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git-svn-id: http://svn2.nishi.boats/svn/milsko/trunk@543 b9cfdab3-6d41-4d17-bbe4-086880011989
This commit is contained in:
NishiOwO
2025-11-01 04:25:22 +00:00
parent 0626cb3527
commit 98143415ba
12 changed files with 467 additions and 64 deletions
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56
src/math/default.c
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@@ -34,14 +34,14 @@ static void default_multiply_u8(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.u8.h = a->un.u8.h * b->un.u8.h;
};
static void default_reciprocal_u8(MwLLVec* a, MwLLVec* out) {
out->un.u8.a = powf(a->un.u8.a, -1);
out->un.u8.b = powf(a->un.u8.b, -1);
out->un.u8.c = powf(a->un.u8.c, -1);
out->un.u8.d = powf(a->un.u8.d, -1);
out->un.u8.e = powf(a->un.u8.e, -1);
out->un.u8.f = powf(a->un.u8.f, -1);
out->un.u8.g = powf(a->un.u8.g, -1);
out->un.u8.h = powf(a->un.u8.h, -1);
out->un.u8.a = nbsd_pow(a->un.u8.a, -1);
out->un.u8.b = nbsd_pow(a->un.u8.b, -1);
out->un.u8.c = nbsd_pow(a->un.u8.c, -1);
out->un.u8.d = nbsd_pow(a->un.u8.d, -1);
out->un.u8.e = nbsd_pow(a->un.u8.e, -1);
out->un.u8.f = nbsd_pow(a->un.u8.f, -1);
out->un.u8.g = nbsd_pow(a->un.u8.g, -1);
out->un.u8.h = nbsd_pow(a->un.u8.h, -1);
};
static void default_squareRoot_u8(MwLLVec* a, MwLLVec* out) {
out->un.u8.a = sqrt(a->un.u8.a);
@@ -123,10 +123,10 @@ static void default_multiply_u16(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.u16.d = a->un.u16.d * b->un.u16.d;
}
static void default_reciprocal_u16(MwLLVec* a, MwLLVec* out) {
out->un.u16.a = powf(a->un.u16.a, -1);
out->un.u16.b = powf(a->un.u16.b, -1);
out->un.u16.c = powf(a->un.u16.c, -1);
out->un.u16.d = powf(a->un.u16.d, -1);
out->un.u16.a = nbsd_pow(a->un.u16.a, -1);
out->un.u16.b = nbsd_pow(a->un.u16.b, -1);
out->un.u16.c = nbsd_pow(a->un.u16.c, -1);
out->un.u16.d = nbsd_pow(a->un.u16.d, -1);
};
static void default_squareRoot_u16(MwLLVec* a, MwLLVec* out) {
out->un.u16.a = sqrt(a->un.u16.a);
@@ -184,8 +184,8 @@ static void default_multiply_u32(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.u32.b = a->un.u32.b * b->un.u32.b;
}
static void default_reciprocal_u32(MwLLVec* a, MwLLVec* out) {
out->un.u32.a = powf(a->un.u32.a, -1);
out->un.u32.b = powf(a->un.u32.b, -1);
out->un.u32.a = nbsd_pow(a->un.u32.a, -1);
out->un.u32.b = nbsd_pow(a->un.u32.b, -1);
};
static void default_squareRoot_u32(MwLLVec* a, MwLLVec* out) {
out->un.u32.a = sqrt(a->un.u32.a);
@@ -251,14 +251,14 @@ static void default_multiply_i8(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.i8.h = a->un.i8.h * b->un.i8.h;
};
static void default_reciprocal_i8(MwLLVec* a, MwLLVec* out) {
out->un.i8.a = powf(a->un.i8.a, -1);
out->un.i8.b = powf(a->un.i8.b, -1);
out->un.i8.c = powf(a->un.i8.c, -1);
out->un.i8.d = powf(a->un.i8.d, -1);
