1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2.c */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
12 * Optimized by Bruce D. Evans.
16 * return the remainder of x rem pi/2 in y[0]+y[1]
17 * use __rem_pio2_large() for large x
23 * invpio2: 53 bits of 2/pi
24 * pio2_1: first 33 bit of pi/2
25 * pio2_1t: pi/2 - pio2_1
26 * pio2_2: second 33 bit of pi/2
27 * pio2_2t: pi/2 - (pio2_1+pio2_2)
28 * pio2_3: third 33 bit of pi/2
29 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
32 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
33 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
34 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
35 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
36 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
37 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
38 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
39 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
40 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
42 /* caller must handle the case when reduction is not needed: |x| ~<= pi/4 */
43 int __rem_pio2(double x, double *y)
47 int32_t e0,i,j,nx,n,ix,hx;
52 if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */
53 if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */
54 goto medium; /* cancellation -- use medium case */
55 if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */
57 z = x - pio2_1; /* one round good to 85 bits */
59 y[1] = (z-y[0]) - pio2_1t;
64 y[1] = (z-y[0]) + pio2_1t;
71 y[1] = (z-y[0]) - 2*pio2_1t;
76 y[1] = (z-y[0]) + 2*pio2_1t;
81 if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */
82 if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */
83 if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */
88 y[1] = (z-y[0]) - 3*pio2_1t;
93 y[1] = (z-y[0]) + 3*pio2_1t;
97 if (ix == 0x401921fb) /* |x| ~= 4pi/2 */
101 y[0] = z - 4*pio2_1t;
102 y[1] = (z-y[0]) - 4*pio2_1t;
106 y[0] = z + 4*pio2_1t;
107 y[1] = (z-y[0]) + 4*pio2_1t;
112 if (ix < 0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */
115 /* Use a specialized rint() to get fn. Assume round-to-nearest. */
116 STRICT_ASSIGN(double, fn, x*invpio2 + 0x1.8p52);
119 #ifdef HAVE_EFFICIENT_IRINT
125 w = fn*pio2_1t; /* 1st round, good to 85 bits */
128 GET_HIGH_WORD(high,y[0]);
129 i = j - ((high>>20)&0x7ff);
130 if (i > 16) { /* 2nd round, good to 118 bits */
134 w = fn*pio2_2t - ((t-r)-w);
136 GET_HIGH_WORD(high,y[0]);
137 i = j - ((high>>20)&0x7ff);
138 if (i > 49) { /* 3rd round, good to 151 bits, covers all cases */
142 w = fn*pio2_3t - ((t-r)-w);
150 * all other (large) arguments
152 if (ix >= 0x7ff00000) { /* x is inf or NaN */
156 /* set z = scalbn(|x|,ilogb(x)-23) */
158 e0 = (ix>>20) - 1046; /* e0 = ilogb(z)-23; */
159 INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low);
160 for (i=0; i<2; i++) {
161 tx[i] = (double)((int32_t)(z));
166 while (tx[nx-1] == zero) nx--; /* skip zero term */
167 n = __rem_pio2_large(tx,ty,e0,nx,1);