Updated math code from the uClibc 0.9.33 release
This commit is contained in:
Sam Lantinga
parent
554d129015
commit
fd9bdc8766
18 changed files with 945 additions and 1198 deletions
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@ -1,4 +1,3 @@
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/* @(#)k_rem_pio2.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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@ -10,11 +9,6 @@
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* ====================================================
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*/
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#if defined(LIBM_SCCS) && !defined(lint)
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static const char rcsid[] =
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"$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $";
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#endif
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/*
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* __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
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* double x[],y[]; int e0,nx,prec; int ipio2[];
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@ -134,235 +128,171 @@ static const char rcsid[] =
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#include "math_libm.h"
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#include "math_private.h"
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#include "SDL_assert.h"
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static const int init_jk[] = {2,3,4,6}; /* initial value for jk */
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libm_hidden_proto(scalbn)
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libm_hidden_proto(floor)
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#ifdef __STDC__
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static const int init_jk[] = { 2, 3, 4, 6 }; /* initial value for jk */
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#else
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static int init_jk[] = { 2, 3, 4, 6 };
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#endif
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#ifdef __STDC__
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static const double PIo2[] = {
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#else
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static double PIo2[] = {
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#endif
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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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3.28200341580791294123e-22, /* 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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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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3.28200341580791294123e-22, /* 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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#ifdef __STDC__
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static const double
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#else
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static double
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#endif
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zero = 0.0, one = 1.0, two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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zero = 0.0,
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one = 1.0,
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two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
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twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */
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#ifdef __STDC__
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int attribute_hidden
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__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec,
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const int32_t * ipio2)
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#else
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int attribute_hidden
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__kernel_rem_pio2(x, y, e0, nx, prec, ipio2)
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double x[], y[];
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int e0, nx, prec;
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int32_t ipio2[];
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#endif
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int attribute_hidden __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2)
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{
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int32_t 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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int32_t 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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SDL_assert((prec >= 0) && (prec < SDL_arraysize(init_jk)));
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jk = init_jk[prec];
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SDL_assert((jk >= 2) && (jk <= 6));
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jp = jk;
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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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SDL_assert(nx > 0);
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jx = nx - 1;
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jv = (e0 - 3) / 24;
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if (jv < 0)
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jv = 0;
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q0 = e0 - 24 * (jv + 1);
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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;
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m = jx + jk;
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for (i = 0; i <= m; i++, j++)
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f[i] = (j < 0) ? zero : (double) ipio2[j];
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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++) {
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const int32_t idx = jx + i - j;
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SDL_assert(idx >= 0);
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SDL_assert(idx < 20);
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SDL_assert(idx <= m);
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fw += x[j] * f[idx];
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}
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q[i] = fw;
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}
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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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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) ((int32_t) (twon24 * z));
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iq[i] = (int32_t) (z - two24 * fw);
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z = q[j - 1] + fw;
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}
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for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
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fw = (double)((int32_t)(twon24* z));
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iq[i] = (int32_t)(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, 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 = (int32_t) 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));
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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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} else if (q0 == 0)
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ih = iq[jz - 1] >> 23;
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else if (z >= 0.5)
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ih = 2;
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z = scalbn(z,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 = (int32_t) 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;
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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;
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iq[i] = 0x1000000 - j;
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}
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} else
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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;
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break;
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case 2:
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iq[jz - 1] &= 0x3fffff;
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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)
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z -= scalbn(one, q0);
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}
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}
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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,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--)
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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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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++)
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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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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;
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q0 -= 24;
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while (iq[jz] == 0) {
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jz--;
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q0 -= 24;
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}
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} else { /* break z into 24-bit if necessary */
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z = scalbn(z, -q0);
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if (z >= two24) {
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fw = (double) ((int32_t) (twon24 * z));
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iq[jz] = (int32_t) (z - two24 * fw);
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jz += 1;
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q0 += 24;
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iq[jz] = (int32_t) fw;
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} else
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iq[jz] = (int32_t) z;
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}
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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,-q0);
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if(z>=two24) {
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fw = (double)((int32_t)(twon24*z));
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iq[jz] = (int32_t)(z-two24*fw);
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jz += 1; q0 += 24;
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iq[jz] = (int32_t) fw;
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} else iq[jz] = (int32_t) z ;
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}
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/* convert integer "bit" chunk to floating-point value */
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fw = scalbn(one, q0);
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for (i = jz; i >= 0; i--) {
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q[i] = fw * (double) iq[i];
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fw *= twon24;
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}
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fw = scalbn(one,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++)
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fw += PIo2[k] * q[i + k];
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fq[jz - i] = fw;
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}
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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--)
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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--)
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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++)
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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--)
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fw += fq[i];
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if (ih == 0) {
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y[0] = fq[0];
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y[1] = fq[1];
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y[2] = fw;
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} else {
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y[0] = -fq[0];
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y[1] = -fq[1];
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y[2] = -fw;
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}
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}
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return n & 7;
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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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