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- Implemented fmin()/fminf(), fmax()/fmaxf(), fdim()/fdimf() for C99.

Browse Source 
- Ported acosf(), asinf(), atan2f(), atanf(), ceilf(), expf(), floorf(),
  fmodf(), frexpf(), ldexpf(), log10f(), logbf(), logf(), modff(), powf(), sqrtf(),
  scalbn() and scalbnf() for C99.

- Ported cbrt(), cbrtf(), erf(), erff(), erfc(), erfcf(), expm1(),
  expm1f(), ilogb(), ilogbf(), log1p() and log1pf() for C99.


git-svn-id: file:///Users/olsen/Code/migration-svn-zu-git/logical-line-staging/clib2/trunk@14963 87f5fb63-7c3d-0410-a384-fd976d0f7a62
This commit is contained in:
Olaf Barthel
2005-05-29 14:45:33 +00:00
parent 49e98713d4
commit 3c220c3939
36 changed files with 2501 additions and 161 deletions
Download Patch File Download Diff File Expand all files Collapse all files

46
library/GNUmakefile.68k
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@@ -1,5 +1,5 @@
#
# $Id: GNUmakefile.68k,v 1.55 2005-05-14 10:52:31 obarthel Exp $
# $Id: GNUmakefile.68k,v 1.56 2005-05-29 14:45:28 obarthel Exp $
#
# :ts=8
#
@@ -520,45 +520,75 @@ MATH_LIB = \
complex_crealf.o \
complex_creall.o \
math_acos.o \
math_acosf.o \
math_asin.o \
math_asinf.o \
math_atan.o \
math_atan2.o \
math_atan2f.o \
math_atanf.o \
math_cbrt.o \
math_cbrtf.o \
math_ceil.o \
math_cos.o \
math_cosh.o \
math_ceilf.o \
math_copysign.o \
math_copysignf.o \
math_cos.o \
math_cosh.o \
math_erf.o \
math_erfc.o \
math_erfcf.o \
math_erff.o \
math_exp.o \
math_expf.o \
math_expm1.o \
math_expm1f.o \
math_fabs.o \
math_fabsf.o \
math_floor.o \
math_floorf.o \
math_fmod.o \
math_fmodf.o \
math_fpclassify.o \
math_inf.o \
math_inff.o \
math_isfinite.o \
math_isunordered.o \
math_signbit.o \
math_frexp.o \
math_frexpf.o \
math_huge_val.o \
math_huge_valf.o \
math_hypot.o \
math_ilogb.o \
math_ilogbf.o \
math_inf.o \
math_inff.o \
math_init_exit.o \
math_isfinite.o \
math_isunordered.o \
math_ldexp.o \
math_ldexpf.o \
math_log.o \
math_log10.o \
math_log10f.o \
math_log1p.o \
math_log1pf.o \
math_logb.o \
math_logbf.o \
math_logf.o \
math_modf.o \
math_modff.o \
math_nan.o \
math_nanf.o \
math_nextafter.o \
math_nextafterf.o \
math_pow.o \
math_powf.o \
math_rint.o \
math_rintf.o \
math_scalbn.o \
math_scalbnf.o \
math_signbit.o \
math_sin.o \
math_sinh.o \
math_sqrt.o \
math_sqrtf.o \
math_tan.o \
math_tanh.o \
stdio_asprintf.o \

58
library/GNUmakefile.os4
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@@ -1,5 +1,5 @@
#
# $Id: GNUmakefile.os4,v 1.59 2005-05-14 10:52:31 obarthel Exp $
# $Id: GNUmakefile.os4,v 1.60 2005-05-29 14:45:29 obarthel Exp $
#
# :ts=8
#
@@ -520,53 +520,83 @@ MATH_LIB = \
complex_crealf.o \
complex_creall.o \
math_acos.o \
math_acosf.o \
math_asin.o \
math_asinf.o \
math_atan.o \
math_atan2.o \
math_atan2f.o \
math_atanf.o \
math_cbrt.o \
math_cbrtf.o \
math_ceil.o \
math_cos.o \
math_cosh.o \
math_ceilf.o \
math_copysign.o \
math_copysignf.o \
math_cos.o \
math_cosh.o \
math_erf.o \
math_erfc.o \
math_erfcf.o \
math_erff.o \
math_exp.o \
math_expf.o \
math_expm1.o \
math_expm1f.o \
math_fabs.o \
math_fabsf.o \
math_floor.o \
math_floorf.o \
math_fmod.o \
math_fmodf.o \
math_fpclassify.o \
math_inf.o \
math_inff.o \
math_isfinite.o \
math_isunordered.o \
math_signbit.o \
math_frexp.o \
math_frexpf.o \
math_huge_val.o \
math_huge_valf.o \
math_hypot.o \
math_ilogb.o \
math_ilogbf.o \
math_inf.o \
math_inff.o \
math_init_exit.o \
math_isfinite.o \
math_isunordered.o \
math_kernel_cos.o \
math_kernel_expm1.o \
math_kernel_rem_pio2.o \
math_kernel_scalbn.o \
math_kernel_sin.o \
math_kernel_tan.o \
math_ldexp.o \
math_ldexpf.o \
math_log.o \
math_log10.o \
math_log10f.o \
math_log1p.o \
math_log1pf.o \
math_logb.o \
math_logbf.o \
math_logf.o \
math_modf.o \
math_modff.o \
math_nan.o \
math_nanf.o \
math_nextafter.o \
math_nextafterf.o \
math_pow.o \
math_powf.o \
math_rint.o \
math_rintf.o \
math_scalbn.o \
math_scalbnf.o \
math_signbit.o \
math_sin.o \
math_sinh.o \
math_sqrt.o \
math_sqrtf.o \
math_tan.o \
math_tanh.o \
math_kernel_expm1.o \
math_kernel_scalbn.o \
math_kernel_tan.o \
math_kernel_cos.o \
math_kernel_rem_pio2.o \
math_kernel_sin.o \
stdio_asprintf.o \
stdio_flush.o \
stdio_flush_all_files.o \

44
library/TODO
View File

@@ -1,51 +1,43 @@
C99 math functions:
("float"-versions of existing "double" functions)
acosf
asinf
atan2f
atanf
ceilf
cosf
expf
floorf
fmodf
frexpf
hypotf
ldexpf
log10f
logbf
logf
modff
powf
sinf
sqrtf
tanf
(functions generally missing, plus their "float" counterparts)
(functions generally missing, including their "float" counterparts)
acosh
acoshf
asinh
cbrt
erfc
asinhf
exp2
expm1
fdim
exp2f
fma
fmax
fmin
ilogb
fmaf
lgamma
log1p
lgammaf
log2
log2f
lrint
lrintf
lround
lroundf
nearbyint
nearbyintf
nexttoward
nexttowardf
remainder
remainderf
remquo
remquof
round
scalbn
roundf
sinh
sinhf
tanh
tanhf
tgamma
tgammaf
trunc
truncf

10
library/changes
View File

@@ -61,7 +61,15 @@
tanhf(), tgamma(), tgammaf(), trunc() and truncf(), to be filled in
later...
- Implemented fmin()/fminf(), fmax()/fmaxf(), fdim()/fdimf() (C99).
- Implemented fmin()/fminf(), fmax()/fmaxf(), fdim()/fdimf() for C99.
- Ported acosf(), asinf(), atan2f(), atanf(), ceilf(), expf(), floorf(),
fmodf(), frexpf(), ldexpf(), log10f(), logbf(), logf(), modff(), powf(), sqrtf(),
scalbn() and scalbnf() for C99.
- Ported cbrt(), cbrtf(), erf(), erff(), erfc(), erfcf(), expm1(),
expm1f(), ilogb(), ilogbf(), log1p() and log1pf() for C99.
c.lib 1.192 (12.5.2005)

