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 //__FBSDID("$FreeBSD: src/lib/msun/ld80/e_rem_pio2l.h,v 1.3 2011/06/18 13:56:33 benl Exp $");
17
18 /* ld80 version of __ieee754_rem_pio2l(x,y)
19 *
20 * return the remainder of x rem pi/2 in y[0]+y[1]
21 * use __kernel_rem_pio2()
22 */
23
24 #include "../math_ld.h"
25
26 #define BIAS (LDBL_MAX_EXP - 1)
27
28 /*
29 * invpio2: 64 bits of 2/pi
30 * pio2_1: first 39 bits of pi/2
31 * pio2_1t: pi/2 - pio2_1
32 * pio2_2: second 39 bits of pi/2
33 * pio2_2t: pi/2 - (pio2_1+pio2_2)
34 * pio2_3: third 39 bits of pi/2
35 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
36 */
37
38 static const double
39 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
40 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
41 pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
42 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
43 pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
44
45 #if defined(__amd64__) || defined(__i386__)
46 /* Long double constants are slow on these arches, and broken on i386. */
47 static const volatile double
48 invpio2hi = 6.3661977236758138e-01, /* 0x145f306dc9c883.0p-53 */
49 invpio2lo = -3.9356538861223811e-17, /* -0x16b00000000000.0p-107 */
50 pio2_1thi = -1.0746346554971943e-12, /* -0x12e7b9676733af.0p-92 */
51 pio2_1tlo = 8.8451028997905949e-29, /* 0x1c080000000000.0p-146 */
52 pio2_2thi = 6.3683171635109499e-25, /* 0x18a2e03707344a.0p-133 */
53 pio2_2tlo = 2.3183081793789774e-41, /* 0x10280000000000.0p-187 */
54 pio2_3thi = -2.7529965190440717e-37, /* -0x176b7ed8fbbacc.0p-174 */
55 pio2_3tlo = -4.2006647512740502e-54; /* -0x19c00000000000.0p-230 */
56 #define invpio2 ((long double)invpio2hi + (long double)invpio2lo)
57 #define pio2_1t ((long double)pio2_1thi + (long double)pio2_1tlo)
58 #define pio2_2t ((long double)pio2_2thi + (long double)pio2_2tlo)
59 #define pio2_3t ((long double)pio2_3thi + (long double)pio2_3tlo)
60 #else
61 static const long double
62 invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
63 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
64 pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
65 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
66 #endif
67
68 //VBS
69 //static inline __always_inline int
70 //__ieee754_rem_pio2l(long double x, long double *y)
71
72 static inline int
__ieee754_rem_pio2l(long double x,long double * y)73 __ieee754_rem_pio2l(long double x, long double *y)
74 {
75 union IEEEl2bits u,u1;
76 long double z,w,t,r,fn;
77 double tx[3],ty[2];
78 int e0,ex,i,j,nx,n;
79 int16_t expsign;
80
81 u.e = x;
82 expsign = u.xbits.expsign;
83 ex = expsign & 0x7fff;
84 if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
85 /* |x| ~< 2^25*(pi/2), medium size */
86 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
87 fn = x*invpio2+0x1.8p63L;
88 fn = fn-0x1.8p63L;
89 #ifdef HAVE_EFFICIENT_IRINT
90 n = irint(fn);
91 #else
92 n = fn;
93 #endif
94 r = x-fn*(long double)pio2_1;
95 w = fn*pio2_1t; /* 1st round good to 102 bit */
96 {
97 union IEEEl2bits u2;
98 int ex1;
99 j = ex;
100 y[0] = r-w;
101 u2.e = y[0];
102 ex1 = u2.xbits.expsign & 0x7fff;
103 i = j-ex1;
104 if(i>22) { /* 2nd iteration needed, good to 141 */
105 t = r;
106 w = fn*(long double)pio2_2;
107 r = t-w;
108 w = fn*pio2_2t-((t-r)-w);
109 y[0] = r-w;
110 u2.e = y[0];
111 ex1 = u2.xbits.expsign & 0x7fff;
112 i = j-ex1;
113 if(i>61) { /* 3rd iteration need, 180 bits acc */
114 t = r; /* will cover all possible cases */
115 w = fn*(long double)pio2_3;
116 r = t-w;
117 w = fn*pio2_3t-((t-r)-w);
118 y[0] = r-w;
119 }
120 }
121 }
122 y[1] = (r-y[0])-w;
123 return n;
124 }
125 /*
126 * all other (large) arguments
127 */
128 if(ex==0x7fff) { /* x is inf or NaN */
129 y[0]=y[1]=x-x; return 0;
130 }
131 /* set z = scalbn(|x|,ilogb(x)-23) */
132 u1.e = x;
133 e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
134 u1.xbits.expsign = ex - e0;
135 z = u1.e;
136 for(i=0;i<2;i++) {
137 tx[i] = (double)((int32_t)(z));
138 z = (z-(long double)tx[i])*(long double)two24;
139 }
140 tx[2] = z;
141 nx = 3;
142 while(tx[nx-1]==zero) nx--; /* skip zero term */
143 n = __kernel_rem_pio2(tx,ty,e0,nx,2);
144 r = (long double)ty[0] + (long double)ty[1];
145 w = (long double)ty[1] - (r - (long double)ty[0]);
146 if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
147 y[0] = r; y[1] = w; return n;
148 }
149
