
|
|
|
749 |
|
|
54876
|
750 |
FT_BASE_DEF( FT_Bool )
|
|
|
751 |
FT_Matrix_Check( const FT_Matrix* matrix )
|
|
|
752 |
{
|
|
|
753 |
FT_Matrix m;
|
|
|
754 |
FT_Fixed val[4];
|
|
|
755 |
FT_Fixed nonzero_minval, maxval;
|
|
|
756 |
FT_Fixed temp1, temp2;
|
|
|
757 |
FT_UInt i;
|
|
|
758 |
|
|
|
759 |
|
|
|
760 |
if ( !matrix )
|
|
|
761 |
return 0;
|
|
|
762 |
|
|
|
763 |
val[0] = FT_ABS( matrix->xx );
|
|
|
764 |
val[1] = FT_ABS( matrix->xy );
|
|
|
765 |
val[2] = FT_ABS( matrix->yx );
|
|
|
766 |
val[3] = FT_ABS( matrix->yy );
|
|
|
767 |
|
|
|
768 |
/*
|
|
|
769 |
* To avoid overflow, we ensure that each value is not larger than
|
|
|
770 |
*
|
|
|
771 |
* int(sqrt(2^31 / 4)) = 23170 ;
|
|
|
772 |
*
|
|
|
773 |
* we also check that no value becomes zero if we have to scale.
|
|
|
774 |
*/
|
|
|
775 |
|
|
|
776 |
maxval = 0;
|
|
|
777 |
nonzero_minval = FT_LONG_MAX;
|
|
|
778 |
|
|
|
779 |
for ( i = 0; i < 4; i++ )
|
|
|
780 |
{
|
|
|
781 |
if ( val[i] > maxval )
|
|
|
782 |
maxval = val[i];
|
|
|
783 |
if ( val[i] && val[i] < nonzero_minval )
|
|
|
784 |
nonzero_minval = val[i];
|
|
|
785 |
}
|
|
|
786 |
|
|
|
787 |
/* we only handle 32bit values */
|
|
|
788 |
if ( maxval > 0x7FFFFFFFL )
|
|
|
789 |
return 0;
|
|
|
790 |
|
|
|
791 |
if ( maxval > 23170 )
|
|
|
792 |
{
|
|
|
793 |
FT_Fixed scale = FT_DivFix( maxval, 23170 );
|
|
|
794 |
|
|
|
795 |
|
|
|
796 |
if ( !FT_DivFix( nonzero_minval, scale ) )
|
|
|
797 |
return 0; /* value range too large */
|
|
|
798 |
|
|
|
799 |
m.xx = FT_DivFix( matrix->xx, scale );
|
|
|
800 |
m.xy = FT_DivFix( matrix->xy, scale );
|
|
|
801 |
m.yx = FT_DivFix( matrix->yx, scale );
|
|
|
802 |
m.yy = FT_DivFix( matrix->yy, scale );
|
|
|
803 |
}
|
|
|
804 |
else
|
|
|
805 |
m = *matrix;
|
|
|
806 |
|
|
|
807 |
temp1 = FT_ABS( m.xx * m.yy - m.xy * m.yx );
|
|
|
808 |
temp2 = m.xx * m.xx + m.xy * m.xy + m.yx * m.yx + m.yy * m.yy;
|
|
|
809 |
|
|
|
810 |
if ( temp1 == 0 ||
|
|
|
811 |
temp2 / temp1 > 50 )
|
|
|
812 |
return 0;
|
|
|
813 |
|
|
|
814 |
return 1;
|
|
|
815 |
}
|
|
|
816 |
|
|
|
817 |
|
|
|
818 |
/* documentation is in ftcalc.h */
|
|
|
819 |
|
|
49234
|
820 |
FT_BASE_DEF( void )
|
|
|
821 |
FT_Vector_Transform_Scaled( FT_Vector* vector,
|
|
|
822 |
const FT_Matrix* matrix,
|
|
|
823 |
FT_Long scaling )
|
|
|
824 |
{
|
|
|
825 |
FT_Pos xz, yz;
|
|
|
826 |
|
|
|
827 |
FT_Long val = 0x10000L * scaling;
|
|
|
828 |
|
|
|
829 |
|
|
|
830 |
if ( !vector || !matrix )
|
|
|
831 |
return;
|
|
|
832 |
|
|
|
833 |
xz = ADD_LONG( FT_MulDiv( vector->x, matrix->xx, val ),
|
|
|
834 |
FT_MulDiv( vector->y, matrix->xy, val ) );
|
|
|
835 |
yz = ADD_LONG( FT_MulDiv( vector->x, matrix->yx, val ),
