sinl.c

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Author : Bruno Haible
Date : 2003-02-18 17:05:23
Hash : 5657b253
Message : Transcendental functions for 'long double', from Paolo Bonzini.
lib/sinl.c
/* s_sinl.c -- long double version of s_sin.c.
 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
 */

/*
 * ====================================================
 * 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.
 * ====================================================
 */

/* sinl(x)
 * Return sine function of x.
 *
 * kernel function:
 *	__kernel_sinl		... sine function on [-pi/4,pi/4]
 *	__kernel_cosl		... cose function on [-pi/4,pi/4]
 *	__ieee754_rem_pio2l	... argument reduction routine
 *
 * Method.
 *      Let S,C and T denote the sin, cos and tan respectively on
 *	[-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
 *	in [-pi/4 , +pi/4], and let n = k mod 4.
 *	We have
 *
 *          n        sin(x)      cos(x)        tan(x)
 *     ----------------------------------------------------------
 *	    0	       S	   C		 T
 *	    1	       C	  -S		-1/T
 *	    2	      -S	  -C		 T
 *	    3	      -C	   S		-1/T
 *     ----------------------------------------------------------
 *
 * Special cases:
 *      Let trig be any of sin, cos, or tan.
 *      trig(+-INF)  is NaN, with signals;
 *      trig(NaN)    is that NaN;
 *
 * Accuracy:
 *	TRIG(x) returns trig(x) nearly rounded
 */

#include <math.h>

#include "mathl.h"

#include "trigl.h"
#include "trigl.c"
#include "sincosl.c"

long double
sinl (long double x)
{
  long double y[2], z = 0.0L;
  int n;

  /* |x| ~< pi/4 */
  if (x >= -0.7853981633974483096156608458198757210492 &&
      x <= 0.7853981633974483096156608458198757210492)
    return kernel_sinl (x, z, 0);

    /* sinl(Inf or NaN) is NaN, sinl(0) is 0 */
  else if (x + x == x || x != x)
    return x - x;		/* NaN */

  /* argument reduction needed */
  else
    {
      n = ieee754_rem_pio2l (x, y);
      switch (n & 3)
	{
	case 0:
	  return kernel_sinl (y[0], y[1], 1);
	case 1:
	  return kernel_cosl (y[0], y[1]);
	case 2:
	  return -kernel_sinl (y[0], y[1], 1);
	default:
	  return -kernel_cosl (y[0], y[1]);
	}
    }
}

#if 0
int
main ()
{
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *29));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *2));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *30));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *4));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *32));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *2/3));
  printf ("%.16Lg\n", sinl(0.7853981633974483096156608458198757210492 *4/3));
}
#endif
kc3-lang/gnulib/lib/sinl.c

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