Am 24.06.2014 22:28, schrieb Kai Tietz:
> 2014-06-22 14:38 GMT+02:00 André Hentschel <[email protected]>:
>> -----BEGIN PGP SIGNED MESSAGE-----
>> Hash: SHA1
>>
>> Am 21.06.2014 22:06, schrieb Kai Tietz:
>>> 2014-06-21 18:10 GMT+02:00 André Hentschel <[email protected]>:
>>>> Am 21.06.2014 17:10, schrieb André Hentschel:
>>>>> Hi,
>>>>> this time i just put some commits on github for review [1],
>>>>> so please review, then i'll commit it except of the temporary tests.
>>>>> (btw, this is the work of more than two weeks...)
>>>>>
>>>>> [1] https://github.com/AndreRH/mingw-w64/commits/master
>>>>>
>>>>
>>>> Here it is as patch (without Makefile.in)
>>>
>>> Patch is ok. Only thing we might want to change here is softfloat.c.
>>> I don't think we should have one file implementing many math functions
>>> without need. So functions, which can go into own files, should be
>>> isolated, and it might be of interest to make out of softfloat.c
>>> instead an include file.
>>
>> 1) Why is it so bad to have all in one file?
> Because that reasons to link all functions into binary at once.
> Without LTO you get a lot of stuff you might not need into your
> executable.
>> 2) How do you want it exactly? sin.def.h and so on? which functions could
>> stay in softfloat.c?
> Well, something like implementation file. I wouldn't name them .h.
> Call them sin.c ... which includes the shared stuff from (best static
> or inline) softfloat.h. The none-inline version of those shared
> function could be placed into softfloat.c.
>
> Kai
OK, how is that?
commit 1a2aaad2b7b768f9009b8244a53e66d0a3b93753
Author: André Hentschel <[email protected]>
Date: Wed Jun 25 23:14:01 2014 +0200
softmath: Add initial softmath implementation by adding cosf
diff --git a/mingw-w64-crt/Makefile.am b/mingw-w64-crt/Makefile.am
index b530a7b..53da0ae 100644
--- a/mingw-w64-crt/Makefile.am
+++ b/mingw-w64-crt/Makefile.am
@@ -195,6 +195,7 @@ src_msvcrt32=\
$(src_msvcrt) \
misc/lc_locale_func.c
+# These mingwex sources are target independent:
src_libmingwex=\
crt/dllentry.c crt/dllmain.c \
\
@@ -229,7 +230,7 @@ src_libmingwex=\
math/asinh.c math/asinhf.c math/asinhl.c math/asinl.c math/atan2f.c math/atan2l.c \
math/atanf.c math/atanh.c math/atanhf.c math/atanhl.c math/atanl.c math/cbrt.c \
math/cbrtf.c math/cbrtl.c math/cephes_emath.c math/copysign.c math/copysignf.c math/cos.c \
- math/cosf.c math/coshf.c math/coshl.c math/cosl.c math/cossin.c math/erfl.c \
+ math/coshf.c math/coshl.c math/cosl.c math/cossin.c math/erfl.c \
math/exp.c math/expf.c math/expl.c math/expm1.c math/expm1f.c math/expm1l.c \
math/fabs.c math/fabsf.c math/fabsl.c math/fdim.c math/fdimf.c math/fdiml.c \
math/fmal.c math/fmax.c math/fmaxf.c math/fmaxl.c math/fmin.c math/fminf.c \
@@ -292,6 +293,20 @@ src_libmingwex=\
stdio/vscanf.c stdio/vsnprintf.c stdio/vsnprintf_s.c stdio/vsnwprintf.c stdio/vsscanf.c \
stdio/vswscanf.c stdio/vwscanf.c stdio/wtoll.c stdio/mingw_asprintf.c stdio/mingw_vasprintf.c
+# these only go into the 64 bit version:
+src_libmingwex64=\
+ math/cosf.c
+
+# these only go into the 32 bit version:
+src_libmingwex32=\
+ math/cosf.c
+
+# these only go into the ARM32 version:
+src_libmingwexarm32=\
+ math/softmath/e_fmodf.c math/softmath/e_powf.c \
+ math/softmath/cosf.c
+
+
# These intrinsics are target independent:
src_intrincs= \
intrincs/__movsb.c intrincs/__movsd.c intrincs/__movsw.c intrincs/__stosb.c intrincs/__stosd.c \
@@ -513,7 +528,7 @@ lib32_libmingw32_a_SOURCES = $(src_libmingw32)
lib32_LIBRARIES += lib32/libmingwex.a
lib32_libmingwex_a_CPPFLAGS=$(CPPFLAGS32) $(extra_include) $(AM_CPPFLAGS)
-lib32_libmingwex_a_SOURCES = $(src_libmingwex) $(src_dfp_math)
+lib32_libmingwex_a_SOURCES = $(src_libmingwex) $(src_libmingwex32) $(src_dfp_math)
lib32_libmingwex_a_LIBADD = $(obj_dfpsrc32)
lib32_LIBRARIES += lib32/libmoldname.a
@@ -758,7 +773,7 @@ lib64_libmingw32_a_SOURCES = $(src_libmingw32)
lib64_LIBRARIES += lib64/libmingwex.a
lib64_libmingwex_a_CPPFLAGS=$(CPPFLAGS64) $(extra_include) $(AM_CPPFLAGS)