out->un.i8.e = powf(a->un.i8.e, -1);
out->un.i8.f = powf(a->un.i8.f, -1);
out->un.i8.g = powf(a->un.i8.g, -1);
out->un.i8.h = powf(a->un.i8.h, -1);
out->un.i8.a = nbsd_pow(a->un.i8.a, -1);
out->un.i8.b = nbsd_pow(a->un.i8.b, -1);
out->un.i8.c = nbsd_pow(a->un.i8.c, -1);
out->un.i8.d = nbsd_pow(a->un.i8.d, -1);
out->un.i8.e = nbsd_pow(a->un.i8.e, -1);
out->un.i8.f = nbsd_pow(a->un.i8.f, -1);
out->un.i8.g = nbsd_pow(a->un.i8.g, -1);
out->un.i8.h = nbsd_pow(a->un.i8.h, -1);
};
static void default_squareRoot_i8(MwLLVec* a, MwLLVec* out) {
out->un.i8.a = sqrt(a->un.i8.a);
@@ -321,10 +321,10 @@ static void default_multiply_i16(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.i16.d = a->un.i16.d * b->un.i16.d;
}
static void default_reciprocal_i16(MwLLVec* a, MwLLVec* out) {
out->un.i16.a = powf(a->un.i16.a, -1);
out->un.i16.b = powf(a->un.i16.b, -1);
out->un.i16.c = powf(a->un.i16.c, -1);
out->un.i16.d = powf(a->un.i16.d, -1);
out->un.i16.a = nbsd_pow(a->un.i16.a, -1);
out->un.i16.b = nbsd_pow(a->un.i16.b, -1);
out->un.i16.c = nbsd_pow(a->un.i16.c, -1);
out->un.i16.d = nbsd_pow(a->un.i16.d, -1);
};
static void default_squareRoot_i16(MwLLVec* a, MwLLVec* out) {
out->un.i16.a = sqrt(a->un.i16.a);
@@ -370,8 +370,8 @@ static void default_multiply_i32(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.i32.b = a->un.i32.b * b->un.i32.b;
}
static void default_reciprocal_i32(MwLLVec* a, MwLLVec* out) {
out->un.i32.a = powf(a->un.i32.a, -1);
out->un.i32.b = powf(a->un.i32.b, -1);
out->un.i32.a = nbsd_pow(a->un.i32.a, -1);
out->un.i32.b = nbsd_pow(a->un.i32.b, -1);
};
static void default_squareRoot_i32(MwLLVec* a, MwLLVec* out) {
out->un.i32.a = sqrt(a->un.i32.a);

54
src/math/math.c
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@@ -3,7 +3,7 @@
#include "math_internal.h"
MwLLVec _MwLLVecCreateGeneric(MwLLVecType ty, ...) {
MwLLVec _MwLLVecCreateGeneric(int ty, ...) {
MwLLVecUnion un;
MwLLVec vec;
va_list va;
@@ -59,16 +59,16 @@ static MwBool hasMMX(void) {
}
static MwLLMathVTable** mwLLMultiTable;
static MwLLMathVTable* multiTableSetupAndGet(MwLLVecType ty);
static MwLLMathVTable* multiTableGet(MwLLVecType ty);
static MwLLMathVTable* multiTableSetupAndGet(int ty);
static MwLLMathVTable* multiTableGet(int ty);
static MwLLMathVTable* (*mwLLmathFunc)(MwLLVecType ty) = multiTableSetupAndGet;
static MwLLMathVTable* (*mwLLmathFunc)(int ty) = multiTableSetupAndGet;
static MwLLMathVTable* getMultiTable(MwLLVecType ty) {
static MwLLMathVTable* getMultiTable(int ty) {
return mwLLmathFunc(ty);
}
static MwLLMathVTable* multiTableSetupAndGet(MwLLVecType ty) {
static MwLLMathVTable* multiTableSetupAndGet(int ty) {
mwLLMultiTable = default_multi_table();
#if defined(__i386__) || defined(__x86_64__)
@@ -81,50 +81,50 @@ static MwLLMathVTable* multiTableSetupAndGet(MwLLVecType ty) {