55
library/include/math.h
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@@ -1,5 +1,5 @@
/*
* $Id: math.h,v 1.12 2005-05-29 12:41:04 obarthel Exp $
* $Id: math.h,v 1.13 2005-05-29 14:45:33 obarthel Exp $
*
* :ts=4
*
@@ -224,7 +224,25 @@ extern int __isunordered_double(double x,double y);
/****************************************************************************/
extern float acosf(float x);
extern float asinf(float x);
extern float atanf(float x);
extern float atan2f(float y, float x);
extern float ceilf(float x);
extern float expf(float x);
extern float fabsf(float x);
extern float floorf(float x);
extern float fmodf(float x, float y);
extern float frexpf(float x, int *eptr);
extern float ldexp(float x,int exp);
extern float logf(float x);
extern float log10f(float x);
extern float logbf(float x);
extern float modff(float x, float *iptr);
extern float powf(float x, float y);
extern float sqrtf(float x);
/****************************************************************************/
@@ -258,6 +276,41 @@ extern double fmax(double x,double y);
/****************************************************************************/
extern float scalbnf (float x, int n);
extern double scalbn (double x, int n);
/****************************************************************************/
extern float cbrtf(float x);
extern double cbrt(double x);
/****************************************************************************/
extern float erff(float x);
extern double erf(double x);
/****************************************************************************/
extern float erfcf(float x);
extern double erfc(double x);
/****************************************************************************/
extern float expm1f(float x);
extern double expm1(double x);
/****************************************************************************/
extern int ilogbf(float x);
extern int ilogb(double x);
/****************************************************************************/
extern float log1pf(float x);
extern double log1p(double x);
/****************************************************************************/
#define FLT_EVAL_METHOD 0
/****************************************************************************/

71
library/math_acosf.c
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@@ -1,5 +1,5 @@
/*
* $Id: math_acosf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_acosf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,64 @@
/****************************************************************************/
static const float
one = 1.0000000000e+00, /* 0x3F800000 */
pi = 3.1415925026e+00, /* 0x40490fda */
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
pS3 = -4.0055535734e-02, /* 0xbd241146 */
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
qS1 = -2.4033949375e+00, /* 0xc019d139 */
qS2 = 2.0209457874e+00, /* 0x4001572d */
qS3 = -6.8828397989e-01, /* 0xbf303361 */
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
float
acosf(float x)
{
/* ZZZ unimplemented */
return(0);
float z,p,q,r,w,s,c,df;
LONG hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) { /* |x|==1 */
if(hx>0) return 0.0; /* acos(1) = 0 */
else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */
} else if(ix>0x3f800000) { /* |x| >= 1 */
return (x-x)/(x-x); /* acos(|x|>1) is NaN */
}
if(ix<0x3f000000) { /* |x| < 0.5 */
if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/
z = x*x;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
return pio2_hi - (x - (pio2_lo-x*r));
} else if (hx<0) { /* x < -0.5 */
z = (one+x)*(float)0.5;
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
s = sqrtf(z);
r = p/q;
w = r*s-pio2_lo;
return pi - (float)2.0*(s+w);
} else { /* x > 0.5 */
LONG idf;
z = (one-x)*(float)0.5;
s = sqrtf(z);
df = s;
GET_FLOAT_WORD(idf,df);
SET_FLOAT_WORD(df,idf&0xfffff000U);
c = (z-df*df)/(s+df);
p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
r = p/q;
w = r*s+c;
return (float)2.0*(df+w);
}
}
/****************************************************************************/

74
library/math_asinf.c
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@@ -1,5 +1,5 @@
/*
* $Id: math_asinf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_asinf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,67 @@
/****************************************************************************/
static const float
one = 1.0000000000e+00, /* 0x3F800000 */
huge = 1.000e+30,
pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */
pio2_lo = 7.5497894159e-08, /* 0x33a22168 */
pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */
/* coefficient for R(x^2) */
pS0 = 1.6666667163e-01, /* 0x3e2aaaab */
pS1 = -3.2556581497e-01, /* 0xbea6b090 */
pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */
pS3 = -4.0055535734e-02, /* 0xbd241146 */
pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */
pS5 = 3.4793309169e-05, /* 0x3811ef08 */
qS1 = -2.4033949375e+00, /* 0xc019d139 */
qS2 = 2.0209457874e+00, /* 0x4001572d */
qS3 = -6.8828397989e-01, /* 0xbf303361 */
qS4 = 7.7038154006e-02; /* 0x3d9dc62e */
float
asinf(float x)
{
/* ZZZ unimplemented */
return(0);
float t=0.0,w,p,q,c,r,s;
LONG hx,ix;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix==0x3f800000) {
/* asin(1)=+-pi/2 with inexact */
return x*pio2_hi+x*pio2_lo;
} else if(ix> 0x3f800000) { /* |x|>= 1 */
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
} else if (ix<0x3f000000) { /* |x|<0.5 */
if(ix<0x32000000) { /* if |x| < 2**-27 */
if(huge+x>one) return x;/* return x with inexact if x!=0*/
} else
t = x*x;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
w = p/q;
return x+x*w;
}
/* 1> |x|>= 0.5 */
w = one-fabsf(x);
t = w*(float)0.5;
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
s = sqrtf(t);
if(ix>=0x3F79999A) { /* if |x| > 0.975 */
w = p/q;
t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo);
} else {
LONG iw;
w = s;
GET_FLOAT_WORD(iw,w);
SET_FLOAT_WORD(w,iw&0xfffff000U);
c = (t-w*w)/(s+w);
r = p/q;
p = (float)2.0*s*r-(pio2_lo-(float)2.0*c);
q = pio4_hi-(float)2.0*w;
t = pio4_hi-(p-q);
}
if(hx>0) return t; else return -t;
}
/****************************************************************************/

96
library/math_atan2f.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_atan2f.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_atan2f.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,87 @@
/****************************************************************************/
static const float
tiny = 1.0e-30,
zero = 0.0,
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
pi = 3.1415925026e+00, /* 0x40490fda */
pi_lo = 1.5099578832e-07; /* 0x34222168 */
float
atan2f(float y,float x)
atan2f(float y, float x)
{
/* ZZZ unimplemented */
return(0);
float z;
LONG k,m,hx,hy,ix,iy;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
GET_FLOAT_WORD(hy,y);
iy = hy&0x7fffffff;
if((ix>0x7f800000)||
(iy>0x7f800000)) /* x or y is NaN */
return x+y;
if(hx==0x3f800000) return atanf(y); /* x=1.0 */
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if(iy==0) {
switch(m) {
case 0:
case 1: return y; /* atan(+-0,+anything)=+-0 */
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7f800000) {
if(iy==0x7f800000) {
switch(m) {
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
}
} else {
switch(m) {
case 0: return zero ; /* atan(+...,+INF) */
case 1: /* atan(-...,+INF) */
{
/* Make sure we return -0, not +0. If we
say "return -zero;", GCC might optimize
that with FLDZ, which we don't want. */
return copysignf(zero, -1);
}
case 2: return pi+tiny ; /* atan(+...,-INF) */
case 3: return -pi-tiny ; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = (iy-ix)>>23;
if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
else z=atanf(fabsf(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
__uint32_t zh;
GET_FLOAT_WORD(zh,z);
SET_FLOAT_WORD(z,zh ^ 0x80000000U);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
/****************************************************************************/

