1/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 * Debugged and optimized by Bruce D. Evans.
5 */
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16/* __rem_pio2f(x,y)
17 *
18 * return the remainder of x rem pi/2 in *y
19 * use double precision for everything except passing x
20 * use __rem_pio2_large() for large x
21 */
22
23#include "libm.h"
24
25#if FLT_EVAL_METHOD == 0 || FLT_EVAL_METHOD == 1
26#define EPS DBL_EPSILON
27#elif FLT_EVAL_METHOD == 2
28#define EPS LDBL_EPSILON
29#endif
30
31/*
32 * invpio2:  53 bits of 2/pi
33 * pio2_1:   first 25 bits of pi/2
34 * pio2_1t:  pi/2 - pio2_1
35 */
36static const double toint = 1.5 / EPS,
37                    invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
38    pio2_1 = 1.57079631090164184570e+00,                  /* 0x3FF921FB, 0x50000000 */
39    pio2_1t = 1.58932547735281966916e-08;                 /* 0x3E5110b4, 0x611A6263 */
40
41int __rem_pio2f(float x, double* y) {
42    union {
43        float f;
44        uint32_t i;
45    } u = {x};
46    double tx[1], ty[1];
47    double_t fn;
48    uint32_t ix;
49    int n, sign, e0;
50
51    ix = u.i & 0x7fffffff;
52    /* 25+53 bit pi is good enough for medium size */
53    if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
54        /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
55        fn = (double_t)x * invpio2 + toint - toint;
56        n = (int32_t)fn;
57        *y = x - fn * pio2_1 - fn * pio2_1t;
58        return n;
59    }
60    if (ix >= 0x7f800000) { /* x is inf or NaN */
61        *y = x - x;
62        return 0;
63    }
64    /* scale x into [2^23, 2^24-1] */
65    sign = u.i >> 31;
66    e0 = (ix >> 23) - (0x7f + 23); /* e0 = ilogb(|x|)-23, positive */
67    u.i = ix - (e0 << 23);
68    tx[0] = u.f;
69    n = __rem_pio2_large(tx, ty, e0, 1, 0);
70    if (sign) {
71        *y = -ty[0];
72        return -n;
73    }
74    *y = ty[0];
75    return n;
76}
77