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#if defined(LIBM_SCCS) && !defined(lint)
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static char rcsid[] =
"$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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#include "math.h"
00134
#include "mathP.h"
00135
00136
#ifdef __STDC__
00137
static const int init_jk[] = {2,3,4,6};
00138
#else
00139 static int init_jk[] = {2,3,4,6};
00140
#endif
00141
00142
#ifdef __STDC__
00143
static const double PIo2[] = {
00144
#else
00145 static double PIo2[] = {
00146
#endif
00147
1.57079625129699707031e+00,
00148 7.54978941586159635335e-08,
00149 5.39030252995776476554e-15,
00150 3.28200341580791294123e-22,
00151 1.27065575308067607349e-29,
00152 1.22933308981111328932e-36,
00153 2.73370053816464559624e-44,
00154 2.16741683877804819444e-51,
00155 };
00156
00157
#ifdef __STDC__
00158
static const double
00159
#else
00160
static double
00161
#endif
00162 zero = 0.0,
00163 one = 1.0,
00164 two24 = 1.67772160000000000000e+07,
00165 twon24 = 5.96046447753906250000e-08;
00166
00167
#ifdef __STDC__
00168
int __kernel_rem_pio2(
double *x,
double *y,
int e0,
int nx,
int prec,
const int32_t *ipio2)
00169 #
else
00170 int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2)
00171 double x[], y[];
int e0,nx,prec; int32_t ipio2[];
00172 #endif
00173 {
00174 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
00175
double z,fw,f[20],fq[20],q[20];
00176
00177
00178 jk =
init_jk[prec];
00179 jp = jk;
00180
00181
00182 jx = nx-1;
00183 jv = (e0-3)/24;
if(jv<0) jv=0;
00184 q0 = e0-24*(jv+1);
00185
00186
00187 j = jv-jx; m = jx+jk;
00188
for(i=0;i<=m;i++,j++) f[i] = (j<0)?
zero : (
double) ipio2[j];
00189
00190
00191
for (i=0;i<=jk;i++) {
00192
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
00193 }
00194
00195 jz = jk;
00196 recompute:
00197
00198
for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
00199 fw = (
double)((int32_t)(twon24* z));
00200 iq[i] = (int32_t)(z-two24*fw);
00201 z = q[j-1]+fw;
00202 }
00203
00204
00205 z =
scalbn(z,q0);
00206 z -= 8.0*
floor(z*0.125);
00207 n = (int32_t) z;
00208 z -= (
double)n;
00209 ih = 0;
00210
if(q0>0) {
00211 i = (iq[jz-1]>>(24-q0)); n += i;
00212 iq[jz-1] -= i<<(24-q0);
00213 ih = iq[jz-1]>>(23-q0);
00214 }
00215
else if(q0==0) ih = iq[jz-1]>>23;
00216
else if(z>=0.5) ih=2;
00217
00218
if(ih>0) {
00219 n += 1; carry = 0;
00220
for(i=0;i<jz ;i++) {
00221 j = iq[i];
00222
if(carry==0) {
00223
if(j!=0) {
00224 carry = 1; iq[i] = 0x1000000- j;
00225 }
00226 }
else iq[i] = 0xffffff - j;
00227 }
00228
if(q0>0) {
00229
switch(q0) {
00230
case 1:
00231 iq[jz-1] &= 0x7fffff;
break;
00232
case 2:
00233 iq[jz-1] &= 0x3fffff;
break;
00234 }
00235 }
00236
if(ih==2) {
00237 z = one - z;
00238
if(carry!=0) z -=
scalbn(one,q0);
00239 }
00240 }
00241
00242
00243
if(z==
zero) {
00244 j = 0;
00245
for (i=jz-1;i>=jk;i--) j |= iq[i];
00246
if(j==0) {
00247
for(k=1;iq[jk-k]==0;k++);
00248
00249
for(i=jz+1;i<=jz+k;i++) {
00250 f[jx+i] = (
double) ipio2[jv+i];
00251
for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
00252 q[i] = fw;
00253 }
00254 jz += k;
00255
goto recompute;
00256 }
00257 }
00258
00259
00260
if(z==0.0) {
00261 jz -= 1; q0 -= 24;
00262
while(iq[jz]==0) { jz--; q0-=24;}
00263 }
else {
00264 z =
scalbn(z,-q0);
00265
if(z>=two24) {
00266 fw = (
double)((int32_t)(twon24*z));
00267 iq[jz] = (int32_t)(z-two24*fw);
00268 jz += 1; q0 += 24;
00269 iq[jz] = (int32_t) fw;
00270 }
else iq[jz] = (int32_t) z ;
00271 }
00272
00273
00274 fw =
scalbn(one,q0);
00275
for(i=jz;i>=0;i--) {
00276 q[i] = fw*(
double)iq[i]; fw*=twon24;
00277 }
00278
00279
00280
for(i=jz;i>=0;i--) {
00281
for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw +=
PIo2[k]*q[i+k];
00282 fq[jz-i] = fw;
00283 }
00284
00285
00286
switch(prec) {
00287
case 0:
00288 fw = 0.0;
00289
for (i=jz;i>=0;i--) fw += fq[i];
00290 y[0] = (ih==0)? fw: -fw;
00291
break;
00292
case 1:
00293
case 2:
00294 fw = 0.0;
00295
for (i=jz;i>=0;i--) fw += fq[i];
00296 y[0] = (ih==0)? fw: -fw;
00297 fw = fq[0]-fw;
00298
for (i=1;i<=jz;i++) fw += fq[i];
00299 y[1] = (ih==0)? fw: -fw;
00300
break;
00301
case 3:
00302
for (i=jz;i>0;i--) {
00303 fw = fq[i-1]+fq[i];
00304 fq[i] += fq[i-1]-fw;
00305 fq[i-1] = fw;
00306 }
00307
for (i=jz;i>1;i--) {
00308 fw = fq[i-1]+fq[i];
00309 fq[i] += fq[i-1]-fw;
00310 fq[i-1] = fw;
00311 }
00312
for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
00313
if(ih==0) {
00314 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
00315 }
else {
00316 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
00317 }
00318 }
00319
return n&7;
00320 }