return mwLLMultiTable[ty];
}
static MwLLMathVTable* multiTableGet(MwLLVecType ty) {
static MwLLMathVTable* multiTableGet(int ty) {
return mwLLMultiTable[ty];
}
void MwLLMathAdd(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->Add(a, b, out);
};
getMultiTable(a->ty)->Add(a, b, out);
}
void MwLLMathSub(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->Sub(a, b, out);
};
getMultiTable(a->ty)->Sub(a, b, out);
}
void MwLLMathMultiply(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->Multiply(a, b, out);
};
getMultiTable(a->ty)->Multiply(a, b, out);
}
void MwLLMathReciprocal(MwLLVec* a, MwLLVec* out) {
assert(a->ty == out->ty);
return getMultiTable(a->ty)->Reciprocal(a, out);
};
getMultiTable(a->ty)->Reciprocal(a, out);
}
void MwLLMathSquareRoot(MwLLVec* a, MwLLVec* out) {
assert(a->ty == out->ty);
return getMultiTable(a->ty)->SquareRoot(a, out);
};
getMultiTable(a->ty)->SquareRoot(a, out);
}
void MwLLMathShiftRight(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->ShiftRight(a, b, out);
};
getMultiTable(a->ty)->ShiftRight(a, b, out);
}
void MwLLMathShiftLeft(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->ShiftLeft(a, b, out);
};
getMultiTable(a->ty)->ShiftLeft(a, b, out);
}
void MwLLMathEqual(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->Equal(a, b, out);
};
getMultiTable(a->ty)->Equal(a, b, out);
}
void MwLLMathGreaterThen(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
assert(a->ty == b->ty && a->ty == out->ty && b->ty == out->ty);
return getMultiTable(a->ty)->GreaterThen(a, b, out);
};
getMultiTable(a->ty)->GreaterThen(a, b, out);
}
void MwLLMathAnd(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.all = a->un.all & b->un.all;
};
}
void MwLLMathOr(MwLLVec* a, MwLLVec* b, MwLLVec* out) {
out->un.all = a->un.all | b->un.all;
};
}

3
src/math/math_internal.h
View File

@@ -5,6 +5,8 @@
#include <Mw/LowLevelMath.h>
#include "nbsd_math.h"
struct _MwLLMathVTable {
void (*Add)(MwLLVec* a, MwLLVec* b, MwLLVec* out);
void (*Multiply)(MwLLVec* a, MwLLVec* b, MwLLVec* out);
@@ -24,5 +26,6 @@ typedef struct _MwLLMathVTable MwLLMathVTable;
MwLLMathVTable** default_multi_table(void);
void mmx_apply(MwLLMathVTable**);
double nbsd_pow(double a, double b);
#endif

2
src/math/mmx.c
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@@ -1,4 +1,5 @@
/* $Id$ */
#ifdef GUARD
#include <Mw/LowLevelMath.h>
#include "math_internal.h"
@@ -101,3 +102,4 @@ void mmx_apply(MwLLMathVTable** t) {
t[_MwLLVecTypeI32x2]->ShiftLeft = mmx_shiftLeft_u32;
t[_MwLLVecTypeI32x2]->ShiftRight = mmx_shiftRight_u32;
}
#endif

1
src/math/mmx_guard.c
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@@ -1,5 +1,6 @@
/* $Id$ */
#if defined(__WATCOMC__) || defined(__i386__) || defined(__amd64__)
#define GUARD
#include "mmx.c"
#else