89
library/math_atanf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_atanf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_atanf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,82 @@
/****************************************************************************/
static const float atanhi[] = {
4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */
7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */
9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */
1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */
};
static const float atanlo[] = {
5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */
3.7748947079e-08, /* atan(1.0)lo 0x33222168 */
3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */
7.5497894159e-08, /* atan(inf)lo 0x33a22168 */
};
static const float aT[] = {
3.3333334327e-01, /* 0x3eaaaaaa */
-2.0000000298e-01, /* 0xbe4ccccd */
1.4285714924e-01, /* 0x3e124925 */
-1.1111110449e-01, /* 0xbde38e38 */
9.0908870101e-02, /* 0x3dba2e6e */
-7.6918758452e-02, /* 0xbd9d8795 */
6.6610731184e-02, /* 0x3d886b35 */
-5.8335702866e-02, /* 0xbd6ef16b */
4.9768779427e-02, /* 0x3d4bda59 */
-3.6531571299e-02, /* 0xbd15a221 */
1.6285819933e-02, /* 0x3c8569d7 */
};
static const float
one = 1.0,
huge = 1.0e30;
float
atanf(float x)
{
/* ZZZ unimplemented */
return(0);
float w,s1,s2,z;
LONG ix,hx,id;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x50800000) { /* if |x| >= 2^34 */
if(ix>0x7f800000)
return x+x; /* NaN */
if(hx>0) return atanhi[3]+atanlo[3];
else return -atanhi[3]-atanlo[3];
} if (ix < 0x3ee00000) { /* |x| < 0.4375 */
if (ix < 0x31000000) { /* |x| < 2^-29 */
if(huge+x>one) return x; /* raise inexact */
}
id = -1;
} else {
x = fabsf(x);
if (ix < 0x3f980000) { /* |x| < 1.1875 */
if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */
id = 0; x = ((float)2.0*x-one)/((float)2.0+x);
} else { /* 11/16<=|x|< 19/16 */
id = 1; x = (x-one)/(x+one);
}
} else {
if (ix < 0x401c0000) { /* |x| < 2.4375 */
id = 2; x = (x-(float)1.5)/(one+(float)1.5*x);
} else { /* 2.4375 <= |x| < 2^66 */
id = 3; x = -(float)1.0/x;
}
}}
/* end of argument reduction */
z = x*x;
w = z*z;
/* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
if (id<0) return x - x*(s1+s2);
else {
z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
return (hx<0)? -z:z;
}
}
/****************************************************************************/

68
library/math_cbrt.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_cbrt.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_cbrt.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,64 @@
/****************************************************************************/
static const ULONG
B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */
B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */
static const double
C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */
D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */
E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */
F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */
G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */
double
cbrt(double x)
{
/* ZZZ unimplemented */
return(0);
LONG hx;
double r,s,t=0.0,w;
ULONG sign;
ULONG high,low;
GET_HIGH_WORD(hx,x);
sign=hx&0x80000000U; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */
GET_LOW_WORD(low,x);
if((hx|low)==0)
return(x); /* cbrt(0) is itself */
SET_HIGH_WORD(x,hx); /* x <- |x| */
/* rough cbrt to 5 bits */
if(hx<0x00100000) /* subnormal number */
{SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */
t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2);
}
else
SET_HIGH_WORD(t,hx/3+B1);
/* new cbrt to 23 bits, may be implemented in single precision */
r=t*t/x;
s=C+r*t;
t*=G+F/(s+E+D/s);
/* chopped to 20 bits and make it larger than cbrt(x) */
GET_HIGH_WORD(high,t);
INSERT_WORDS(t,high+0x00000001,0);
/* one step newton iteration to 53 bits with error less than 0.667 ulps */
s=t*t; /* t*t is exact */
r=x/s;
w=t+t;
r=(r-t)/(w+r); /* r-s is exact */
t=t+t*r;
/* retore the sign bit */
GET_HIGH_WORD(high,t);
SET_HIGH_WORD(t,high|sign);
return(t);
}
/****************************************************************************/

57
library/math_cbrtf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_cbrtf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_cbrtf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,50 @@
/****************************************************************************/
static const ULONG
B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */
B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */
static const float
C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */
D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */
E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */
F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */
G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */
float
cbrtf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG hx;
float r,s,t;
ULONG sign;
ULONG high;
GET_FLOAT_WORD(hx,x);
sign=hx&0x80000000U; /* sign= sign(x) */
hx ^=sign;
if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */
if(hx==0)
return(x); /* cbrt(0) is itself */
SET_FLOAT_WORD(x,hx); /* x <- |x| */
/* rough cbrt to 5 bits */
if(hx<0x00800000) /* subnormal number */
{SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */
t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2);
}
else
SET_FLOAT_WORD(t,hx/3+B1);
/* new cbrt to 23 bits */
r=t*t/x;
s=C+r*t;
t*=G+F/(s+E+D/s);
/* retore the sign bit */
GET_FLOAT_WORD(high,t);
SET_FLOAT_WORD(t,high|sign);
return(t);
}
/****************************************************************************/

42
library/math_ceilf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_ceilf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_ceilf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,35 @@
/****************************************************************************/
static const float huge = 1.0e30;
float
ceilf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG i0,j_0;
ULONG i;
GET_FLOAT_WORD(i0,x);
j_0 = ((i0>>23)&0xff)-0x7f;
if(j_0<23) {
if(j_0<0) { /* raise inexact if x != 0 */
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
if(i0<0) {i0=0x80000000U;}
else if(i0!=0) { i0=0x3f800000;}
}
} else {
i = (0x007fffff)>>j_0;
if((i0&i)==0) return x; /* x is integral */
if(huge+x>(float)0.0) { /* raise inexact flag */
if(i0>0) i0 += (0x00800000)>>j_0;
i0 &= (~i);
}
}
} else {
if(j_0==0x80) return x+x; /* inf or NaN */
else return x; /* x is integral */
}
SET_FLOAT_WORD(x,i0);
return x;
}
/****************************************************************************/

135
library/math_erf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_erf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_erf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,131 @@
/****************************************************************************/
static const double
tiny = 1e-300,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
double
erf(double x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,ix,i;
double R,S,P,Q,s,y,z,r;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erf(nan)=nan */
i = ((__uint32_t)hx>>31)<<1;
return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3e300000) { /* |x|<2**-28 */
if (ix < 0x00800000)
return 0.125*(8.0*x+efx8*x); /*avoid underflow */
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40180000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
r = exp(-z*z-0.5625)*exp((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
/****************************************************************************/

145
library/math_erfc.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_erfc.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_erfc.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,141 @@
/****************************************************************************/
static const double
tiny = 1e-300,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */
pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */
qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */
qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */
qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */
pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */
pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */
pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */
pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */
qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */
qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */
qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */
qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */
ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */
ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */
ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */
ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */
ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */
sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */
sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */
sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */
sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */
sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */
sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */
rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */
rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */
rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */
rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */
sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */
sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */
sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */
sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */
sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */
sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */
sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */
double
erfc(double x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,ix;
double R,S,P,Q,s,y,z,r;
GET_HIGH_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (double)(((ULONG)hx>>31)<<1)+one/x;
}
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3c700000) /* |x|<2**-56 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3fd00000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */
s = fabs(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x403c0000) { /* |x|<28 */
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
r = exp(-z*z-0.5625)*
exp((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}
/****************************************************************************/

148
library/math_erfcf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_erfcf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_erfcf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,141 @@
/****************************************************************************/
static const float
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
pp2 = -2.8481749818e-02, /* 0xbce9528f */
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
qq4 = 1.3249473704e-04, /* 0x390aee49 */
qq5 = -3.9602282413e-06, /* 0xb684e21a */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
qa4 = 1.2617121637e-01, /* 0x3e013307 */
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
ra2 = -1.0558626175e+01, /* 0xc128f022 */
ra3 = -6.2375331879e+01, /* 0xc2798057 */
ra4 = -1.6239666748e+02, /* 0xc322658c */
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
ra7 = -9.8143291473e+00, /* 0xc11d077e */
sa1 = 1.9651271820e+01, /* 0x419d35ce */
sa2 = 1.3765776062e+02, /* 0x4309a863 */
sa3 = 4.3456588745e+02, /* 0x43d9486f */
sa4 = 6.4538726807e+02, /* 0x442158c9 */
sa5 = 4.2900814819e+02, /* 0x43d6810b */
sa6 = 1.0863500214e+02, /* 0x42d9451f */
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
rb2 = -1.7757955551e+01, /* 0xc18e104b */
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
rb5 = -1.0250950928e+03, /* 0xc480230b */
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
sb3 = 1.5367296143e+03, /* 0x44c01759 */
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
sb5 = 2.5530502930e+03, /* 0x451f90ce */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
float
erfcf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,ix;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erfc(nan)=nan */
/* erfc(+-inf)=0,2 */
return (float)(((ULONG)hx>>31)<<1)+one/x;
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x23800000) /* |x|<2**-56 */
return one-x;
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
if(hx < 0x3e800000) { /* x<1/4 */
return one-(x+x*y);
} else {
r = x*y;
r += (x-half);
return half - r ;
}
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
z = erx+P/Q; return one+z;
}
}
if (ix < 0x41e00000) { /* |x|<28 */
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000U);
r = expf(-z*z-(float)0.5625)*
expf((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}
/****************************************************************************/

