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