![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to pow.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 pow.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[] = "@(#)pow.c 5.6 (Berkeley) 6/1/90";
27: #endif /* not lint */
28:
29: /* POW(X,Y)
30: * RETURN X**Y
31: * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
32: * CODED IN C BY K.C. NG, 1/8/85;
33: * REVISED BY K.C. NG on 7/10/85.
34: *
35: * Required system supported functions:
36: * scalb(x,n)
37: * logb(x)
38: * copysign(x,y)
39: * finite(x)
40: * drem(x,y)
41: *
42: * Required kernel functions:
43: * exp__E(a,c) ...return exp(a+c) - 1 - a*a/2
44: * log__L(x) ...return (log(1+x) - 2s)/s, s=x/(2+x)
45: * pow_p(x,y) ...return +(anything)**(finite non zero)
46: *
47: * Method
48: * 1. Compute and return log(x) in three pieces:
49: * log(x) = n*ln2 + hi + lo,
50: * where n is an integer.
51: * 2. Perform y*log(x) by simulating muti-precision arithmetic and
52: * return the answer in three pieces:
53: * y*log(x) = m*ln2 + hi + lo,
54: * where m is an integer.
55: * 3. Return x**y = exp(y*log(x))
56: * = 2^m * ( exp(hi+lo) ).
57: *
58: * Special cases:
59: * (anything) ** 0 is 1 ;
60: * (anything) ** 1 is itself;
61: * (anything) ** NaN is NaN;
62: * NaN ** (anything except 0) is NaN;
63: * +-(anything > 1) ** +INF is +INF;
64: * +-(anything > 1) ** -INF is +0;
65: * +-(anything < 1) ** +INF is +0;
66: * +-(anything < 1) ** -INF is +INF;
67: * +-1 ** +-INF is NaN and signal INVALID;
68: * +0 ** +(anything except 0, NaN) is +0;
69: * -0 ** +(anything except 0, NaN, odd integer) is +0;
70: * +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO;
71: * -0 ** -(anything except 0, NaN, odd integer) is +INF with signal;
72: * -0 ** (odd integer) = -( +0 ** (odd integer) );
73: * +INF ** +(anything except 0,NaN) is +INF;
74: * +INF ** -(anything except 0,NaN) is +0;
75: * -INF ** (odd integer) = -( +INF ** (odd integer) );
76: * -INF ** (even integer) = ( +INF ** (even integer) );
77: * -INF ** -(anything except integer,NaN) is NaN with signal;
78: * -(x=anything) ** (k=integer) is (-1)**k * (x ** k);
79: * -(anything except 0) ** (non-integer) is NaN with signal;
80: *
81: * Accuracy:
82: * pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX,
83: * and a Zilog Z8000,
84: * pow(integer,integer)
85: * always returns the correct integer provided it is representable.
86: * In a test run with 100,000 random arguments with 0 < x, y < 20.0
87: * on a VAX, the maximum observed error was 1.79 ulps (units in the
88: * last place).
89: *
90: * Constants :
91: * The hexadecimal values are the intended ones for the following constants.
92: * The decimal values may be used, provided that the compiler will convert
93: * from decimal to binary accurately enough to produce the hexadecimal values
94: * shown.
