1 /* kf_rem_pio2.c -- float version of k_rem_pio2.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) 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 "fdlibm.h" 17 18 /* In the float version, the input parameter x contains 8 bit 19 integers, not 24 bit integers. 113 bit precision is not supported. */ 20 21 #ifdef __STDC__ 22 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 23 #else 24 static int init_jk[] = {4,7,9}; 25 #endif 26 27 #ifdef __STDC__ 28 static const float PIo2[] = { 29 #else 30 static float PIo2[] = { 31 #endif 32 1.5703125000e+00, /* 0x3fc90000 */ 33 4.5776367188e-04, /* 0x39f00000 */ 34 2.5987625122e-05, /* 0x37da0000 */ 35 7.5437128544e-08, /* 0x33a20000 */ 36 6.0026650317e-11, /* 0x2e840000 */ 37 7.3896444519e-13, /* 0x2b500000 */ 38 5.3845816694e-15, /* 0x27c20000 */ 39 5.6378512969e-18, /* 0x22d00000 */ 40 8.3009228831e-20, /* 0x1fc40000 */ 41 3.2756352257e-22, /* 0x1bc60000 */ 42 6.3331015649e-25, /* 0x17440000 */ 43 }; 44 45 #ifdef __STDC__ 46 static const float 47 #else 48 static float 49 #endif 50 zero = 0.0, 51 one = 1.0, 52 two8 = 2.5600000000e+02, /* 0x43800000 */ 53 twon8 = 3.9062500000e-03; /* 0x3b800000 */ 54 55 #ifdef __STDC__ 56 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2) 57 #else 58 int __kernel_rem_pio2f(x,y,e0,nx,prec,ipio2) 59 float x[], y[]; int e0,nx,prec; __int32_t ipio2[]; 60 #endif 61 { 62 __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 63 float z,fw,f[20],fq[20],q[20]; 64 65 /* initialize jk*/ 66 jk = init_jk[prec]; 67 jp = jk; 68 69 /* determine jx,jv,q0, note that 3>q0 */ 70 jx = nx-1; 71 jv = (e0-3)/8; if(jv<0) jv=0; 72 q0 = e0-8*(jv+1); 73 74 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 75 j = jv-jx; m = jx+jk; 76 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 77 78 /* compute q[0],q[1],...q[jk] */ 79 for (i=0;i<=jk;i++) { 80 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 81 } 82 83 jz = jk; 84 recompute: 85 /* distill q[] into iq[] reversingly */ 86 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 87 fw = (float)((__int32_t)(twon8* z)); 88 iq[i] = (__int32_t)(z-two8*fw); 89 z = q[j-1]+fw; 90 } 91 92 /* compute n */ 93 z = scalbnf(z,(int)q0); /* actual value of z */ 94 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 95 n = (__int32_t) z; 96 z -= (float)n; 97 ih = 0; 98 if(q0>0) { /* need iq[jz-1] to determine n */ 99 i = (iq[jz-1]>>(8-q0)); n += i; 100 iq[jz-1] -= i<<(8-q0); 101 ih = iq[jz-1]>>(7-q0); 102 } 103 else if(q0==0) ih = iq[jz-1]>>8; 104 else if(z>=(float)0.5) ih=2; 105 106 if(ih>0) { /* q > 0.5 */ 107 n += 1; carry = 0; 108 for(i=0;i<jz ;i++) { /* compute 1-q */ 109 j = iq[i]; 110 if(carry==0) { 111 if(j!=0) { 112 carry = 1; iq[i] = 0x100- j; 113 } 114 } else iq[i] = 0xff - j; 115 } 116 if(q0>0) { /* rare case: chance is 1 in 12 */ 117 switch(q0) { 118 case 1: 119 iq[jz-1] &= 0x7f; break; 120 case 2: 121 iq[jz-1] &= 0x3f; break; 122 } 123 } 124 if(ih==2) { 125 z = one - z; 126 if(carry!=0) z -= scalbnf(one,(int)q0); 127 } 128 } 129 130 /* check if recomputation is needed */ 131 if(z==zero) { 132 j = 0; 133 for (i=jz-1;i>=jk;i--) j |= iq[i]; 134 if(j==0) { /* need recomputation */ 135 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 136 137 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 138 f[jx+i] = (float) ipio2[jv+i]; 139 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 140 q[i] = fw; 141 } 142 jz += k; 143 goto recompute; 144 } 145 } 146 147 /* chop off zero terms */ 148 if(z==(float)0.0) { 149 jz -= 1; q0 -= 8; 150 while(iq[jz]==0) { jz--; q0-=8;} 151 } else { /* break z into 8-bit if necessary */ 152 z = scalbnf(z,-(int)q0); 153 if(z>=two8) { 154 fw = (float)((__int32_t)(twon8*z)); 155 iq[jz] = (__int32_t)(z-two8*fw); 156 jz += 1; q0 += 8; 157 iq[jz] = (__int32_t) fw; 158 } else iq[jz] = (__int32_t) z ; 159 } 160 161 /* convert integer "bit" chunk to floating-point value */ 162 fw = scalbnf(one,(int)q0); 163 for(i=jz;i>=0;i--) { 164 q[i] = fw*(float)iq[i]; fw*=twon8; 165 } 166 167 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 168 for(i=jz;i>=0;i--) { 169 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 170 fq[jz-i] = fw; 171 } 172 173 /* compress fq[] into y[] */ 174 switch(prec) { 175 case 0: 176 fw = 0.0; 177 for (i=jz;i>=0;i--) fw += fq[i]; 178 y[0] = (ih==0)? fw: -fw; 179 break; 180 case 1: 181 case 2: 182 fw = 0.0; 183 for (i=jz;i>=0;i--) fw += fq[i]; 184 y[0] = (ih==0)? fw: -fw; 185 fw = fq[0]-fw; 186 for (i=1;i<=jz;i++) fw += fq[i]; 187 y[1] = (ih==0)? fw: -fw; 188 break; 189 case 3: /* painful */ 190 for (i=jz;i>0;i--) { 191 fw = fq[i-1]+fq[i]; 192 fq[i] += fq[i-1]-fw; 193 fq[i-1] = fw; 194 } 195 for (i=jz;i>1;i--) { 196 fw = fq[i-1]+fq[i]; 197 fq[i] += fq[i-1]-fw; 198 fq[i-1] = fw; 199 } 200 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 201 if(ih==0) { 202 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 203 } else { 204 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 205 } 206 } 207 return n&7; 208 } 209
