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 #if defined(LIBM_SCCS) && !defined(lint) 17 static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc 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 26 #ifdef __STDC__ 27 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 28 #else 29 static int init_jk[] = {4,7,9}; 30 #endif 31 32 #ifdef __STDC__ 33 static const float PIo2[] = { 34 #else 35 static float PIo2[] = { 36 #endif 37 1.5703125000e+00, /* 0x3fc90000 */ 38 4.5776367188e-04, /* 0x39f00000 */ 39 2.5987625122e-05, /* 0x37da0000 */ 40 7.5437128544e-08, /* 0x33a20000 */ 41 6.0026650317e-11, /* 0x2e840000 */ 42 7.3896444519e-13, /* 0x2b500000 */ 43 5.3845816694e-15, /* 0x27c20000 */ 44 5.6378512969e-18, /* 0x22d00000 */ 45 8.3009228831e-20, /* 0x1fc40000 */ 46 3.2756352257e-22, /* 0x1bc60000 */ 47 6.3331015649e-25, /* 0x17440000 */ 48 }; 49 50 #ifdef __STDC__ 51 static const float 52 #else 53 static float 54 #endif 55 zero = 0.0, 56 one = 1.0, 57 two8 = 2.5600000000e+02, /* 0x43800000 */ 58 twon8 = 3.9062500000e-03; /* 0x3b800000 */ 59 60 #ifdef __STDC__ 61 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 62 #else 63 int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) 64 float x[], y[]; int e0,nx,prec; int32_t ipio2[]; 65 #endif 66 { 67 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 68 float z,fw,f[20],fq[20],q[20]; 69 70 /* initialize jk*/ 71 jk = init_jk[prec]; 72 jp = jk; 73 74 /* determine jx,jv,q0, note that 3>q0 */ 75 jx = nx-1; 76 jv = (e0-3)/8; if(jv<0) jv=0; 77 q0 = e0-8*(jv+1); 78 79 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 80 j = jv-jx; m = jx+jk; 81 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 82 83 /* compute q[0],q[1],...q[jk] */ 84 for (i=0;i<=jk;i++) { 85 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 86 } 87 88 jz = jk; 89 recompute: 90 /* distill q[] into iq[] reversingly */ 91 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 92 fw = (float)((int32_t)(twon8* z)); 93 iq[i] = (int32_t)(z-two8*fw); 94 z = q[j-1]+fw; 95 } 96 97 /* compute n */ 98 z = scalbnf(z,q0); /* actual value of z */ 99 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 100 n = (int32_t) z; 101 z -= (float)n; 102 ih = 0; 103 if(q0>0) { /* need iq[jz-1] to determine n */ 104 i = (iq[jz-1]>>(8-q0)); n += i; 105 iq[jz-1] -= i<<(8-q0); 106 ih = iq[jz-1]>>(7-q0); 107 } 108 else if(q0==0) ih = iq[jz-1]>>8; 109 else if(z>=(float)0.5) ih=2; 110 111 if(ih>0) { /* q > 0.5 */ 112 n += 1; carry = 0; 113 for(i=0;i<jz ;i++) { /* compute 1-q */ 114 j = iq[i]; 115 if(carry==0) { 116 if(j!=0) { 117 carry = 1; iq[i] = 0x100- j; 118 } 119 } else iq[i] = 0xff - j; 120 } 121 if(q0>0) { /* rare case: chance is 1 in 12 */ 122 switch(q0) { 123 case 1: 124 iq[jz-1] &= 0x7f; break; 125 case 2: 126 iq[jz-1] &= 0x3f; break; 127 } 128 } 129 if(ih==2) { 130 z = one - z; 131 if(carry!=0) z -= scalbnf(one,q0); 132 } 133 } 134 135 /* check if recomputation is needed */ 136 if(z==zero) { 137 j = 0; 138 for (i=jz-1;i>=jk;i--) j |= iq[i]; 139 if(j==0) { /* need recomputation */ 140 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 141 142 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 143 f[jx+i] = (float) ipio2[jv+i]; 144 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 145 q[i] = fw; 146 } 147 jz += k; 148 goto recompute; 149 } 150 } 151 152 /* chop off zero terms */ 153 if(z==(float)0.0) { 154 jz -= 1; q0 -= 8; 155 while(iq[jz]==0) { jz--; q0-=8;} 156 } else { /* break z into 8-bit if necessary */ 157 z = scalbnf(z,-q0); 158 if(z>=two8) { 159 fw = (float)((int32_t)(twon8*z)); 160 iq[jz] = (int32_t)(z-two8*fw); 161 jz += 1; q0 += 8; 162 iq[jz] = (int32_t) fw; 163 } else iq[jz] = (int32_t) z ; 164 } 165 166 /* convert integer "bit" chunk to floating-point value */ 167 fw = scalbnf(one,q0); 168 for(i=jz;i>=0;i--) { 169 q[i] = fw*(float)iq[i]; fw*=twon8; 170 } 171 172 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 173 for(i=jz;i>=0;i--) { 174 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 175 fq[jz-i] = fw; 176 } 177 178 /* compress fq[] into y[] */ 179 switch(prec) { 180 case 0: 181 fw = 0.0; 182 for (i=jz;i>=0;i--) fw += fq[i]; 183 y[0] = (ih==0)? fw: -fw; 184 break; 185 case 1: 186 case 2: 187 fw = 0.0; 188 for (i=jz;i>=0;i--) fw += fq[i]; 189 y[0] = (ih==0)? fw: -fw; 190 fw = fq[0]-fw; 191 for (i=1;i<=jz;i++) fw += fq[i]; 192 y[1] = (ih==0)? fw: -fw; 193 break; 194 case 3: /* painful */ 195 for (i=jz;i>0;i--) { 196 fw = fq[i-1]+fq[i]; 197 fq[i] += fq[i-1]-fw; 198 fq[i-1] = fw; 199 } 200 for (i=jz;i>1;i--) { 201 fw = fq[i-1]+fq[i]; 202 fq[i] += fq[i-1]-fw; 203 fq[i-1] = fw; 204 } 205 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 206 if(ih==0) { 207 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 208 } else { 209 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 210 } 211 } 212 return n&7; 213 } 214