1 #include "FEATURE/uwin"
2
3 #if !_UWIN || _lib_expm1
4
_STUB_expm1()5 void _STUB_expm1(){}
6
7 #else
8
9 /*
10 * Copyright (c) 1985, 1993
11 * The Regents of the University of California. All rights reserved.
12 *
13 * Redistribution and use in source and binary forms, with or without
14 * modification, are permitted provided that the following conditions
15 * are met:
16 * 1. Redistributions of source code must retain the above copyright
17 * notice, this list of conditions and the following disclaimer.
18 * 2. Redistributions in binary form must reproduce the above copyright
19 * notice, this list of conditions and the following disclaimer in the
20 * documentation and/or other materials provided with the distribution.
21 * 3. Neither the name of the University nor the names of its contributors
22 * may be used to endorse or promote products derived from this software
23 * without specific prior written permission.
24 *
25 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
26 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
27 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
28 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
29 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
30 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
31 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
32 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
33 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
34 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
35 * SUCH DAMAGE.
36 */
37
38 #ifndef lint
39 static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93";
40 #endif /* not lint */
41
42 /* EXPM1(X)
43 * RETURN THE EXPONENTIAL OF X MINUS ONE
44 * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
45 * CODED IN C BY K.C. NG, 1/19/85;
46 * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
47 *
48 * Required system supported functions:
49 * scalb(x,n)
50 * copysign(x,y)
51 * finite(x)
52 *
53 * Kernel function:
54 * exp__E(x,c)
55 *
56 * Method:
57 * 1. Argument Reduction: given the input x, find r and integer k such
58 * that
59 * x = k*ln2 + r, |r| <= 0.5*ln2 .
60 * r will be represented as r := z+c for better accuracy.
61 *
62 * 2. Compute EXPM1(r)=exp(r)-1 by
63 *
64 * EXPM1(r=z+c) := z + exp__E(z,c)
65 *
66 * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ).
67 *
68 * Remarks:
69 * 1. When k=1 and z < -0.25, we use the following formula for
70 * better accuracy:
71 * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
72 * 2. To avoid rounding error in 1-2^-k where k is large, we use
73 * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
74 * when k>56.
75 *
76 * Special cases:
77 * EXPM1(INF) is INF, EXPM1(NaN) is NaN;
78 * EXPM1(-INF)= -1;
79 * for finite argument, only EXPM1(0)=0 is exact.
80 *
81 * Accuracy:
82 * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
83 * 1,166,000 random arguments on a VAX, the maximum observed error was
84 * .872 ulps (units of the last place).
85 *
86 * Constants:
87 * The hexadecimal values are the intended ones for the following constants.
88 * The decimal values may be used, provided that the compiler will convert
89 * from decimal to binary accurately enough to produce the hexadecimal values
90 * shown.
91 */
92
93 #include "mathimpl.h"
94
95 vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
96 vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
97 vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
98 vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
99
100 ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
101 ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
102 ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
103 ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
104
105 #ifdef vccast
106 #define ln2hi vccast(ln2hi)
107 #define ln2lo vccast(ln2lo)
108 #define lnhuge vccast(lnhuge)
109 #define invln2 vccast(invln2)
110 #endif
111
112 extern double expm1(x)
113 double x;
114 {
115 const static double one=1.0, half=1.0/2.0;
116 double z,hi,lo,c;
117 int k;
118 #if defined(vax)||defined(tahoe)
119 static prec=56;
120 #else /* defined(vax)||defined(tahoe) */
121 static prec=53;
122 #endif /* defined(vax)||defined(tahoe) */
123
124 #if !defined(vax)&&!defined(tahoe)
125 if(x!=x) return(x); /* x is NaN */
126 #endif /* !defined(vax)&&!defined(tahoe) */
127
128 if( x <= lnhuge ) {
129 if( x >= -40.0 ) {
130
131 /* argument reduction : x - k*ln2 */
132 k= (int)(invln2*x)+copysign(0.5,x); /* k=NINT(x/ln2) */
133 hi=x-k*ln2hi ;
134 z=hi-(lo=k*ln2lo);
135 c=(hi-z)-lo;
136
137 if(k==0) return(z+__exp__E(z,c));
138 if(k==1)
139 if(z< -0.25)
140 {x=z+half;x +=__exp__E(z,c); return(x+x);}
141 else
142 {z+=__exp__E(z,c); x=half+z; return(x+x);}
143 /* end of k=1 */
144
145 else {
146 if(k<=prec)
147 { x=one-scalb(one,-k); z += __exp__E(z,c);}
148 else if(k<100)
149 { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
150 else
151 { x = __exp__E(z,c)+z; z=one;}
152
153 return (scalb(x+z,k));
154 }
155 }
156 /* end of x > lnunfl */
157
158 else
159 /* expm1(-big#) rounded to -1 (inexact) */
160 if(finite(x))
161 { ln2hi+ln2lo; return(-one);}
162
163 /* expm1(-INF) is -1 */
164 else return(-one);
165 }
166 /* end of x < lnhuge */
167
168 else
169 /* expm1(INF) is INF, expm1(+big#) overflows to INF */
170 return( finite(x) ? scalb(one,5000) : x);
171 }
172
173 #endif
174