mirror of
https://github.com/adtools/clib2.git
synced 2025-12-08 14:59:05 +00:00
91bcdea2a2
git-svn-id: file:///Users/olsen/Code/migration-svn-zu-git/logical-line-staging/clib2/trunk@14685 87f5fb63-7c3d-0410-a384-fd976d0f7a62
352 lines
11 KiB
C
352 lines
11 KiB
C
/*
|
|
* $Id: math_kernel_rem_pio2.c,v 1.1.1.1 2004-07-26 16:30:47 obarthel Exp $
|
|
*
|
|
* :ts=4
|
|
*
|
|
* Portable ISO 'C' (1994) runtime library for the Amiga computer
|
|
* Copyright (c) 2002-2004 by Olaf Barthel <olsen@sourcery.han.de>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
*
|
|
* - Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
*
|
|
* - Neither the name of Olaf Barthel nor the names of contributors
|
|
* may be used to endorse or promote products derived from this
|
|
* software without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
|
* AND ANY EXPRESS 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 OWNER OR CONTRIBUTORS 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.
|
|
*
|
|
*
|
|
* 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
|
|
#include "math_headers.h"
|
|
#endif /* _MATH_HEADERS_H */
|
|
|
|
/****************************************************************************/
|
|
|
|
#if defined(FLOATING_POINT_SUPPORT) && defined(PPC_FLOATING_POINT_SUPPORT)
|
|
|
|
/****************************************************************************/
|
|
|
|
static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
|
|
static const double PIo2[] = {
|
|
1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
|
|
7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
|
|
5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
|
|
3.28200341580791294123e422, /* 0x3B78CC51, 0x60000000 */
|
|
1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
|
|
1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
|
|
2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
|
|
2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
|
|
};
|
|
|
|
static const double
|
|
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
|
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
|
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
|
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
|
twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
|
|
|
|
INLINE static int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
|
|
{
|
|
int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
|
|
double z,fw,f[20],fq[20],q[20];
|
|
|
|
/* initialize jk*/
|
|
jk = init_jk[prec];
|
|
jp = jk;
|
|
|
|
/* determine jx,jv,q0, note that 3>q0 */
|
|
jx = nx-1;
|
|
jv = (e0-3)/24; if(jv<0) jv=0;
|
|
q0 = e0-24*(jv+1);
|
|
|
|
/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
|
|
j = jv-jx; m = jx+jk;
|
|
for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
|
|
|
|
/* compute q[0],q[1],...q[jk] */
|
|
for (i=0;i<=jk;i++) {
|
|
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
|
|
}
|
|
|
|
jz = jk;
|
|
recompute:
|
|
/* distill q[] into iq[] reversingly */
|
|
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
|
|
fw = (double)((int)(twon24* z));
|
|
iq[i] = (int)(z-two24*fw);
|
|
z = q[j-1]+fw;
|
|
}
|
|
|
|
/* compute n */
|
|
z = __scalbn(z,(int)q0); /* actual value of z */
|
|
z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
|
|
n = (int) z;
|
|
z -= (double)n;
|
|
ih = 0;
|
|
if(q0>0) { /* need iq[jz-1] to determine n */
|
|
i = (iq[jz-1]>>(24-q0)); n += i;
|
|
iq[jz-1] -= i<<(24-q0);
|
|
ih = iq[jz-1]>>(23-q0);
|
|
}
|
|
else if(q0==0) ih = iq[jz-1]>>23;
|
|
else if(z>=0.5) ih=2;
|
|
|
|
if(ih>0) { /* q > 0.5 */
|
|
n += 1; carry = 0;
|
|
for(i=0;i<jz ;i++) { /* compute 1-q */
|
|
j = iq[i];
|
|
if(carry==0) {
|
|
if(j!=0) {
|
|
carry = 1; iq[i] = 0x1000000- j;
|
|
}
|
|
} else iq[i] = 0xffffff - j;
|
|
}
|
|
if(q0>0) { /* rare case: chance is 1 in 12 */
|
|
switch(q0) {
|
|
case 1:
|
|
iq[jz-1] &= 0x7fffff; break;
|
|
case 2:
|
|
iq[jz-1] &= 0x3fffff; break;
|
|
}
|
|
}
|
|
if(ih==2) {
|
|
z = one - z;
|
|
if(carry!=0) z -= __scalbn(one,(int)q0);
|
|
}
|
|
}
|
|
|
|
/* check if recomputation is needed */
|
|
if(z==zero) {
|
|
j = 0;
|
|
for (i=jz-1;i>=jk;i--) j |= iq[i];
|
|
if(j==0) { /* need recomputation */
|
|
for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
|
|
|
|
for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
|
|
f[jx+i] = (double) ipio2[jv+i];
|
|
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
|
|
q[i] = fw;
|
|
}
|
|
jz += k;
|
|
goto recompute;
|
|
}
|
|
}
|
|
|
|
/* chop off zero terms */
|
|
if(z==0.0) {
|
|
jz -= 1; q0 -= 24;
|
|
while(iq[jz]==0) { jz--; q0-=24;}
|
|
} else { /* break z into 24-bit if necessary */
|
|
z = __scalbn(z,-(int)q0);
|
|
if(z>=two24) {
|
|
fw = (double)((int)(twon24*z));
|
|
iq[jz] = (int)(z-two24*fw);
|
|
jz += 1; q0 += 24;
|
|
iq[jz] = (int) fw;
|
|
} else iq[jz] = (int) z ;
|
|
}
|
|
|
|
/* convert integer "bit" chunk to floating-point value */
|
|
fw = __scalbn(one,(int)q0);
|
|
for(i=jz;i>=0;i--) {
|
|
q[i] = fw*(double)iq[i]; fw*=twon24;
|
|
}
|
|
|
|
/* compute PIo2[0,...,jp]*q[jz,...,0] */
