511 lines
13 KiB
C
511 lines
13 KiB
C
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/****************************************************************************
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*
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* ftcalc.h
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*
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* Arithmetic computations (specification).
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*
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* Copyright (C) 1996-2020 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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#ifndef FTCALC_H_
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#define FTCALC_H_
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#include <ft2build.h>
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#include FT_FREETYPE_H
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FT_BEGIN_HEADER
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/**************************************************************************
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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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#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
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/* Provide assembler fragments for performance-critical functions. */
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/* These must be defined `static __inline__' with GCC. */
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#if defined( __CC_ARM ) || defined( __ARMCC__ ) /* RVCT */
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#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
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/* documentation is in freetype.h */
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static __inline FT_Int32
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FT_MulFix_arm( FT_Int32 a,
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FT_Int32 b )
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{
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FT_Int32 t, t2;
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__asm
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{
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smull t2, t, b, a /* (lo=t2,hi=t) = a*b */
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mov a, t, asr #31 /* a = (hi >> 31) */
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add a, a, #0x8000 /* a += 0x8000 */
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adds t2, t2, a /* t2 += a */
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adc t, t, #0 /* t += carry */
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mov a, t2, lsr #16 /* a = t2 >> 16 */
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orr a, a, t, lsl #16 /* a |= t << 16 */
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}
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return a;
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}
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#endif /* __CC_ARM || __ARMCC__ */
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#ifdef __GNUC__
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#if defined( __arm__ ) && \
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( !defined( __thumb__ ) || defined( __thumb2__ ) ) && \
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!( defined( __CC_ARM ) || defined( __ARMCC__ ) )
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#define FT_MULFIX_ASSEMBLER FT_MulFix_arm
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/* documentation is in freetype.h */
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static __inline__ FT_Int32
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FT_MulFix_arm( FT_Int32 a,
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FT_Int32 b )
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{
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FT_Int32 t, t2;
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__asm__ __volatile__ (
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"smull %1, %2, %4, %3\n\t" /* (lo=%1,hi=%2) = a*b */
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"mov %0, %2, asr #31\n\t" /* %0 = (hi >> 31) */
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#if defined( __clang__ ) && defined( __thumb2__ )
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"add.w %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
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#else
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"add %0, %0, #0x8000\n\t" /* %0 += 0x8000 */
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#endif
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"adds %1, %1, %0\n\t" /* %1 += %0 */
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"adc %2, %2, #0\n\t" /* %2 += carry */
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"mov %0, %1, lsr #16\n\t" /* %0 = %1 >> 16 */
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"orr %0, %0, %2, lsl #16\n\t" /* %0 |= %2 << 16 */
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: "=r"(a), "=&r"(t2), "=&r"(t)
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: "r"(a), "r"(b)
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: "cc" );
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return a;
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}
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#endif /* __arm__ && */
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/* ( __thumb2__ || !__thumb__ ) && */
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/* !( __CC_ARM || __ARMCC__ ) */
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#if defined( __i386__ )
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#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
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/* documentation is in freetype.h */
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static __inline__ FT_Int32
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FT_MulFix_i386( FT_Int32 a,
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FT_Int32 b )
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{
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FT_Int32 result;
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__asm__ __volatile__ (
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"imul %%edx\n"
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"movl %%edx, %%ecx\n"
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"sarl $31, %%ecx\n"
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"addl $0x8000, %%ecx\n"
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"addl %%ecx, %%eax\n"
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"adcl $0, %%edx\n"
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"shrl $16, %%eax\n"
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"shll $16, %%edx\n"
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"addl %%edx, %%eax\n"
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: "=a"(result), "=d"(b)
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: "a"(a), "d"(b)
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: "%ecx", "cc" );
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return result;
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}
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#endif /* i386 */
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#endif /* __GNUC__ */
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#ifdef _MSC_VER /* Visual C++ */
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#ifdef _M_IX86
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#define FT_MULFIX_ASSEMBLER FT_MulFix_i386
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/* documentation is in freetype.h */
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static __inline FT_Int32
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FT_MulFix_i386( FT_Int32 a,
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FT_Int32 b )
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{
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FT_Int32 result;
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__asm
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{
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mov eax, a
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mov edx, b
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imul edx
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mov ecx, edx
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sar ecx, 31
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add ecx, 8000h
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add eax, ecx
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adc edx, 0
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shr eax, 16
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shl edx, 16
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add eax, edx
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mov result, eax
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}
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return result;
