src/libm/k_tan.c
author Ryan C. Gordon <icculus@icculus.org>
Fri, 12 Aug 2016 19:59:00 -0400
changeset 10266 c09f06c4e8c8
parent 8840 9b6ddcbdea65
permissions -rw-r--r--
emscripten: send fake mouse events for touches, like other targets do. (This really should be handled at the higher level and not in the individual targets, but this fixes the immediate bug.)

/*
 * ====================================================
 * 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_tan( x, y, k )
 * kernel tan 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 k indicates whether tan (if k=1) or
 * -1/tan (if k= -1) is returned.
 *
 * Algorithm
 *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
 *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
 *	3. tan(x) is approximated by a odd polynomial of degree 27 on
 *	   [0,0.67434]
 *		  	         3             27
 *	   	tan(x) ~ x + T1*x + ... + T13*x
 *	   where
 *
 * 	        |tan(x)         2     4            26   |     -59.2
 * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
 * 	        |  x 					|
 *
 *	   Note: tan(x+y) = tan(x) + tan'(x)*y
 *		          ~ tan(x) + (1+x*x)*y
 *	   Therefore, for better accuracy in computing tan(x+y), let
 *		     3      2      2       2       2
 *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
 *	   then
 *		 		    3    2
 *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
 *
 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
 *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
 *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
 */

#include "math_libm.h"
#include "math_private.h"

static const double
one   =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pio4  =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
pio4lo=  3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
T[] =  {
  3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
  1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
  5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
  2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
  8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
  3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
  1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
  5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
  2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
  7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
  7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
 -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
  2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
};

double __kernel_tan(double x, double y, int iy)
{
	double z,r,v,w,s;
	int32_t ix,hx;
	GET_HIGH_WORD(hx,x);
	ix = hx&0x7fffffff;	/* high word of |x| */
	if(ix<0x3e300000)			/* x < 2**-28 */
	    {if((int)x==0) {			/* generate inexact */
	        u_int32_t low;
		GET_LOW_WORD(low,x);
		if(((ix|low)|(iy+1))==0) return one/fabs(x);
		else return (iy==1)? x: -one/x;
	    }
	    }
	if(ix>=0x3FE59428) { 			/* |x|>=0.6744 */
	    if(hx<0) {x = -x; y = -y;}
	    z = pio4-x;
	    w = pio4lo-y;
	    x = z+w; y = 0.0;
	}
	z	=  x*x;
	w 	=  z*z;
    /* Break x^5*(T[1]+x^2*T[2]+...) into
     *	  x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
     *	  x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
     */
	r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11]))));
	v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12])))));
	s = z*x;
	r = y + z*(s*(r+v)+y);
	r += T[0]*s;
	w = x+r;
	if(ix>=0x3FE59428) {
	    v = (double)iy;
	    return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r)));
	}
	if(iy==1) return w;
	else {		/* if allow error up to 2 ulp,
			   simply return -1.0/(x+r) here */
     /*  compute -1.0/(x+r) accurately */
	    double a,t;
	    z  = w;
	    SET_LOW_WORD(z,0);
	    v  = r-(z - x); 	/* z+v = r+x */
	    t = a  = -1.0/w;	/* a = -1.0/w */
	    SET_LOW_WORD(t,0);
	    s  = 1.0+t*z;
	    return t+a*(s+t*v);
	}
}