95: */
96:
97: #include <errno.h>
98: #include "mathimpl.h"
99:
100: vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000)
101: vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
102: vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1)
103: vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65)
104:
105: ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000)
106: ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76)
107: ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE)
108: ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD)
109:
110: #ifdef vccast
111: #define ln2hi vccast(ln2hi)
112: #define ln2lo vccast(ln2lo)
113: #define invln2 vccast(invln2)
114: #define sqrt2 vccast(sqrt2)
115: #endif
116:
117: const static double zero=0.0, half=1.0/2.0, one=1.0, two=2.0, negone= -1.0;
118:
119: static double pow_p();
120:
121: double pow(x,y)
122: double x,y;
123: {
124: double t;
125:
126: if (y==zero) return(one);
127: else if(y==one
128: #if !defined(vax)&&!defined(tahoe)
129: ||x!=x
130: #endif /* !defined(vax)&&!defined(tahoe) */
131: ) return( x ); /* if x is NaN or y=1 */
132: #if !defined(vax)&&!defined(tahoe)
133: else if(y!=y) return( y ); /* if y is NaN */
134: #endif /* !defined(vax)&&!defined(tahoe) */
135: else if(!finite(y)) /* if y is INF */
136: if((t=copysign(x,one))==one) return(zero/zero);
137: else if(t>one) return((y>zero)?y:zero);
138: else return((y<zero)?-y:zero);
139: else if(y==two) return(x*x);
140: else if(y==negone) return(one/x);
141:
142: /* sign(x) = 1 */
143: else if(copysign(one,x)==one) return(pow_p(x,y));
144:
145: /* sign(x)= -1 */
146: /* if y is an even integer */
147: else if ( (t=drem(y,two)) == zero) return( pow_p(-x,y) );
148:
149: /* if y is an odd integer */
150: else if (copysign(t,one) == one) return( -pow_p(-x,y) );
151:
152: /* Henceforth y is not an integer */
153: else if(x==zero) /* x is -0 */
154: return((y>zero)?-x:one/(-x));
155: else { /* return NaN */
156: #if defined(vax)||defined(tahoe)
157: return (infnan(EDOM)); /* NaN */
158: #else /* defined(vax)||defined(tahoe) */
159: return(zero/zero);
160: #endif /* defined(vax)||defined(tahoe) */
161: }
162: }
163:
164: #ifndef mc68881
165: /* pow_p(x,y) return x**y for x with sign=1 and finite y */
166: static double pow_p(x,y)
167: double x,y;
168: {
169: double c,s,t,z,tx,ty;
170: #ifdef tahoe
171: double tahoe_tmp;
172: #endif /* tahoe */
173: float sx,sy;
174: long k=0;
175: int n,m;
176:
177: if(x==zero||!finite(x)) { /* if x is +INF or +0 */
178: #if defined(vax)||defined(tahoe)
179: return((y>zero)?x:infnan(ERANGE)); /* if y<zero, return +INF */
180: #else /* defined(vax)||defined(tahoe) */
181: return((y>zero)?x:one/x);
182: #endif /* defined(vax)||defined(tahoe) */
183: }
184: if(x==1.0) return(x); /* if x=1.0, return 1 since y is finite */
185:
186: /* reduce x to z in [sqrt(1/2)-1, sqrt(2)-1] */
187: z=scalb(x,-(n=logb(x)));
188: #if !defined(vax)&&!defined(tahoe) /* IEEE double; subnormal number */
189: if(n <= -1022) {n += (m=logb(z)); z=scalb(z,-m);}
190: #endif /* !defined(vax)&&!defined(tahoe) */
191: if(z >= sqrt2 ) {n += 1; z *= half;} z -= one ;
192:
193: /* log(x) = nlog2+log(1+z) ~ nlog2 + t + tx */
194: s=z/(two+z); c=z*z*half; tx=s*(c+log__L(s*s));
195: t= z-(c-tx); tx += (z-t)-c;
196:
197: /* if y*log(x) is neither too big nor too small */
198: if((s=logb(y)+logb(n+t)) < 12.0)
199: if(s>-60.0) {
200:
201: /* compute y*log(x) ~ mlog2 + t + c */
202: s=y*(n+invln2*t);
203: m=s+copysign(half,s); /* m := nint(y*log(x)) */
204: k=y;
205: if((double)k==y) { /* if y is an integer */
206: k = m-k*n;
207: sx=t; tx+=(t-sx); }
208: else { /* if y is not an integer */
209: k =m;
210: tx+=n*ln2lo;
211: sx=(c=n*ln2hi)+t; tx+=(c-sx)+t; }
212: /* end of checking whether k==y */
213:
214: sy=y; ty=y-sy; /* y ~ sy + ty */
215: #ifdef tahoe
216: s = (tahoe_tmp = sx)*sy-k*ln2hi;
217: #else /* tahoe */
218: s=(double)sx*sy-k*ln2hi; /* (sy+ty)*(sx+tx)-kln2 */
219: #endif /* tahoe */
220: z=(tx*ty-k*ln2lo);
221: tx=tx*sy; ty=sx*ty;
222: t=ty+z; t+=tx; t+=s;
223: c= -((((t-s)-tx)-ty)-z);
224:
225: /* return exp(y*log(x)) */
226: t += exp__E(t,c); return(scalb(one+t,m));
227: }
228: /* end of if log(y*log(x)) > -60.0 */
229:
230: else
231: /* exp(+- tiny) = 1 with inexact flag */
232: {ln2hi+ln2lo; return(one);}
233: else if(copysign(one,y)*(n+invln2*t) <zero)
234: /* exp(-(big#)) underflows to zero */
235: return(scalb(one,-5000));
236: else
237: /* exp(+(big#)) overflows to INF */
238: return(scalb(one, 5000));
239:
240: }
241: #endif /* mc68881 */
This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.