/* 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,
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.  Assume round-to-nearest. */
                fn = (double_t)x*invpio2 + toint - toint;
                n  = (int32_t)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;
}