1/* k_rem_pio2f.c -- float version of k_rem_pio2.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 3 */ 4 5/* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16#include <sys/cdefs.h> 17#if defined(LIBM_SCCS) && !defined(lint) 18__RCSID("$NetBSD: k_rem_pio2f.c,v 1.7 2002/05/26 22:01:53 wiz Exp $"); 19#endif 20 21#include "namespace.h" 22#include "math.h" 23#include "math_private.h" 24 25/* In the float version, the input parameter x contains 8 bit 26 integers, not 24 bit integers. 113 bit precision is not supported. */ 27 28static const int init_jk[] = {4,7,9}; /* initial value for jk */ 29 30static const float PIo2[] = { 31 1.5703125000e+00, /* 0x3fc90000 */ 32 4.5776367188e-04, /* 0x39f00000 */ 33 2.5987625122e-05, /* 0x37da0000 */ 34 7.5437128544e-08, /* 0x33a20000 */ 35 6.0026650317e-11, /* 0x2e840000 */ 36 7.3896444519e-13, /* 0x2b500000 */ 37 5.3845816694e-15, /* 0x27c20000 */ 38 5.6378512969e-18, /* 0x22d00000 */ 39 8.3009228831e-20, /* 0x1fc40000 */ 40 3.2756352257e-22, /* 0x1bc60000 */ 41 6.3331015649e-25, /* 0x17440000 */ 42}; 43 44static const float 45zero = 0.0, 46one = 1.0, 47two8 = 2.5600000000e+02, /* 0x43800000 */ 48twon8 = 3.9062500000e-03; /* 0x3b800000 */ 49 50int 51__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 52{ 53 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 54 float z,fw,f[20],fq[20],q[20]; 55 56 /* initialize jk*/ 57 jk = init_jk[prec]; 58 jp = jk; 59 60 /* determine jx,jv,q0, note that 3>q0 */ 61 jx = nx-1; 62 jv = (e0-3)/8; if(jv<0) jv=0; 63 q0 = e0-8*(jv+1); 64 65 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 66 j = jv-jx; m = jx+jk; 67 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 68 69 /* compute q[0],q[1],...q[jk] */ 70 for (i=0;i<=jk;i++) { 71 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 72 } 73 74 jz = jk; 75recompute: 76 /* distill q[] into iq[] reversingly */ 77 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 78 fw = (float)((int32_t)(twon8* z)); 79 iq[i] = (int32_t)(z-two8*fw); 80 z = q[j-1]+fw; 81 } 82 83 /* compute n */ 84 z = scalbnf(z,q0); /* actual value of z */ 85 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 86 n = (int32_t) z; 87 z -= (float)n; 88 ih = 0; 89 if(q0>0) { /* need iq[jz-1] to determine n */ 90 i = (iq[jz-1]>>(8-q0)); n += i; 91 iq[jz-1] -= i<<(8-q0); 92 ih = iq[jz-1]>>(7-q0); 93 } 94 else if(q0==0) ih = iq[jz-1]>>8; 95 else if(z>=(float)0.5) ih=2; 96 97 if(ih>0) { /* q > 0.5 */ 98 n += 1; carry = 0; 99 for(i=0;i<jz ;i++) { /* compute 1-q */ 100 j = iq[i]; 101 if(carry==0) { 102 if(j!=0) { 103 carry = 1; iq[i] = 0x100- j; 104 } 105 } else iq[i] = 0xff - j; 106 } 107 if(q0>0) { /* rare case: chance is 1 in 12 */ 108 switch(q0) { 109 case 1: 110 iq[jz-1] &= 0x7f; break; 111 case 2: 112 iq[jz-1] &= 0x3f; break; 113 } 114 } 115 if(ih==2) { 116 z = one - z; 117 if(carry!=0) z -= scalbnf(one,q0); 118 } 119 } 120 121 /* check if recomputation is needed */ 122 if(z==zero) { 123 j = 0; 124 for (i=jz-1;i>=jk;i--) j |= iq[i]; 125 if(j==0) { /* need recomputation */ 126 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 127 128 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 129 f[jx+i] = (float) ipio2[jv+i]; 130 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 131 q[i] = fw; 132 } 133 jz += k; 134 goto recompute; 135 } 136 } 137 138 /* chop off zero terms */ 139 if(z==(float)0.0) { 140 jz -= 1; q0 -= 8; 141 while(iq[jz]==0) { jz--; q0-=8;} 142 } else { /* break z into 8-bit if necessary */ 143 z = scalbnf(z,-q0); 144 if(z>=two8) { 145 fw = (float)((int32_t)(twon8*z)); 146 iq[jz] = (int32_t)(z-two8*fw); 147 jz += 1; q0 += 8; 148 iq[jz] = (int32_t) fw; 149 } else iq[jz] = (int32_t) z ; 150 } 151 152 /* convert integer "bit" chunk to floating-point value */ 153 fw = scalbnf(one,q0); 154 for(i=jz;i>=0;i--) { 155 q[i] = fw*(float)iq[i]; fw*=twon8; 156 } 157 158 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 159 for(i=jz;i>=0;i--) { 160 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 161 fq[jz-i] = fw; 162 } 163 164 /* compress fq[] into y[] */ 165 switch(prec) { 166 case 0: 167 fw = 0.0; 168 for (i=jz;i>=0;i--) fw += fq[i]; 169 y[0] = (ih==0)? fw: -fw; 170 break; 171 case 1: 172 case 2: 173 fw = 0.0; 174 for (i=jz;i>=0;i--) fw += fq[i]; 175 y[0] = (ih==0)? fw: -fw; 176 fw = fq[0]-fw; 177 for (i=1;i<=jz;i++) fw += fq[i]; 178 y[1] = (ih==0)? fw: -fw; 179 break; 180 case 3: /* painful */ 181 for (i=jz;i>0;i--) { 182 fw = fq[i-1]+fq[i]; 183 fq[i] += fq[i-1]-fw; 184 fq[i-1] = fw; 185 } 186 for (i=jz;i>1;i--) { 187 fw = fq[i-1]+fq[i]; 188 fq[i] += fq[i-1]-fw; 189 fq[i-1] = fw; 190 } 191 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 192 if(ih==0) { 193 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 194 } else { 195 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 196 } 197 } 198 return n&7; 199} 200