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 1.10 2023/08/08 06:31:17 mrg 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 /* if nx < 2, fq[0] may be accessed uninitialised */ 57 if (nx < 2) { 58 fq[0] = 0; 59 } 60 61 /* initialize jk*/ 62 jk = init_jk[prec]; 63 jp = jk; 64 65 /* determine jx,jv,q0, note that 3>q0 */ 66 jx = nx-1; 67 jv = (e0-3)/8; if(jv<0) jv=0; 68 q0 = e0-8*(jv+1); 69 70 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 71 j = jv-jx; m = jx+jk; 72 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 73 74 /* compute q[0],q[1],...q[jk] */ 75 for (i=0;i<=jk;i++) { 76 for(j=0,fw=0.0;j<=jx;j++) 77 fw += x[j]*f[jx+i-j]; 78 q[i] = fw; 79 } 80 81 jz = jk; 82recompute: 83 /* distill q[] into iq[] reversingly */ 84 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 85 fw = (float)((int32_t)(twon8* z)); 86 iq[i] = (int32_t)(z-two8*fw); 87 z = q[j-1]+fw; 88 } 89 90 /* compute n */ 91 z = scalbnf(z,q0); /* actual value of z */ 92 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 93 n = (int32_t) z; 94 z -= (float)n; 95 ih = 0; 96 if(q0>0) { /* need iq[jz-1] to determine n */ 97 i = (iq[jz-1]>>(8-q0)); n += i; 98 iq[jz-1] -= i<<(8-q0); 99 ih = iq[jz-1]>>(7-q0); 100 } 101 else if(q0==0) ih = iq[jz-1]>>8; 102 else if(z>=(float)0.5) ih=2; 103 104 if(ih>0) { /* q > 0.5 */ 105 n += 1; carry = 0; 106 for(i=0;i<jz ;i++) { /* compute 1-q */ 107 j = iq[i]; 108 if(carry==0) { 109 if(j!=0) { 110 carry = 1; iq[i] = 0x100- j; 111 } 112 } else iq[i] = 0xff - j; 113 } 114 if(q0>0) { /* rare case: chance is 1 in 12 */ 115 switch(q0) { 116 case 1: 117 iq[jz-1] &= 0x7f; break; 118 case 2: 119 iq[jz-1] &= 0x3f; break; 120 } 121 } 122 if(ih==2) { 123 z = one - z; 124 if(carry!=0) z -= scalbnf(one,q0); 125 } 126 } 127 128 /* check if recomputation is needed */ 129 if(z==zero) { 130 j = 0; 131 for (i=jz-1;i>=jk;i--) j |= iq[i]; 132 if(j==0) { /* need recomputation */ 133 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 134 135 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 136 f[jx+i] = (float) ipio2[jv+i]; 137 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 138 q[i] = fw; 139 } 140 jz += k; 141 goto recompute; 142 } 143 } 144 145 /* chop off zero terms */ 146 if(z==(float)0.0) { 147 jz -= 1; q0 -= 8; 148 while(iq[jz]==0) { jz--; q0-=8;} 149 } else { /* break z into 8-bit if necessary */ 150 z = scalbnf(z,-q0); 151 if(z>=two8) { 152 fw = (float)((int32_t)(twon8*z)); 153 iq[jz] = (int32_t)(z-two8*fw); 154 jz += 1; q0 += 8; 155 iq[jz] = (int32_t) fw; 156 } else iq[jz] = (int32_t) z ; 157 } 158 159 /* convert integer "bit" chunk to floating-point value */ 160 fw = scalbnf(one,q0); 161 for(i=jz;i>=0;i--) { 162 q[i] = fw*(float)iq[i]; fw*=twon8; 163 } 164 165 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 166 for(i=jz;i>=0;i--) { 167 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 168 fq[jz-i] = fw; 169 } 170 171 /* compress fq[] into y[] */ 172 switch(prec) { 173 case 0: 174 fw = 0.0; 175 for (i=jz;i>=0;i--) fw += fq[i]; 176 y[0] = (ih==0)? fw: -fw; 177 break; 178 case 1: 179 case 2: 180 fw = 0.0; 181 for (i=jz;i>=0;i--) fw += fq[i]; 182 y[0] = (ih==0)? fw: -fw; 183 fw = fq[0]-fw; 184 for (i=1;i<=jz;i++) fw += fq[i]; 185 y[1] = (ih==0)? fw: -fw; 186 break; 187 case 3: /* painful */ 188 for (i=jz;i>0;i--) { 189 fw = fq[i-1]+fq[i]; 190 fq[i] += fq[i-1]-fw; 191 fq[i-1] = fw; 192 } 193 for (i=jz;i>1;i--) { 194 fw = fq[i-1]+fq[i]; 195 fq[i] += fq[i-1]-fw; 196 fq[i-1] = fw; 197 } 198 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 199 if(ih==0) { 200 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 201 } else { 202 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 203 } 204 } 205 return n&7; 206} 207