-lib64_libmingwex_a_SOURCES = $(src_libmingwex) $(src_dfp_math)
+lib64_libmingwex_a_SOURCES = $(src_libmingwex) $(src_libmingwex64) $(src_dfp_math)
lib64_libmingwex_a_LIBADD = $(obj_dfpsrc64)
lib64_LIBRARIES += lib64/libmoldname.a
@@ -1269,7 +1284,7 @@ libarm32_libmingw32_a_SOURCES = $(src_libmingw32)
libarm32_LIBRARIES += libarm32/libmingwex.a
libarm32_libmingwex_a_CPPFLAGS=$(CPPFLAGSARM32) $(extra_include) $(AM_CPPFLAGS)
-libarm32_libmingwex_a_SOURCES = $(src_libmingwex) $(src_dfp_math)
+libarm32_libmingwex_a_SOURCES = $(src_libmingwex) $(src_libmingwexarm32) $(src_dfp_math)
libarm32_libmingwex_a_LIBADD = $(obj_dfpsrc32)
libarm32_LIBRARIES += libarm32/libmoldname.a
diff --git a/mingw-w64-crt/math/softmath/cosf.c b/mingw-w64-crt/math/softmath/cosf.c
new file mode 100644
index 0000000..05ee998
--- /dev/null
+++ b/mingw-w64-crt/math/softmath/cosf.c
@@ -0,0 +1,69 @@
+/*
+ This Software is provided under the Zope Public License (ZPL) Version 2.1.
+
+ Copyright (c) 2014 by the mingw-w64 project
+
+ See the AUTHORS file for the list of contributors to the mingw-w64 project.
+
+ This license has been certified as open source. It has also been designated
+ as GPL compatible by the Free Software Foundation (FSF).
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions are met:
+
+ 1. Redistributions in source code must retain the accompanying copyright
+ notice, this list of conditions, and the following disclaimer.
+ 2. Redistributions in binary form must reproduce the accompanying
+ copyright notice, this list of conditions, and the following disclaimer
+ in the documentation and/or other materials provided with the
+ distribution.
+ 3. Names of the copyright holders must not be used to endorse or promote
+ products derived from this software without prior written permission
+ from the copyright holders.
+ 4. The right to distribute this software or to use it for any purpose does
+ not give you the right to use Servicemarks (sm) or Trademarks (tm) of
+ the copyright holders. Use of them is covered by separate agreement
+ with the copyright holders.
+ 5. If any files are modified, you must cause the modified files to carry
+ prominent notices stating that you changed the files and the date of
+ any change.
+
+ Disclaimer
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED
+ OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
+ EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+ LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
+ OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN 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.
+*/
+
+#include "softmath_private.h"
+
+float cosf(float x)
+{
+ float result = 0.0, neg = (x < 0) ? -1 : 1;
+ int n, quadrant;
+
+ x *= neg;
+ quadrant = (int)(x / M_PI_2) % 4;
+
+ x = bsd__ieee754_fmodf(x, M_PI_2);
+ if (quadrant == 1 || quadrant == 3)
+ x = M_PI_2 - x;
+
+ for(n = 0; n < 5; n++)
+ {
+ float sign = (n % 2 == 0) ? 1 : -1;
+ result += sign * (bsd__ieee754_powf(x, (2 * n)) / softmath_fact(2 * n));
+ }
+
+ if (quadrant == 1 || quadrant == 2)
+ result *= -1;
+
+ return result;
+}
diff --git a/mingw-w64-crt/math/softmath/e_fmodf.c b/mingw-w64-crt/math/softmath/e_fmodf.c
new file mode 100644
index 0000000..c57daf4
--- /dev/null
+++ b/mingw-w64-crt/math/softmath/e_fmodf.c
@@ -0,0 +1,94 @@
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+/*
+ * __ieee754_fmodf(x,y)
+ * Return x mod y in exact arithmetic
+ * Method: shift and subtract
+ */
+
+#include "math.h"
+#include "softmath_private.h"
+
+float bsd__ieee754_fmodf(float x, float y)
+{
+ int32_t n,hx,hy,hz,ix,iy,sx,i;
+
+ GET_FLOAT_WORD(hx,x);
+ GET_FLOAT_WORD(hy,y);
+ sx = hx&0x80000000; /* 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[(u_int32_t)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[(u_int32_t)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[(u_int32_t)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 */
+}
diff --git a/mingw-w64-crt/math/softmath/e_powf.c b/mingw-w64-crt/math/softmath/e_powf.c
new file mode 100644
index 0000000..faaf3dd
