1 /* origin: FreeBSD /usr/src/lib/msun/ld80/e_rem_pio2.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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
11 * ====================================================
13 * Optimized by Bruce D. Evans.
16 #if LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
17 /* ld80 version of __rem_pio2(x,y)
19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __rem_pio2_large() for large x
23 #define BIAS (LDBL_MAX_EXP - 1)
26 * invpio2: 64 bits of 2/pi
27 * pio2_1: first 39 bits of pi/2
28 * pio2_1t: pi/2 - pio2_1
29 * pio2_2: second 39 bits of pi/2
30 * pio2_2t: pi/2 - (pio2_1+pio2_2)
31 * pio2_3: third 39 bits of pi/2
32 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
35 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
36 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
37 pio2_1 = 1.57079632679597125389e+00, /* 0x3FF921FB, 0x54444000 */
38 pio2_2 = -1.07463465549783099519e-12, /* -0x12e7b967674000.0p-92 */
39 pio2_3 = 6.36831716351370313614e-25; /* 0x18a2e037074000.0p-133 */
41 static const long double
42 invpio2 = 6.36619772367581343076e-01L, /* 0xa2f9836e4e44152a.0p-64 */
43 pio2_1t = -1.07463465549719416346e-12L, /* -0x973dcb3b399d747f.0p-103 */
44 pio2_2t = 6.36831716351095013979e-25L, /* 0xc51701b839a25205.0p-144 */
45 pio2_3t = -2.75299651904407171810e-37L; /* -0xbb5bf6c7ddd660ce.0p-185 */
47 static inline int __rem_pio2l(long double x, long double *y)
49 union IEEEl2bits u,u1;
50 long double z,w,t,r,fn;
56 expsign = u.xbits.expsign;
57 ex = expsign & 0x7fff;
58 if (ex < BIAS + 25 || (ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2)) {
62 /* |x| ~< 2^25*(pi/2), medium size */
63 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
64 fn = x*invpio2 + 0x1.8p63;
67 //#ifdef HAVE_EFFICIENT_IRINT
73 w = fn*pio2_1t; /* 1st round good to 102 bit */
77 ex1 = u2.xbits.expsign & 0x7fff;
79 if (i > 22) { /* 2nd iteration needed, good to 141 */
83 w = fn*pio2_2t-((t-r)-w);
86 ex1 = u2.xbits.expsign & 0x7fff;
88 if (i > 61) { /* 3rd iteration need, 180 bits acc */
89 t = r; /* will cover all possible cases */
92 w = fn*pio2_3t-((t-r)-w);
96 y[1] = (r - y[0]) - w;
100 * all other (large) arguments
102 if (ex == 0x7fff) { /* x is inf or NaN */
106 /* set z = scalbn(|x|,ilogb(x)-23) */
108 e0 = ex - BIAS - 23; /* e0 = ilogb(|x|)-23; */
109 u1.xbits.expsign = ex - e0;
111 for (i=0; i<2; i++) {
112 tx[i] = (double)(int32_t)z;
117 while (tx[nx-1] == zero)
118 nx--; /* skip zero term */
119 n = __rem_pio2_large(tx,ty,e0,nx,2);
120 r = (long double)ty[0] + ty[1];
121 w = ty[1] - (r - ty[0]);