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qmath.h
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/* ==== ArtNouveaU Quick Math ~ qmath.h ==================================
WATCOM C/C++ Standard Libraries replacement for tiny code.
Copyright (C) 1997 by the gang at ArtNouveaU, All Rights Reserved.
Microsoft Visual C/C++ Standard Libraries replacement for tiny code.
Copyright (C) 2002 by Gabriele Scibilia, All Rights Reserved.
author : <G>SZ ~ ArtNouveaU
file creation : 30 March 1997
file description : fast floating point math intrinsics
revision history :
(30/03/97) the beginning
(24/10/97) renamed WATCOM C/C++ tinymath.h
(26/10/97) added sincos intrinsic
(30/10/97) added acos and asin intrinsics
(31/10/97) added ceil and floor ones
(01/11/97) added hypot, cosh, sinh, acosh, asinh atanh ones
(02/11/97) added tanh intrinsic
(09/01/98) added M_ constants
(27/08/02) renamed MS Visual C/C++ qmath.h
(11/01/04) modified qmathTan() - J.Bennett <[email protected]>
references :
ArtNouveaU Tiny Library,
tinymath WATCOM C/C++ intrinsics for math functions,
Gabriele Scibilia, 24 October 1997.
Pascal/Cubic math intrinsics, 1997.
WATCOM C/C++ v11.0 Math Library, 1997.
RTLIB2 small math run time library replacement,
"Art" 64k demo by Farbrausch and Scoopex, 2001.
notes : pow returns NaN with non-positive arguments
For those who hates "naked" convention
try modifing each function as the following
ie.
i- changing float loads
ii- removing inlined "ret" statement
double _QMATH_LINK qmathSqrt(double __x)
{
__asm fld qword ptr __x
__asm fsqrt
}
When single precision floating point support
is required...
_QMATH_NAKED _QMATH_INLINE
float _QMATH_LINK qmathSinFloat(float __x)
{
__asm fld dword ptr [esp + 4]
__asm fsin
__asm ret 4
}
======================================================================== */
#ifndef _QUICKMATH_H_INCLUDED
#define _QUICKMATH_H_INCLUDED
#include <math.h>
#ifdef __cplusplus
extern "C" {
#endif
// Commented out in AutoHotkey v1.0.40.02 to help reduce code size:
//static char quickmath_id[] = "$Id: qmath.h,v 1.1 2004/01/15 19:50:35 jonbennett Exp $";
// for silly C compilers allowing inlining
// try using "static" definition otherwise
#define _QMATH_INLINE __inline
// functions are emitted without prolog or epilog code
#define _QMATH_NAKED __declspec(naked)
// argument-passing right to left
// called function pops its own arguments from the stack
#define _QMATH_LINK __stdcall
#define FIST_MAGIC (((65536.0 * 65536.0 * 16) + 32768.0) * 65536.0)
#define FIST_M0131 (65536.0 * 24.0 * 2.0)
#define FIST_M0230 (65536.0 * 24.0 * 4.0)
#define FIST_M0329 (65536.0 * 24.0 * 8.0)
#define FIST_M0428 (65536.0 * 24.0 * 16.0)
#define FIST_M0527 (65536.0 * 24.0 * 32.0)
#define FIST_M0626 (65536.0 * 24.0 * 64.0)
#define FIST_M0725 (65536.0 * 24.0 * 128.0)
#define FIST_M0824 (65536.0 * 24.0 * 256.0)
#define FIST_M0923 (65536.0 * 24.0 * 512.0)
#define FIST_M1022 (65536.0 * 24.0 * 1024.0)
#define FIST_M1121 (65536.0 * 24.0 * 2048.0)
#define FIST_M1220 (65536.0 * 24.0 * 4096.0)
#define FIST_M1319 (65536.0 * 24.0 * 8192.0)
#define FIST_M1418 (65536.0 * 24.0 * 16384.0)
#define FIST_M1517 (65536.0 * 24.0 * 32768.0)
#define FIST_M1616 (65536.0 * 65536.0 * 24.0 * 1.0)
#define FIST_M1715 (65536.0 * 65536.0 * 24.0 * 2.0)
#define FIST_M1814 (65536.0 * 65536.0 * 24.0 * 4.0)
#define FIST_M1913 (65536.0 * 65536.0 * 24.0 * 8.0)
#define FIST_M2012 (65536.0 * 65536.0 * 24.0 * 16.0)
#define FIST_M2111 (65536.0 * 65536.0 * 24.0 * 32.0)
#define FIST_M2210 (65536.0 * 65536.0 * 24.0 * 64.0)
#define FIST_M2309 (65536.0 * 65536.0 * 24.0 * 128.0)
#define FIST_M2408 (65536.0 * 65536.0 * 24.0 * 256.0)
#define FIST_M2507 (65536.0 * 65536.0 * 24.0 * 512.0)
#define FIST_M2606 (65536.0 * 65536.0 * 24.0 * 1024.0)
#define FIST_M2705 (65536.0 * 65536.0 * 24.0 * 2048.0)
#define FIST_M2804 (65536.0 * 65536.0 * 24.0 * 4096.0)
#define FIST_M2903 (65536.0 * 65536.0 * 24.0 * 8192.0)
#define FIST_M3002 (65536.0 * 65536.0 * 24.0 * 16384.0)
