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

     1  /* origin: FreeBSD /usr/src/lib/msun/src/s_sin.c */
     2  /*
     3   * ====================================================
     4   * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
     5   *
     6   * Developed at SunPro, a Sun Microsystems, Inc. business.
     7   * Permission to use, copy, modify, and distribute this
     8   * software is freely granted, provided that this notice
     9   * is preserved.
    10   * ====================================================
    11   */
    12  /* sin(x)
    13   * Return sine function of x.
    14   *
    15   * kernel function:
    16   *      __sin            ... sine function on [-pi/4,pi/4]
    17   *      __cos            ... cose function on [-pi/4,pi/4]
    18   *      __rem_pio2       ... argument reduction routine
    19   *
    20   * Method.
    21   *      Let S,C and T denote the sin, cos and tan respectively on
    22   *      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
    23   *      in [-pi/4 , +pi/4], and let n = k mod 4.
    24   *      We have
    25   *
    26   *          n        sin(x)      cos(x)        tan(x)
    27   *     ----------------------------------------------------------
    28   *          0          S           C             T
    29   *          1          C          -S            -1/T
    30   *          2         -S          -C             T
    31   *          3         -C           S            -1/T
    32   *     ----------------------------------------------------------
    33   *
    34   * Special cases:
    35   *      Let trig be any of sin, cos, or tan.
    36   *      trig(+-INF)  is NaN, with signals;
    37   *      trig(NaN)    is that NaN;
    38   *
    39   * Accuracy:
    40   *      TRIG(x) returns trig(x) nearly rounded
    41   */
    42  
    43  #include "libm.h"
    44  
    45  double sin(double x)
    46  {
    47  	double y[2];
    48  	uint32_t ix;
    49  	unsigned n;
    50  
    51  	/* High word of x. */
    52  	GET_HIGH_WORD(ix, x);
    53  	ix &= 0x7fffffff;
    54  
    55  	/* |x| ~< pi/4 */
    56  	if (ix <= 0x3fe921fb) {
    57  		if (ix < 0x3e500000) {  /* |x| < 2**-26 */
    58  			/* raise inexact if x != 0 and underflow if subnormal*/
    59  			FORCE_EVAL(ix < 0x00100000 ? x/0x1p120f : x+0x1p120f);
    60  			return x;
    61  		}
    62  		return __sin(x, 0.0, 0);
    63  	}
    64  
    65  	/* sin(Inf or NaN) is NaN */
    66  	if (ix >= 0x7ff00000)
    67  		return x - x;
    68  
    69  	/* argument reduction needed */
    70  	n = __rem_pio2(x, y);
    71  	switch (n&3) {
    72  	case 0: return  __sin(y[0], y[1], 1);
    73  	case 1: return  __cos(y[0], y[1]);
    74  	case 2: return -__sin(y[0], y[1], 1);
    75  	default:
    76  		return -__cos(y[0], y[1]);
    77  	}
    78  }