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 1.10 2023/08/08 06:31:17 mrg 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
__kernel_rem_pio2f(float * x,float * y,int e0,int nx,int prec,const int32_t * ipio2)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 /* if nx < 2, fq[0] may be accessed uninitialised */
57 if (nx < 2) {
58 fq[0] = 0;
59 }
60
61 /* initialize jk*/
62 jk = init_jk[prec];
63 jp = jk;
64
65 /* determine jx,jv,q0, note that 3>q0 */
66 jx = nx-1;
67 jv = (e0-3)/8; if(jv<0) jv=0;
68 q0 = e0-8*(jv+1);
69
70 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
71 j = jv-jx; m = jx+jk;
72 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
73
74 /* compute q[0],q[1],...q[jk] */
75 for (i=0;i<=jk;i++) {
76 for(j=0,fw=0.0;j<=jx;j++)
77 fw += x[j]*f[jx+i-j];
78 q[i] = fw;
79 }
80
81 jz = jk;
82 recompute:
83 /* distill q[] into iq[] reversingly */
84 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
85 fw = (float)((int32_t)(twon8* z));
86 iq[i] = (int32_t)(z-two8*fw);
87 z = q[j-1]+fw;
88 }
89
90 /* compute n */
91 z = scalbnf(z,q0); /* actual value of z */
92 z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
93 n = (int32_t) z;
94 z -= (float)n;
95 ih = 0;
96 if(q0>0) { /* need iq[jz-1] to determine n */
97 i = (iq[jz-1]>>(8-q0)); n += i;
98 iq[jz-1] -= i<<(8-q0);
99 ih = iq[jz-1]>>(7-q0);
100 }
101 else if(q0==0) ih = iq[jz-1]>>8;
102 else if(z>=(float)0.5) ih=2;
103
104 if(ih>0) { /* q > 0.5 */
105 n += 1; carry = 0;
106 for(i=0;i<jz ;i++) { /* compute 1-q */
107 j = iq[i];
108 if(carry==0) {
109 if(j!=0) {
110 carry = 1; iq[i] = 0x100- j;
111 }
112 } else iq[i] = 0xff - j;
113 }
114 if(q0>0) { /* rare case: chance is 1 in 12 */
115 switch(q0) {
116 case 1:
117 iq[jz-1] &= 0x7f; break;
118 case 2:
119 iq[jz-1] &= 0x3f; break;
120 }
121 }
122 if(ih==2) {
123 z = one - z;
124 if(carry!=0) z -= scalbnf(one,q0);
125 }
126 }
127
128 /* check if recomputation is needed */
129 if(z==zero) {
130 j = 0;
131 for (i=jz-1;i>=jk;i--) j |= iq[i];
132 if(j==0) { /* need recomputation */
133 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
134
135 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
136 f[jx+i] = (float) ipio2[jv+i];
137 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
138 q[i] = fw;
139 }
140 jz += k;
141 goto recompute;
142 }
143 }
144
145 /* chop off zero terms */
146 if(z==(float)0.0) {
147 jz -= 1; q0 -= 8;
148 while(iq[jz]==0) { jz--; q0-=8;}
149 } else { /* break z into 8-bit if necessary */
150 z = scalbnf(z,-q0);
151 if(z>=two8) {
152 fw = (float)((int32_t)(twon8*z));
153 iq[jz] = (int32_t)(z-two8*fw);
154 jz += 1; q0 += 8;
155 iq[jz] = (int32_t) fw;
156 } else iq[jz] = (int32_t) z ;
157 }
158
159 /* convert integer "bit" chunk to floating-point value */
160 fw = scalbnf(one,q0);
161 for(i=jz;i>=0;i--) {
162 q[i] = fw*(float)iq[i]; fw*=twon8;
163 }
164
165 /* compute PIo2[0,...,jp]*q[jz,...,0] */
166 for(i=jz;i>=0;i--) {
167 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
168 fq[jz-i] = fw;
169 }
170
171 /* compress fq[] into y[] */
172 switch(prec) {
173 case 0:
174 fw = 0.0;
175 for (i=jz;i>=0;i--) fw += fq[i];
176 y[0] = (ih==0)? fw: -fw;
177 break;
178 case 1:
179 case 2:
180 fw = 0.0;
181 for (i=jz;i>=0;i--) fw += fq[i];
182 y[0] = (ih==0)? fw: -fw;
183 fw = fq[0]-fw;
184 for (i=1;i<=jz;i++) fw += fq[i];
185 y[1] = (ih==0)? fw: -fw;
186 break;
187 case 3: /* painful */
188 for (i=jz;i>0;i--) {
189 fw = fq[i-1]+fq[i];
190 fq[i] += fq[i-1]-fw;
191 fq[i-1] = fw;
192 }
193 for (i=jz;i>1;i--) {
194 fw = fq[i-1]+fq[i];
195 fq[i] += fq[i-1]-fw;
196 fq[i-1] = fw;
197 }
198 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
199 if(ih==0) {
200 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
201 } else {
202 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
203 }
204 }
205 return n&7;
206 }
207