text: /*
   * ====================================================
   * 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.
   * ====================================================
   */
  
  /* __kernel_sin( x, y, iy)
   * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
   * Input x is assumed to be bounded by ~pi/4 in magnitude.
   * Input y is the tail of x.
   * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
   *
   * Algorithm
   *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
   *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
   *	3. sin(x) is approximated by a polynomial of degree 13 on
   *	   [0,pi/4]
   *		  	         3            13
   *	   	sin(x) ~ x + S1*x + ... + S6*x
   *	   where
   *
   * 	|sin(x)         2     4     6     8     10     12  |     -58
   * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
   * 	|  x 					           |
   *
   *	4. sin(x+y) = sin(x) + sin'(x')*y
   *		    ~ sin(x) + (1-x*x/2)*y
   *	   For better accuracy, let
   *		     3      2      2      2      2
   *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
   *	   then                   3    2
   *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
   */
  
  #include "math_libm.h"
  #include "math_private.h"
  
  static const double
  half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
  S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
  S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
  S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
  S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
  S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
  S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
  
  double attribute_hidden __kernel_sin(double x, double y, int iy)
  {
  	double z,r,v;
  	int32_t ix;
  	GET_HIGH_WORD(ix,x);
  	ix &= 0x7fffffff;			/* high word of x */
  	if(ix<0x3e400000)			/* |x| < 2**-27 */
  	   {if((int)x==0) return x;}		/* generate inexact */
  	z	=  x*x;
  	v	=  z*x;
  	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
  	if(iy==0) return x+v*(S1+z*r);
  	else      return x-((z*(half*y-v*r)-y)-v*S1);
  }
  