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#ifndef lint 17static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_rem_pio2f.c,v 1.8 2005/10/11 07:56:05 bde Exp $"; 18#endif 19 20#include "math.h" 21#include "math_private.h" 22 23/* In the float version, the input parameter x contains 8 bit 24 integers, not 24 bit integers. 113 bit precision is not supported. */ 25 26static const int init_jk[] = {4,7,9}; /* initial value for jk */ 27 28static const float PIo2[] = { 29 1.5703125000e+00, /* 0x3fc90000 */ 30 4.5776367188e-04, /* 0x39f00000 */ 31 2.5987625122e-05, /* 0x37da0000 */ 32 7.5437128544e-08, /* 0x33a20000 */ 33 6.0026650317e-11, /* 0x2e840000 */ 34 7.3896444519e-13, /* 0x2b500000 */ 35 5.3845816694e-15, /* 0x27c20000 */ 36 5.6378512969e-18, /* 0x22d00000 */ 37 8.3009228831e-20, /* 0x1fc40000 */ 38 3.2756352257e-22, /* 0x1bc60000 */ 39 6.3331015649e-25, /* 0x17440000 */ 40}; 41 42static const float 43zero = 0.0, 44one = 1.0, 45two8 = 2.5600000000e+02, /* 0x43800000 */ 46twon8 = 3.9062500000e-03; /* 0x3b800000 */ 47 48 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 49{ 50 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 51 float z,fw,f[20],fq[20],q[20]; 52 53 /* initialize jk*/ 54 jk = init_jk[prec]; 55 jp = jk; 56 57 /* determine jx,jv,q0, note that 3>q0 */ 58 jx = nx-1; 59 jv = (e0-3)/8; if(jv<0) jv=0; 60 q0 = e0-8*(jv+1); 61 62 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 63 j = jv-jx; m = jx+jk; 64 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 65 66 /* compute q[0],q[1],...q[jk] */ 67 for (i=0;i<=jk;i++) { 68 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 69 } 70 71 jz = jk; 72recompute: 73 /* distill q[] into iq[] reversingly */ 74 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 75 fw = (float)((int32_t)(twon8* z)); 76 iq[i] = (int32_t)(z-two8*fw); 77 z = q[j-1]+fw; 78 } 79 80 /* compute n */ 81 z = scalbnf(z,q0); /* actual value of z */ 82 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 83 n = (int32_t) z; 84 z -= (float)n; 85 ih = 0; 86 if(q0>0) { /* need iq[jz-1] to determine n */ 87 i = (iq[jz-1]>>(8-q0)); n += i; 88 iq[jz-1] -= i<<(8-q0); 89 ih = iq[jz-1]>>(7-q0); 90 } 91 else if(q0==0) ih = iq[jz-1]>>7; 92 else if(z>=(float)0.5) ih=2; 93 94 if(ih>0) { /* q > 0.5 */ 95 n += 1; carry = 0; 96 for(i=0;i<jz ;i++) { /* compute 1-q */ 97 j = iq[i]; 98 if(carry==0) { 99 if(j!=0) { 100 carry = 1; iq[i] = 0x100- j; 101 } 102 } else iq[i] = 0xff - j; 103 } 104 if(q0>0) { /* rare case: chance is 1 in 12 */ 105 switch(q0) { 106 case 1: 107 iq[jz-1] &= 0x7f; break; 108 case 2: 109 iq[jz-1] &= 0x3f; break; 110 } 111 } 112 if(ih==2) { 113 z = one - z; 114 if(carry!=0) z -= scalbnf(one,q0); 115 } 116 } 117 118 /* check if recomputation is needed */ 119 if(z==zero) { 120 j = 0; 121 for (i=jz-1;i>=jk;i--) j |= iq[i]; 122 if(j==0) { /* need recomputation */ 123 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 124 125 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 126 f[jx+i] = (float) ipio2[jv+i]; 127 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 128 q[i] = fw; 129 } 130 jz += k; 131 goto recompute; 132 } 133 } 134 135 /* chop off zero terms */ 136 if(z==(float)0.0) { 137 jz -= 1; q0 -= 8; 138 while(iq[jz]==0) { jz--; q0-=8;} 139 } else { /* break z into 8-bit if necessary */ 140 z = scalbnf(z,-q0); 141 if(z>=two8) { 142 fw = (float)((int32_t)(twon8*z)); 143 iq[jz] = (int32_t)(z-two8*fw); 144 jz += 1; q0 += 8; 145 iq[jz] = (int32_t) fw; 146 } else iq[jz] = (int32_t) z ; 147 } 148 149 /* convert integer "bit" chunk to floating-point value */ 150 fw = scalbnf(one,q0); 151 for(i=jz;i>=0;i--) { 152 q[i] = fw*(float)iq[i]; fw*=twon8; 153 } 154 155 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 156 for(i=jz;i>=0;i--) { 157 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 158 fq[jz-i] = fw; 159 } 160 161 /* compress fq[] into y[] */ 162 switch(prec) { 163 case 0: 164 fw = 0.0; 165 for (i=jz;i>=0;i--) fw += fq[i]; 166 y[0] = (ih==0)? fw: -fw; 167 break; 168 case 1: 169 case 2: 170 fw = 0.0; 171 for (i=jz;i>=0;i--) fw += fq[i]; 172 fw = *(volatile float *)&fw; /* clip any extra precision */ 173 y[0] = (ih==0)? fw: -fw; 174 fw = fq[0]-fw; 175 for (i=1;i<=jz;i++) fw += fq[i]; 176 y[1] = (ih==0)? fw: -fw; 177 break; 178 case 3: /* painful */ 179 for (i=jz;i>0;i--) { 180 fw = fq[i-1]+fq[i]; 181 fq[i] += fq[i-1]-fw; 182 fq[i-1] = fw; 183 } 184 for (i=jz;i>1;i--) { 185 fw = fq[i-1]+fq[i]; 186 fq[i] += fq[i-1]-fw; 187 fq[i-1] = fw; 188 } 189 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 190 if(ih==0) { 191 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 192 } else { 193 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 194 } 195 } 196 return n&7; 197} 198