void mmx_apply(MwLLMathVTable** t) {

87
src/math/nbsd_math.h Normal file
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@@ -0,0 +1,87 @@
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/*
* from: @(#)fdlibm.h 5.1 93/09/24
* $NetBSD: math_private.h,v 1.34 2024/07/17 12:00:13 riastradh Exp $
*/
/* $Id$ */
#ifndef __NBSD_MATH__
#define __NBSD_MATH__
#include <Mw/BaseTypes.h>
typedef union _ieee_double_shape_type
{
double value;
struct
{
MwU32 lsw;
MwU32 msw;
} parts;
struct
{
MwU64 w;
} xparts;
} ieee_double_shape_type;
/* Get two 32-bit integers from a double. */
#define EXTRACT_WORDS(ix0,ix1,d) \
do { \
ieee_double_shape_type ew_u; \
ew_u.value = (d); \
(ix0) = ew_u.parts.msw; \
(ix1) = ew_u.parts.lsw; \
} while (0)
/* Get the more significant 32-bit integer from a double. */
#define GET_HIGH_WORD(i,d) \
do { \
ieee_double_shape_type gh_u; \
gh_u.value = (d); \
(i) = gh_u.parts.msw; \
} while (0)
/* Get the less significant 32-bit integer from a double. */
#define GET_LOW_WORD(i,d) \
do { \
ieee_double_shape_type gl_u; \
gl_u.value = (d); \
(i) = gl_u.parts.lsw; \
} while (0)
/* Set the more significant 32 bits of a double from an integer. */
#define SET_HIGH_WORD(d,v) \
do { \
ieee_double_shape_type sh_u; \
sh_u.value = (d); \
sh_u.parts.msw = (v); \
(d) = sh_u.value; \
} while (0)
/* Set the less significant 32 bits of a double from an integer. */
#define SET_LOW_WORD(d,v) \
do { \
ieee_double_shape_type sl_u; \
sl_u.value = (d); \
sl_u.parts.lsw = (v); \
(d) = sl_u.value; \
} while (0)
#endif

303
src/math/nbsd_pow.c Normal file
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@@ -0,0 +1,303 @@
/* @(#)e_pow.c 1.5 04/04/22 SMI */
/*
* ====================================================
* Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
*
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#include <Mw/BaseTypes.h>
#include "math_internal.h"
/* __ieee754_pow(x,y) return x**y
*
* n
* Method: Let x = 2 * (1+f)
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
* 2. Perform y*log2(x) = n+y' by simulating multi-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
* 3. (anything) ** NAN is NAN except 1 ** NAN = 1
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
* 9. +-1 ** +-INF is 1
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
* 13. -0 ** (-anything except 0, NAN, odd integer) is +INF
* 14. -0 ** (odd integer) = -( +0 ** (odd integer) )
* 15. +INF ** (+anything except 0,NAN) is +INF
* 16. +INF ** (-anything except 0,NAN) is +0
* 17. -INF ** (anything) = -0 ** (-anything)
* 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
* 19. (-anything except 0 and inf) ** (non-integer) is NAN
*
* Accuracy:
* pow(x,y) returns x**y nearly rounded. In particular
* pow(integer,integer)
* always returns the correct integer provided it is
* representable.
