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 1.9 2017/06/22 12:43:43 maya Exp $"); 19 #endif 20 21 #include "namespace.h" 22 #include "math.h" 23 #include "math_private.h" 24 25 /* In the float version, the input parameter x contains 8 bit 26 integers, not 24 bit integers. 113 bit precision is not supported. */ 27 28 static const int init_jk[] = {4,7,9}; /* initial value for jk */ 29 30 static const float PIo2[] = { 31 1.5703125000e+00, /* 0x3fc90000 */ 32 4.5776367188e-04, /* 0x39f00000 */ 33 2.5987625122e-05, /* 0x37da0000 */ 34 7.5437128544e-08, /* 0x33a20000 */ 35 6.0026650317e-11, /* 0x2e840000 */ 36 7.3896444519e-13, /* 0x2b500000 */ 37 5.3845816694e-15, /* 0x27c20000 */ 38 5.6378512969e-18, /* 0x22d00000 */ 39 8.3009228831e-20, /* 0x1fc40000 */ 40 3.2756352257e-22, /* 0x1bc60000 */ 41 6.3331015649e-25, /* 0x17440000 */ 42 }; 43 44 static const float 45 zero = 0.0, 46 one = 1.0, 47 two8 = 2.5600000000e+02, /* 0x43800000 */ 48 twon8 = 3.9062500000e-03; /* 0x3b800000 */ 49 50 int 51 __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) 52 { 53 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; 54 float z,fw,f[20],fq[20],q[20]; 55 56 /* initialize jk*/ 57 jk = init_jk[prec]; 58 jp = jk; 59 60 /* determine jx,jv,q0, note that 3>q0 */ 61 jx = nx-1; 62 jv = (e0-3)/8; if(jv<0) jv=0; 63 q0 = e0-8*(jv+1); 64 65 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ 66 j = jv-jx; m = jx+jk; 67 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; 68 69 /* compute q[0],q[1],...q[jk] */ 70 for (i=0;i<=jk;i++) { 71 for(j=0,fw=0.0;j<=jx;j++) 72 fw += x[j]*f[jx+i-j]; 73 q[i] = fw; 74 } 75 76 jz = jk; 77 recompute: 78 /* distill q[] into iq[] reversingly */ 79 for(i=0,j=jz,z=q[jz];j>0;i++,j--) { 80 fw = (float)((int32_t)(twon8* z)); 81 iq[i] = (int32_t)(z-two8*fw); 82 z = q[j-1]+fw; 83 } 84 85 /* compute n */ 86 z = scalbnf(z,q0); /* actual value of z */ 87 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ 88 n = (int32_t) z; 89 z -= (float)n; 90 ih = 0; 91 if(q0>0) { /* need iq[jz-1] to determine n */ 92 i = (iq[jz-1]>>(8-q0)); n += i; 93 iq[jz-1] -= i<<(8-q0); 94 ih = iq[jz-1]>>(7-q0); 95 } 96 else if(q0==0) ih = iq[jz-1]>>8; 97 else if(z>=(float)0.5) ih=2; 98 99 if(ih>0) { /* q > 0.5 */ 100 n += 1; carry = 0; 101 for(i=0;i<jz ;i++) { /* compute 1-q */ 102 j = iq[i]; 103 if(carry==0) { 104 if(j!=0) { 105 carry = 1; iq[i] = 0x100- j; 106 } 107 } else iq[i] = 0xff - j; 108 } 109 if(q0>0) { /* rare case: chance is 1 in 12 */ 110 switch(q0) { 111 case 1: 112 iq[jz-1] &= 0x7f; break; 113 case 2: 114 iq[jz-1] &= 0x3f; break; 115 } 116 } 117 if(ih==2) { 118 z = one - z; 119 if(carry!=0) z -= scalbnf(one,q0); 120 } 121 } 122 123 /* check if recomputation is needed */ 124 if(z==zero) { 125 j = 0; 126 for (i=jz-1;i>=jk;i--) j |= iq[i]; 127 if(j==0) { /* need recomputation */ 128 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ 129 130 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ 131 f[jx+i] = (float) ipio2[jv+i]; 132 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; 133 q[i] = fw; 134 } 135 jz += k; 136 goto recompute; 137 } 138 } 139 140 /* chop off zero terms */ 141 if(z==(float)0.0) { 142 jz -= 1; q0 -= 8; 143 while(iq[jz]==0) { jz--; q0-=8;} 144 } else { /* break z into 8-bit if necessary */ 145 z = scalbnf(z,-q0); 146 if(z>=two8) { 147 fw = (float)((int32_t)(twon8*z)); 148 iq[jz] = (int32_t)(z-two8*fw); 149 jz += 1; q0 += 8; 150 iq[jz] = (int32_t) fw; 151 } else iq[jz] = (int32_t) z ; 152 } 153 154 /* convert integer "bit" chunk to floating-point value */ 155 fw = scalbnf(one,q0); 156 for(i=jz;i>=0;i--) { 157 q[i] = fw*(float)iq[i]; fw*=twon8; 158 } 159 160 /* compute PIo2[0,...,jp]*q[jz,...,0] */ 161 for(i=jz;i>=0;i--) { 162 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; 163 fq[jz-i] = fw; 164 } 165 166 /* compress fq[] into y[] */ 167 switch(prec) { 168 case 0: 169 fw = 0.0; 170 for (i=jz;i>=0;i--) fw += fq[i]; 171 y[0] = (ih==0)? fw: -fw; 172 break; 173 case 1: 174 case 2: 175 fw = 0.0; 176 for (i=jz;i>=0;i--) fw += fq[i]; 177 y[0] = (ih==0)? fw: -fw; 178 fw = fq[0]-fw; 179 for (i=1;i<=jz;i++) fw += fq[i]; 180 y[1] = (ih==0)? fw: -fw; 181 break; 182 case 3: /* painful */ 183 for (i=jz;i>0;i--) { 184 fw = fq[i-1]+fq[i]; 185 fq[i] += fq[i-1]-fw; 186 fq[i-1] = fw; 187 } 188 for (i=jz;i>1;i--) { 189 fw = fq[i-1]+fq[i]; 190 fq[i] += fq[i-1]-fw; 191 fq[i-1] = fw; 192 } 193 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; 194 if(ih==0) { 195 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; 196 } else { 197 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; 198 } 199 } 200 return n&7; 201 } 202