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#include <libc-internal.h>
23
24/* In the float version, the input parameter x contains 8 bit
25 integers, not 24 bit integers. 113 bit precision is not supported. */
26
27static const int init_jk[] = {4,7,9}; /* initial value for jk */
28
29static const float PIo2[] = {
30 1.5703125000e+00, /* 0x3fc90000 */
31 4.5776367188e-04, /* 0x39f00000 */
32 2.5987625122e-05, /* 0x37da0000 */
33 7.5437128544e-08, /* 0x33a20000 */
34 6.0026650317e-11, /* 0x2e840000 */
35 7.3896444519e-13, /* 0x2b500000 */
36 5.3845816694e-15, /* 0x27c20000 */
37 5.6378512969e-18, /* 0x22d00000 */
38 8.3009228831e-20, /* 0x1fc40000 */
39 3.2756352257e-22, /* 0x1bc60000 */
40 6.3331015649e-25, /* 0x17440000 */
41};
42
43static const float
44zero = 0.0,
45one = 1.0,
46two8 = 2.5600000000e+02, /* 0x43800000 */
47twon8 = 3.9062500000e-03; /* 0x3b800000 */
48
49int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2)
50{
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];
53
54 /* initialize jk*/
55 jk = init_jk[prec];
56 jp = jk;
57
58 /* determine jx,jv,q0, note that 3>q0 */
59 jx = nx-1;
60 jv = (e0-3)/8; if(jv<0) jv=0;
61 q0 = e0-8*(jv+1);
62
63 /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
64 j = jv-jx; m = jx+jk;
65 for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
66
67 /* compute q[0],q[1],...q[jk] */
68 for (i=0;i<=jk;i++) {
69 for(j=0,fw=0.0;j<=jx;j++)
70 fw += x[j]*f[jx+i-j];
71 q[i] = fw;
72 }
73
74 jz = jk;
75recompute:
76 /* distill q[] into iq[] reversingly */
77 for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
78 fw = (float)((int32_t)(twon8* z));
79 iq[i] = (int32_t)(z-two8*fw);
80 z = q[j-1]+fw;
81 }
82
83 /* compute n */
84 z = __scalbnf(z,q0); /* actual value of z */
85 z -= (float)8.0*__floorf(z*(float)0.125); /* trim off integer >= 8 */
86 n = (int32_t) z;
87 z -= (float)n;
88 ih = 0;
89 if(q0>0) { /* need iq[jz-1] to determine n */
90 i = (iq[jz-1]>>(8-q0)); n += i;
91 iq[jz-1] -= i<<(8-q0);
92 ih = iq[jz-1]>>(7-q0);
93 }
94 else if(q0==0) ih = iq[jz-1]>>7;
95 else if(z>=(float)0.5) ih=2;
96
97 if(ih>0) { /* q > 0.5 */
98 n += 1; carry = 0;
99 for(i=0;i<jz ;i++) { /* compute 1-q */
100 j = iq[i];
101 if(carry==0) {
102 if(j!=0) {
103 carry = 1; iq[i] = 0x100- j;
104 }
105 } else iq[i] = 0xff - j;
106 }
107 if(q0>0) { /* rare case: chance is 1 in 12 */
108 switch(q0) {
109 case 1:
110 iq[jz-1] &= 0x7f; break;
111 case 2:
112 iq[jz-1] &= 0x3f; break;
113 }
114 }
115 if(ih==2) {
116 z = one - z;
117 if(carry!=0) z -= __scalbnf(one,q0);
118 }
119 }
120
121 /* check if recomputation is needed */
122 if(z==zero) {
123 j = 0;
124 for (i=jz-1;i>=jk;i--) j |= iq[i];
125 if(j==0) { /* need recomputation */
126 /* On s390x gcc 6.1 -O3 produces the warning "array subscript is
127 below array bounds [-Werror=array-bounds]". Only
128 __ieee754_rem_pio2f calls __kernel_rem_pio2f for normal
129 numbers and |x| ~> 2^7*(pi/2). Thus x can't be zero and
130 ipio2 is not zero, too. Thus not all iq[] values can't be
131 zero. */
132 DIAG_PUSH_NEEDS_COMMENT;
133 DIAG_IGNORE_NEEDS_COMMENT (6.1, "-Warray-bounds");
134 for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
135 DIAG_POP_NEEDS_COMMENT;
136
137 for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
138 f[jx+i] = (float) ipio2[jv+i];
139 for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
140 q[i] = fw;
141 }
142 jz += k;
143 goto recompute;
144 }
145 }
146
147 /* chop off zero terms */
148 if(z==(float)0.0) {
149 jz -= 1; q0 -= 8;
150 while(iq[jz]==0) { jz--; q0-=8;}
151 } else { /* break z into 8-bit if necessary */
152 z = __scalbnf(z,-q0);
153 if(z>=two8) {
154 fw = (float)((int32_t)(twon8*z));
155 iq[jz] = (int32_t)(z-two8*fw);
156 jz += 1; q0 += 8;
157 iq[jz] = (int32_t) fw;
158 } else iq[jz] = (int32_t) z ;
159 }
160
161 /* convert integer "bit" chunk to floating-point value */
162 fw = __scalbnf(one,q0);
163 for(i=jz;i>=0;i--) {
164 q[i] = fw*(float)iq[i]; fw*=twon8;
165 }
166
167 /* compute PIo2[0,...,jp]*q[jz,...,0] */
168 for(i=jz;i>=0;i--) {
169 for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
170 fq[jz-i] = fw;
171 }
172
173 /* compress fq[] into y[] */
174 switch(prec) {
175 case 0:
176 fw = 0.0;
177 for (i=jz;i>=0;i--) fw += fq[i];
178 y[0] = (ih==0)? fw: -fw;
179 break;
180 case 1:
181 case 2:;
182 float fv = 0.0;
183 for (i=jz;i>=0;i--) fv = math_narrow_eval (fv + fq[i]);
184 y[0] = (ih==0)? fv: -fv;
185 fv = math_narrow_eval (fq[0]-fv);
186 for (i=1;i<=jz;i++) fv = math_narrow_eval (fv + fq[i]);
187 y[1] = (ih==0)? fv: -fv;
188 break;
189 case 3: /* painful */
190 for (i=jz;i>0;i--) {
191 float fv = math_narrow_eval (fq[i-1]+fq[i]);
192 fq[i] += fq[i-1]-fv;
193 fq[i-1] = fv;
194 }
195 for (i=jz;i>1;i--) {
196 float fv = math_narrow_eval (fq[i-1]+fq[i]);
197 fq[i] += fq[i-1]-fv;
198 fq[i-1] = fv;
199 }
200 for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
201 if(ih==0) {
202 y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
203 } else {
204 y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
205 }
206 }
207 return n&7;
208}
209