/* 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;
}