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.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
17 #include "math_private.h"
19 /* In the float version, the input parameter x contains 8 bit
20 integers, not 24 bit integers. 113 bit precision is not supported. */
22 static const int init_jk[] = {4,7,9}; /* initial value for jk */
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 */
41 two8 = 2.5600000000e+02, /* 0x43800000 */
42 twon8 = 3.9062500000e-03; /* 0x3b800000 */
44 int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
46 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
47 float z,fw,f[20],fq[20],q[20];
53 /* determine jx,jv,q0, note that 3>q0 */
55 jv = (e0-3)/8; if(jv<0) jv=0;
58 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
60 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
62 /* compute q[0],q[1],...q[jk] */
64 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
69 /* distill q[] into iq[] reversingly */
70 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
71 fw = (float)((int32_t)(twon8* z));
72 iq[i] = (int32_t)(z-two8*fw);
77 z = scalbnf(z,q0); /* actual value of z */
78 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
82 if(q0>0) { /* need iq[jz-1] to determine n */
83 i = (iq[jz-1]>>(8-q0)); n += i;
84 iq[jz-1] -= i<<(8-q0);
85 ih = iq[jz-1]>>(7-q0);
87 else if(q0==0) ih = iq[jz-1]>>7;
88 else if(z>=(float)0.5) ih=2;
90 if(ih>0) { /* q > 0.5 */
92 for(i=0;i<jz ;i++) { /* compute 1-q */
96 carry = 1; iq[i] = 0x100- j;
98 } else iq[i] = 0xff - j;
100 if(q0>0) { /* rare case: chance is 1 in 12 */
103 iq[jz-1] &= 0x7f; break;
105 iq[jz-1] &= 0x3f; break;
110 if(carry!=0) z -= scalbnf(one,q0);
114 /* check if recomputation is needed */
117 for (i=jz-1;i>=jk;i--) j |= iq[i];
118 if(j==0) { /* need recomputation */
119 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
121 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
122 f[jx+i] = (float) ipio2[jv+i];
123 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
131 /* chop off zero terms */
134 while(iq[jz]==0) { jz--; q0-=8;}
135 } else { /* break z into 8-bit if necessary */
138 fw = (float)((int32_t)(twon8*z));
139 iq[jz] = (int32_t)(z-two8*fw);
141 iq[jz] = (int32_t) fw;
142 } else iq[jz] = (int32_t) z ;
145 /* convert integer "bit" chunk to floating-point value */
146 fw = scalbnf(one,q0);
148 q[i] = fw*(float)iq[i]; fw*=twon8;
151 /* compute PIo2[0,...,jp]*q[jz,...,0] */
153 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
157 /* compress fq[] into y[] */
161 for (i=jz;i>=0;i--) fw += fq[i];
162 y[0] = (ih==0)? fw: -fw;
167 for (i=jz;i>=0;i--) fw += fq[i];
168 y[0] = (ih==0)? fw: -fw;
170 for (i=1;i<=jz;i++) fw += fq[i];
171 y[1] = (ih==0)? fw: -fw;
173 case 3: /* painful */
184 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
186 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
188 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;