139
library/math_erff.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_erff.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_erff.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,132 @@
/****************************************************************************/
static const float
tiny = 1e-30,
half= 5.0000000000e-01, /* 0x3F000000 */
one = 1.0000000000e+00, /* 0x3F800000 */
two = 2.0000000000e+00, /* 0x40000000 */
/* c = (subfloat)0.84506291151 */
erx = 8.4506291151e-01, /* 0x3f58560b */
/*
* Coefficients for approximation to erf on [0,0.84375]
*/
efx = 1.2837916613e-01, /* 0x3e0375d4 */
efx8= 1.0270333290e+00, /* 0x3f8375d4 */
pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
pp1 = -3.2504209876e-01, /* 0xbea66beb */
pp2 = -2.8481749818e-02, /* 0xbce9528f */
pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
qq2 = 6.5022252500e-02, /* 0x3d852a63 */
qq3 = 5.0813062117e-03, /* 0x3ba68116 */
qq4 = 1.3249473704e-04, /* 0x390aee49 */
qq5 = -3.9602282413e-06, /* 0xb684e21a */
/*
* Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
pa1 = 4.1485610604e-01, /* 0x3ed46805 */
pa2 = -3.7220788002e-01, /* 0xbebe9208 */
pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
qa4 = 1.2617121637e-01, /* 0x3e013307 */
qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
/*
* Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.8649440333e-03, /* 0xbc21a093 */
ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
ra2 = -1.0558626175e+01, /* 0xc128f022 */
ra3 = -6.2375331879e+01, /* 0xc2798057 */
ra4 = -1.6239666748e+02, /* 0xc322658c */
ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
ra6 = -8.1287437439e+01, /* 0xc2a2932b */
ra7 = -9.8143291473e+00, /* 0xc11d077e */
sa1 = 1.9651271820e+01, /* 0x419d35ce */
sa2 = 1.3765776062e+02, /* 0x4309a863 */
sa3 = 4.3456588745e+02, /* 0x43d9486f */
sa4 = 6.4538726807e+02, /* 0x442158c9 */
sa5 = 4.2900814819e+02, /* 0x43d6810b */
sa6 = 1.0863500214e+02, /* 0x42d9451f */
sa7 = 6.5702495575e+00, /* 0x40d23f7c */
sa8 = -6.0424413532e-02, /* 0xbd777f97 */
/*
* Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.8649431020e-03, /* 0xbc21a092 */
rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
rb2 = -1.7757955551e+01, /* 0xc18e104b */
rb3 = -1.6063638306e+02, /* 0xc320a2ea */
rb4 = -6.3756646729e+02, /* 0xc41f6441 */
rb5 = -1.0250950928e+03, /* 0xc480230b */
rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
sb1 = 3.0338060379e+01, /* 0x41f2b459 */
sb2 = 3.2579251099e+02, /* 0x43a2e571 */
sb3 = 1.5367296143e+03, /* 0x44c01759 */
sb4 = 3.1998581543e+03, /* 0x4547fdbb */
sb5 = 2.5530502930e+03, /* 0x451f90ce */
sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
sb7 = -2.2440952301e+01; /* 0xc1b38712 */
float
erff(float x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,ix,i;
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
if(ix>=0x7f800000) { /* erf(nan)=nan */
i = ((ULONG)hx>>31)<<1;
return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
if(ix < 0x31800000) { /* |x|<2**-28 */
if (ix < 0x04000000)
/*avoid underflow */
return (float)0.125*((float)8.0*x+efx8*x);
return x + efx*x;
}
z = x*x;
r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
y = r/s;
return x + x*y;
}
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40c00000) { /* inf>|x|>=6 */
if(hx>=0) return one-tiny; else return tiny-one;
}
x = fabsf(x);
s = one/(x*x);
if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
ra5+s*(ra6+s*ra7))))));
S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
sa5+s*(sa6+s*(sa7+s*sa8)))))));
} else { /* |x| >= 1/0.35 */
R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
rb5+s*rb6)))));
S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
sb5+s*(sb6+s*sb7))))));
}
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(z,ix&0xfffff000U);
r = expf(-z*z-(float)0.5625)*expf((z-x)*(z+x)+R/S);
if(hx>=0) return one-r/x; else return r/x-one;
}
/****************************************************************************/

89
library/math_expf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_expf.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_expf.c,v 1.2 2005-05-29 14:45:29 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,82 @@
/****************************************************************************/
static const float
one = 1.0,
halF[2] = {0.5,-0.5,},
huge = 1.0e+30,
twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */
o_threshold= 8.872283911e+01, /* 0x42b17218 */
u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */
ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */
-6.9313812256e-01,}, /* 0xbf317180 */
ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */
-9.0580006145e-06,}, /* 0xb717f7d1 */
invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08; /* 0x3331bb4c */
float
expf(float x)
{
/* ZZZ unimplemented */
return(0);
float y,hi=0.0,lo=0.0,c,t;
LONG k=0,xsb;
ULONG hx;
GET_FLOAT_WORD(hx,x);
xsb = (hx>>31)&1; /* sign bit of x */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out non-finite argument */
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
if(hx == 0x42b17218) { /* if |x| == 88.7228... */
if (xsb == 0)
return FLT_MAX;
}
if(hx>0x7f800000)
return x+x; /* NaN */
if(hx==0x7f800000)
return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
if(x > o_threshold) return huge*huge; /* overflow */
if(x < u_threshold) return twom100*twom100; /* underflow */
}
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
} else {
k = invln2*x+halF[xsb];
t = k;
hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
lo = t*ln2LO[0];
}
x = hi - lo;
}
else if(hx < 0x31800000) { /* when |x|<2**-28 */
if(huge+x>one) return one+x;/* trigger inexact */
}
else k = 0;
/* x is now in primary range */
t = x*x;
c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
if(k==0) return one-((x*c)/(c-(float)2.0)-x);
else y = one-((lo-(x*c)/((float)2.0-c))-hi);
if(k >= -125) {
ULONG hy;
GET_FLOAT_WORD(hy,y);
SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */
return y;
} else {
ULONG hy;
GET_FLOAT_WORD(hy,y);
SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */
return y*twom100;
}
}
/****************************************************************************/

