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.
4 * $FreeBSD: src/lib/msun/src/k_rem_pio2f.c,v 1.5 1999/08/28 00:06:41 peter Exp $
5 * $DragonFly: src/lib/msun/src/Attic/k_rem_pio2f.c,v 1.3 2004/12/29 15:22:57 asmodai Exp $
9 * ====================================================
10 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
12 * Developed at SunPro, a Sun Microsystems, Inc. business.
13 * Permission to use, copy, modify, and distribute this
14 * software is freely granted, provided that this notice
16 * ====================================================
20 #include "math_private.h"
22 /* In the float version, the input parameter x contains 8 bit
23 integers, not 24 bit integers. 113 bit precision is not supported. */
25 static const int init_jk[] = {4,7,9}; /* initial value for jk */
27 static const float PIo2[] = {
28 1.5703125000e+00, /* 0x3fc90000 */
29 4.5776367188e-04, /* 0x39f00000 */
30 2.5987625122e-05, /* 0x37da0000 */
31 7.5437128544e-08, /* 0x33a20000 */
32 6.0026650317e-11, /* 0x2e840000 */
33 7.3896444519e-13, /* 0x2b500000 */
34 5.3845816694e-15, /* 0x27c20000 */
35 5.6378512969e-18, /* 0x22d00000 */
36 8.3009228831e-20, /* 0x1fc40000 */
37 3.2756352257e-22, /* 0x1bc60000 */
38 6.3331015649e-25, /* 0x17440000 */
44 two8 = 2.5600000000e+02, /* 0x43800000 */
45 twon8 = 3.9062500000e-03; /* 0x3b800000 */
48 __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec,
51 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
52 float z,fw,f[20],fq[20],q[20];
58 /* determine jx,jv,q0, note that 3>q0 */
60 jv = (e0-3)/8; if(jv<0) jv=0;
63 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
65 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
67 /* compute q[0],q[1],...q[jk] */
69 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
74 /* distill q[] into iq[] reversingly */
75 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
76 fw = (float)((int32_t)(twon8* z));
77 iq[i] = (int32_t)(z-two8*fw);
82 z = scalbnf(z,q0); /* actual value of z */
83 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
87 if(q0>0) { /* need iq[jz-1] to determine n */
88 i = (iq[jz-1]>>(8-q0)); n += i;
89 iq[jz-1] -= i<<(8-q0);
90 ih = iq[jz-1]>>(7-q0);
92 else if(q0==0) ih = iq[jz-1]>>8;
93 else if(z>=(float)0.5) ih=2;
95 if(ih>0) { /* q > 0.5 */
97 for(i=0;i<jz ;i++) { /* compute 1-q */
101 carry = 1; iq[i] = 0x100- j;
103 } else iq[i] = 0xff - j;
105 if(q0>0) { /* rare case: chance is 1 in 12 */
108 iq[jz-1] &= 0x7f; break;
110 iq[jz-1] &= 0x3f; break;
115 if(carry!=0) z -= scalbnf(one,q0);
119 /* check if recomputation is needed */
122 for (i=jz-1;i>=jk;i--) j |= iq[i];
123 if(j==0) { /* need recomputation */
124 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
126 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
127 f[jx+i] = (float) ipio2[jv+i];
128 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
136 /* chop off zero terms */
139 while(iq[jz]==0) { jz--; q0-=8;}
140 } else { /* break z into 8-bit if necessary */
143 fw = (float)((int32_t)(twon8*z));
144 iq[jz] = (int32_t)(z-two8*fw);
146 iq[jz] = (int32_t) fw;
147 } else iq[jz] = (int32_t) z ;
150 /* convert integer "bit" chunk to floating-point value */
151 fw = scalbnf(one,q0);
153 q[i] = fw*(float)iq[i]; fw*=twon8;
156 /* compute PIo2[0,...,jp]*q[jz,...,0] */
158 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
162 /* compress fq[] into y[] */
166 for (i=jz;i>=0;i--) fw += fq[i];
167 y[0] = (ih==0)? fw: -fw;
172 for (i=jz;i>=0;i--) fw += fq[i];
173 y[0] = (ih==0)? fw: -fw;
175 for (i=1;i<=jz;i++) fw += fq[i];
176 y[1] = (ih==0)? fw: -fw;
178 case 3: /* painful */
189 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
191 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
193 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;