GCC Code Coverage Report
Directory: ./ Exec Total Coverage
File: lib/libm/src/k_cos.c Lines: 14 15 93.3 %
Date: 2017-11-13 Branches: 5 8 62.5 %

Line Branch Exec Source
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/* @(#)k_cos.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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/*
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 * __kernel_cos( x,  y )
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 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
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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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 *
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 * Algorithm
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 *	1. Since cos(-x) = cos(x), we need only to consider positive x.
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 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
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 *	3. cos(x) is approximated by a polynomial of degree 14 on
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 *	   [0,pi/4]
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 *		  	                 4            14
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 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
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 *	   where the Remes error is
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 *
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 * 	|              2     4     6     8     10    12     14 |     -58
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 * 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
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 * 	|    					               |
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 *
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 * 	               4     6     8     10    12     14
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 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
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 *	       cos(x) = 1 - x*x/2 + r
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 *	   since cos(x+y) ~ cos(x) - sin(x)*y
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 *			  ~ cos(x) - x*y,
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 *	   a correction term is necessary in cos(x) and hence
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 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
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 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
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 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
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 *	   Then
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 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
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 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
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 *	   magnitude of the latter is at least a quarter of x*x/2,
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 *	   thus, reducing the rounding error in the subtraction.
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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
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one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
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C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
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C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
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C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
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C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
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C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
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double
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__kernel_cos(double x, double y)
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{
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	double a,hz,z,r,qx;
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	int32_t ix;
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1812
	GET_HIGH_WORD(ix,x);
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906
	ix &= 0x7fffffff;			/* ix = |x|'s high word*/
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	if(ix<0x3e400000) {			/* if x < 2**27 */
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	    if(((int)x)==0) return one;		/* generate inexact */
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	}
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	z  = x*x;
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	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
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	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
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	    return one - (0.5*z - (z*r - x*y));
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	else {
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	    if(ix > 0x3fe90000) {		/* x > 0.78125 */
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		qx = 0.28125;
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	    } else {
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	        INSERT_WORDS(qx,ix-0x00200000,0);	/* x/4 */
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	    }
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	    hz = 0.5*z-qx;
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	    a  = one-qx;
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	    return a - (hz - (z*r-x*y));
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	}
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}