*
* Constants :
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
static const double
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
zero = 0.0,
one = 1.0,
two = 2.0,
two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */
hugev = 1.0e300,
tinyv = 1.0e-300,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/
double
nbsd_pow(double x, double y)
{
double z,ax,z_h,z_l,p_h,p_l;
double yy1,t1,t2,r,s,t,u,v,w;
MwI32 i,j,k,yisint,n;
MwI32 hx,hy,ix,iy;
MwU32 lx,ly;
EXTRACT_WORDS(hx,lx,x);
EXTRACT_WORDS(hy,ly,y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if((iy|ly)==0) return one;
/* x==1: 1**y = 1, even if y is NaN */
if (hx==0x3ff00000 && lx == 0) return one;
/* y!=zero: result is NaN if either arg is NaN */
if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
return (x+0.0)+(y+0.0);
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if(hx<0) {
if(iy>=0x43400000) yisint = 2; /* even integer y */
else if(iy>=0x3ff00000) {
k = (iy>>20)-0x3ff; /* exponent */
if(k>20) {
j = ly>>(52-k);
if((uint32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
} else if(ly==0) {
j = iy>>(20-k);
if((j<<(20-k))==iy) yisint = 2-(j&1);
}
}
}
/* special value of y */
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
return one; /* (-1)**+-inf is 1 */
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3ff00000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3fe00000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return sqrt(x);
}
}
ax = fabs(x);
/* special value of x */
if(lx==0) {
if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3ff00000)|yisint)==0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if(yisint==1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
}
/* CYGNUS LOCAL + fdlibm-5.3 fix: This used to be
n = (hx>>31)+1;
but ANSI C says a right shift of a signed negative quantity is
implementation defined. */
n = ((MwU32)hx>>31)-1;
/* (x<0)**(non-int) is NaN */
if((n|yisint)==0) return (x-x)/(x-x);
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */
/* |y| is hugev */
if(iy>0x41e00000) { /* if |y| > 2**31 */
if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */
if(ix<=0x3fefffff) return (hy<0)? hugev*hugev:tinyv*tinyv;
if(ix>=0x3ff00000) return (hy>0)? hugev*hugev:tinyv*tinyv;
}
/* over/underflow if x is not close to one */
if(ix<0x3fefffff) return (hy<0)? s*hugev*hugev:s*tinyv*tinyv;
if(ix>0x3ff00000) return (hy>0)? s*hugev*hugev:s*tinyv*tinyv;
/* now |1-x| is tinyv <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax-one; /* t has 20 trailing zeros */
w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
u = ivln2_h*t; /* ivln2_h has 21 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
SET_LOW_WORD(t1,0);
t2 = v-(t1-u);
} else {
double ss,s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x00100000)
{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
n += ((ix)>>20)-0x3ff;
j = ix&0x000fffff;
/* determine interval */
ix = j|0x3ff00000; /* normalize ix */
if(j<=0x3988E) k=0; /* |x|<sqrt(3/2) */
else if(j<0xBB67A) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00100000;}
SET_HIGH_WORD(ax,ix);
/* compute ss = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax-bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = one/(ax+bp[k]);
ss = u*v;
s_h = ss;
SET_LOW_WORD(s_h,0);
/* t_h=ax+bp[k] High */
t_h = zero;
SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = ss*ss;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+ss);
s2 = s_h*s_h;
t_h = 3.0+s2+r;
SET_LOW_WORD(t_h,0);
t_l = r-((t_h-3.0)-s2);
/* u+v = ss*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*ss;
/* 2/(3log2)*(ss+...) */
p_h = u+v;
SET_LOW_WORD(p_h,0);
p_l = v-(p_h-u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h+p_l*cp+dp_l[k];
/* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (double)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
SET_LOW_WORD(t1,0);
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
/* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */
yy1 = y;
SET_LOW_WORD(yy1,0);
p_l = (y-yy1)*t1+y*t2;
p_h = yy1*t1;
z = p_l+p_h;
EXTRACT_WORDS(j,i,z);
if (j>=0x40900000) { /* z >= 1024 */
if(((j-0x40900000)|i)!=0) /* if z > 1024 */
return s*hugev*hugev; /* overflow */
else {
if(p_l+ovt>z-p_h) return s*hugev*hugev; /* overflow */
}
} else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */
if(((j-0xc090cc00)|i)!=0) /* z < -1075 */
return s*tinyv*tinyv; /* underflow */
else {
if(p_l<=z-p_h) return s*tinyv*tinyv; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
k = (i>>20)-0x3ff;
n = 0;
if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00100000>>(k+1));
k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */
t = zero;
SET_HIGH_WORD(t,n&~(0x000fffff>>k));
n = ((n&0x000fffff)|0x00100000)>>(20-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
SET_LOW_WORD(t,0);
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2+t*lg2_l;
z = u+v;
w = v-(z-u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-two)-(w+z*w);
z = one-(r-z);
GET_HIGH_WORD(j,z);
j += (n<<20);
if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */
else SET_HIGH_WORD(z,j);
return s*z;
}