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git-svn-id: file:///Users/olsen/Code/migration-svn-zu-git/logical-line-staging/clib2/trunk@15079 87f5fb63-7c3d-0410-a384-fd976d0f7a62
354 lines
11 KiB
C
354 lines
11 KiB
C
/*
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* $Id: math_kernel_rem_pio2.c,v 1.5 2006-01-08 12:04:23 obarthel Exp $
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*
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* :ts=4
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*
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* Portable ISO 'C' (1994) runtime library for the Amiga computer
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* Copyright (c) 2002-2006 by Olaf Barthel <olsen (at) sourcery.han.de>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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*
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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*
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* - Neither the name of Olaf Barthel nor the names of contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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*
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*
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* PowerPC math library based in part on work by Sun Microsystems
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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*/
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#ifndef _MATH_HEADERS_H
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#include "math_headers.h"
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#endif /* _MATH_HEADERS_H */
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/****************************************************************************/
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#if defined(FLOATING_POINT_SUPPORT) && defined(PPC_FLOATING_POINT_SUPPORT)
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/****************************************************************************/
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static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
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static const double PIo2[] = {
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1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */
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7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */
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5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */
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3.28200341580791294123e422, /* 0x3B78CC51, 0x60000000 */
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1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */
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1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */
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2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */
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2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */
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};
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static const double
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zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
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half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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INLINE STATIC int kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2)
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{
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int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
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double z,fw,f[20],fq[20],q[20];
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/* initialize jk*/
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jk = init_jk[prec];
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jp = jk;
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/* determine jx,jv,q0, note that 3>q0 */
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jx = nx-1;
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jv = (e0-3)/24; if(jv<0) jv=0;
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q0 = e0-24*(jv+1);
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/* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
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j = jv-jx; m = jx+jk;
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for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j];
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/* compute q[0],q[1],...q[jk] */
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for (i=0;i<=jk;i++) {
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for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
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}
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jz = jk;
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recompute:
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/* distill q[] into iq[] reversingly */
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for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
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fw = (double)((int)(twon24* z));
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iq[i] = (int)(z-two24*fw);
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z = q[j-1]+fw;
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}
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/* compute n */
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z = __scalbn(z,(int)q0); /* actual value of z */
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z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */
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n = (int) z;
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z -= (double)n;
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ih = 0;
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if(q0>0) { /* need iq[jz-1] to determine n */
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i = (iq[jz-1]>>(24-q0)); n += i;
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iq[jz-1] -= i<<(24-q0);
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ih = iq[jz-1]>>(23-q0);
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}
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else if(q0==0) ih = iq[jz-1]>>23;
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else if(z>=0.5) ih=2;
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if(ih>0) { /* q > 0.5 */
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n += 1; carry = 0;
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for(i=0;i<jz ;i++) { /* compute 1-q */
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j = iq[i];
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if(carry==0) {
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if(j!=0) {
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carry = 1; iq[i] = 0x1000000- j;
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}
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} else iq[i] = 0xffffff - j;
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}
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if(q0>0) { /* rare case: chance is 1 in 12 */
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switch(q0) {
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case 1:
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iq[jz-1] &= 0x7fffff; break;
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case 2:
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iq[jz-1] &= 0x3fffff; break;
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}
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}
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if(ih==2) {
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z = one - z;
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if(carry!=0) z -= __scalbn(one,(int)q0);
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}
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}
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/* check if recomputation is needed */
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if(z==zero) {
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j = 0;
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for (i=jz-1;i>=jk;i--) j |= iq[i];
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if(j==0) { /* need recomputation */
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for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
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for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
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f[jx+i] = (double) ipio2[jv+i];
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for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
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q[i] = fw;
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}
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jz += k;
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goto recompute;
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}
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}
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/* chop off zero terms */
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if(z==0.0) {
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jz -= 1; q0 -= 24;
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while(iq[jz]==0) { jz--; q0-=24;}
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} else { /* break z into 24-bit if necessary */
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z = __scalbn(z,-(int)q0);
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if(z>=two24) {
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fw = (double)((int)(twon24*z));
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iq[jz] = (int)(z-two24*fw);
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jz += 1; q0 += 24;
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iq[jz] = (int) fw;
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} else iq[jz] = (int) z ;
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}
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/* convert integer "bit" chunk to floating-point value */
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fw = __scalbn(one,(int)q0);
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for(i=jz;i>=0;i--) {
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q[i] = fw*(double)iq[i]; fw*=twon24;
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}
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/* compute PIo2[0,...,jp]*q[jz,...,0] */
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for(i=jz;i>=0;i--) {
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for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
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fq[jz-i] = fw;
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}
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/* compress fq[] into y[] */
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switch(prec) {
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case 0:
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fw = 0.0;
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for (i=jz;i>=0;i--) fw += fq[i];
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y[0] = (ih==0)? fw: -fw;
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break;
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case 1:
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case 2:
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fw = 0.0;
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for (i=jz;i>=0;i--) fw += fq[i];
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y[0] = (ih==0)? fw: -fw;
