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k_rem_pio2f.c (5017B)
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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 #ifndef lint
17 static char rcsid[] = "$FreeBSD: src/lib/msun/src/k_rem_pio2f.c,v 1.6 2002/05/28 17:51:46 alfred 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
26 static const int init_jk[] = {4,7,9}; /* initial value for jk */
27
28 static 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
42 static const float
43 zero = 0.0,
44 one = 1.0,
45 two8 = 2.5600000000e+02, /* 0x43800000 */
46 twon8 = 3.9062500000e-03; /* 0x3b800000 */
47
48 int __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++) fw += x[j]*f[jx+i-j]; q[i] = fw;
69 }
70
71 jz = jk;
72 recompute:
73 /* distill q[] into iq[] reversingly */
74 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
75 fw = (float)((int32_t)(twon8* z));
76 iq[i] = (int32_t)(z-two8*fw);
77 z = q[j-1]+fw;
78 }
79
80 /* compute n */
81 z = scalbnf(z,q0); /* actual value of z */
82 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
83 n = (int32_t) z;
84 z -= (float)n;
85 ih = 0;
86 if(q0>0) { /* need iq[jz-1] to determine n */
87 i = (iq[jz-1]>>(8-q0)); n += i;
88 iq[jz-1] -= i<<(8-q0);
89 ih = iq[jz-1]>>(7-q0);
90 }
91 else if(q0==0) ih = iq[jz-1]>>8;
92 else if(z>=(float)0.5) ih=2;
93
94 if(ih>0) { /* q > 0.5 */
95 n += 1; carry = 0;
96 for(i=0;i<jz ;i++) { /* compute 1-q */
97 j = iq[i];
98 if(carry==0) {
99 if(j!=0) {
100 carry = 1; iq[i] = 0x100- j;
101 }
102 } else iq[i] = 0xff - j;
103 }
104 if(q0>0) { /* rare case: chance is 1 in 12 */
105 switch(q0) {
106 case 1:
107 iq[jz-1] &= 0x7f; break;
108 case 2:
109 iq[jz-1] &= 0x3f; break;
110 }
111 }
112 if(ih==2) {
113 z = one - z;
114 if(carry!=0) z -= scalbnf(one,q0);
115 }
116 }
117
118 /* check if recomputation is needed */
119 if(z==zero) {
120 j = 0;
121 for (i=jz-1;i>=jk;i--) j |= iq[i];
122 if(j==0) { /* need recomputation */
123 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
124
125 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
126 f[jx+i] = (float) ipio2[jv+i];
127 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
128 q[i] = fw;
129 }
130 jz += k;
131 goto recompute;
132 }
133 }
134
135 /* chop off zero terms */
136 if(z==(float)0.0) {
137 jz -= 1; q0 -= 8;
138 while(iq[jz]==0) { jz--; q0-=8;}
139 } else { /* break z into 8-bit if necessary */
140 z = scalbnf(z,-q0);
141 if(z>=two8) {
142 fw = (float)((int32_t)(twon8*z));
143 iq[jz] = (int32_t)(z-two8*fw);
144 jz += 1; q0 += 8;
145 iq[jz] = (int32_t) fw;
146 } else iq[jz] = (int32_t) z ;
147 }
148
149 /* convert integer "bit" chunk to floating-point value */
150 fw = scalbnf(one,q0);
151 for(i=jz;i>=0;i--) {
152 q[i] = fw*(float)iq[i]; fw*=twon8;
153 }
154
155 /* compute PIo2[0,...,jp]*q[jz,...,0] */
156 for(i=jz;i>=0;i--) {
157 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
158 fq[jz-i] = fw;
159 }
160
161 /* compress fq[] into y[] */
162 switch(prec) {
163 case 0:
164 fw = 0.0;
165 for (i=jz;i>=0;i--) fw += fq[i];
166 y[0] = (ih==0)? fw: -fw;
167 break;
168 case 1:
169 case 2:
170 fw = 0.0;
171 for (i=jz;i>=0;i--) fw += fq[i];
172 y[0] = (ih==0)? fw: -fw;
173 fw = fq[0]-fw;
174 for (i=1;i<=jz;i++) fw += fq[i];
175 y[1] = (ih==0)? fw: -fw;
176 break;
177 case 3: /* painful */
178 for (i=jz;i>0;i--) {
179 fw = fq[i-1]+fq[i];
180 fq[i] += fq[i-1]-fw;
181 fq[i-1] = fw;
182 }
183 for (i=jz;i>1;i--) {
184 fw = fq[i-1]+fq[i];
185 fq[i] += fq[i-1]-fw;
186 fq[i-1] = fw;
187 }
188 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
189 if(ih==0) {
190 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
191 } else {
192 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
193 }
194 }
195 return n&7;
196 }