kc3-lang/libquadmath/math/sinq.c

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• Hash : 4f659ab9
  Author : Thomas de Grivel
  Date : 2025-11-02T19:33:45
  

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• math/sinq.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.
   * ====================================================
   */
  
  /* sinq(x)
   * Return sine function of x.
   *
   * kernel function:
   *	__quadmath_kernel_sinq		... sine function on [-pi/4,pi/4]
   *	__quadmath_kernel_cosq		... cose function on [-pi/4,pi/4]
   *	__quadmath_rem_pio2q	... 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 "quadmath-imp.h"
  
  __float128 sinq(__float128 x)
  {
  	__float128 y[2],z=0;
  	int64_t n, ix;
  
      /* High word of x. */
  	GET_FLT128_MSW64(ix,x);
  
      /* |x| ~< pi/4 */
  	ix &= 0x7fffffffffffffffLL;
  	if(ix <= 0x3ffe921fb54442d1LL)
  	  return __quadmath_kernel_sinq(x,z,0);
  
      /* sin(Inf or NaN) is NaN */
  	else if (ix>=0x7fff000000000000LL) {
  	    if (ix == 0x7fff000000000000LL) {
  		GET_FLT128_LSW64(n,x);
  		if (n == 0)
  		    errno = EDOM;
  	    }
  	    return x-x;
  	}
  
      /* argument reduction needed */
  	else {
  	    n = __quadmath_rem_pio2q(x,y);
  	    switch(n&3) {
  		case 0: return  __quadmath_kernel_sinq(y[0],y[1],1);
  		case 1: return  __quadmath_kernel_cosq(y[0],y[1]);
  		case 2: return -__quadmath_kernel_sinq(y[0],y[1],1);
  		default:
  			return -__quadmath_kernel_cosq(y[0],y[1]);
  	    }
  	}
  }
  

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