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 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 27 28 static 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 42 static const float 43 zero = 0.0, 44 one = 1.0, 45 two8 = 2.5600000000e+02, /* 0x43800000 */ 46 twon8 = 3.9062500000e-03; /* 0x3b800000 */ 47 48 int 49 __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, 50 const int32_t *ipio2) 51 { 52 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 53 float z,fw,f[20],fq[20],q[20]; 54 55 /* initialize jk*/ 56 jk = init_jk[prec]; 57 jp = jk; 58 59 /* determine jx,jv,q0, note that 3>q0 */ 60 jx = nx-1; 61 jv = (e0-3)/8; if(jv<0) jv=0; 62 q0 = e0-8*(jv+1); 63 64 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 65 j = jv-jx; m = jx+jk; 66 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 67 68 /* compute q[0],q[1],...q[jk] */ 69 for (i=0;i<=jk;i++) { 70 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; 71 } 72 73 jz = jk; 74 recompute: 75 /* distill q[] into iq[] reversingly */ 76 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 77 fw = (float)((int32_t)(twon8* z)); 78 iq[i] = (int32_t)(z-two8*fw); 79 z = q[j-1]+fw; 80 } 81 82 /* compute n */ 83 z = scalbnf(z,q0); /* actual value of z */ 84 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 85 n = (int32_t) z; 86 z -= (float)n; 87 ih = 0; 88 if(q0>0) { /* need iq[jz-1] to determine n */ 89 i = (iq[jz-1]>>(8-q0)); n += i; 90 iq[jz-1] -= i<<(8-q0); 91 ih = iq[jz-1]>>(7-q0); 92 } 93 else if(q0==0) ih = iq[jz-1]>>8; 94 else if(z>=(float)0.5) ih=2; 95 96 if(ih>0) { /* q > 0.5 */ 97 n += 1; carry = 0; 98 for(i=0;i<jz ;i++) { /* compute 1-q */ 99 j = iq[i]; 100 if(carry==0) { 101 if(j!=0) { 102 carry = 1; iq[i] = 0x100- j; 103 } 104 } else iq[i] = 0xff - j; 105 } 106 if(q0>0) { /* rare case: chance is 1 in 12 */ 107 switch(q0) { 108 case 1: 109 iq[jz-1] &= 0x7f; break; 110 case 2: 111 iq[jz-1] &= 0x3f; break; 112 } 113 } 114 if(ih==2) { 115 z = one - z; 116 if(carry!=0) z -= scalbnf(one,q0); 117 } 118 } 119 120 /* check if recomputation is needed */ 121 if(z==zero) { 122 j = 0; 123 for (i=jz-1;i>=jk;i--) j |= iq[i]; 124 if(j==0) { /* need recomputation */ 125 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 126 127 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 128 f[jx+i] = (float) ipio2[jv+i]; 129 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 130 q[i] = fw; 131 } 132 jz += k; 133 goto recompute; 134 } 135 } 136 137 /* chop off zero terms */ 138 if(z==(float)0.0) { 139 jz -= 1; q0 -= 8; 140 while(iq[jz]==0) { jz--; q0-=8;} 141 } else { /* break z into 8-bit if necessary */ 142 z = scalbnf(z,-q0); 143 if(z>=two8) { 144 fw = (float)((int32_t)(twon8*z)); 145 iq[jz] = (int32_t)(z-two8*fw); 146 jz += 1; q0 += 8; 147 iq[jz] = (int32_t) fw; 148 } else iq[jz] = (int32_t) z ; 149 } 150 151 /* convert integer "bit" chunk to floating-point value */ 152 fw = scalbnf(one,q0); 153 for(i=jz;i>=0;i--) { 154 q[i] = fw*(float)iq[i]; fw*=twon8; 155 } 156 157 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 158 for(i=jz;i>=0;i--) { 159 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 160 fq[jz-i] = fw; 161 } 162 163 /* compress fq[] into y[] */ 164 switch(prec) { 165 case 0: 166 fw = 0.0; 167 for (i=jz;i>=0;i--) fw += fq[i]; 168 y[0] = (ih==0)? fw: -fw; 169 break; 170 case 1: 171 case 2: 172 fw = 0.0; 173 for (i=jz;i>=0;i--) fw += fq[i]; 174 y[0] = (ih==0)? fw: -fw; 175 fw = fq[0]-fw; 176 for (i=1;i<=jz;i++) fw += fq[i]; 177 y[1] = (ih==0)? fw: -fw; 178 break; 179 case 3: /* painful */ 180 for (i=jz;i>0;i--) { 181 fw = fq[i-1]+fq[i]; 182 fq[i] += fq[i-1]-fw; 183 fq[i-1] = fw; 184 } 185 for (i=jz;i>1;i--) { 186 fw = fq[i-1]+fq[i]; 187 fq[i] += fq[i-1]-fw; 188 fq[i-1] = fw; 189 } 190 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 191 if(ih==0) { 192 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 193 } else { 194 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 195 } 196 } 197 return n&7; 198 } 199