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
37toint   = 1.5/EPS,
38#ifdef __wasilibc_unmodified_upstream // Wasm doesn't have alternate rounding modes
39pio4    = 0x1.921fb6p-1,
40#endif
41invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
42pio2_1  = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
43pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
44
45int __rem_pio2f(float x, double *y)
46{
47	union {float f; uint32_t i;} u = {x};
48	double tx[1],ty[1];
49	double_t fn;
50	uint32_t ix;
51	int n, sign, e0;
52
53	ix = u.i & 0x7fffffff;
54	/* 25+53 bit pi is good enough for medium size */
55	if (ix < 0x4dc90fdb) {  /* |x| ~< 2^28*(pi/2), medium size */
56		/* Use a specialized rint() to get fn. */
57		fn = (double_t)x*invpio2 + toint - toint;
58		n  = (int32_t)fn;
59		*y = x - fn*pio2_1 - fn*pio2_1t;
60#ifdef __wasilibc_unmodified_upstream // Wasm doesn't have alternate rounding modes
61		/* Matters with directed rounding. */
62		if (predict_false(*y < -pio4)) {
63			n--;
64			fn--;
65			*y = x - fn*pio2_1 - fn*pio2_1t;
66		} else if (predict_false(*y > pio4)) {
67			n++;
68			fn++;
69			*y = x - fn*pio2_1 - fn*pio2_1t;
70		}
71#endif
72		return n;
73	}
74	if(ix>=0x7f800000) {  /* x is inf or NaN */
75		*y = x-x;
76		return 0;
77	}
78	/* scale x into [2^23, 2^24-1] */
79	sign = u.i>>31;
80	e0 = (ix>>23) - (0x7f+23);  /* e0 = ilogb(|x|)-23, positive */
81	u.i = ix - (e0<<23);
82	tx[0] = u.f;
83	n  =  __rem_pio2_large(tx,ty,e0,1,0);
84	if (sign) {
85		*y = -ty[0];
86		return -n;
87	}
88	*y = ty[0];
89	return n;
90}