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 1.5 1997/10/09 11:30:22 lukem Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 /* In the float version, the input parameter x contains 8 bit 25 integers, not 24 bit integers. 113 bit precision is not supported. */ 26 27 #ifdef __STDC__ 28 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 29 #else 30 static int init_jk[] = {4,7,9}; 31 #endif 32 33 #ifdef __STDC__ 34 static const float PIo2[] = { 35 #else 36 static float PIo2[] = { 37 #endif 38 1.5703125000e+00, /* 0x3fc90000 */ 39 4.5776367188e-04, /* 0x39f00000 */ 40 2.5987625122e-05, /* 0x37da0000 */ 41 7.5437128544e-08, /* 0x33a20000 */ 42 6.0026650317e-11, /* 0x2e840000 */ 43 7.3896444519e-13, /* 0x2b500000 */ 44 5.3845816694e-15, /* 0x27c20000 */ 45 5.6378512969e-18, /* 0x22d00000 */ 46 8.3009228831e-20, /* 0x1fc40000 */ 47 3.2756352257e-22, /* 0x1bc60000 */ 48 6.3331015649e-25, /* 0x17440000 */ 49 }; 50 51 #ifdef __STDC__ 52 static const float 53 #else 54 static float 55 #endif 56 zero = 0.0, 57 one = 1.0, 58 two8 = 2.5600000000e+02, /* 0x43800000 */ 59 twon8 = 3.9062500000e-03; /* 0x3b800000 */ 60 61 #ifdef __STDC__ 62 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 63 #else 64 int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) 65 float x[], y[]; int e0,nx,prec; int32_t ipio2[]; 66 #endif 67 { 68 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 69 float z,fw,f[20],fq[20],q[20]; 70 71 /* initialize jk*/ 72 jk = init_jk[prec]; 73 jp = jk; 74 75 /* determine jx,jv,q0, note that 3>q0 */ 76 jx = nx-1; 77 jv = (e0-3)/8; if(jv<0) jv=0; 78 q0 = e0-8*(jv+1); 79 80 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 81 j = jv-jx; m = jx+jk; 82 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 83 84 /* compute q[0],q[1],...q[jk] */ 85 for (i=0;i<=jk;i++) { 86 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 87 } 88 89 jz = jk; 90 recompute: 91 /* distill q[] into iq[] reversingly */ 92 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 93 fw = (float)((int32_t)(twon8* z)); 94 iq[i] = (int32_t)(z-two8*fw); 95 z = q[j-1]+fw; 96 } 97 98 /* compute n */ 99 z = scalbnf(z,q0); /* actual value of z */ 100 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 101 n = (int32_t) z; 102 z -= (float)n; 103 ih = 0; 104 if(q0>0) { /* need iq[jz-1] to determine n */ 105 i = (iq[jz-1]>>(8-q0)); n += i; 106 iq[jz-1] -= i<<(8-q0); 107 ih = iq[jz-1]>>(7-q0); 108 } 109 else if(q0==0) ih = iq[jz-1]>>8; 110 else if(z>=(float)0.5) ih=2; 111 112 if(ih>0) { /* q > 0.5 */ 113 n += 1; carry = 0; 114 for(i=0;i<jz ;i++) { /* compute 1-q */ 115 j = iq[i]; 116 if(carry==0) { 117 if(j!=0) { 118 carry = 1; iq[i] = 0x100- j; 119 } 120 } else iq[i] = 0xff - j; 121 } 122 if(q0>0) { /* rare case: chance is 1 in 12 */ 123 switch(q0) { 124 case 1: 125 iq[jz-1] &= 0x7f; break; 126 case 2: 127 iq[jz-1] &= 0x3f; break; 128 } 129 } 130 if(ih==2) { 131 z = one - z; 132 if(carry!=0) z -= scalbnf(one,q0); 133 } 134 } 135 136 /* check if recomputation is needed */ 137 if(z==zero) { 138 j = 0; 139 for (i=jz-1;i>=jk;i--) j |= iq[i]; 140 if(j==0) { /* need recomputation */ 141 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 142 143 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 144 f[jx+i] = (float) ipio2[jv+i]; 145 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 146 q[i] = fw; 147 } 148 jz += k; 149 goto recompute; 150 } 151 } 152 153 /* chop off zero terms */ 154 if(z==(float)0.0) { 155 jz -= 1; q0 -= 8; 156 while(iq[jz]==0) { jz--; q0-=8;} 157 } else { /* break z into 8-bit if necessary */ 158 z = scalbnf(z,-q0); 159 if(z>=two8) { 160 fw = (float)((int32_t)(twon8*z)); 161 iq[jz] = (int32_t)(z-two8*fw); 162 jz += 1; q0 += 8; 163 iq[jz] = (int32_t) fw; 164 } else iq[jz] = (int32_t) z ; 165 } 166 167 /* convert integer "bit" chunk to floating-point value */ 168 fw = scalbnf(one,q0); 169 for(i=jz;i>=0;i--) { 170 q[i] = fw*(float)iq[i]; fw*=twon8; 171 } 172 173 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 174 for(i=jz;i>=0;i--) { 175 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 176 fq[jz-i] = fw; 177 } 178 179 /* compress fq[] into y[] */ 180 switch(prec) { 181 case 0: 182 fw = 0.0; 183 for (i=jz;i>=0;i--) fw += fq[i]; 184 y[0] = (ih==0)? fw: -fw; 185 break; 186 case 1: 187 case 2: 188 fw = 0.0; 189 for (i=jz;i>=0;i--) fw += fq[i]; 190 y[0] = (ih==0)? fw: -fw; 191 fw = fq[0]-fw; 192 for (i=1;i<=jz;i++) fw += fq[i]; 193 y[1] = (ih==0)? fw: -fw; 194 break; 195 case 3: /* painful */ 196 for (i=jz;i>0;i--) { 197 fw = fq[i-1]+fq[i]; 198 fq[i] += fq[i-1]-fw; 199 fq[i-1] = fw; 200 } 201 for (i=jz;i>1;i--) { 202 fw = fq[i-1]+fq[i]; 203 fq[i] += fq[i-1]-fw; 204 fq[i-1] = fw; 205 } 206 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 207 if(ih==0) { 208 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 209 } else { 210 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 211 } 212 } 213 return n&7; 214 } 215