|
|
|
836 |
FT_MulDiv( vector->y, matrix->yy, val ) );
|
|
|
837 |
|
|
|
838 |
vector->x = xz;
|
|
|
839 |
vector->y = yz;
|
|
|
840 |
}
|
|
|
841 |
|
|
|
842 |
|
|
|
843 |
/* documentation is in ftcalc.h */
|
|
|
844 |
|
|
|
845 |
FT_BASE_DEF( FT_UInt32 )
|
|
|
846 |
FT_Vector_NormLen( FT_Vector* vector )
|
|
|
847 |
{
|
|
|
848 |
FT_Int32 x_ = vector->x;
|
|
|
849 |
FT_Int32 y_ = vector->y;
|
|
|
850 |
FT_Int32 b, z;
|
|
|
851 |
FT_UInt32 x, y, u, v, l;
|
|
|
852 |
FT_Int sx = 1, sy = 1, shift;
|
|
|
853 |
|
|
|
854 |
|
|
|
855 |
x = (FT_UInt32)x_;
|
|
|
856 |
y = (FT_UInt32)y_;
|
|
|
857 |
|
|
|
858 |
FT_MOVE_SIGN( x_, x, sx );
|
|
|
859 |
FT_MOVE_SIGN( y_, y, sy );
|
|
|
860 |
|
|
|
861 |
/* trivial cases */
|
|
|
862 |
if ( x == 0 )
|
|
|
863 |
{
|
|
|
864 |
if ( y > 0 )
|
|
|
865 |
vector->y = sy * 0x10000;
|
|
|
866 |
return y;
|
|
|
867 |
}
|
|
|
868 |
else if ( y == 0 )
|
|
|
869 |
{
|
|
|
870 |
if ( x > 0 )
|
|
|
871 |
vector->x = sx * 0x10000;
|
|
|
872 |
return x;
|
|
|
873 |
}
|
|
|
874 |
|
|
|
875 |
/* Estimate length and prenormalize by shifting so that */
|
|
|
876 |
/* the new approximate length is between 2/3 and 4/3. */
|
|
|
877 |
/* The magic constant 0xAAAAAAAAUL (2/3 of 2^32) helps */
|
|
|
878 |
/* achieve this in 16.16 fixed-point representation. */
|
|
|
879 |
l = x > y ? x + ( y >> 1 )
|
|
|
880 |
: y + ( x >> 1 );
|
|
|
881 |
|
|
|
882 |
shift = 31 - FT_MSB( l );
|
|
|
883 |
shift -= 15 + ( l >= ( 0xAAAAAAAAUL >> shift ) );
|
|
|
884 |
|
|
|
885 |
if ( shift > 0 )
|
|
|
886 |
{
|
|
|
887 |
x <<= shift;
|
|
|
888 |
y <<= shift;
|
|
|
889 |
|
|
|
890 |
/* re-estimate length for tiny vectors */
|
|
|
891 |
l = x > y ? x + ( y >> 1 )
|
|
|
892 |
: y + ( x >> 1 );
|
|
|
893 |
}
|
|
|
894 |
else
|
|
|
895 |
{
|
|
|
896 |
x >>= -shift;
|
|
|
897 |
y >>= -shift;
|
|
|
898 |
l >>= -shift;
|
|
|
899 |
}
|
|
|
900 |
|
|
|
901 |
/* lower linear approximation for reciprocal length minus one */
|
|
|
902 |
b = 0x10000 - (FT_Int32)l;
|
|
|
903 |
|
|
|
904 |
x_ = (FT_Int32)x;
|
|
|
905 |
y_ = (FT_Int32)y;
|
|
|
906 |
|
|
|
907 |
/* Newton's iterations */
|
|
|
908 |
do
|
|
|
909 |
{
|
|
|
910 |
u = (FT_UInt32)( x_ + ( x_ * b >> 16 ) );
|
|
|
911 |
v = (FT_UInt32)( y_ + ( y_ * b >> 16 ) );
|
|
|
912 |
|
|
|
913 |
/* Normalized squared length in the parentheses approaches 2^32. */
|
|
|
914 |
/* On two's complement systems, converting to signed gives the */
|
|
|
915 |
/* difference with 2^32 even if the expression wraps around. */
|
|
|
916 |
z = -(FT_Int32)( u * u + v * v ) / 0x200;
|
|
|
917 |
z = z * ( ( 0x10000 + b ) >> 8 ) / 0x10000;
|
|
|
918 |
|
|
|
919 |
b += z;