#define FIST_M3101 (65536.0 * 65536.0 * 24.0 * 32768.0)
#define FIST_SHORT (14680064.0f)
/*
The following ASM code will convert quickly from a floating point value
to a 16.16 fixed point number.
This code comes complements of Chris Babcock (a.k.a. "VOR")
i_bignum dq 04238000000000000h
FADD [i_bignum]
...
FSTP [qword ptr i_temp]
...
MOV eax,[dword ptr i_temp] ; eax = 16.16
*/
_QMATH_INLINE long qmathFtstNeg(float inval)
{
return ((*(long *) &inval) > 0x80000000);
}
_QMATH_INLINE long qmathFtstPos(float inval)
{
return ((*(long *) &inval) < 0x80000000);
}
_QMATH_INLINE long qmathFtstZero(float inval)
{
return ((*(long *) &inval) + (*(long *) &inval));
}
_QMATH_INLINE long qmathFcompGreatThan(float invala, float invalb)
{
return ((*(long *) &invala) > (*(long *) &invalb));
}
_QMATH_INLINE long qmathFcompLessThan(float invala, float invalb)
{
return ((*(long *) &invala) < (*(long *) &invalb));
}
_QMATH_INLINE short qmathFistShort(float inval)
{
float dtemp = FIST_SHORT + inval;
return ((*(short *) &dtemp) & 0x1FFFFF);
}
_QMATH_INLINE long qmathFistLong(float inval)
{
double dtemp = FIST_MAGIC + inval;
return ((*(long *) &dtemp) - 0x80000000);
}
_QMATH_INLINE long qmathFist0131(float inval)
{
double dtemp = FIST_M0131 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0230(float inval)
{
double dtemp = FIST_M0230 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0329(float inval)
{
double dtemp = FIST_M0329 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0428(float inval)
{
double dtemp = FIST_M0428 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0527(float inval)
{
double dtemp = FIST_M0527 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0626(float inval)
{
double dtemp = FIST_M0626 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0725(float inval)
{
double dtemp = FIST_M0725 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0824(float inval)
{
double dtemp = FIST_M0824 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist0923(float inval)
{
double dtemp = FIST_M0923 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1022(float inval)
{
double dtemp = FIST_M1022 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1121(float inval)
{
double dtemp = FIST_M1121 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1220(float inval)
{
double dtemp = FIST_M1220 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1319(float inval)
{
double dtemp = FIST_M1319 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1418(float inval)
{
double dtemp = FIST_M1418 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1517(float inval)
{
double dtemp = FIST_M1517 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1616(float inval)
{
double dtemp = FIST_M1616 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1715(float inval)
{
double dtemp = FIST_M1715 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1814(float inval)
{
double dtemp = FIST_M1814 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist1913(float inval)
{
double dtemp = FIST_M1913 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2012(float inval)
{
double dtemp = FIST_M2012 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2111(float inval)
{
double dtemp = FIST_M2111 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2210(float inval)
{
double dtemp = FIST_M2210 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2309(float inval)
{
double dtemp = FIST_M2309 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2408(float inval)
{
double dtemp = FIST_M2408 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2507(float inval)
{
double dtemp = FIST_M2507 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2606(float inval)
{
double dtemp = FIST_M2606 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2705(float inval)
{
double dtemp = FIST_M2705 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2804(float inval)
{
double dtemp = FIST_M2804 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist2903(float inval)
