1 |
|
|
/* $OpenBSD: b_exp__D.c,v 1.6 2016/09/12 04:39:47 guenther Exp $ */ |
2 |
|
|
/* |
3 |
|
|
* Copyright (c) 1985, 1993 |
4 |
|
|
* The Regents of the University of California. All rights reserved. |
5 |
|
|
* |
6 |
|
|
* Redistribution and use in source and binary forms, with or without |
7 |
|
|
* modification, are permitted provided that the following conditions |
8 |
|
|
* are met: |
9 |
|
|
* 1. Redistributions of source code must retain the above copyright |
10 |
|
|
* notice, this list of conditions and the following disclaimer. |
11 |
|
|
* 2. Redistributions in binary form must reproduce the above copyright |
12 |
|
|
* notice, this list of conditions and the following disclaimer in the |
13 |
|
|
* documentation and/or other materials provided with the distribution. |
14 |
|
|
* 3. Neither the name of the University nor the names of its contributors |
15 |
|
|
* may be used to endorse or promote products derived from this software |
16 |
|
|
* without specific prior written permission. |
17 |
|
|
* |
18 |
|
|
* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND |
19 |
|
|
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
20 |
|
|
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
21 |
|
|
* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE |
22 |
|
|
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
23 |
|
|
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
24 |
|
|
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
25 |
|
|
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
26 |
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
27 |
|
|
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
28 |
|
|
* SUCH DAMAGE. |
29 |
|
|
*/ |
30 |
|
|
|
31 |
|
|
/* EXP(X) |
32 |
|
|
* RETURN THE EXPONENTIAL OF X |
33 |
|
|
* DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) |
34 |
|
|
* CODED IN C BY K.C. NG, 1/19/85; |
35 |
|
|
* REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. |
36 |
|
|
* |
37 |
|
|
* Required system supported functions: |
38 |
|
|
* scalb(x,n) |
39 |
|
|
* copysign(x,y) |
40 |
|
|
* isfinite(x) |
41 |
|
|
* |
42 |
|
|
* Method: |
43 |
|
|
* 1. Argument Reduction: given the input x, find r and integer k such |
44 |
|
|
* that |
45 |
|
|
* x = k*ln2 + r, |r| <= 0.5*ln2 . |
46 |
|
|
* r will be represented as r := z+c for better accuracy. |
47 |
|
|
* |
48 |
|
|
* 2. Compute exp(r) by |
49 |
|
|
* |
50 |
|
|
* exp(r) = 1 + r + r*R1/(2-R1), |
51 |
|
|
* where |
52 |
|
|
* R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). |
53 |
|
|
* |
54 |
|
|
* 3. exp(x) = 2^k * exp(r) . |
55 |
|
|
* |
56 |
|
|
* Special cases: |
57 |
|
|
* exp(INF) is INF, exp(NaN) is NaN; |
58 |
|
|
* exp(-INF)= 0; |
59 |
|
|
* for finite argument, only exp(0)=1 is exact. |
60 |
|
|
* |
61 |
|
|
* Accuracy: |
62 |
|
|
* exp(x) returns the exponential of x nearly rounded. In a test run |
63 |
|
|
* with 1,156,000 random arguments on a VAX, the maximum observed |
64 |
|
|
* error was 0.869 ulps (units in the last place). |
65 |
|
|
*/ |
66 |
|
|
|
67 |
|
|
#include "math.h" |
68 |
|
|
#include "math_private.h" |
69 |
|
|
|
70 |
|
|
static const double p1 = 0x1.555555555553ep-3; |
71 |
|
|
static const double p2 = -0x1.6c16c16bebd93p-9; |
72 |
|
|
static const double p3 = 0x1.1566aaf25de2cp-14; |
73 |
|
|
static const double p4 = -0x1.bbd41c5d26bf1p-20; |
74 |
|
|
static const double p5 = 0x1.6376972bea4d0p-25; |
75 |
|
|
static const double ln2hi = 0x1.62e42fee00000p-1; |
76 |
|
|
static const double ln2lo = 0x1.a39ef35793c76p-33; |
77 |
|
|
static const double lnhuge = 0x1.6602b15b7ecf2p9; |
78 |
|
|
static const double lntiny = -0x1.77af8ebeae354p9; |
79 |
|
|
static const double invln2 = 0x1.71547652b82fep0; |
80 |
|
|
|
81 |
|
|
/* returns exp(r = x + c) for |c| < |x| with no overlap. */ |
82 |
|
|
|
83 |
|
|
double |
84 |
|
|
__exp__D(double x, double c) |
85 |
|
|
{ |
86 |
|
|
double z, hi, lo; |
87 |
|
|
int k; |
88 |
|
|
|
89 |
✗✓ |
20 |
if (isnan(x)) /* x is NaN */ |
90 |
|
|
return(x); |
91 |
✓✗ |
10 |
if ( x <= lnhuge ) { |
92 |
✓✗ |
10 |
if ( x >= lntiny ) { |
93 |
|
|
|
94 |
|
|
/* argument reduction : x --> x - k*ln2 */ |
95 |
|
10 |
z = invln2*x; |
96 |
|
10 |
k = z + copysign(.5, x); |
97 |
|
|
|
98 |
|
|
/* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ |
99 |
|
|
|
100 |
|
10 |
hi=(x-k*ln2hi); /* Exact. */ |
101 |
|
10 |
x= hi - (lo = k*ln2lo-c); |
102 |
|
|
/* return 2^k*[1+x+x*c/(2+c)] */ |
103 |
|
10 |
z=x*x; |
104 |
|
10 |
c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); |
105 |
|
10 |
c = (x*c)/(2.0-c); |
106 |
|
|
|
107 |
|
10 |
return scalb(1.+(hi-(lo - c)), k); |
108 |
|
|
} |
109 |
|
|
/* end of x > lntiny */ |
110 |
|
|
|
111 |
|
|
else |
112 |
|
|
/* exp(-big#) underflows to zero */ |
113 |
|
|
if(isfinite(x)) return(scalb(1.0,-5000)); |
114 |
|
|
|
115 |
|
|
/* exp(-INF) is zero */ |
116 |
|
|
else return(0.0); |
117 |
|
|
} |
118 |
|
|
/* end of x < lnhuge */ |
119 |
|
|
|
120 |
|
|
else |
121 |
|
|
/* exp(INF) is INF, exp(+big#) overflows to INF */ |
122 |
|
|
return( isfinite(x) ? scalb(1.0,5000) : x); |
123 |
|
10 |
} |