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}
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#endif /* _M_IX86 */
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#endif /* _MSC_VER */
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#if defined( __GNUC__ ) && defined( __x86_64__ )
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#define FT_MULFIX_ASSEMBLER FT_MulFix_x86_64
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static __inline__ FT_Int32
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FT_MulFix_x86_64( FT_Int32 a,
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FT_Int32 b )
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{
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/* Temporarily disable the warning that C90 doesn't support */
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/* `long long'. */
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#if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
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#pragma GCC diagnostic push
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#pragma GCC diagnostic ignored "-Wlong-long"
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#endif
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#if 1
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/* Technically not an assembly fragment, but GCC does a really good */
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/* job at inlining it and generating good machine code for it. */
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long long ret, tmp;
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ret = (long long)a * b;
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tmp = ret >> 63;
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ret += 0x8000 + tmp;
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return (FT_Int32)( ret >> 16 );
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#else
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/* For some reason, GCC 4.6 on Ubuntu 12.04 generates invalid machine */
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/* code from the lines below. The main issue is that `wide_a' is not */
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/* properly initialized by sign-extending `a'. Instead, the generated */
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/* machine code assumes that the register that contains `a' on input */
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/* can be used directly as a 64-bit value, which is wrong most of the */
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/* time. */
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long long wide_a = (long long)a;
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long long wide_b = (long long)b;
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long long result;
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__asm__ __volatile__ (
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"imul %2, %1\n"
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"mov %1, %0\n"
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"sar $63, %0\n"
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"lea 0x8000(%1, %0), %0\n"
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"sar $16, %0\n"
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: "=&r"(result), "=&r"(wide_a)
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: "r"(wide_b)
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: "cc" );
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return (FT_Int32)result;
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#endif
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#if __GNUC__ > 4 || ( __GNUC__ == 4 && __GNUC_MINOR__ >= 6 )
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#pragma GCC diagnostic pop
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#endif
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}
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#endif /* __GNUC__ && __x86_64__ */
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#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
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#ifdef FT_CONFIG_OPTION_INLINE_MULFIX
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#ifdef FT_MULFIX_ASSEMBLER
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#define FT_MulFix( a, b ) FT_MULFIX_ASSEMBLER( (FT_Int32)(a), (FT_Int32)(b) )
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#endif
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#endif
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/**************************************************************************
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*
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* @function:
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* FT_MulDiv_No_Round
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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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* (without rounding) with maximum accuracy (it uses a 64-bit
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* intermediate integer 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 ::
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* The first multiplier.
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* b ::
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* The second multiplier.
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* c ::
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* 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 on
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* the signs of 'a' and 'b'.
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*/
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FT_BASE( 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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* A variant of FT_Matrix_Multiply which scales its result afterwards. The
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* idea is that both `a' and `b' are scaled by factors of 10 so that the
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* values are as precise as possible to get a correct result during the
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* 64bit multiplication. Let `sa' and `sb' be the scaling factors of `a'
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* and `b', respectively, then the scaling factor of the result is `sa*sb'.
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*/
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FT_BASE( void )
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FT_Matrix_Multiply_Scaled( const FT_Matrix* a,
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FT_Matrix *b,
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FT_Long scaling );
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/*
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* Check a matrix. If the transformation would lead to extreme shear or
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* extreme scaling, for example, return 0. If everything is OK, return 1.
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*
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* Based on geometric considerations we use the following inequality to
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* identify a degenerate matrix.
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*
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* 50 * abs(xx*yy - xy*yx) < xx^2 + xy^2 + yx^2 + yy^2
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*
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* Value 50 is heuristic.
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*/
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FT_BASE( FT_Bool )
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FT_Matrix_Check( const FT_Matrix* matrix );
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/*
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* A variant of FT_Vector_Transform. See comments for
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* FT_Matrix_Multiply_Scaled.
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*/
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FT_BASE( void )
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FT_Vector_Transform_Scaled( FT_Vector* vector,
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const FT_Matrix* matrix,
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FT_Long scaling );
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/*
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* This function normalizes a vector and returns its original length. The
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* normalized vector is a 16.16 fixed-point unit vector with length close
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* to 0x10000. The accuracy of the returned length is limited to 16 bits
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* also. The function utilizes quick inverse square root approximation
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* without divisions and square roots relying on Newton's iterations
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* instead.
