github.com/afumu/libc@v0.0.6/musl/src/math/__rem_pio2f.c (about)

     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   */
    36  static const double
    37  toint   = 1.5/EPS,
    38  pio4    = 0x1.921fb6p-1,
    39  invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
    40  pio2_1  = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
    41  pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
    42  
    43  int __rem_pio2f(float x, double *y)
    44  {
    45  	union {float f; uint32_t i;} u = {x};
    46  	double tx[1],ty[1];
    47  	double_t fn;
    48  	uint32_t ix;
    49  	int n, sign, e0;
    50  
    51  	ix = u.i & 0x7fffffff;
    52  	/* 25+53 bit pi is good enough for medium size */
    53  	if (ix < 0x4dc90fdb) {  /* |x| ~< 2^28*(pi/2), medium size */
    54  		/* Use a specialized rint() to get fn. */
    55  		fn = (double_t)x*invpio2 + toint - toint;
    56  		n  = (int32_t)fn;
    57  		*y = x - fn*pio2_1 - fn*pio2_1t;
    58  		/* Matters with directed rounding. */
    59  		if (predict_false(*y < -pio4)) {
    60  			n--;
    61  			fn--;
    62  			*y = x - fn*pio2_1 - fn*pio2_1t;
    63  		} else if (predict_false(*y > pio4)) {
    64  			n++;
    65  			fn++;
    66  			*y = x - fn*pio2_1 - fn*pio2_1t;
    67  		}
    68  		return n;
    69  	}
    70  	if(ix>=0x7f800000) {  /* x is inf or NaN */
    71  		*y = x-x;
    72  		return 0;
    73  	}
    74  	/* scale x into [2^23, 2^24-1] */
    75  	sign = u.i>>31;
    76  	e0 = (ix>>23) - (0x7f+23);  /* e0 = ilogb(|x|)-23, positive */
    77  	u.i = ix - (e0<<23);
    78  	tx[0] = u.f;
    79  	n  =  __rem_pio2_large(tx,ty,e0,1,0);
    80  	if (sign) {
    81  		*y = -ty[0];
    82  		return -n;
    83  	}
    84  	*y = ty[0];
    85  	return n;
    86  }