986
|
1 |
|
|
2 |
/* @(#)e_rem_pio2.c 1.4 95/01/18 */
|
|
3 |
/*
|
|
4 |
* ====================================================
|
|
5 |
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
6 |
*
|
|
7 |
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
8 |
* Permission to use, copy, modify, and distribute this
|
|
9 |
* software is freely granted, provided that this notice
|
|
10 |
* is preserved.
|
|
11 |
* ====================================================
|
|
12 |
*
|
|
13 |
*/
|
|
14 |
|
|
15 |
/* __ieee754_rem_pio2(x,y)
|
|
16 |
*
|
|
17 |
* return the remainder of x rem pi/2 in y[0]+y[1]
|
|
18 |
* use __kernel_rem_pio2()
|
|
19 |
*/
|
|
20 |
|
|
21 |
#include "fdlibm.h"
|
|
22 |
|
|
23 |
/*
|
|
24 |
* Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
|
|
25 |
*/
|
|
26 |
#ifdef __STDC__
|
|
27 |
static const int two_over_pi[] = {
|
|
28 |
#else
|
|
29 |
static int two_over_pi[] = {
|
|
30 |
#endif
|
|
31 |
0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
|
|
32 |
0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
|
|
33 |
0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
|
|
34 |
0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
|
|
35 |
0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
|
|
36 |
0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
|
|
37 |
0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
|
|
38 |
0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
|
|
39 |
0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
|
|
40 |
0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
|
|
41 |
0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
|
|
42 |
};
|
|
43 |
|
|
44 |
#ifdef __STDC__
|
|
45 |
static const int npio2_hw[] = {
|
|
46 |
#else
|
|
47 |
static int npio2_hw[] = {
|
|
48 |
#endif
|
|
49 |
0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
|
|
50 |
0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
|
|
51 |
0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
|
|
52 |
0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
|
|
53 |
0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
|
|
54 |
0x404858EB, 0x404921FB,
|
|
55 |
};
|
|
56 |
|
|
57 |
/*
|
|
58 |
* invpio2: 53 bits of 2/pi
|
|
59 |
* pio2_1: first 33 bit of pi/2
|
|
60 |
* pio2_1t: pi/2 - pio2_1
|
|
61 |
* pio2_2: second 33 bit of pi/2
|
|
62 |
* pio2_2t: pi/2 - (pio2_1+pio2_2)
|
|
63 |
* pio2_3: third 33 bit of pi/2
|
|
64 |
* pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
|
65 |
*/
|
|
66 |
|
|
67 |
#ifdef __STDC__
|
|
68 |
static const double
|
|
69 |
#else
|
|
70 |
static double
|
|
71 |
#endif
|
|
72 |
zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
|
|
73 |
half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
|
|
74 |
two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
|
|
75 |
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
|
|
76 |
pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
|
|
77 |
pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
|
|
78 |
pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
|
|
79 |
pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
|
|
80 |
pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
|
|
81 |
pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
|
|
82 |
|
|
83 |
#ifdef __STDC__
|
|
84 |
int __ieee754_rem_pio2(double x, double *y)
|
|
85 |
#else
|
|
86 |
int __ieee754_rem_pio2(x,y)
|
|
87 |
double x,y[];
|
|
88 |
#endif
|
|
89 |
{
|
|
90 |
double z,w,t,r,fn;
|
|
91 |
double tx[3];
|
|
92 |
int e0,i,j,nx,n,ix,hx;
|
|
93 |
|
|
94 |
hx = __HI(x); /* high word of x */
|
|
95 |
ix = hx&0x7fffffff;
|
|
96 |
if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
|
|
97 |
{y[0] = x; y[1] = 0; return 0;}
|
|
98 |
if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
|
|
99 |
if(hx>0) {
|
|
100 |
z = x - pio2_1;
|
|
101 |
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
|
102 |
y[0] = z - pio2_1t;
|
|
103 |
y[1] = (z-y[0])-pio2_1t;
|
|
104 |
} else { /* near pi/2, use 33+33+53 bit pi */
|
|
105 |
z -= pio2_2;
|
|
106 |
y[0] = z - pio2_2t;
|
|
107 |
y[1] = (z-y[0])-pio2_2t;
|
|
108 |
}
|
|
109 |
return 1;
|
|
110 |
} else { /* negative x */
|
|
111 |
z = x + pio2_1;
|
|
112 |
if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
|
|
113 |
y[0] = z + pio2_1t;
|
|
114 |
y[1] = (z-y[0])+pio2_1t;
|
|
115 |
} else { /* near pi/2, use 33+33+53 bit pi */
|
|
116 |
z += pio2_2;
|
|
117 |
y[0] = z + pio2_2t;
|
|
118 |
y[1] = (z-y[0])+pio2_2t;
|
|
119 |
}
|
|
120 |
return -1;
|
|
121 |
}
|
|
122 |
}
|
|
123 |
if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
|
|
124 |
t = fabs(x);
|
|
125 |
n = (int) (t*invpio2+half);
|
|
126 |
fn = (double)n;
|
|
127 |
r = t-fn*pio2_1;
|
|
128 |
w = fn*pio2_1t; /* 1st round good to 85 bit */
|
|
129 |
if(n<32&&ix!=npio2_hw[n-1]) {
|
|
130 |
y[0] = r-w; /* quick check no cancellation */
|
|
131 |
} else {
|
|
132 |
j = ix>>20;
|
|
133 |
y[0] = r-w;
|
|
134 |
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
|
135 |
if(i>16) { /* 2nd iteration needed, good to 118 */
|
|
136 |
t = r;
|
|
137 |
w = fn*pio2_2;
|
|
138 |
r = t-w;
|
|
139 |
w = fn*pio2_2t-((t-r)-w);
|
|
140 |
y[0] = r-w;
|
|
141 |
i = j-(((__HI(y[0]))>>20)&0x7ff);
|
|
142 |
if(i>49) { /* 3rd iteration need, 151 bits acc */
|
|
143 |
t = r; /* will cover all possible cases */
|
|
144 |
w = fn*pio2_3;
|
|
145 |
r = t-w;
|
|
146 |
w = fn*pio2_3t-((t-r)-w);
|
|
147 |
y[0] = r-w;
|
|
148 |
}
|
|
149 |
}
|
|
150 |
}
|
|
151 |
y[1] = (r-y[0])-w;
|
|
152 |
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
153 |
else return n;
|
|
154 |
}
|
|
155 |
/*
|
|
156 |
* all other (large) arguments
|
|
157 |
*/
|
|
158 |
if(ix>=0x7ff00000) { /* x is inf or NaN */
|
|
159 |
y[0]=y[1]=x-x; return 0;
|
|
160 |
}
|
|
161 |
/* set z = scalbn(|x|,ilogb(x)-23) */
|
|
162 |
__LO(z) = __LO(x);
|
|
163 |
e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
|
|
164 |
__HI(z) = ix - (e0<<20);
|
|
165 |
for(i=0;i<2;i++) {
|
|
166 |
tx[i] = (double)((int)(z));
|
|
167 |
z = (z-tx[i])*two24;
|
|
168 |
}
|
|
169 |
tx[2] = z;
|
|
170 |
nx = 3;
|
|
171 |
while(tx[nx-1]==zero) nx--; /* skip zero term */
|
|
172 |
n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
|
|
173 |
if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
|
|
174 |
return n;
|
|
175 |
}
|