GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/k_tan.c Lines: 0 45 0.0 %
Date: 2017-11-13 Branches: 0 16 0.0 %

Line Branch Exec Source
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/* @(#)k_tan.c 5.1 93/09/24 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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/* __kernel_tan( x, y, k )
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 * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
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 * Input x is assumed to be bounded by ~pi/4 in magnitude.
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 * Input y is the tail of x.
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 * Input k indicates whether tan (if k=1) or
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 * -1/tan (if k= -1) is returned.
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 *
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 * Algorithm
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 *	1. Since tan(-x) = -tan(x), we need only to consider positive x.
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 *	2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
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 *	3. tan(x) is approximated by a odd polynomial of degree 27 on
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 *	   [0,0.67434]
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 *		  	         3             27
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 *	   	tan(x) ~ x + T1*x + ... + T13*x
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 *	   where
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 *
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 * 	        |tan(x)         2     4            26   |     -59.2
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 * 	        |----- - (1+T1*x +T2*x +.... +T13*x    )| <= 2
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 * 	        |  x 					|
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 *
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 *	   Note: tan(x+y) = tan(x) + tan'(x)*y
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 *		          ~ tan(x) + (1+x*x)*y
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 *	   Therefore, for better accuracy in computing tan(x+y), let
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 *		     3      2      2       2       2
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 *		r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
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 *	   then
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 *		 		    3    2
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 *		tan(x+y) = x + (T1*x + (x *(r+y)+y))
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 *
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 *      4. For x in [0.67434,pi/4],  let y = pi/4 - x, then
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 *		tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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 *		       = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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 */
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#include "math.h"
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#include "math_private.h"
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static const double xxx[] = {
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		 3.33333333333334091986e-01,	/* 3FD55555, 55555563 */
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		 1.33333333333201242699e-01,	/* 3FC11111, 1110FE7A */
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		 5.39682539762260521377e-02,	/* 3FABA1BA, 1BB341FE */
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		 2.18694882948595424599e-02,	/* 3F9664F4, 8406D637 */
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		 8.86323982359930005737e-03,	/* 3F8226E3, E96E8493 */
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		 3.59207910759131235356e-03,	/* 3F6D6D22, C9560328 */
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		 1.45620945432529025516e-03,	/* 3F57DBC8, FEE08315 */
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		 5.88041240820264096874e-04,	/* 3F4344D8, F2F26501 */
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		 2.46463134818469906812e-04,	/* 3F3026F7, 1A8D1068 */
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		 7.81794442939557092300e-05,	/* 3F147E88, A03792A6 */
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		 7.14072491382608190305e-05,	/* 3F12B80F, 32F0A7E9 */
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		-1.85586374855275456654e-05,	/* BEF375CB, DB605373 */
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		 2.59073051863633712884e-05,	/* 3EFB2A70, 74BF7AD4 */
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/* one */	 1.00000000000000000000e+00,	/* 3FF00000, 00000000 */
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/* pio4 */	 7.85398163397448278999e-01,	/* 3FE921FB, 54442D18 */
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/* pio4lo */	 3.06161699786838301793e-17	/* 3C81A626, 33145C07 */
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};
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#define	one	xxx[13]
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#define	pio4	xxx[14]
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#define	pio4lo	xxx[15]
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#define	T	xxx
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double
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__kernel_tan(double x, double y, int iy)
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{
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	double z, r, v, w, s;
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	int32_t ix, hx;
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	GET_HIGH_WORD(hx, x);	/* high word of x */
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	ix = hx & 0x7fffffff;			/* high word of |x| */
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	if (ix < 0x3e300000) {			/* x < 2**-28 */
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		if ((int) x == 0) {		/* generate inexact */
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			u_int32_t low;
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			GET_LOW_WORD(low, x);
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			if(((ix | low) | (iy + 1)) == 0)
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				return one / fabs(x);
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			else {
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				if (iy == 1)
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					return x;
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				else {	/* compute -1 / (x+y) carefully */
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					double a, t;
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					z = w = x + y;
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					SET_LOW_WORD(z, 0);
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					v = y - (z - x);
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					t = a = -one / w;
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					SET_LOW_WORD(t, 0);
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					s = one + t * z;
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					return t + a * (s + t * v);
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				}
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			}
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		}
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	}
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	if (ix >= 0x3FE59428) {	/* |x| >= 0.6744 */
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		if (hx < 0) {
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			x = -x;
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			y = -y;
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		}
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		z = pio4 - x;
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		w = pio4lo - y;
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		x = z + w;
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		y = 0.0;
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	}
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	z = x * x;
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	w = z * z;
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	/*
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	 * Break x^5*(T[1]+x^2*T[2]+...) into
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	 * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
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	 * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
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	 */
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	r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
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		w * T[11]))));
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	v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
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		w * T[12])))));
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	s = z * x;
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	r = y + z * (s * (r + v) + y);
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	r += T[0] * s;
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	w = x + r;
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	if (ix >= 0x3FE59428) {
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		v = (double) iy;
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		return (double) (1 - ((hx >> 30) & 2)) *
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			(v - 2.0 * (x - (w * w / (w + v) - r)));
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	}
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	if (iy == 1)
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		return w;
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	else {
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		/*
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		 * if allow error up to 2 ulp, simply return
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		 * -1.0 / (x+r) here
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		 */
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		/* compute -1.0 / (x+r) accurately */
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		double a, t;
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		z = w;
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		SET_LOW_WORD(z, 0);
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		v = r - (z - x);	/* z+v = r+x */
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		t = a = -1.0 / w;	/* a = -1.0/w */
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		SET_LOW_WORD(t, 0);
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		s = 1.0 + t * z;
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		return t + a * (s + t * v);
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	}
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}