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*/
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FT_BASE( FT_UInt32 )
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FT_Vector_NormLen( FT_Vector* vector );
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/*
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* Return -1, 0, or +1, depending on the orientation of a given corner. We
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* use the Cartesian coordinate system, with positive vertical values going
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* upwards. The function returns +1 if the corner turns to the left, -1 to
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* the right, and 0 for undecidable cases.
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*/
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FT_BASE( FT_Int )
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ft_corner_orientation( FT_Pos in_x,
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FT_Pos in_y,
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FT_Pos out_x,
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FT_Pos out_y );
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/*
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* Return TRUE if a corner is flat or nearly flat. This is equivalent to
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* saying that the corner point is close to its neighbors, or inside an
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* ellipse defined by the neighbor focal points to be more precise.
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*/
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FT_BASE( FT_Int )
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ft_corner_is_flat( FT_Pos in_x,
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FT_Pos in_y,
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FT_Pos out_x,
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FT_Pos out_y );
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/*
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* Return the most significant bit index.
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*/
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#ifndef FT_CONFIG_OPTION_NO_ASSEMBLER
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#if defined( __GNUC__ ) && \
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( __GNUC__ > 3 || ( __GNUC__ == 3 && __GNUC_MINOR__ >= 4 ) )
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#if FT_SIZEOF_INT == 4
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#define FT_MSB( x ) ( 31 - __builtin_clz( x ) )
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#elif FT_SIZEOF_LONG == 4
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#define FT_MSB( x ) ( 31 - __builtin_clzl( x ) )
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#endif /* __GNUC__ */
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#elif defined( _MSC_VER ) && ( _MSC_VER >= 1400 )
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#if FT_SIZEOF_INT == 4
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#include <intrin.h>
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#pragma intrinsic( _BitScanReverse )
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static __inline FT_Int32
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FT_MSB_i386( FT_UInt32 x )
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{
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unsigned long where;
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_BitScanReverse( &where, x );
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|
||
|
|
return (FT_Int32)where;
|
||
|
|
}
|
||
|
|
|
||
|
|
#define FT_MSB( x ) ( FT_MSB_i386( x ) )
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|
||
|
|
#endif /* _MSC_VER */
|
||
|
|
|
||
|
|
|
||
|
|
#endif /* !FT_CONFIG_OPTION_NO_ASSEMBLER */
|
||
|
|
|
||
|
|
#ifndef FT_MSB
|
||
|
|
|
||
|
|
FT_BASE( FT_Int )
|
||
|
|
FT_MSB( FT_UInt32 z );
|
||
|
|
|
||
|
|
#endif
|
||
|
|
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Return sqrt(x*x+y*y), which is the same as `FT_Vector_Length' but uses
|
||
|
|
* two fixed-point arguments instead.
|
||
|
|
*/
|
||
|
|
FT_BASE( FT_Fixed )
|
||
|
|
FT_Hypot( FT_Fixed x,
|
||
|
|
FT_Fixed y );
|
||
|
|
|
||
|
|
|
||
|
|
#if 0
|
||
|
|
|
||
|
|
/**************************************************************************
|
||
|
|
*
|
||
|
|
* @function:
|
||
|
|
* FT_SqrtFixed
|
||
|
|
*
|
||
|
|
* @description:
|
||
|
|
* Computes the square root of a 16.16 fixed-point value.
|
||
|
|
*
|
||
|
|
* @input:
|
||
|
|
* x ::
|
||
|
|
* The value to compute the root for.
|
||
|
|
*
|
||
|
|
* @return:
|
||
|
|
* The result of 'sqrt(x)'.
|
||
|
|
*
|
||
|
|
* @note:
|
||
|
|
* This function is not very fast.