--- /dev/null
+++ b/mingw-w64-crt/math/softmath/e_powf.c
@@ -0,0 +1,208 @@
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include "math.h"
+#include "softmath_private.h"
+
+float bsd__ieee754_powf(float x, float y)
+{
+ float z,ax,z_h,z_l,p_h,p_l;
+ float y1,t1,t2,r,s,sn,t,u,v,w;
+ int32_t i,j,k,yisint,n;
+ int32_t 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;
+
+ /* x==1: 1**y = 1, even if y is NaN */
+ if (hx==0x3f800000) return one;
+
+ /* y!=zero: result is NaN if either arg is NaN */
+ if(ix > 0x7f800000 ||
+ iy > 0x7f800000)
+ return (x+0.0F)+(y+0.0F);
+
+ /* 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 one; /* (-1)**+-inf 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;
+ }
+
+ n = ((u_int32_t)hx>>31)-1;
+
+ /* (x<0)**(non-int) is NaN */
+ if((n|yisint)==0) return (x-x)/(x-x);
+
+ sn = one; /* s (sign of result -ve**odd) = -1 else = 1 */
+ if((n|(yisint-1))==0) sn = -one; /* (-ve)**(odd int) */
+
+ /* |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)? sn*huge*huge:sn*tiny*tiny;
+ if(ix>0x3f800007) return (hy>0)? sn*huge*huge:sn*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 = ax-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&0xfffff000);
+ 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&0xfffff000);
+ /* t_h=ax+bp[k] High */
+ is = ((ix>>1)&0xfffff000)|0x20000000;
+ SET_FLOAT_WORD(t_h,is+0x00400000+(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&0xfffff000);
+ 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&0xfffff000);
+ 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&0xfffff000);
+ t2 = z_l-(((t1-t)-dp_h[k])-z_h);
+ }
+
+ /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
+ GET_FLOAT_WORD(is,y);
+ SET_FLOAT_WORD(y1,is&0xfffff000);
+ p_l = (y-y1)*t1+y*t2;
+ p_h = y1*t1;
+ z = p_l+p_h;
+ GET_FLOAT_WORD(j,z);
+ if (j>0x43000000) /* if z > 128 */
+ return sn*huge*huge; /* overflow */
+ else if (j==0x43000000) { /* if z == 128 */
+ if(p_l+ovt>z-p_h) return sn*huge*huge; /* overflow */
+ }
+ else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */
+ return sn*tiny*tiny; /* underflow */
+ else if ((j&0xffffffff)==0xc3160000){ /* z == -150 */
+ if(p_l<=z-p_h) return sn*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&0xffff8000);
+ 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,n); /* subnormal output */
+ else SET_FLOAT_WORD(z,j);
+ return sn*z;
+}
diff --git a/mingw-w64-crt/math/softmath/softmath_private.h b/mingw-w64-crt/math/softmath/softmath_private.h
new file mode 100644
index 0000000..60a2094
--- /dev/null
+++ b/mingw-w64-crt/math/softmath/softmath_private.h
@@ -0,0 +1,79 @@
+/*
+* ====================================================
+* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+*
+* Developed at SunPro, a Sun Microsystems, Inc. business.
+* Permission to use, copy, modify, and distribute this
+* software is freely granted, provided that this notice
+* is preserved.
+* ====================================================
+*/
+
+#include <math.h>
+#include <inttypes.h>
+
+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, -0.0,},
+ 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 = 9.6191406250e-01, /* 0x3f764000 =12b cp */
+ cp_l = -1.1736857402e-04, /* 0xb8f623c6 =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*/
+
+typedef unsigned int u_int32_t;
+
+typedef union {
+ float value;
+ u_int32_t word;
+} ieee_float_shape_type;
+
+#define GET_FLOAT_WORD(i,d) do \
+{ \
+ ieee_float_shape_type gf_u; \
+ gf_u.value = (d); \
+ (i) = gf_u.word; \
+} while(0)
+
+#define SET_FLOAT_WORD(d,i) do \
+{ \
+ ieee_float_shape_type gf_u; \
+ gf_u.word = (i); \
+ (d) = gf_u.value; \
+} while(0)
+
+static inline double softmath_fact(double number)
+{
+ if (number <= 0)
+ return 1;
+
+ return number * softmath_fact(number - 1);
+}
+
+extern float bsd__ieee754_fmodf(float, float);
+extern float bsd__ieee754_powf(float, float);
------------------------------------------------------------------------------
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