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