{
double dtemp = FIST_M2903 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist3002(float inval)
{
double dtemp = FIST_M3002 + inval;
return (*(long *) &dtemp);
}
_QMATH_INLINE long qmathFist3101(float inval)
{
double dtemp = FIST_M3101 + inval;
return (*(long *) &dtemp);
}
// M_ constants
#define M_E (2.71828182845904523536)
#define M_LOG2E (1.44269504088896340736)
#define M_LOG10E (0.434294481903251827651)
#define M_LN2 (0.693147180559945309417)
#define M_LN10 (2.30258509299404568402)
#define M_PI (3.14159265358979323846)
#define M_PI_2 (1.57079632679489661923)
#define M_PI_4 (0.785398163397448309616)
#define M_1_PI (0.318309886183790671538)
#define M_2_PI (0.636619772367581343076)
#define M_1_SQRTPI (0.564189583547756286948)
#define M_2_SQRTPI (1.12837916709551257390)
#define M_SQRT2 (1.41421356237309504880)
#define M_SQRT_2 (0.707106781186547524401)
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathSin(double __x){sin(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fsin
__asm ret 8
}
*/
static double einhalb = 0.5;
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAsin(double __x){asin(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld st
__asm fabs
__asm fcom dword ptr [einhalb]
__asm fstsw ax
__asm sahf
__asm jbe asin_kleiner
__asm fld1
__asm fsubrp st(1), st(0)
__asm fld st
__asm fadd st(0), st(0)
__asm fxch st(1)
__asm fmul st(0), st(0)
__asm fsubp st(1), st(0)
__asm jmp asin_exit
asin_kleiner:
__asm fstp st(0)
__asm fld st(0)
__asm fmul st(0), st(0)
__asm fld1
__asm fsubrp st(1), st(0)
asin_exit:
__asm fsqrt
__asm fpatan
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathCos(double __x){cos(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fcos
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAcos(double __x){acos(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld1
__asm fchs
__asm fcomp st(1)
__asm fstsw ax
__asm je acos_suckt
__asm fld st(0)
__asm fld1
__asm fsubrp st(1), st(0)
__asm fxch st(1)
__asm fld1
__asm faddp st(1), st(0)
__asm fdivp st(1), st(0)
__asm fsqrt
__asm fld1
__asm jmp acos_exit
acos_suckt:
__asm fld1
__asm fldz
acos_exit:
__asm fpatan
__asm fadd st(0), st(0)
__asm ret 8
}
*/
/* J.Bennett - added fstp in tan function to remove 1.0 it pushes onto the stack */
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathTan(double __x){return tan(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fptan
__asm fstp st(0)
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAtan(double __x){return atan(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld1
__asm fpatan
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAtan2(double __y, double __x){return atan2(__x, __y);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld qword ptr [esp + 12]
__asm fpatan
__asm ret 16
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathExp(double __x){return exp(__x);}
/*
{
__asm fld qword ptr [esp + 4];
__asm fldl2e
__asm fmulp st(1), st
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathExp2(double __x){return exp2(__x);}
/*
{
__asm fld qword ptr [esp + 4];
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathExp10(double __x){return pow(10, __x);}
/*
{
__asm fld qword ptr [esp + 4];
__asm fldl2t
__asm fmulp st(1), st
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathLog(double __x){return log(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fldln2
__asm fxch
__asm fyl2x
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathLog2(double __x){return log2(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld1
__asm fxch
__asm fyl2x
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathLog10(double __x){return log10(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fldlg2
__asm fxch
__asm fyl2x
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathFabs(double __x){return fabs(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fabs
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathPow(double __x, double __y){return pow(__x, __y);}
