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f28ff572 ZAL |
1 | /* |
2 | * Copyright (c) 1985 Regents of the University of California. | |
3 | * | |
4 | * Use and reproduction of this software are granted in accordance with | |
5 | * the terms and conditions specified in the Berkeley Software License | |
6 | * Agreement (in particular, this entails acknowledgement of the programs' | |
7 | * source, and inclusion of this notice) with the additional understanding | |
8 | * that all recipients should regard themselves as participants in an | |
9 | * ongoing research project and hence should feel obligated to report | |
10 | * their experiences (good or bad) with these elementary function codes, | |
11 | * using "sendbug 4bsd-bugs@BERKELEY", to the authors. | |
12 | */ | |
13 | ||
14 | #ifndef lint | |
15 | static char sccsid[] = "@(#)exp.c 1.1 (ELEFUNT) %G%"; | |
16 | #endif not lint | |
17 | ||
18 | /* EXP(X) | |
19 | * RETURN THE EXPONENTIAL OF X | |
20 | * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) | |
21 | * CODED IN C BY K.C. NG, 1/19/85; | |
22 | * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85. | |
23 | * | |
24 | * Required system supported functions: | |
25 | * scalb(x,n) | |
26 | * copysign(x,y) | |
27 | * finite(x) | |
28 | * | |
29 | * Kernel function: | |
30 | * exp__E(x,c) | |
31 | * | |
32 | * Method: | |
33 | * 1. Argument Reduction: given the input x, find r and integer k such | |
34 | * that | |
35 | * x = k*ln2 + r, |r| <= 0.5*ln2 . | |
36 | * r will be represented as r := z+c for better accuracy. | |
37 | * | |
38 | * 2. Compute expm1(r)=exp(r)-1 by | |
39 | * | |
40 | * expm1(r=z+c) := z + exp__E(z,r) | |
41 | * | |
42 | * 3. exp(x) = 2^k * ( expm1(r) + 1 ). | |
43 | * | |
44 | * Special cases: | |
45 | * exp(INF) is INF, exp(NaN) is NaN; | |
46 | * exp(-INF)= 0; | |
47 | * for finite argument, only exp(0)=1 is exact. | |
48 | * | |
49 | * Accuracy: | |
50 | * exp(x) returns the exponential of x nearly rounded. In a test run | |
51 | * with 1,156,000 random arguments on a VAX, the maximum observed | |
52 | * error was .768 ulps (units in the last place). | |
53 | * | |
54 | * Constants: | |
55 | * The hexadecimal values are the intended ones for the following constants. | |
56 | * The decimal values may be used, provided that the compiler will convert | |
57 | * from decimal to binary accurately enough to produce the hexadecimal values | |
58 | * shown. | |
59 | */ | |
60 | ||
61 | #ifdef VAX /* VAX D format */ | |
62 | /* double static */ | |
63 | /* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */ | |
64 | /* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */ | |
65 | /* lnhuge = 9.4961163736712506989E1 , Hex 2^ 7 * .BDEC1DA73E9010 */ | |
66 | /* lntiny = -9.5654310917272452386E1 , Hex 2^ 7 * -.BF4F01D72E33AF */ | |
67 | /* invln2 = 1.4426950408889634148E0 ; Hex 2^ 1 * .B8AA3B295C17F1 */ | |
68 | static long ln2hix[] = { 0x72174031, 0x0000f7d0}; | |
69 | static long ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1}; | |
70 | static long lnhugex[] = { 0xec1d43bd, 0x9010a73e}; | |
71 | static long lntinyx[] = { 0x4f01c3bf, 0x33afd72e}; | |
72 | static long invln2x[] = { 0xaa3b40b8, 0x17f1295c}; | |
73 | #define ln2hi (*(double*)ln2hix) | |
74 | #define ln2lo (*(double*)ln2lox) | |
75 | #define lnhuge (*(double*)lnhugex) | |
76 | #define lntiny (*(double*)lntinyx) | |
77 | #define invln2 (*(double*)invln2x) | |
78 | #else /* IEEE double */ | |
79 | double static | |
80 | ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */ | |
81 | ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */ | |
82 | lnhuge = 7.1602103751842355450E2 , /*Hex 2^ 9 * 1.6602B15B7ECF2 */ | |
83 | lntiny = -7.5137154372698068983E2 , /*Hex 2^ 9 * -1.77AF8EBEAE354 */ | |
84 | invln2 = 1.4426950408889633870E0 ; /*Hex 2^ 0 * 1.71547652B82FE */ | |
85 | #endif | |
86 | ||
87 | double exp(x) | |
88 | double x; | |
89 | { | |
90 | double scalb(), copysign(), exp__E(), z,hi,lo,c; | |
91 | int k,finite(); | |
92 | ||
93 | #ifndef VAX | |
94 | if(x!=x) return(x); /* x is NaN */ | |
95 | #endif | |
96 | if( x <= lnhuge ) { | |
97 | if( x >= lntiny ) { | |
98 | ||
99 | /* argument reduction : x --> x - k*ln2 */ | |
100 | ||
101 | k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ | |
102 | ||
103 | /* express x-k*ln2 as z+c */ | |
104 | hi=x-k*ln2hi; | |
105 | z=hi-(lo=k*ln2lo); | |
106 | c=(hi-z)-lo; | |
107 | ||
108 | /* return 2^k*[expm1(x) + 1] */ | |
109 | z += exp__E(z,c); | |
110 | return (scalb(z+1.0,k)); | |
111 | } | |
112 | /* end of x > lntiny */ | |
113 | ||
114 | else | |
115 | /* exp(-big#) underflows to zero */ | |
116 | if(finite(x)) return(scalb(1.0,-5000)); | |
117 | ||
118 | /* exp(-INF) is zero */ | |
119 | else return(0.0); | |
120 | } | |
121 | /* end of x < lnhuge */ | |
122 | ||
123 | else | |
124 | /* exp(INF) is INF, exp(+big#) overflows to INF */ | |
125 | return( finite(x) ? scalb(1.0,5000) : x); | |
126 | } |