1570af302Sopenharmony_ci/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
2570af302Sopenharmony_ci/*
3570af302Sopenharmony_ci * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4570af302Sopenharmony_ci * Debugged and optimized by Bruce D. Evans.
5570af302Sopenharmony_ci */
6570af302Sopenharmony_ci/*
7570af302Sopenharmony_ci * ====================================================
8570af302Sopenharmony_ci * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9570af302Sopenharmony_ci *
10570af302Sopenharmony_ci * Developed at SunPro, a Sun Microsystems, Inc. business.
11570af302Sopenharmony_ci * Permission to use, copy, modify, and distribute this
12570af302Sopenharmony_ci * software is freely granted, provided that this notice
13570af302Sopenharmony_ci * is preserved.
14570af302Sopenharmony_ci * ====================================================
15570af302Sopenharmony_ci */
16570af302Sopenharmony_ci/* __rem_pio2f(x,y)
17570af302Sopenharmony_ci *
18570af302Sopenharmony_ci * return the remainder of x rem pi/2 in *y
19570af302Sopenharmony_ci * use double precision for everything except passing x
20570af302Sopenharmony_ci * use __rem_pio2_large() for large x
21570af302Sopenharmony_ci */
22570af302Sopenharmony_ci
23570af302Sopenharmony_ci#include "libm.h"
24570af302Sopenharmony_ci
25570af302Sopenharmony_ci#if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
26570af302Sopenharmony_ci#define EPS DBL_EPSILON
27570af302Sopenharmony_ci#elif FLT_EVAL_METHOD==2
28570af302Sopenharmony_ci#define EPS LDBL_EPSILON
29570af302Sopenharmony_ci#endif
30570af302Sopenharmony_ci
31570af302Sopenharmony_ci/*
32570af302Sopenharmony_ci * invpio2:  53 bits of 2/pi
33570af302Sopenharmony_ci * pio2_1:   first 25 bits of pi/2
34570af302Sopenharmony_ci * pio2_1t:  pi/2 - pio2_1
35570af302Sopenharmony_ci */
36570af302Sopenharmony_cistatic const double
37570af302Sopenharmony_citoint   = 1.5/EPS,
38570af302Sopenharmony_cipio4    = 0x1.921fb6p-1,
39570af302Sopenharmony_ciinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
40570af302Sopenharmony_cipio2_1  = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
41570af302Sopenharmony_cipio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
42570af302Sopenharmony_ci
43570af302Sopenharmony_ciint __rem_pio2f(float x, double *y)
44570af302Sopenharmony_ci{
45570af302Sopenharmony_ci	union {float f; uint32_t i;} u = {x};
46570af302Sopenharmony_ci	double tx[1],ty[1];
47570af302Sopenharmony_ci	double_t fn;
48570af302Sopenharmony_ci	uint32_t ix;
49570af302Sopenharmony_ci	int n, sign, e0;
50570af302Sopenharmony_ci
51570af302Sopenharmony_ci	ix = u.i & 0x7fffffff;
52570af302Sopenharmony_ci	/* 25+53 bit pi is good enough for medium size */
53570af302Sopenharmony_ci	if (ix < 0x4dc90fdb) {  /* |x| ~< 2^28*(pi/2), medium size */
54570af302Sopenharmony_ci		/* Use a specialized rint() to get fn. */
55570af302Sopenharmony_ci		fn = (double_t)x*invpio2 + toint - toint;
56570af302Sopenharmony_ci		n  = (int32_t)fn;
57570af302Sopenharmony_ci		*y = x - fn*pio2_1 - fn*pio2_1t;
58570af302Sopenharmony_ci		/* Matters with directed rounding. */
59570af302Sopenharmony_ci		if (predict_false(*y < -pio4)) {
60570af302Sopenharmony_ci			n--;
61570af302Sopenharmony_ci			fn--;
62570af302Sopenharmony_ci			*y = x - fn*pio2_1 - fn*pio2_1t;
63570af302Sopenharmony_ci		} else if (predict_false(*y > pio4)) {
64570af302Sopenharmony_ci			n++;
65570af302Sopenharmony_ci			fn++;
66570af302Sopenharmony_ci			*y = x - fn*pio2_1 - fn*pio2_1t;
67570af302Sopenharmony_ci		}
68570af302Sopenharmony_ci		return n;
69570af302Sopenharmony_ci	}
70570af302Sopenharmony_ci	if(ix>=0x7f800000) {  /* x is inf or NaN */
71570af302Sopenharmony_ci		*y = x-x;
72570af302Sopenharmony_ci		return 0;
73570af302Sopenharmony_ci	}
74570af302Sopenharmony_ci	/* scale x into [2^23, 2^24-1] */
75570af302Sopenharmony_ci	sign = u.i>>31;
76570af302Sopenharmony_ci	e0 = (ix>>23) - (0x7f+23);  /* e0 = ilogb(|x|)-23, positive */
77570af302Sopenharmony_ci	u.i = ix - (e0<<23);
78570af302Sopenharmony_ci	tx[0] = u.f;
79570af302Sopenharmony_ci	n  =  __rem_pio2_large(tx,ty,e0,1,0);
80570af302Sopenharmony_ci	if (sign) {
81570af302Sopenharmony_ci		*y = -ty[0];
82570af302Sopenharmony_ci		return -n;
83570af302Sopenharmony_ci	}
84570af302Sopenharmony_ci	*y = ty[0];
85570af302Sopenharmony_ci	return n;
86570af302Sopenharmony_ci}
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