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libm: add trunc+log

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This commit is contained in:
Mark Poliakov 2024-11-01 19:07:53 +02:00
parent 3e605b3b11
commit a7f727b58e
6 changed files with 325 additions and 10 deletions
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23
lib/runtime/build.rs
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@ -33,19 +33,22 @@ fn build_libm() {
.flag("-ffreestanding")
.flag("-nostdlib");
add_file(&mut build, "libm/s_truncf.c");
add_file(&mut build, "libm/s_ceilf.c");
add_file(&mut build, "libm/s_floorf.c");
add_file(&mut build, "libm/s_fabsf.c");
add_file(&mut build, "libm/s_scalbnf.c");
add_file(&mut build, "libm/s_copysignf.c");
add_file(&mut build, "libm/e_fmodf.c");
add_file(&mut build, "libm/e_hypotf.c");
add_file(&mut build, "libm/e_log.c");
add_file(&mut build, "libm/e_powf.c");
add_file(&mut build, "libm/e_sqrtf.c");
add_file(&mut build, "libm/e_hypotf.c");
add_file(&mut build, "libm/e_fmodf.c");
add_file(&mut build, "libm/w_powf.c");
add_file(&mut build, "libm/w_hypotf.c");
add_file(&mut build, "libm/s_ceilf.c");
add_file(&mut build, "libm/s_copysignf.c");
add_file(&mut build, "libm/s_fabsf.c");
add_file(&mut build, "libm/s_floorf.c");
add_file(&mut build, "libm/s_scalbnf.c");
add_file(&mut build, "libm/s_trunc.c");
add_file(&mut build, "libm/s_truncf.c");
add_file(&mut build, "libm/w_fmodf.c");
add_file(&mut build, "libm/w_hypotf.c");
add_file(&mut build, "libm/w_log.c");
add_file(&mut build, "libm/w_powf.c");
build.compile("m");
}

135
lib/runtime/libm/e_log.c Normal file
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@ -0,0 +1,135 @@
/* @(#)e_log.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#include <stdint.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $");
#endif
/* __ieee754_log(x)
* Return the logrithm of x
*
* Method :
* 1. Argument Reduction: find k and f such that
* x = 2^k * (1+f),
* where sqrt(2)/2 < 1+f < sqrt(2) .
*
* 2. Approximation of log(1+f).
* Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
* = 2s + 2/3 s**3 + 2/5 s**5 + .....,
* = 2s + s*R
* We use a special Reme algorithm on [0,0.1716] to generate
* a polynomial of degree 14 to approximate R The maximum error
* of this polynomial approximation is bounded by 2**-58.45. In
* other words,
* 2 4 6 8 10 12 14
* R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s
* (the values of Lg1 to Lg7 are listed in the program)
* and
* | 2 14 | -58.45
* | Lg1*s +...+Lg7*s - R(z) | <= 2
* | |
* Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
* In order to guarantee error in log below 1ulp, we compute log
* by
* log(1+f) = f - s*(f - R) (if f is not too large)
* log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
*
* 3. Finally, log(x) = k*ln2 + log(1+f).
* = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
* Here ln2 is split into two floating point number:
* ln2_hi + ln2_lo,
* where n*ln2_hi is always exact for |n| < 2000.
*
* Special cases:
* log(x) is NaN with signal if x < 0 (including -INF) ;
* log(+INF) is +INF; log(0) is -INF with signal;
* log(NaN) is that NaN with no signal.
*
* Accuracy:
* according to an error analysis, the error is always less than
* 1 ulp (unit in the last place).
*
* 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.
*/
#include "private.h"
static const double
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static const double zero = 0.0;
double
__ieee754_log(double x)
{
double hfsq,f,s,z,R,w,t1,t2,dk;
int32_t k,hx,i,j;
uint32_t lx;
EXTRACT_WORDS(hx,lx,x);
k=0;
if (hx < 0x00100000) { /* x < 2**-1022 */
if (((hx&0x7fffffff)|lx)==0)
return -two54/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 54; x *= two54; /* subnormal number, scale up x */
GET_HIGH_WORD(hx,x);
}
if (hx >= 0x7ff00000) return x+x;
k += (hx>>20)-1023;
hx &= 0x000fffff;
i = (hx+0x95f64)&0x100000;
SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */
k += (i>>20);
f = x-1.0;
if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero; else {dk=(double)k;
return dk*ln2_hi+dk*ln2_lo;}
}
R = f*f*(0.5-0.33333333333333333*f);
if(k==0) return f-R; else {dk=(double)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/(2.0+f);
dk = (double)k;
z = s*s;
i = hx-0x6147a;
w = z*z;
j = 0x6b851-hx;
t1= w*(Lg2+w*(Lg4+w*Lg6));
t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
i |= j;
R = t2+t1;
if(i>0) {
hfsq=0.5*f*f;
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
} else {
if(k==0) return f-s*(f-R); else
return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
}
}

