![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to exp__E.c CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [CSRG BSD Unix] / 43BSDTahoe / usr.lib / libm|
Return to exp__E.c CVS log | Up to [CSRG BSD Unix] / 43BSDTahoe / usr.lib / libm |
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 the above copyright notice and this paragraph are
7: * duplicated in all such forms and that any documentation,
8: * advertising materials, and other materials related to such
9: * distribution and use acknowledge that the software was developed
10: * by the University of California, Berkeley. The name of the
11: * University may not be used to endorse or promote products derived
12: * from this software without specific prior written permission.
13: * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
14: * IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
15: * WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
16: *
17: * All recipients should regard themselves as participants in an ongoing
18: * research project and hence should feel obligated to report their
19: * experiences (good or bad) with these elementary function codes, using
20: * the sendbug(8) program, to the authors.
21: */
22:
23: #ifndef lint
24: static char sccsid[] = "@(#)exp__E.c 5.3 (Berkeley) 6/30/88";
25: #endif /* not lint */
26:
27: /* exp__E(x,c)
28: * ASSUMPTION: c << x SO THAT fl(x+c)=x.
29: * (c is the correction term for x)
30: * exp__E RETURNS
31: *
32: * / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
33: * exp__E(x,c) = |
34: * \ 0 , |x| < 1E-19.
35: *
36: * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
37: * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
38: * CODED IN C BY K.C. NG, 1/31/85;
39: * REVISED BY K.C. NG on 3/16/85, 4/16/85.
40: *
41: * Required system supported function:
42: * copysign(x,y)
43: *
44: * Method:
45: * 1. Rational approximation. Let r=x+c.
46: * Based on
47: * 2 * sinh(r/2)
48: * exp(r) - 1 = ---------------------- ,
49: * cosh(r/2) - sinh(r/2)
50: * exp__E(r) is computed using
51: * x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
52: * --- + (c + x*[---------------------------------- + c ])
53: * 2 1 - W
54: * where P := p1*x^2 + p2*x^4,
55: * Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
56: * W := x/2-(Q-x*P),
57: *
58: * (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
59: * nomials P and Q may be regarded as the approximations to sinh
60: * and cosh :
61: * sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
62: *
63: * The coefficients were obtained by a special Remez algorithm.
64: *
65: * Approximation error:
66: *
67: * | exp(x) - 1 | 2**(-57), (IEEE double)
68: * | ------------ - (exp__E(x,0)+x)/x | <=
69: * | x | 2**(-69). (VAX D)
70: *
71: * Constants:
72: * The hexadecimal values are the intended ones for the following constants.
73: * The decimal values may be used, provided that the compiler will convert
74: * from decimal to binary accurately enough to produce the hexadecimal values
75: * shown.
76: */
77:
78: #if defined(vax)||defined(tahoe) /* VAX D format */
79: #ifdef vax
80: #define _0x(A,B) 0x/**/A/**/B
81: #else /* vax */
82: #define _0x(A,B) 0x/**/B/**/A
83: #endif /* vax */
84: /* static double */
85: /* p1 = 1.5150724356786683059E-2 , Hex 2^ -6 * .F83ABE67E1066A */
86: /* p2 = 6.3112487873718332688E-5 , Hex 2^-13 * .845B4248CD0173 */
87: /* q1 = 1.1363478204690669916E-1 , Hex 2^ -3 * .E8B95A44A2EC45 */
88: /* q2 = 1.2624568129896839182E-3 , Hex 2^ -9 * .A5790572E4F5E7 */
89: /* q3 = 1.5021856115869022674E-6 ; Hex 2^-19 * .C99EB4604AC395 */
90: static long p1x[] = { _0x(3abe,3d78), _0x(066a,67e1)};
91: static long p2x[] = { _0x(5b42,3984), _0x(0173,48cd)};
92: static long q1x[] = { _0x(b95a,3ee8), _0x(ec45,44a2)};
93: static long q2x[] = { _0x(7905,3ba5), _0x(f5e7,72e4)};
94: static long q3x[] = { _0x(9eb4,36c9), _0x(c395,604a)};
95: #define p1 (*(double*)p1x)
96: #define p2 (*(double*)p2x)
97: #define q1 (*(double*)q1x)
98: #define q2 (*(double*)q2x)
99: #define q3 (*(double*)q3x)
100: #else /* defined(vax)||defined(tahoe) */
101: static double
102: p1 = 1.3887401997267371720E-2 , /*Hex 2^ -7 * 1.C70FF8B3CC2CF */
103: p2 = 3.3044019718331897649E-5 , /*Hex 2^-15 * 1.15317DF4526C4 */
104: q1 = 1.1110813732786649355E-1 , /*Hex 2^ -4 * 1.C719538248597 */
105: q2 = 9.9176615021572857300E-4 ; /*Hex 2^-10 * 1.03FC4CB8C98E8 */
106: #endif /* defined(vax)||defined(tahoe) */
107:
108: double exp__E(x,c)
109: double x,c;
110: {
111: static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
112: double copysign(),z,p,q,xp,xh,w;
113: if(copysign(x,one)>small) {
114: z = x*x ;
115: p = z*( p1 +z* p2 );
116: #if defined(vax)||defined(tahoe)
117: q = z*( q1 +z*( q2 +z* q3 ));
118: #else /* defined(vax)||defined(tahoe) */
119: q = z*( q1 +z* q2 );
120: #endif /* defined(vax)||defined(tahoe) */
121: xp= x*p ;
122: xh= x*half ;
123: w = xh-(q-xp) ;
124: p = p+p;
125: c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
126: return(z*half+c);
127: }
128: /* end of |x| > small */
129:
130: else {
131: if(x!=zero) one+small; /* raise the inexact flag */
132: return(copysign(zero,x));
133: }
134: }
This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.