|
|
for(i=jz;i>=0;i--) {
|
|
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
|
|
fq[jz-i] = fw;
|
|
}
|
|
|
|
/* compress fq[] into y[] */
|
|
switch(prec) {
|
|
case 0:
|
|
fw = 0.0;
|
|
for (i=jz;i>=0;i--) fw += fq[i];
|
|
y[0] = (ih==0)? fw: -fw;
|
|
break;
|
|
case 1:
|
|
case 2:
|
|
fw = 0.0;
|
|
for (i=jz;i>=0;i--) fw += fq[i];
|
|
y[0] = (ih==0)? fw: -fw;
|
|
fw = fq[0]-fw;
|
|
for (i=1;i<=jz;i++) fw += fq[i];
|
|
y[1] = (ih==0)? fw: -fw;
|
|
break;
|
|
case 3: /* painful */
|
|
for (i=jz;i>0;i--) {
|
|
fw = fq[i-1]+fq[i];
|
|
fq[i] += fq[i-1]-fw;
|
|
fq[i-1] = fw;
|
|
}
|
|
for (i=jz;i>1;i--) {
|
|
fw = fq[i-1]+fq[i];
|
|
fq[i] += fq[i-1]-fw;
|
|
fq[i-1] = fw;
|
|
}
|
|
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
|
|
if(ih==0) {
|
|
y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
|
|
} else {
|
|
y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
|
|
}
|
|
}
|
|
return n&7;
|
|
}
|
|
|
|
static const int two_over_pi[] = {
|
|
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
|
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
|
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
|
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
|
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
|
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
|
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
|
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
|
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
|
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
|
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
|
};
|
|
|
|
static const int npio2_hw[] = {
|
|
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
|
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
|
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
|
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
|
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
|
0x404858EB, 0x404921FB,
|
|
};
|
|
|
|
static const double
|
|
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
|
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
|
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
|
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
|
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
|
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
|
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
|
|
|
int __rem_pio2(double x, double *y)
|
|
{
|
|
double z,w,t,r,fn;
|
|
double tx[3];
|
|
int i,j,n,ix,hx;
|
|
int e0,nx;
|
|
unsigned int low;
|
|
|
|
GET_HIGH_WORD(hx,x); /* high word of x */
|
|
ix = hx&0x7fffffff;
|
|
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
|
{y[0] = x; y[1] = 0; return 0;}
|
|
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
|
if(hx>0) {
|
|
z = x - pio2_1;
|
|
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
|
y[0] = z - pio2_1t;
|
|
y[1] = (z-y[0])-pio2_1t;
|
|
} else { /* near pi/2, use 33+33+53 bit pi */
|
|
z -= pio2_2;
|
|
y[0] = z - pio2_2t;
|
|
y[1] = (z-y[0])-pio2_2t;
|
|
}
|
|
return 1;
|
|
} else { /* negative x */
|
|
z = x + pio2_1;
|
|
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
|
y[0] = z + pio2_1t;
|
|
y[1] = (z-y[0])+pio2_1t;
|
|
} else { /* near pi/2, use 33+33+53 bit pi */
|
|
z += pio2_2;
|
|
y[0] = z + pio2_2t;
|
|
y[1] = (z-y[0])+pio2_2t;
|
|
}
|
|
return -1;
|
|
}
|
|
}
|
|
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
|
t = fabs(x);
|
|
n = (int) (t*invpio2+half);
|
|
fn = (double)n;
|
|
r = t-fn*pio2_1;
|
|
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
|
if(n<32&&ix!=npio2_hw[n-1]) {
|
|
y[0] = r-w; /* quick check no cancellation */
|
|
} else {
|
|
unsigned int high;
|
|
j = ix>>20;
|
|
y[0] = r-w;
|
|
GET_HIGH_WORD(high,y[0]);
|
|
i = j-((high>>20)&0x7ff);
|
|
if(i>16) { /* 2nd iteration needed, good to 118 */
|
|
t = r;
|
|
w = fn*pio2_2;
|
|
r = t-w;
|
|
w = fn*pio2_2t-((t-r)-w);
|
|
y[0] = r-w;
|
|
GET_HIGH_WORD(high,y[0]);
|
|
i = j-((high>>20)&0x7ff);
|
|
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
|
t = r; /* will cover all possible cases */
|
|
w = fn*pio2_3;
|
|
r = t-w;
|
|
w = fn*pio2_3t-((t-r)-w);
|
|
y[0] = r-w;
|
|
}
|
|
}
|
|
}
|
|
y[1] = (r-y[0])-w;
|
|
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
else return n;
|
|
}
|
|
/*
|
|
* all other (large) arguments
|
|
*/
|
|
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
|
y[0]=y[1]=x-x; return 0;
|
|
}
|
|
/* set z = __scalbn(|x|,ilogb(x)-23) */
|
|
GET_LOW_WORD(low,x);
|
|
SET_LOW_WORD(z,low);
|
|
e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */
|
|
SET_HIGH_WORD(z, ix - ((int)e0<<20));
|
|
for(i=0;i<2;i++) {
|
|
tx[i] = (double)((int)(z));
|
|
z = (z-tx[i])*two24;
|
|
}
|
|
tx[2] = z;
|
|
nx = 3;
|
|
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
|
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
|
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
return n;
|
|
}
|
|
|
|
/****************************************************************************/
|
|
|
|
#endif /* FLOATING_POINT_SUPPORT && PPC_FLOATING_POINT_SUPPORT */
|