0
lib/runtime/libm/log.c Normal file
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70
lib/runtime/libm/private.h
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@ -6,6 +6,74 @@ typedef union
uint32_t word;
} ieee_float_shape_type;
typedef union
{
double value;
struct
{
uint32_t lsw;
uint32_t msw;
} parts;
} ieee_double_shape_type;
/* Get two 32 bit ints 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 (/*CONSTCOND*/0)
/* Get the more significant 32 bit int 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 (/*CONSTCOND*/0)
/* Get the less significant 32 bit int 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 (/*CONSTCOND*/0)
/* Set a double from two 32 bit ints. */
#define INSERT_WORDS(d,ix0,ix1) \
do { \
ieee_double_shape_type iw_u; \
iw_u.parts.msw = (ix0); \
iw_u.parts.lsw = (ix1); \
(d) = iw_u.value; \
} while (/*CONSTCOND*/0)
/* Set the more significant 32 bits of a double from an int. */
#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 (/*CONSTCOND*/0)
/* Set the less significant 32 bits of a double from an int. */
#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 (/*CONSTCOND*/0)
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(i,d) \
@ -32,3 +100,5 @@ float __ieee754_fmodf(float x, float y);
float scalbnf(float x, int n);
float copysignf(float x, float y);
float fabsf(float x);
double __ieee754_log(double x);

65
lib/runtime/libm/s_trunc.c Normal file
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@ -0,0 +1,65 @@
/* @(#)s_floor.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#include <stdint.h>
#if 0
__FBSDID("$FreeBSD: src/lib/msun/src/s_trunc.c,v 1.1 2004/06/20 09:25:43 das Exp $");
#endif
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: s_trunc.c,v 1.3 2008/04/25 22:21:53 christos Exp $");
#endif
/*
* trunc(x)
* Return x rounded toward 0 to integral value
* Method:
* Bit twiddling.
* Exception:
* Inexact flag raised if x not equal to trunc(x).
*/
#include "private.h"
static const double huge = 1.0e300;
double
trunc(double x)
{
int32_t i0,i1,jj0;
uint32_t i;
EXTRACT_WORDS(i0,i1,x);
jj0 = ((i0>>20)&0x7ff)-0x3ff;
if(jj0<20) {
if(jj0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* |x|<1, so return 0*sign(x) */
i0 &= 0x80000000U;
i1 = 0;
}
} else {
i = (0x000fffff)>>jj0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
i0 &= (~i); i1=0;
}
}
} else if (jj0>51) {
if(jj0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((uint32_t)(0xffffffff))>>(jj0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) /* raise inexact flag */
i1 &= (~i);
}
INSERT_WORDS(x,i0,i1);
return x;
}

42
lib/runtime/libm/w_log.c Normal file
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@ -0,0 +1,42 @@
/* @(#)w_log.c 5.1 93/09/24 */
/*
* ====================================================
* 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.
* ====================================================
*/
#include <stdint.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: w_log.c,v 1.10 2007/08/20 16:01:40 drochner Exp $");
#endif
/*
* wrapper log(x)
*/
#include "private.h"
#ifdef __weak_alias
__weak_alias(log, _log)
#endif
double
log(double x) /* wrapper log */
{
// #ifdef _IEEE_LIBM
return __ieee754_log(x);
// #else
// double z;
// z = __ieee754_log(x);
// if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z;
// if(x==0.0)
// return __kernel_standard(x,x,16); /* log(0) */
// else
// return __kernel_standard(x,x,17); /* log(x<0) */
// #endif
}