116
library/math_expm1.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_expm1.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_expm1.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,112 @@
/****************************************************************************/
static const double
one = 1.0,
huge = 1.0e+300,
tiny = 1.0e-300,
o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */
ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */
ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */
invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */
/* scaled coefficients related to expm1 */
Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */
Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */
Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */
Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */
Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */
double
expm1(double x)
{
/* ZZZ unimplemented */
return(0);
double y,hi,lo,c=0.0,t,e,hxs,hfx,r1;
LONG k,xsb;
ULONG hx;
GET_HIGH_WORD(hx,x);
xsb = hx&0x80000000U; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */
if(hx >= 0x40862E42) { /* if |x|>=709.78... */
if(hx>=0x7ff00000) {
ULONG low;
GET_LOW_WORD(low,x);
if(((hx&0xfffff)|low)!=0)
return x+x; /* NaN */
else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
}
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */
if(x+tiny<0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?0.5:-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi - lo;
c = (hi-x)-lo;
}
else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = 0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = 3.0-r1*hfx;
e = hxs*((r1-t)/(6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return 0.5*(x-e)-0.5;
if(k==1) {
if(x < -0.25) return -2.0*(e-(x+0.5));
else return one+2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
ULONG high;
y = one-(e-x);
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<20) {
ULONG high;
SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */
y = t-(e-x);
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
} else {
ULONG high;
SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */
y = x-(e+t);
y += one;
GET_HIGH_WORD(high,y);
SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */
}
}
return y;
}
/****************************************************************************/

116
library/math_expm1f.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_expm1f.c,v 1.1 2005-05-29 11:19:00 obarthel Exp $
* $Id: math_expm1f.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,109 @@
/****************************************************************************/
static const float
one = 1.0,
huge = 1.0e+30,
tiny = 1.0e-30,
o_threshold = 8.8721679688e+01,/* 0x42b17180 */
ln2_hi = 6.9313812256e-01,/* 0x3f317180 */
ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */
invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */
/* scaled coefficients related to expm1 */
Q1 = -3.3333335072e-02, /* 0xbd088889 */
Q2 = 1.5873016091e-03, /* 0x3ad00d01 */
Q3 = -7.9365076090e-05, /* 0xb8a670cd */
Q4 = 4.0082177293e-06, /* 0x36867e54 */
Q5 = -2.0109921195e-07; /* 0xb457edbb */
float
expm1f(float x)
{
/* ZZZ unimplemented */
return(0);
float y,hi,lo,c=0.0,t,e,hxs,hfx,r1;
LONG k,xsb;
ULONG hx;
GET_FLOAT_WORD(hx,x);
xsb = hx&0x80000000U; /* sign bit of x */
if(xsb==0) y=x; else y= -x; /* y = |x| */
hx &= 0x7fffffff; /* high word of |x| */
/* filter out huge and non-finite argument */
if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */
if(hx >= 0x42b17218) { /* if |x|>=88.721... */
if(hx>0x7f800000)
return x+x; /* NaN */
if(hx==0x7f800000)
return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */
if(x > o_threshold) return huge*huge; /* overflow */
}
if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */
if(x+tiny<(float)0.0) /* raise inexact */
return tiny-one; /* return -1 */
}
}
/* argument reduction */
if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
if(xsb==0)
{hi = x - ln2_hi; lo = ln2_lo; k = 1;}
else
{hi = x + ln2_hi; lo = -ln2_lo; k = -1;}
} else {
k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
t = k;
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
lo = t*ln2_lo;
}
x = hi - lo;
c = (hi-x)-lo;
}
else if(hx < 0x33000000) { /* when |x|<2**-25, return x */
t = huge+x; /* return x with inexact flags when x!=0 */
return x - (t-(huge+x));
}
else k = 0;
/* x is now in primary range */
hfx = (float)0.5*x;
hxs = x*hfx;
r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5))));
t = (float)3.0-r1*hfx;
e = hxs*((r1-t)/((float)6.0 - x*t));
if(k==0) return x - (x*e-hxs); /* c is 0 */
else {
e = (x*(e-c)-c);
e -= hxs;
if(k== -1) return (float)0.5*(x-e)-(float)0.5;
if(k==1) {
if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5));
else return one+(float)2.0*(x-e);
}
if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */
LONG i;
y = one-(e-x);
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
return y-one;
}
t = one;
if(k<23) {
LONG i;
SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
y = t-(e-x);
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
} else {
LONG i;
SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */
y = x-(e+t);
y += one;
GET_FLOAT_WORD(i,y);
SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */
}
}
return y;
}
/****************************************************************************/

31
library/math_floorf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_floorf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_floorf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -41,11 +41,36 @@
/****************************************************************************/
static const float huge = 1.0e30;
float
floorf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG i0,j_0;
ULONG i;
GET_FLOAT_WORD(i0,x);
j_0 = ((i0>>23)&0xff)-0x7f;
if(j_0<23) {
if(j_0<0) { /* raise inexact if x != 0 */
if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {i0=0;}
else if((i0&0x7fffffff)!=0)
{ i0=0xbf800000U;}
}
} else {
i = (0x007fffff)>>j_0;
if((i0&i)==0) return x; /* x is integral */
if(huge+x>(float)0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00800000)>>j_0;
i0 &= (~i);
}
}
} else {
if(j_0==0x80) return x+x; /* inf or NaN */
else return x; /* x is integral */
}
SET_FLOAT_WORD(x,i0);
return x;
}
/****************************************************************************/

48
library/math_fmodf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_fmodf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_fmodf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,39 @@
/****************************************************************************/
static const float one = 1.0;
float
fmodf(float x,float y)
modff(float x, float *iptr)
{
/* ZZZ unimplemented */
return(0);
LONG i0,j_0;
ULONG i;
GET_FLOAT_WORD(i0,x);
j_0 = ((i0>>23)&0xff)-0x7f; /* exponent of x */
if(j_0<23) { /* integer part in x */
if(j_0<0) { /* |x|<1 */
SET_FLOAT_WORD(*iptr,i0&0x80000000U); /* *iptr = +-0 */
return x;
} else {
i = (0x007fffff)>>j_0;
if((i0&i)==0) { /* x is integral */
ULONG ix;
*iptr = x;
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(x,ix&0x80000000U); /* return +-0 */
return x;
} else {
SET_FLOAT_WORD(*iptr,i0&(~i));
return x - *iptr;
}
}
} else { /* no fraction part */
ULONG ix;
*iptr = x*one;
GET_FLOAT_WORD(ix,x);
SET_FLOAT_WORD(x,ix&0x80000000U); /* return +-0 */
return x;
}
}
/****************************************************************************/

35
library/math_frexpf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_frexpf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_frexpf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,26 @@
/****************************************************************************/
static const float two25 = 3.3554432000e+07; /* 0x4c000000 */
float
frexpf(float value,int * exp)
frexpf(float x, int *eptr)
{
/* ZZZ unimplemented */
return(0);
LONG hx, ix;
GET_FLOAT_WORD(hx,x);
ix = 0x7fffffff&hx;
*eptr = 0;
if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */
if (ix<0x00800000) { /* subnormal */
x *= two25;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
*eptr = -25;
}
*eptr += (ix>>23)-126;
hx = (hx&0x807fffffU)|0x3f000000;
SET_FLOAT_WORD(x,hx);
return x;
}
/****************************************************************************/

32
library/math_ilogb.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_ilogb.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_ilogb.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,26 @@
/****************************************************************************/
double
int
ilogb(double x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,lx,ix;
EXTRACT_WORDS(hx,lx,x);
hx &= 0x7fffffff;
if(hx<0x00100000) {
if((hx|lx)==0)
return - INT_MAX; /* ilogb(0) = 0x80000001 */
else /* subnormal x */
if(hx==0) {
for (ix = -1043; lx>0; lx<<=1) ix -=1;
} else {
for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1;
}
return ix;
}
else if (hx<0x7ff00000) return (hx>>20)-1023;
else return INT_MAX;
}
/****************************************************************************/

31
library/math_ilogbf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_ilogbf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_ilogbf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,22 @@
/****************************************************************************/
float
int
ilogbf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG hx,ix;
GET_FLOAT_WORD(hx,x);
hx &= 0x7fffffff;
if(hx<0x00800000) {
if(hx==0)
return - INT_MAX; /* ilogb(0) = 0x80000001 */
else /* subnormal x */
for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1;
return ix;
}
else if (hx<0x7f800000) return (hx>>23)-127;
else return INT_MAX;
}
/****************************************************************************/