|
|
|
920 |
|
|
|
921 |
} while ( z > 0 );
|
|
|
922 |
|
|
|
923 |
vector->x = sx < 0 ? -(FT_Pos)u : (FT_Pos)u;
|
|
|
924 |
vector->y = sy < 0 ? -(FT_Pos)v : (FT_Pos)v;
|
|
|
925 |
|
|
|
926 |
/* Conversion to signed helps to recover from likely wrap around */
|
|
|
927 |
/* in calculating the prenormalized length, because it gives the */
|
|
|
928 |
/* correct difference with 2^32 on two's complement systems. */
|
|
|
929 |
l = (FT_UInt32)( 0x10000 + (FT_Int32)( u * x + v * y ) / 0x10000 );
|
|
|
930 |
if ( shift > 0 )
|
|
|
931 |
l = ( l + ( 1 << ( shift - 1 ) ) ) >> shift;
|
|
|
932 |
else
|
|
|
933 |
l <<= -shift;
|
|
|
934 |
|
|
|
935 |
return l;
|
|
|
936 |
}
|
|
|
937 |
|
|
|
938 |
|
|
|
939 |
#if 0
|
|
|
940 |
|
|
|
941 |
/* documentation is in ftcalc.h */
|
|
|
942 |
|
|
|
943 |
FT_BASE_DEF( FT_Int32 )
|
|
|
944 |
FT_SqrtFixed( FT_Int32 x )
|
|
|
945 |
{
|
|
|
946 |
FT_UInt32 root, rem_hi, rem_lo, test_div;
|
|
|
947 |
FT_Int count;
|
|
|
948 |
|
|
|
949 |
|
|
|
950 |
root = 0;
|
|
|
951 |
|
|
|
952 |
if ( x > 0 )
|
|
|
953 |
{
|
|
|
954 |
rem_hi = 0;
|
|
|
955 |
rem_lo = (FT_UInt32)x;
|
|
|
956 |
count = 24;
|
|
|
957 |
do
|
|
|
958 |
{
|
|
|
959 |
rem_hi = ( rem_hi << 2 ) | ( rem_lo >> 30 );
|
|
|
960 |
rem_lo <<= 2;
|
|
|
961 |
root <<= 1;
|
|
|
962 |
test_div = ( root << 1 ) + 1;
|
|
|
963 |
|
|
|
964 |
if ( rem_hi >= test_div )
|
|
|
965 |
{
|
|
|
966 |
rem_hi -= test_div;
|
|
|
967 |
root += 1;
|
|
|
968 |
}
|
|
|
969 |
} while ( --count );
|
|
|
970 |
}
|
|
|
971 |
|
|
|
972 |
return (FT_Int32)root;
|
|
|
973 |
}
|
|
|
974 |
|
|
|
975 |
#endif /* 0 */
|
|
|
976 |
|
|
|
977 |
|
|
|
978 |
/* documentation is in ftcalc.h */
|
|
|
979 |
|
|
|
980 |
FT_BASE_DEF( FT_Int )
|
|
|
981 |
ft_corner_orientation( FT_Pos in_x,
|
|
|
982 |
FT_Pos in_y,
|
|
|
983 |
FT_Pos out_x,
|
|
|
984 |
FT_Pos out_y )
|
|
|
985 |
{
|
|
54876
|
986 |
/* we silently ignore overflow errors since such large values */
|
|
|
987 |
/* lead to even more (harmless) rendering errors later on */
|
|
|
988 |
|
|
49234
|
989 |
#ifdef FT_LONG64
|
|
|
990 |
|
|
54876
|
991 |
FT_Int64 delta = SUB_INT64( MUL_INT64( in_x, out_y ),
|
|
|
992 |
MUL_INT64( in_y, out_x ) );
|
|
49234
|
993 |
|
|
|
994 |
|
|
|
995 |
return ( delta > 0 ) - ( delta < 0 );
|
|
|
996 |
|
|
|
997 |
#else
|
|
|
998 |
|
|
|
999 |
FT_Int result;
|
|
|
1000 |
|
|
|
1001 |
|
|
|
1002 |
if ( ADD_LONG( FT_ABS( in_x ), FT_ABS( out_y ) ) <= 131071L &&
|
|
|
1003 |
ADD_LONG( FT_ABS( in_y ), FT_ABS( out_x ) ) <= 131071L )
|
|
|
1004 |
{
|
|
|
1005 |
FT_Long z1 = MUL_LONG( in_x, out_y );
|
|
|
1006 |
FT_Long z2 = MUL_LONG( in_y, out_x );
|
|
|
1007 |
|
|
|
1008 |
|
|
|
1009 |
