1 /* From: @(#)e_rem_pio2.c 1.4 95/01/18 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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 * Optimized by Bruce D. Evans.
14 */
15
16
17 /* ld80 version of __ieee754_rem_pio2l(x,y)
18 *
19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __kernel_rem_pio2()
21 */
22
23 #include "../math_ld.h"
24
25 #define BIAS (LDBL_MAX_EXP - 1)
26
27 /*
28 * invpio2: 64 bits of 2/pi
29 * pio2_1: first 39 bits of pi/2
30 * pio2_1t: pi/2 - pio2_1
31 * pio2_2: second 39 bits of pi/2
32 * pio2_2t: pi/2 - (pio2_1+pio2_2)
33 * pio2_3: third 39 bits of pi/2
34 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
35 */
36
37 static const double
38 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
39 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
40 pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
41 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
42 pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
43
44 #if defined(__amd64__) || defined(__i386__)
45 /* Long double constants are slow on these arches, and broken on i386. */
46 static const volatile double
47 invpio2hi = 6.3661977236758138e-01, /* 0x145f306dc9c883.0p-53 */
48 invpio2lo = -3.9356538861223811e-17, /* -0x16b00000000000.0p-107 */
49 pio2_1thi = -1.0746346554971943e-12, /* -0x12e7b9676733af.0p-92 */
50 pio2_1tlo = 8.8451028997905949e-29, /* 0x1c080000000000.0p-146 */
51 pio2_2thi = 6.3683171635109499e-25, /* 0x18a2e03707344a.0p-133 */
52 pio2_2tlo = 2.3183081793789774e-41, /* 0x10280000000000.0p-187 */
53 pio2_3thi = -2.7529965190440717e-37, /* -0x176b7ed8fbbacc.0p-174 */
54 pio2_3tlo = -4.2006647512740502e-54; /* -0x19c00000000000.0p-230 */
55 #define invpio2 ((long double)invpio2hi + (long double)invpio2lo)
56 #define pio2_1t ((long double)pio2_1thi + (long double)pio2_1tlo)
57 #define pio2_2t ((long double)pio2_2thi + (long double)pio2_2tlo)
58 #define pio2_3t ((long double)pio2_3thi + (long double)pio2_3tlo)
59 #else
60 static const long double
61 invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
62 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
63 pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
64 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
65 #endif
66
67 //VBS
68 //static inline __always_inline int
69 //__ieee754_rem_pio2l(long double x, long double *y)
70
71 static inline int
__ieee754_rem_pio2l(long double x,long double * y)72 __ieee754_rem_pio2l(long double x, long double *y)
73 {
74 union IEEEl2bits u,u1;
75 long double z,w,t,r,fn;
76 double tx[3],ty[2];
77 int e0,ex,i,j,nx,n;
78 int16_t expsign;
79
80 u.e = x;
81 expsign = u.xbits.expsign;
82 ex = expsign & 0x7fff;
83 if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
84 /* |x| ~< 2^25*(pi/2), medium size */
85 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
86 fn = x*invpio2+0x1.8p63L;
87 fn = fn-0x1.8p63L;
88 #ifdef HAVE_EFFICIENT_IRINT
89 n = irint(fn);
90 #else
91 n = fn;
92 #endif
93 r = x-fn*(long double)pio2_1;
94 w = fn*pio2_1t; /* 1st round good to 102 bit */
95 {
96 union IEEEl2bits u2;
97 int ex1;
98 j = ex;
99 y[0] = r-w;
100 u2.e = y[0];
101 ex1 = u2.xbits.expsign & 0x7fff;
102 i = j-ex1;
103 if(i>22) { /* 2nd iteration needed, good to 141 */
104 t = r;
105 w = fn*(long double)pio2_2;
106 r = t-w;
107 w = fn*pio2_2t-((t-r)-w);
108 y[0] = r-w;
109 u2.e = y[0];
110 ex1 = u2.xbits.expsign & 0x7fff;
111 i = j-ex1;
112 if(i>61) { /* 3rd iteration need, 180 bits acc */
113 t = r; /* will cover all possible cases */
114 w = fn*(long double)pio2_3;
115 r = t-w;
116 w = fn*pio2_3t-((t-r)-w);
117 y[0] = r-w;
118 }
119 }
120 }
121 y[1] = (r-y[0])-w;
122 return n;
123 }
124 /*
125 * all other (large) arguments
126 */
127 if(ex==0x7fff) { /* x is inf or NaN */
128 y[0]=y[1]=x-x; return 0;
129 }
130 /* set z = scalbn(|x|,ilogb(x)-23) */
131 u1.e = x;
132 e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
133 u1.xbits.expsign = ex - e0;
134 z = u1.e;
135 for(i=0;i<2;i++) {
136 tx[i] = (double)((int32_t)(z));
137 z = (z-(long double)tx[i])*(long double)two24;
138 }
139 tx[2] = z;
140 nx = 3;
141 while(tx[nx-1]==zero) nx--; /* skip zero term */
142 n = __kernel_rem_pio2(tx,ty,e0,nx,2);
143 r = (long double)ty[0] + (long double)ty[1];
144 w = (long double)ty[1] - (r - (long double)ty[0]);
145 if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
146 y[0] = r; y[1] = w; return n;
147 }
148