19
library/math_ldexpf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_ldexpf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_ldexpf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -44,8 +44,21 @@
float
ldexpf(float x,int exp)
{
/* ZZZ unimplemented */
return(0);
float result;
if(isinf(x) || fpclassify(x) == FP_ZERO)
{
result = x;
}
else
{
result = scalbnf(x,exp);
if(isinf(result) || (result < FLT_MIN || result > -FLT_MIN))
__set_errno(ERANGE);
}
return(result);
}
/****************************************************************************/

45
library/math_log10f.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_log10f.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_log10f.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,38 @@
/****************************************************************************/
static const float
two25 = 3.3554432000e+07, /* 0x4c000000 */
ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */
log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */
log10_2lo = 7.9034151668e-07; /* 0x355427db */
static const float zero = 0.0;
float
log10f(float x)
{
/* ZZZ unimplemented */
return(0);
float y,z;
LONG i,k,hx;
GET_FLOAT_WORD(hx,x);
k=0;
if (hx < 0x00800000) { /* x < 2**-126 */
if ((hx&0x7fffffff)==0)
return -two25/zero; /* log(+-0)=-inf */
if (hx<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 25; x *= two25; /* subnormal number, scale up x */
GET_FLOAT_WORD(hx,x);
}
if (hx >= 0x7f800000) return x+x;
k += (hx>>23)-127;
i = ((ULONG)k&0x80000000U)>>31;
hx = (hx&0x007fffff)|((0x7f-i)<<23);
y = (float)(k+i);
SET_FLOAT_WORD(x,hx);
z = y*log10_2lo + ivln10*logf(x);
return z+y*log10_2hi;
}
/****************************************************************************/

86
library/math_log1p.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_log1p.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_log1p.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,82 @@
/****************************************************************************/
static const double
ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */
ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */
two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */
Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */
Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */
Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */
Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */
Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */
Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */
static const double zero = 0.0;
double
log1p(double x)
{
/* ZZZ unimplemented */
return(0);
double hfsq,f=0.0,c=0.0,s,z,R;
volatile double u; /* so GCC never optimizes it away */
LONG k,hx,hu=0.0,ax;
GET_HIGH_WORD(hx,x);
ax = hx&0x7fffffff;
k = 1;
if (hx < 0x3FDA827A) { /* x < 0.41422 */
if(ax>=0x3ff00000) /* x <= -1.0 */
return log(1+x); /* log1p(-1) */
if(ax<0x3e200000) { /* |x| < 2**-29 */
if(two54+x>zero /* raise inexact */
&&ax<0x3c900000) /* |x| < 2**-54 */
return x;
else
return x - x*x*0.5;
}
if(hx>0||hx<=((LONG)0xbfd2bec3U)) {
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
}
if (hx >= 0x7ff00000) return x+x;
if(k!=0) {
if(hx<0x43400000) {
u = 1.0+x;
GET_HIGH_WORD(hu,u);
k = (hu>>20)-1023;
c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */
c /= u;
} else {
u = x;
GET_HIGH_WORD(hu,u);
k = (hu>>20)-1023;
c = 0;
}
hu &= 0x000fffff;
if(hu<0x6a09e) {
SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */
} else {
k += 1;
SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */
hu = (0x00100000-hu)>>2;
}
f = u-1.0;
}
hfsq=0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}
}
R = hfsq*(1.0-0.66666666666666666*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
s = f/(2.0+f);
z = s*s;
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}
/****************************************************************************/

90
library/math_log1pf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_log1pf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_log1pf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,83 @@
/****************************************************************************/
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
Lp1 = 6.6666668653e-01, /* 3F2AAAAB */
Lp2 = 4.0000000596e-01, /* 3ECCCCCD */
Lp3 = 2.8571429849e-01, /* 3E924925 */
Lp4 = 2.2222198546e-01, /* 3E638E29 */
Lp5 = 1.8183572590e-01, /* 3E3A3325 */
Lp6 = 1.5313838422e-01, /* 3E1CD04F */
Lp7 = 1.4798198640e-01; /* 3E178897 */
static const float zero = 0.0;
float
log1pf(float x)
{
/* ZZZ unimplemented */
return(0);
float hfsq,f=0.0,c=0.0,s,z,R;
volatile float u; /* so GCC doesn't optimize it away */
LONG k,hx,hu=0.0,ax;
GET_FLOAT_WORD(hx,x);
ax = hx&0x7fffffff;
k = 1;
if (hx < 0x3ed413d7) { /* x < 0.41422 */
if(ax>=0x3f800000) /* x <= -1.0 */
return logf(1+x); /* log1p(x<=-1) */
if(ax<0x31000000) { /* |x| < 2**-29 */
if(two25+x>zero /* raise inexact */
&&ax<0x24800000) /* |x| < 2**-54 */
return x;
else
return x - x*x*(float)0.5;
}
if(hx>0||hx<=((LONG)0xbe95f61fU)) {
k=0;f=x;hu=1;} /* -0.2929<x<0.41422 */
}
if (hx >= 0x7f800000) return x+x;
if(k!=0) {
if(hx<0x5a000000) {
u = (float)1.0+x;
GET_FLOAT_WORD(hu,u);
k = (hu>>23)-127;
/* correction term */
c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0);
c /= u;
} else {
u = x;
GET_FLOAT_WORD(hu,u);
k = (hu>>23)-127;
c = 0;
}
hu &= 0x007fffff;
if(hu<0x3504f7) {
SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */
} else {
k += 1;
SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */
hu = (0x00800000-hu)>>2;
}
f = u-(float)1.0;
}
hfsq=(float)0.5*f*f;
if(hu==0) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}
}
R = hfsq*((float)1.0-(float)0.66666666666666666*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
s = f/((float)2.0+f);
z = s*s;
R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7))))));
if(k==0) return f-(hfsq-s*(hfsq+R)); else
return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f);
}
/****************************************************************************/

25
library/math_logbf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_logbf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_logbf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -44,8 +56,15 @@
float
logbf(float x)
{
/* ZZZ unimplemented */
return(0);
LONG ix;
GET_FLOAT_WORD(ix,x);
ix &= 0x7fffffff; /* high |x| */
if(ix==0) return (float)-1.0/fabsf(x);
if(ix>=0x7f800000) return x*x;
if((ix>>=23)==0) /* IEEE 754 logb */
return -126.0;
else
return (float) (ix-127);
}
/****************************************************************************/

76
library/math_logf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_logf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_logf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,69 @@
/****************************************************************************/
static const float
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
two25 = 3.355443200e+07, /* 0x4c000000 */
Lg1 = 6.6666668653e-01, /* 3F2AAAAB */
Lg2 = 4.0000000596e-01, /* 3ECCCCCD */
Lg3 = 2.8571429849e-01, /* 3E924925 */
Lg4 = 2.2222198546e-01, /* 3E638E29 */
Lg5 = 1.8183572590e-01, /* 3E3A3325 */
Lg6 = 1.5313838422e-01, /* 3E1CD04F */
Lg7 = 1.4798198640e-01; /* 3E178897 */
static const float zero = 0.0;
float
logf(float x)
{
/* ZZZ unimplemented */
return(0);
float hfsq,f,s,z,R,w,t1,t2,dk;
LONG k,ix,i,j;
GET_FLOAT_WORD(ix,x);
k=0;
if (ix < 0x00800000) { /* x < 2**-126 */
if ((ix&0x7fffffff)==0)
return -two25/zero; /* log(+-0)=-inf */
if (ix<0) return (x-x)/zero; /* log(-#) = NaN */
k -= 25; x *= two25; /* subnormal number, scale up x */
GET_FLOAT_WORD(ix,x);
}
if (ix >= 0x7f800000) return x+x;
k += (ix>>23)-127;
ix &= 0x007fffff;
i = (ix+(0x95f64<<3))&0x800000;
SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */
k += (i>>23);
f = x-(float)1.0;
if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */
if(f==zero) { if(k==0) return zero; else {dk=(float)k;
return dk*ln2_hi+dk*ln2_lo;}
}
R = f*f*((float)0.5-(float)0.33333333333333333*f);
if(k==0) return f-R; else {dk=(float)k;
return dk*ln2_hi-((R-dk*ln2_lo)-f);}
}
s = f/((float)2.0+f);
dk = (float)k;
z = s*s;
i = ix-(0x6147a<<3);
w = z*z;
j = (0x6b851<<3)-ix;
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=(float)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);
}
}
/****************************************************************************/

