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#if defined(LIBM_SCCS) && !defined(lint)
17static char rcsid[] = "$NetBSD: k_rem_pio2f.c,v 1.4 1995/05/10 20:46:28 jtc Exp $";
18#endif
19
20#include <math.h>
21#include <math_private.h>
22
23/* In the float version, the input parameter x contains 8 bit
24 integers, not 24 bit integers. 113 bit precision is not supported. */
25
26static const int init_jk[] = {4,7,9}; /* initial value for jk */
27
28static const float PIo2[] = {
29 1.5703125000e+00, /* 0x3fc90000 */
30 4.5776367188e-04, /* 0x39f00000 */
31 2.5987625122e-05, /* 0x37da0000 */
32 7.5437128544e-08, /* 0x33a20000 */
33 6.0026650317e-11, /* 0x2e840000 */
34 7.3896444519e-13, /* 0x2b500000 */
35 5.3845816694e-15, /* 0x27c20000 */
36 5.6378512969e-18, /* 0x22d00000 */
37 8.3009228831e-20, /* 0x1fc40000 */
38 3.2756352257e-22, /* 0x1bc60000 */
39 6.3331015649e-25, /* 0x17440000 */
40};
41
42static const float
43zero = 0.0,
44one = 1.0,
45two8 = 2.5600000000e+02, /* 0x43800000 */
46twon8 = 3.9062500000e-03; /* 0x3b800000 */
47
48int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
49{
50 int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
51 float z,fw,f[20],fq[20],q[20];
52
53 /* initialize jk*/
54 jk = init_jk[prec];
55 jp = jk;
56
57 /* determine jx,jv,q0, note that 3>q0 */
58 jx = nx-1;
59 jv = (e0-3)/8; if(jv<0) jv=0;
60 q0 = e0-8*(jv+1);
61
62 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
63 j = jv-jx; m = jx+jk;
64 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
65
66 /* compute q[0],q[1],...q[jk] */
67 for (i=0;i<=jk;i++) {
68 for(j=0,fw=0.0;j<=jx;j++)
69 fw += x[j]*f[jx+i-j];
70 q[i] = fw;
71 }
72
73 jz = jk;
74recompute:
75 /* distill q[] into iq[] reversingly */
76 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
77 fw = (float)((int32_t)(twon8* z));
78 iq[i] = (int32_t)(z-two8*fw);
79 z = q[j-1]+fw;
80 }
81
82 /* compute n */
83 z = __scalbnf(z,q0); /* actual value of z */
84 z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
85 n = (int32_t) z;
86 z -= (float)n;
87 ih = 0;
88 if(q0>0) { /* need iq[jz-1] to determine n */
89 i = (iq[jz-1]>>(8-q0)); n += i;
90 iq[jz-1] -= i<<(8-q0);
91 ih = iq[jz-1]>>(7-q0);
92 }
93 else if(q0==0) ih = iq[jz-1]>>7;
94 else if(z>=(float)0.5) ih=2;
95
96 if(ih>0) { /* q > 0.5 */
97 n += 1; carry = 0;
98 for(i=0;i<jz ;i++) { /* compute 1-q */
99 j = iq[i];
100 if(carry==0) {
101 if(j!=0) {
102 carry = 1; iq[i] = 0x100- j;
103 }
104 } else iq[i] = 0xff - j;
105 }
106 if(q0>0) { /* rare case: chance is 1 in 12 */
107 switch(q0) {
108 case 1:
109 iq[jz-1] &= 0x7f; break;
110 case 2:
111 iq[jz-1] &= 0x3f; break;
112 }
113 }
114 if(ih==2) {
115 z = one - z;
116 if(carry!=0) z -= __scalbnf(one,q0);
117 }
118 }
119
120 /* check if recomputation is needed */
121 if(z==zero) {
122 j = 0;
123 for (i=jz-1;i>=jk;i--) j |= iq[i];
124 if(j==0) { /* need recomputation */
125 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
126
127 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
128 f[jx+i] = (float) ipio2[jv+i];
129 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
130 q[i] = fw;
131 }
132 jz += k;
133 goto recompute;
134 }
135 }
136
137 /* chop off zero terms */
138 if(z==(float)0.0) {
139 jz -= 1; q0 -= 8;
140 while(iq[jz]==0) { jz--; q0-=8;}
141 } else { /* break z into 8-bit if necessary */
142 z = __scalbnf(z,-q0);
143 if(z>=two8) {
144 fw = (float)((int32_t)(twon8*z));
145 iq[jz] = (int32_t)(z-two8*fw);
146 jz += 1; q0 += 8;
147 iq[jz] = (int32_t) fw;
148 } else iq[jz] = (int32_t) z ;
149 }
150
151 /* convert integer "bit" chunk to floating-point value */
152 fw = __scalbnf(one,q0);
153 for(i=jz;i>=0;i--) {
154 q[i] = fw*(float)iq[i]; fw*=twon8;
155 }
156
157 /* compute PIo2[0,...,jp]*q[jz,...,0] */
158 for(i=jz;i>=0;i--) {
159 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
160 fq[jz-i] = fw;
161 }
162
163 /* compress fq[] into y[] */
164 switch(prec) {
165 case 0:
166 fw = 0.0;
167 for (i=jz;i>=0;i--) fw += fq[i];
168 y[0] = (ih==0)? fw: -fw;
169 break;
170 case 1:
171 case 2:;
172 float fv = 0.0;
173 for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]);
174 y[0] = (ih==0)? fv: -fv;
175 fv = math_narrow_eval (fq[0]-fv);
176 for (i=1;i<=jz;i++) fv = math_narrow_eval (fv + fq[i]);
177 y[1] = (ih==0)? fv: -fv;
178 break;
179 case 3: /* painful */
180 for (i=jz;i>0;i--) {
181 float fv = math_narrow_eval (fq[i-1]+fq[i]);
182 fq[i] += fq[i-1]-fv;
183 fq[i-1] = fv;
184 }
185 for (i=jz;i>1;i--) {
186 float fv = math_narrow_eval (fq[i-1]+fq[i]);
187 fq[i] += fq[i-1]-fv;
188 fq[i-1] = fv;
189 }
190 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
191 if(ih==0) {
192 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
193 } else {
194 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
195 }
196 }
197 return n&7;
198}
199