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fw = fq[0]-fw;
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for (i=1;i<=jz;i++) fw += fq[i];
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y[1] = (ih==0)? fw: -fw;
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break;
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case 3: /* painful */
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for (i=jz;i>0;i--) {
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fw = fq[i-1]+fq[i];
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fq[i] += fq[i-1]-fw;
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fq[i-1] = fw;
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}
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for (i=jz;i>1;i--) {
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fw = fq[i-1]+fq[i];
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fq[i] += fq[i-1]-fw;
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fq[i-1] = fw;
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}
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for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
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if(ih==0) {
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y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
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} else {
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y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
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}
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}
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return n&7;
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}
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static const int two_over_pi[] = {
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0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
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0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
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0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
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0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
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0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
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0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
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0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
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0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
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0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
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0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
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0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
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};
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static const int npio2_hw[] = {
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0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
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0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
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0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
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0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
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0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
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0x404858EB, 0x404921FB,
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};
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static const double
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invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
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pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
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pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
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pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
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pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
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pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
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pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
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int __rem_pio2(double x, double *y)
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{
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double z,w,t,r,fn;
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double tx[3];
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int i,j,n,ix,hx;
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int e0,nx;
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unsigned int low;
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GET_HIGH_WORD(hx,x); /* high word of x */
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ix = hx&0x7fffffff;
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if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
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{y[0] = x; y[1] = 0; return 0;}
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if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
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if(hx>0) {
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z = x - pio2_1;
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
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y[0] = z - pio2_1t;
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y[1] = (z-y[0])-pio2_1t;
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} else { /* near pi/2, use 33+33+53 bit pi */
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z -= pio2_2;
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y[0] = z - pio2_2t;
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y[1] = (z-y[0])-pio2_2t;
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}
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return 1;
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} else { /* negative x */
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z = x + pio2_1;
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if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
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y[0] = z + pio2_1t;
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y[1] = (z-y[0])+pio2_1t;
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} else { /* near pi/2, use 33+33+53 bit pi */
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z += pio2_2;
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y[0] = z + pio2_2t;
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y[1] = (z-y[0])+pio2_2t;
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}
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return -1;
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}
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}
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if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
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t = fabs(x);
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n = (int) (t*invpio2+half);
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fn = (double)n;
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r = t-fn*pio2_1;
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w = fn*pio2_1t; /* 1st round good to 85 bit */
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if(n<32&&ix!=npio2_hw[n-1]) {
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y[0] = r-w; /* quick check no cancellation */
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} else {
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unsigned int high;
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j = ix>>20;
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y[0] = r-w;
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GET_HIGH_WORD(high,y[0]);
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i = j-((high>>20)&0x7ff);
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if(i>16) { /* 2nd iteration needed, good to 118 */
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t = r;
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w = fn*pio2_2;
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r = t-w;
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w = fn*pio2_2t-((t-r)-w);
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y[0] = r-w;
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GET_HIGH_WORD(high,y[0]);
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i = j-((high>>20)&0x7ff);
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if(i>49) { /* 3rd iteration need, 151 bits acc */
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t = r; /* will cover all possible cases */
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w = fn*pio2_3;
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r = t-w;
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w = fn*pio2_3t-((t-r)-w);
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y[0] = r-w;
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}
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}
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}
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y[1] = (r-y[0])-w;
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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else return n;
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}
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/*
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* all other (large) arguments
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*/
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if(ix>=0x7ff00000) { /* x is inf or NaN */
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y[0]=y[1]=x-x; return 0;
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}
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/* keep the compiler happy */
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z = 0;
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/* set z = __scalbn(|x|,ilogb(x)-23) */
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GET_LOW_WORD(low,x);
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SET_LOW_WORD(z,low);
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e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */
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SET_HIGH_WORD(z, ix - ((int)e0<<20));
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for(i=0;i<2;i++) {
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tx[i] = (double)((int)(z));
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z = (z-tx[i])*two24;
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}
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tx[2] = z;
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nx = 3;
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while(tx[nx-1]==zero) nx--; /* skip zero term */
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n = kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
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if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
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return n;
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}
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/****************************************************************************/
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#endif /* FLOATING_POINT_SUPPORT && PPC_FLOATING_POINT_SUPPORT */
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