91
library/math_modff.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_modff.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_modff.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,82 @@
/****************************************************************************/
static const float one = 1.0, Zero[] = {0.0, -0.0,};
float
modff(float value,float *nptr)
fmodf(float x, float y)
{
/* ZZZ unimplemented */
return(0);
LONG n,hx,hy,hz,ix,iy,sx,i;
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
sx = hx&0x80000000U; /* sign of x */
hx ^=sx; /* |x| */
hy &= 0x7fffffff; /* |y| */
/* purge off exception values */
if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */
(hy>0x7f800000)) /* or y is NaN */
return (x*y)/(x*y);
if(hx<hy) return x; /* |x|<|y| return x */
if(hx==hy)
return Zero[(ULONG)sx>>31]; /* |x|=|y| return x*0*/
/* determine ix = ilogb(x) */
if(hx<0x00800000) { /* subnormal x */
for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
} else ix = (hx>>23)-127;
/* determine iy = ilogb(y) */
if(hy<0x00800000) { /* subnormal y */
for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1;
} else iy = (hy>>23)-127;
/* set up {hx,lx}, {hy,ly} and align y to x */
if(ix >= -126)
hx = 0x00800000|(0x007fffff&hx);
else { /* subnormal x, shift x to normal */
n = -126-ix;
hx = hx<<n;
}
if(iy >= -126)
hy = 0x00800000|(0x007fffff&hy);
else { /* subnormal y, shift y to normal */
n = -126-iy;
hy = hy<<n;
}
/* fix point fmod */
n = ix - iy;
while(n--) {
hz=hx-hy;
if(hz<0){hx = hx+hx;}
else {
if(hz==0) /* return sign(x)*0 */
return Zero[(ULONG)sx>>31];
hx = hz+hz;
}
}
hz=hx-hy;
if(hz>=0) {hx=hz;}
/* convert back to floating value and restore the sign */
if(hx==0) /* return sign(x)*0 */
return Zero[(ULONG)sx>>31];
while(hx<0x00800000) { /* normalize x */
hx = hx+hx;
iy -= 1;
}
if(iy>= -126) { /* normalize output */
hx = ((hx-0x00800000)|((iy+127)<<23));
SET_FLOAT_WORD(x,hx|sx);
} else { /* subnormal output */
n = -126 - iy;
hx >>= n;
SET_FLOAT_WORD(x,hx|sx);
x *= one; /* create necessary signal */
}
return x; /* exact output */
}
/****************************************************************************/

238
library/math_powf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_powf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_powf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,229 @@
/****************************************************************************/
static const float
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
zero = 0.0,
one = 1.0,
two = 2.0,
two24 = 16777216.0, /* 0x4b800000 */
huge = 1.0e30,
tiny = 1.0e-30,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01, /* 0x3f19999a */
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
L6 = 2.0697501302e-01, /* 0x3e53f142 */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08, /* 0x3331bb4c */
lg2 = 6.9314718246e-01, /* 0x3f317218 */
lg2_h = 6.93145752e-01, /* 0x3f317200 */
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */
cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
float
powf(float x,float y)
powf(float x, float y)
{
/* ZZZ unimplemented */
return(0);
volatile float z; /* prevent optimizing it out of existence */
float ax,z_h,z_l,p_h,p_l;
float y_1,t1,t2,r,s,t,u,v,w;
LONG i,j,k,yisint,n;
LONG hx,hy,ix,iy,is;
GET_FLOAT_WORD(hx,x);
GET_FLOAT_WORD(hy,y);
ix = hx&0x7fffffff; iy = hy&0x7fffffff;
/* y==zero: x**0 = 1 */
if(iy==0) return one;
/* +-NaN return x+y */
if(ix > 0x7f800000 ||
iy > 0x7f800000)
return x+y;
/* 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>=0x4b800000) yisint = 2; /* even integer y */
else if(iy>=0x3f800000) {
k = (iy>>23)-0x7f; /* exponent */
j = iy>>(23-k);
if((j<<(23-k))==iy) yisint = 2-(j&1);
}
}
/* special value of y */
if (iy==0x7f800000) { /* y is +-inf */
if (ix==0x3f800000)
return y - y; /* inf**+-1 is NaN */
else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
return (hy<0)?-y: zero;
}
if(iy==0x3f800000) { /* y is +-1 */
if(hy<0) return one/x; else return x;
}
if(hy==0x40000000) return x*x; /* y is 2 */
if(hy==0x3f000000) { /* y is 0.5 */
if(hx>=0) /* x >= +0 */
return sqrtf(x);
}
ax = fabsf(x);
/* special value of x */
if(ix==0x7f800000||ix==0||ix==0x3f800000){
z = ax; /*x is +-0,+-inf,+-1*/
if(hy<0) z = one/z; /* z = (1/|x|) */
if(hx<0) {
if(((ix-0x3f800000)|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;
}
/* (x<0)**(non-int) is NaN */
if(((((ULONG)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);
/* |y| is huge */
if(iy>0x4d000000) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny;
if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = x-1; /* t has 20 trailing zeros */
w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25));
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
v = t*ivln2_l-w*ivln2;
t1 = u+v;
GET_FLOAT_WORD(is,t1);
SET_FLOAT_WORD(t1,is&0xfffff000U);
t2 = v-(t1-u);
} else {
float s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if(ix<0x00800000)
{ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); }
n += ((ix)>>23)-0x7f;
j = ix&0x007fffff;
/* determine interval */
ix = j|0x3f800000; /* normalize ix */
if(j<=0x1cc471) k=0; /* |x|<sqrt(3/2) */
else if(j<0x5db3d7) k=1; /* |x|<sqrt(3) */
else {k=0;n+=1;ix -= 0x00800000;}
SET_FLOAT_WORD(ax,ix);
/* compute s = 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]);
s = u*v;
s_h = s;
GET_FLOAT_WORD(is,s_h);
SET_FLOAT_WORD(s_h,is&0xfffff000U);
/* t_h=ax+bp[k] High */
SET_FLOAT_WORD(t_h,((ix>>1)|0x20000000)+0x0040000+(k<<21));
t_l = ax - (t_h-bp[k]);
s_l = v*((u-s_h*t_h)-s_h*t_l);
/* compute log(ax) */
s2 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
s2 = s_h*s_h;
t_h = (float)3.0+s2+r;
GET_FLOAT_WORD(is,t_h);
SET_FLOAT_WORD(t_h,is&0xfffff000U);
t_l = r-((t_h-(float)3.0)-s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h+t_l*s;
/* 2/(3log2)*(s+...) */
p_h = u+v;
GET_FLOAT_WORD(is,p_h);
SET_FLOAT_WORD(p_h,is&0xfffff000U);
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) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (float)n;
t1 = (((z_h+z_l)+dp_h[k])+t);
GET_FLOAT_WORD(is,t1);
SET_FLOAT_WORD(t1,is&0xfffff000U);
t2 = z_l-(((t1-t)-dp_h[k])-z_h);
}
s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
if(((((ULONG)hx>>31)-1)|(yisint-1))==0)
s = -one; /* (-ve)**(odd int) */
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
GET_FLOAT_WORD(is,y);
SET_FLOAT_WORD(y_1,is&0xfffff000U);
p_l = (y-y_1)*t1+y*t2;
p_h = y_1*t1;
z = p_l+p_h;
GET_FLOAT_WORD(j,z);
if (j>0x43000000) /* if z > 128 */
return s*huge*huge; /* overflow */
else if (j==0x43000000) { /* if z == 128 */
if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */
}
else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
return s*tiny*tiny; /* underflow */
else if (j==(LONG)0xc3160000U){ /* z == -150 */
if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */
}
/*
* compute 2**(p_h+p_l)
*/
i = j&0x7fffffff;
k = (i>>23)-0x7f;
n = 0;
if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j+(0x00800000>>(k+1));
k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */
SET_FLOAT_WORD(t,n&~(0x007fffff>>k));
n = ((n&0x007fffff)|0x00800000)>>(23-k);
if(j<0) n = -n;
p_h -= t;
}
t = p_l+p_h;
GET_FLOAT_WORD(is,t);
SET_FLOAT_WORD(t,is&0xfffff000U);
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_FLOAT_WORD(j,z);
j += (n<<23);
if((j>>23)<=0) z = scalbnf(z,(int)n); /* subnormal output */
else SET_FLOAT_WORD(z,j);
return s*z;
}
/****************************************************************************/

