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/* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
/*
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
* Debugged and optimized by Bruce D. Evans.
*/
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __rem_pio2f(x,y)
*
* return the remainder of x rem pi/2 in *y
* use double precision for everything except passing x
* use __rem_pio2_large() for large x
*/
#include "libm.h"
#if FLT_EVAL_METHOD == 0 || FLT_EVAL_METHOD == 1
#define EPS DBL_EPSILON
#elif FLT_EVAL_METHOD == 2
#define EPS LDBL_EPSILON
#endif
/*
* invpio2: 53 bits of 2/pi
* pio2_1: first 25 bits of pi/2
* pio2_1t: pi/2 - pio2_1
*/
static const double toint = 1.5 / EPS, pio4 = 0x1.921fb6p-1,
invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30,
0x6DC9C883 */
pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
int __rem_pio2f(float x, double *y)
{
union {
float f;
uint32_t i;
} u = { x };
double tx[1], ty[1];
double_t fn;
uint32_t ix;
int n, sign, e0;
ix = u.i & 0x7fffffff;
/* 25+53 bit pi is good enough for medium size */
if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
/* Use a specialized rint() to get fn. */
fn = (double_t)x * invpio2 + toint - toint;
n = (int32_t)fn;
*y = x - fn * pio2_1 - fn * pio2_1t;
/* Matters with directed rounding. */
if (predict_false(*y < -pio4)) {
n--;
fn--;
*y = x - fn * pio2_1 - fn * pio2_1t;
} else if (predict_false(*y > pio4)) {
n++;
fn++;
*y = x - fn * pio2_1 - fn * pio2_1t;
}
return n;
}
if (ix >= 0x7f800000) { /* x is inf or NaN */
*y = x - x;
return 0;
}
/* scale x into [2^23, 2^24-1] */
sign = u.i >> 31;
e0 = (ix >> 23) - (0x7f + 23); /* e0 = ilogb(|x|)-23, positive */
u.i = ix - (e0 << 23);
tx[0] = u.f;
n = __rem_pio2_large(tx, ty, e0, 1, 0);
if (sign) {
*y = -ty[0];
return -n;
}
*y = ty[0];
return n;
}
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