Head

GCC Code Coverage Report

Directory:	./		Exec	Total	Coverage
File:	lib/libm/src/ld80/e_expl.c	Lines:	16	17	94.1 %
Date:	2017-11-13	Branches:	5	6	83.3 %


/*	$OpenBSD: e_expl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $	*/

/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */

/*							expl.c
 *
 *	Exponential function, long double precision
 *
 *
 *
 * SYNOPSIS:
 *
 * long double x, y, expl();
 *
 * y = expl( x );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns e (2.71828...) raised to the x power.
 *
 * Range reduction is accomplished by separating the argument
 * into an integer k and fraction f such that
 *
 *     x    k  f
 *    e  = 2  e.
 *
 * A Pade' form of degree 2/3 is used to approximate exp(f) - 1
 * in the basic range [-0.5 ln 2, 0.5 ln 2].
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      +-10000     50000       1.12e-19    2.81e-20
 *
 *
 * Error amplification in the exponential function can be
 * a serious matter.  The error propagation involves
 * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
 * which shows that a 1 lsb error in representing X produces
 * a relative error of X times 1 lsb in the function.
 * While the routine gives an accurate result for arguments
 * that are exactly represented by a long double precision
 * computer number, the result contains amplified roundoff
 * error for large arguments not exactly represented.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * exp underflow    x < MINLOG         0.0
 * exp overflow     x > MAXLOG         MAXNUM
 *
 */

/*	Exponential function	*/

#include <math.h>

#include "math_private.h"

static long double P[3] = {
 1.2617719307481059087798E-4L,
 3.0299440770744196129956E-2L,
 9.9999999999999999991025E-1L,
};
static long double Q[4] = {
 3.0019850513866445504159E-6L,
 2.5244834034968410419224E-3L,
 2.2726554820815502876593E-1L,
 2.0000000000000000000897E0L,
};
static const long double C1 = 6.9314575195312500000000E-1L;
static const long double C2 = 1.4286068203094172321215E-6L;
static const long double MAXLOGL = 1.1356523406294143949492E4L;
static const long double MINLOGL = -1.13994985314888605586758E4L;
static const long double LOG2EL = 1.4426950408889634073599E0L;

long double
expl(long double x)
{
long double px, xx;
int n;

if( isnan(x) )
	return(x);
if( x > MAXLOGL)
	return( INFINITY );

if( x < MINLOGL )
	return(0.0L);

/* Express e**x = e**g 2**n
 *   = e**g e**( n loge(2) )
 *   = e**( g + n loge(2) )
 */
px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */
n = px;
x -= px * C1;
x -= px * C2;


/* rational approximation for exponential
 * of the fractional part:
 * e**x =  1 + 2x P(x**2)/( Q(x**2) - P(x**2) )
 */
xx = x * x;
px = x * __polevll( xx, P, 2 );
x =  px/( __polevll( xx, Q, 3 ) - px );
x = 1.0L + ldexpl( x, 1 );

x = ldexpl( x, n );
return(x);
}
DEF_STD(expl);


Generated by: GCOVR (Version 3.3)

Line	Branch	Exec	Source
1			/* $OpenBSD: e_expl.c,v 1.4 2016/09/12 19:47:02 guenther Exp $ */
2
3			/*
4			* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5			*
6			* Permission to use, copy, modify, and distribute this software for any
7			* purpose with or without fee is hereby granted, provided that the above
8			* copyright notice and this permission notice appear in all copies.
9			*
10			* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11			* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12			* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13			* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14			* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15			* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16			* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17			*/
18
19			/* expl.c
20			*
21			* Exponential function, long double precision
22			*
23			*
24			*
25			* SYNOPSIS:
26			*
27			* long double x, y, expl();
28			*
29			* y = expl( x );
30			*
31			*
32			*
33			* DESCRIPTION:
34			*
35			* Returns e (2.71828...) raised to the x power.
36			*
37			* Range reduction is accomplished by separating the argument
38			* into an integer k and fraction f such that
39			*
40			* x k f
41			* e = 2 e.
42			*
43			* A Pade' form of degree 2/3 is used to approximate exp(f) - 1
44			* in the basic range [-0.5 ln 2, 0.5 ln 2].
45			*
46			*
47			* ACCURACY:
48			*
49			* Relative error:
50			* arithmetic domain # trials peak rms
51			* IEEE +-10000 50000 1.12e-19 2.81e-20
52			*
53			*
54			* Error amplification in the exponential function can be
55			* a serious matter. The error propagation involves
56			* exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
57			* which shows that a 1 lsb error in representing X produces
58			* a relative error of X times 1 lsb in the function.
59			* While the routine gives an accurate result for arguments
60			* that are exactly represented by a long double precision
61			* computer number, the result contains amplified roundoff
62			* error for large arguments not exactly represented.
63			*
64			*
65			* ERROR MESSAGES:
66			*
67			* message condition value returned
68			* exp underflow x < MINLOG 0.0
69			* exp overflow x > MAXLOG MAXNUM
70			*
71			*/
72
73			/* Exponential function */
74
75			#include <math.h>
76
77			#include "math_private.h"
78
79			static long double P[3] = {
80			1.2617719307481059087798E-4L,
81			3.0299440770744196129956E-2L,
82			9.9999999999999999991025E-1L,
83			};
84			static long double Q[4] = {
85			3.0019850513866445504159E-6L,
86			2.5244834034968410419224E-3L,
87			2.2726554820815502876593E-1L,
88			2.0000000000000000000897E0L,
89			};
90			static const long double C1 = 6.9314575195312500000000E-1L;
91			static const long double C2 = 1.4286068203094172321215E-6L;
92			static const long double MAXLOGL = 1.1356523406294143949492E4L;
93			static const long double MINLOGL = -1.13994985314888605586758E4L;
94			static const long double LOG2EL = 1.4426950408889634073599E0L;
95
96			long double
97			expl(long double x)
98			{
99			long double px, xx;
100			int n;
101
102	✗✓	432	if( isnan(x) )
103			return(x);
104	✓✓	216	if( x > MAXLOGL)
105		3	return( INFINITY );
106
107	✓✓	213	if( x < MINLOGL )
108		3	return(0.0L);
109
110			/* Express ex = eg 2**n
111			* = eg e( n loge(2) )
112			* = e**( g + n loge(2) )
113			*/
114		210	px = floorl( LOG2EL * x + 0.5L ); /* floor() truncates toward -infinity. */
115		210	n = px;
116		210	x -= px * C1;
117		210	x -= px * C2;
118
119
120			/* rational approximation for exponential
121			* of the fractional part:
122			* ex = 1 + 2x P(x2)/( Q(x2) - P(x2) )
123			*/
124		210	xx = x * x;
125		210	px = x * __polevll( xx, P, 2 );
126		210	x = px/( __polevll( xx, Q, 3 ) - px );
127		210	x = 1.0L + ldexpl( x, 1 );
128
129		210	x = ldexpl( x, n );
130		210	return(x);
131		216	}
132			DEF_STD(expl);