|
||
|
|
*/
|
||
|
|
FT_BASE( FT_Int32 )
|
||
|
|
FT_SqrtFixed( FT_Int32 x );
|
||
|
|
|
||
|
|
#endif /* 0 */
|
||
|
|
|
||
|
|
|
||
|
|
#define INT_TO_F26DOT6( x ) ( (FT_Long)(x) * 64 ) /* << 6 */
|
||
|
|
#define INT_TO_F2DOT14( x ) ( (FT_Long)(x) * 16384 ) /* << 14 */
|
||
|
|
#define INT_TO_FIXED( x ) ( (FT_Long)(x) * 65536 ) /* << 16 */
|
||
|
|
#define F2DOT14_TO_FIXED( x ) ( (FT_Long)(x) * 4 ) /* << 2 */
|
||
|
|
#define FIXED_TO_INT( x ) ( FT_RoundFix( x ) >> 16 )
|
||
|
|
|
||
|
|
#define ROUND_F26DOT6( x ) ( x >= 0 ? ( ( (x) + 32 ) & -64 ) \
|
||
|
|
: ( -( ( 32 - (x) ) & -64 ) ) )
|
||
|
|
|
||
|
|
/*
|
||
|
|
* The following macros have two purposes.
|
||
|
|
*
|
||
|
|
* - Tag places where overflow is expected and harmless.
|
||
|
|
*
|
||
|
|
* - Avoid run-time sanitizer errors.
|
||
|
|
*
|
||
|
|
* Use with care!
|
||
|
|
*/
|
||
|
|
#define ADD_INT( a, b ) \
|
||
|
|
(FT_Int)( (FT_UInt)(a) + (FT_UInt)(b) )
|
||
|
|
#define SUB_INT( a, b ) \
|
||
|
|
(FT_Int)( (FT_UInt)(a) - (FT_UInt)(b) )
|
||
|
|
#define MUL_INT( a, b ) \
|
||
|
|
(FT_Int)( (FT_UInt)(a) * (FT_UInt)(b) )
|
||
|
|
#define NEG_INT( a ) \
|
||
|
|
(FT_Int)( (FT_UInt)0 - (FT_UInt)(a) )
|
||
|
|
|
||
|
|
#define ADD_LONG( a, b ) \
|
||
|
|
(FT_Long)( (FT_ULong)(a) + (FT_ULong)(b) )
|
||
|
|
#define SUB_LONG( a, b ) \
|
||
|
|
(FT_Long)( (FT_ULong)(a) - (FT_ULong)(b) )
|
||
|
|
#define MUL_LONG( a, b ) \
|
||
|
|
(FT_Long)( (FT_ULong)(a) * (FT_ULong)(b) )
|
||
|
|
#define NEG_LONG( a ) \
|
||
|
|
(FT_Long)( (FT_ULong)0 - (FT_ULong)(a) )
|
||
|
|
|
||
|
|
#define ADD_INT32( a, b ) \
|
||
|
|
(FT_Int32)( (FT_UInt32)(a) + (FT_UInt32)(b) )
|
||
|
|
#define SUB_INT32( a, b ) \
|
||
|
|
(FT_Int32)( (FT_UInt32)(a) - (FT_UInt32)(b) )
|
||
|
|
#define MUL_INT32( a, b ) \
|
||
|
|
(FT_Int32)( (FT_UInt32)(a) * (FT_UInt32)(b) )
|
||
|
|
#define NEG_INT32( a ) \
|
||
|
|
(FT_Int32)( (FT_UInt32)0 - (FT_UInt32)(a) )
|
||
|
|
|
||
|
|
#ifdef FT_LONG64
|
||
|
|
|
||
|
|
#define ADD_INT64( a, b ) \
|
||
|
|
(FT_Int64)( (FT_UInt64)(a) + (FT_UInt64)(b) )
|
||
|
|
#define SUB_INT64( a, b ) \
|
||
|
|
(FT_Int64)( (FT_UInt64)(a) - (FT_UInt64)(b) )
|
||
|
|
#define MUL_INT64( a, b ) \
|
||
|
|
(FT_Int64)( (FT_UInt64)(a) * (FT_UInt64)(b) )
|
||
|
|
#define NEG_INT64( a ) \
|
||
|
|
(FT_Int64)( (FT_UInt64)0 - (FT_UInt64)(a) )
|
||
|
|
|
||
|
|
#endif /* FT_LONG64 */
|
||
|
|
|
||
|
|
|
||
|
|
FT_END_HEADER
|
||
|
|
|
||
|
|
#endif /* FTCALC_H_ */
|
||
|
|
|
||
|
|
|
||
|
|
/* END */
|