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) |
17 | static 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-diag.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 | |
27 | static const int init_jk[] = {4,7,9}; /* initial value for jk */ |
28 | |
29 | static 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 | |
43 | static const float |
44 | zero = 0.0, |
45 | one = 1.0, |
46 | two8 = 2.5600000000e+02, /* 0x43800000 */ |
47 | twon8 = 3.9062500000e-03; /* 0x3b800000 */ |
48 | |
49 | int __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; |
75 | recompute: |
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 | |