if ( z1 > z2 )
|
|
|
1010 |
result = +1;
|
|
|
1011 |
else if ( z1 < z2 )
|
|
|
1012 |
result = -1;
|
|
|
1013 |
else
|
|
|
1014 |
result = 0;
|
|
|
1015 |
}
|
|
|
1016 |
else /* products might overflow 32 bits */
|
|
|
1017 |
{
|
|
|
1018 |
FT_Int64 z1, z2;
|
|
|
1019 |
|
|
|
1020 |
|
|
|
1021 |
/* XXX: this function does not allow 64-bit arguments */
|
|
|
1022 |
ft_multo64( (FT_UInt32)in_x, (FT_UInt32)out_y, &z1 );
|
|
|
1023 |
ft_multo64( (FT_UInt32)in_y, (FT_UInt32)out_x, &z2 );
|
|
|
1024 |
|
|
|
1025 |
if ( z1.hi > z2.hi )
|
|
|
1026 |
result = +1;
|
|
|
1027 |
else if ( z1.hi < z2.hi )
|
|
|
1028 |
result = -1;
|
|
|
1029 |
else if ( z1.lo > z2.lo )
|
|
|
1030 |
result = +1;
|
|
|
1031 |
else if ( z1.lo < z2.lo )
|
|
|
1032 |
result = -1;
|
|
|
1033 |
else
|
|
|
1034 |
result = 0;
|
|
|
1035 |
}
|
|
|
1036 |
|
|
|
1037 |
/* XXX: only the sign of return value, +1/0/-1 must be used */
|
|
|
1038 |
return result;
|
|
|
1039 |
|
|
|
1040 |
#endif
|
|
|
1041 |
}
|
|
|
1042 |
|
|
|
1043 |
|
|
|
1044 |
/* documentation is in ftcalc.h */
|
|
|
1045 |
|
|
|
1046 |
FT_BASE_DEF( FT_Int )
|
|
|
1047 |
ft_corner_is_flat( FT_Pos in_x,
|
|
|
1048 |
FT_Pos in_y,
|
|
|
1049 |
FT_Pos out_x,
|
|
|
1050 |
FT_Pos out_y )
|
|
|
1051 |
{
|
|
|
1052 |
FT_Pos ax = in_x + out_x;
|
|
|
1053 |
FT_Pos ay = in_y + out_y;
|
|
|
1054 |
|
|
|
1055 |
FT_Pos d_in, d_out, d_hypot;
|
|
|
1056 |
|
|
|
1057 |
|
|
|
1058 |
/* The idea of this function is to compare the length of the */
|
|
|
1059 |
/* hypotenuse with the `in' and `out' length. The `corner' */
|
|
|
1060 |
/* represented by `in' and `out' is flat if the hypotenuse's */
|
|
|
1061 |
/* length isn't too large. */
|
|
|
1062 |
/* */
|
|
|
1063 |
/* This approach has the advantage that the angle between */
|
|
|
1064 |
/* `in' and `out' is not checked. In case one of the two */
|
|
|
1065 |
/* vectors is `dominant', this is, much larger than the */
|
|
|
1066 |
/* other vector, we thus always have a flat corner. */
|
|
|
1067 |
/* */
|
|
|
1068 |
/* hypotenuse */
|
|
|
1069 |
/* x---------------------------x */
|
|
|
1070 |
/* \ / */
|
|
|
1071 |
/* \ / */
|
|
|
1072 |
/* in \ / out */
|
|
|
1073 |
/* \ / */
|
|
|
1074 |
/* o */
|
|
|
1075 |
/* Point */
|
|
|
1076 |
|
|
|
1077 |
d_in = FT_HYPOT( in_x, in_y );
|
|
|
1078 |
d_out = FT_HYPOT( out_x, out_y );
|
|
|
1079 |
d_hypot = FT_HYPOT( ax, ay );
|
|
|
1080 |
|
|
|
1081 |
/* now do a simple length comparison: */
|
|
|
1082 |
/* */
|
|
|
1083 |
/* d_in + d_out < 17/16 d_hypot */
|
|
|
1084 |
|
|
|
1085 |
return ( d_in + d_out - d_hypot ) < ( d_hypot >> 4 );
|
|
|
1086 |
}
|
|
|
1087 |
|
|
|
1088 |
|
|
|
1089 |
/* END */
|