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