/*
{
__asm fld qword ptr [esp + 12]
__asm fld qword ptr [esp + 4]
__asm ftst
__asm fstsw ax
__asm sahf
__asm jz pow_zero
__asm fyl2x
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st(0)
__asm fscale
pow_zero:
__asm fstp st(1)
__asm ret 16
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathCeil(double __x){return ceil(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fchs
__asm fld1
__asm fld st(1)
__asm fprem
__asm sub esp, 4
__asm fst dword ptr [esp]
__asm fxch st(2)
__asm mov eax, [esp]
__asm cmp eax, 0x80000000
__asm jbe ceil_exit
__asm fsub st, st(1)
ceil_exit:
__asm fsub st, st(2)
__asm fstp st(1)
__asm fstp st(1)
__asm fchs
__asm pop eax
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathFloor(double __x){return floor(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld1
__asm fld st(1)
__asm fprem
__asm sub esp, 4
__asm fst dword ptr [esp]
__asm fxch st(2)
__asm mov eax, [esp]
__asm cmp eax, 0x80000000
__asm jbe floor_exit
__asm fsub st, st(1)
floor_exit:
__asm fsub st, st(2)
__asm fstp st(1)
__asm fstp st(1)
__asm pop eax
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathFmod(double __x, double __y){return fmod(__x, __y);}
/*
{
__asm fld qword ptr [esp + 12]
__asm fld qword ptr [esp + 4]
__asm fprem
__asm fxch
__asm fstp st
__asm ret 16
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathSqrt(double __x){return sqrt(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fsqrt
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathHypot(double __x, double __y){return hypot(__x, __y);}
/*
{
__asm fld qword ptr [esp + 12]
__asm fld qword ptr [esp + 4]
__asm fmul st, st
__asm fxch
__asm fmul st, st
__asm faddp st(1), st
__asm fsqrt
__asm ret 16
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAcosh(double __x){return acosh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld st
__asm fmul st, st
__asm fld1
__asm fsubp st(1), st
__asm fsqrt
__asm faddp st(1), st
__asm fldln2
__asm fxch
__asm fyl2x
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAsinh(double __x){return asinh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld st
__asm fmul st, st
__asm fld1
__asm faddp st(1), st
__asm fsqrt
__asm faddp st(1), st
__asm fldln2
__asm fxch
__asm fyl2x
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathAtanh(double __x){return atanh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld1
__asm fsub st, st(1)
__asm fld1
__asm faddp st(2), st
__asm fdivrp st(1), st
__asm fldln2
__asm fxch
__asm fyl2x
__asm mov eax, 0xBF000000
__asm push eax
__asm fld dword ptr [esp]
__asm fmulp st(1), st
__asm pop eax
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathCosh(double __x){return cosh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fldl2e
__asm fmulp st(1), st
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm fld1
__asm fdiv st, st(1)
__asm faddp st(1), st
__asm mov eax, 0x3F000000
__asm push eax
__asm fld dword ptr [esp]
__asm fmulp st(1), st
__asm pop eax
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathSinh(double __x){return sinh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fldl2e
__asm fmulp st(1), st
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm fld1
__asm fdiv st, st(1)
__asm fsubp st(1), st
__asm mov eax, 0x3F000000
__asm push eax
__asm fld dword ptr [esp]
__asm fmulp st(1), st
__asm pop eax
__asm ret 8
}
*/
_QMATH_NAKED _QMATH_INLINE
double _QMATH_LINK qmathTanh(double __x){return tanh(__x);}
/*
{
__asm fld qword ptr [esp + 4]
__asm fld st
__asm mov eax, 0x40000000
__asm push eax
__asm fld dword ptr [esp]
__asm fmul st, st(1)
__asm fldl2e
__asm fmulp st(1), st
__asm fld1
__asm fld st(1)
__asm fprem
__asm f2xm1
__asm faddp st(1), st
__asm fscale
__asm fxch
__asm fstp st
__asm fld1
__asm fsub st, st(1)
__asm fchs
__asm fld1
__asm faddp st(2), st
__asm fdivrp st(1), st
__asm pop eax
__asm ret 8
}
*/
#ifdef __cplusplus
};
#endif
#endif // _QUICKMATH_H_INCLUDED