44
library/math_scalbn.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_scalbn.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_scalbn.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,15 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +50,38 @@
/****************************************************************************/
static const double
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
huge = 1.0e+300,
tiny = 1.0e-300;
double
scalbn(double x,int n)
scalbn (double x, int n)
{
/* ZZZ unimplemented */
return(0);
LONG k,hx,lx;
EXTRACT_WORDS(hx,lx,x);
k = (hx&0x7ff00000)>>20; /* extract exponent */
if (k==0) { /* 0 or subnormal x */
if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */
x *= two54;
GET_HIGH_WORD(hx,x);
k = ((hx&0x7ff00000)>>20) - 54;
if (n< -50000) return tiny*x; /*underflow*/
}
if (k==0x7ff) return x+x; /* NaN or Inf */
k = k+n;
if (k > 0x7fe) return copysign(HUGE_VAL,x); /* overflow */
if (k > 0) /* normal result */
{SET_HIGH_WORD(x,(hx&0x800fffffU)|(k<<20)); return x;}
if (k <= -54) {
if (n > 50000) /* in case integer overflow in n+k */
return copysign(HUGE_VAL,x); /*overflow*/
else return tiny*copysign(tiny,x); /*underflow*/
}
k += 54; /* subnormal result */
SET_HIGH_WORD(x,(hx&0x800fffffU)|(k<<20));
return x*twom54;
}
/****************************************************************************/

53
library/math_scalbnf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_scalbnf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_scalbnf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,44 @@
/****************************************************************************/
#if INT_MAX > 50000
#define OVERFLOW_INT 50000
#else
#define OVERFLOW_INT 30000
#endif
static const float
two25 = 3.355443200e+07, /* 0x4c000000 */
twom25 = 2.9802322388e-08, /* 0x33000000 */
huge = 1.0e+30,
tiny = 1.0e-30;
float
scalbnf(float x,int n)
scalbnf (float x, int n)
{
/* ZZZ unimplemented */
return(0);
LONG k,ix;
GET_FLOAT_WORD(ix,x);
k = (ix&0x7f800000)>>23; /* extract exponent */
if (k==0) { /* 0 or subnormal x */
if ((ix&0x7fffffff)==0) return x; /* +-0 */
x *= two25;
GET_FLOAT_WORD(ix,x);
k = ((ix&0x7f800000)>>23) - 25;
if (n< -50000) return tiny*x; /*underflow*/
}
if (k==0xff) return x+x; /* NaN or Inf */
k = k+n;
if (k > 0xfe) return copysignf(__inff(),x); /* overflow */
if (k > 0) /* normal result */
{SET_FLOAT_WORD(x,(ix&0x807fffffU)|(k<<23)); return x;}
if (k <= -25) {
if (n > OVERFLOW_INT) /* in case integer overflow in n+k */
return copysignf(__inff(),x);/*overflow*/
else return tiny*copysignf(tiny,x); /*underflow*/
}
k += 25; /* subnormal result */
SET_FLOAT_WORD(x,(ix&0x807fffffU)|(k<<23));
return x*twom25;
}
/****************************************************************************/

79
library/math_sqrtf.c
View File

@@ -1,5 +1,5 @@
/*
* $Id: math_sqrtf.c,v 1.1 2005-05-29 11:19:01 obarthel Exp $
* $Id: math_sqrtf.c,v 1.2 2005-05-29 14:45:32 obarthel Exp $
*
* :ts=4
*
@@ -29,6 +29,18 @@
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
*
* PowerPC math library based in part on work by Sun Microsystems
* 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.
*
*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
*/
#ifndef _MATH_HEADERS_H
@@ -41,11 +53,72 @@
/****************************************************************************/
static const float one = 1.0, tiny=1.0e-30;
float
sqrtf(float x)
{
/* ZZZ unimplemented */
return(0);
volatile float z; /* to prevent GCC from optimizing it away */
LONG sign = (LONG)0x80000000U;
ULONG r;
LONG ix,s,q,m,t,i;
GET_FLOAT_WORD(ix,x);
/* take care of Inf and NaN */
if((ix&0x7f800000)==0x7f800000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix<=0) {
if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */
else if(ix<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix>>23);
if(m==0) { /* subnormal x */
for(i=0;(ix&0x00800000)==0;i++) ix<<=1;
m -= i-1;
}
m -= 127; /* unbias exponent */
ix = (ix&0x007fffff)|0x00800000;
if(m&1) /* odd m, double x to make it even */
ix += ix;
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix += ix;
q = s = 0; /* q = sqrt(x) */
r = 0x01000000; /* r = moving bit from right to left */
while(r!=0) {
t = s+r;
if(t<=ix) {
s = t+r;
ix -= t;
q += r;
}
ix += ix;
r>>=1;
}
/* use floating add to find out rounding direction */
if(ix!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (z>one)
q += 2;
else
q += (q&1);
}
}
ix = (q>>1)+0x3f000000;
ix += (m <<23);
SET_FLOAT_WORD(z,ix);
return z;
}
/****************************************************************************/

33
library/smakefile
View File

@@ -1,5 +1,5 @@
#
# $Id: smakefile,v 1.43 2005-05-14 10:52:31 obarthel Exp $
# $Id: smakefile,v 1.44 2005-05-29 14:45:32 obarthel Exp $
#
# :ts=8
#
@@ -180,45 +180,62 @@ LOCALE_OBJ = \
MATH_OBJ = \
math_acos.o \
math_acosf.o \
math_asin.o \
math_asinf.o \
math_atan.o \
math_atan2.o \
math_atan2f.o \
math_atanf.o \
math_ceil.o \
math_cos.o \
math_cosh.o \
math_ceilf.o \
math_copysign.o \
math_copysignf.o \
math_cos.o \
math_cosh.o \
math_exp.o \
math_expf.o \
math_fabs.o \
math_fabsf.o \
math_floor.o \
math_floorf.o \
math_fmod.o \
math_fmodf.o \
math_fpclassify.o \
math_inf.o \
math_inff.o \
math_isfinite.o \
math_isunordered.o \
math_signbit.o \
math_frexp.o \
math_frexpf.o \
math_huge_val.o \
math_huge_valf.o \
math_hypot.o \
math_inf.o \
math_inff.o \
math_init_exit.o \
math_isfinite.o \
math_isunordered.o \
math_ldexp.o \
math_log.o \
math_log10.o \
math_log10f.o \
math_logb.o \
math_logbf.o \
math_logf.o \
math_modf.o \
math_modff.o \
math_nan.o \
math_nanf.o \
math_nextafter.o \
math_nextafterf.o \
math_pow.o \
math_powf.o \
math_rint.o \
math_rintf.o \
math_scalbn.o \
math_scalbnf.o \
math_signbit.o \
math_sin.o \
math_sinh.o \
math_sqrt.o \
math_sqrtf.o \
math_tan.o \
math_tanh.o