![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to exp.c CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [CSRG BSD Unix] / 43BSDReno / lib / libm / common_source|
Return to exp.c CVS log | Up to [CSRG BSD Unix] / 43BSDReno / lib / libm / common_source |
1.1 root 1: /*
2: * Copyright (c) 1985 Regents of the University of California.
3: * All rights reserved.
4: *
5: * Redistribution and use in source and binary forms are permitted
6: * provided that: (1) source distributions retain this entire copyright
7: * notice and comment, and (2) distributions including binaries display
8: * the following acknowledgement: ``This product includes software
9: * developed by the University of California, Berkeley and its contributors''
10: * in the documentation or other materials provided with the distribution
11: * and in all advertising materials mentioning features or use of this
12: * software. Neither the name of the University nor the names of its
13: * contributors may be used to endorse or promote products derived
14: * from this software without specific prior written permission.
15: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
16: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
17: * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
18: *
19: * All recipients should regard themselves as participants in an ongoing
20: * research project and hence should feel obligated to report their
21: * experiences (good or bad) with these elementary function codes, using
22: * the sendbug(8) program, to the authors.
23: */
24:
25: #ifndef lint
26: static char sccsid[] = "@(#)exp.c 5.5 (Berkeley) 6/1/90";
27: #endif /* not lint */
28:
29: /* EXP(X)
30: * RETURN THE EXPONENTIAL OF X
31: * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
32: * CODED IN C BY K.C. NG, 1/19/85;
33: * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86.
34: *
35: * Required system supported functions:
36: * scalb(x,n)
37: * copysign(x,y)
38: * finite(x)
39: *
40: * Method:
41: * 1. Argument Reduction: given the input x, find r and integer k such
42: * that
43: * x = k*ln2 + r, |r| <= 0.5*ln2 .
44: * r will be represented as r := z+c for better accuracy.
45: *
46: * 2. Compute exp(r) by
47: *
48: * exp(r) = 1 + r + r*R1/(2-R1),
49: * where
50: * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))).
51: *
52: * 3. exp(x) = 2^k * exp(r) .
53: *
54: * Special cases:
55: * exp(INF) is INF, exp(NaN) is NaN;
56: * exp(-INF)= 0;
57: * for finite argument, only exp(0)=1 is exact.
58: *
59: * Accuracy:
60: * exp(x) returns the exponential of x nearly rounded. In a test run
61: * with 1,156,000 random arguments on a VAX, the maximum observed
62: * error was 0.869 ulps (units in the last place).
63: *
64: * Constants:
65: * The hexadecimal values are the intended ones for the following constants.
66: * The decimal values may be used, provided that the compiler will convert
67: * from decimal to binary accurately enough to produce the hexadecimal values
68: * shown.
69: */
70:
71: #include "mathimpl.h"
72:
73: vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
74: vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
75: vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010)
76: vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF)
77: vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
78: vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1)
79: vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94)
80: vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F)
81: vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84)
82: vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683)
83:
84: #ifdef vccast
85: #define ln2hi vccast(ln2hi)
86: #define ln2lo vccast(ln2lo)
87: #define lnhuge vccast(lnhuge)
88: #define lntiny vccast(lntiny)
89: #define invln2 vccast(invln2)
90: #define p1 vccast(p1)
91: #define p2 vccast(p2)
92: #define p3 vccast(p3)
93: #define p4 vccast(p4)
94: #define p5 vccast(p5)
95: #endif
96:
97: ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E)
98: ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93)
99: ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C)
100: ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1)
101: ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0)
102: ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
103: ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76)
104: ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2)
105: ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354)
106: ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
107:
108: double exp(x)
109: double x;
110: {
111: double z,hi,lo,c;
112: int k;
113:
114: #if !defined(vax)&&!defined(tahoe)
115: if(x!=x) return(x); /* x is NaN */
116: #endif /* !defined(vax)&&!defined(tahoe) */
117: if( x <= lnhuge ) {
118: if( x >= lntiny ) {
119:
120: /* argument reduction : x --> x - k*ln2 */
121:
122: k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */
123:
124: /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */
125:
126: hi=x-k*ln2hi;
127: x=hi-(lo=k*ln2lo);
128:
129: /* return 2^k*[1+x+x*c/(2+c)] */
130: z=x*x;
131: c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5))));
132: return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k);
133:
134: }
135: /* end of x > lntiny */
136:
137: else
138: /* exp(-big#) underflows to zero */
139: if(finite(x)) return(scalb(1.0,-5000));
140:
141: /* exp(-INF) is zero */
142: else return(0.0);
143: }
144: /* end of x < lnhuge */
145:
146: else
147: /* exp(INF) is INF, exp(+big#) overflows to INF */
148: return( finite(x) ? scalb(1.0,5000) : x);
149: }
This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.