```   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[] = "@(#)log.c	4.5 (Berkeley) 8/21/85";
16: #endif not lint
17:
18: /* LOG(X)
19:  * RETURN THE LOGARITHM OF x
20:  * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
21:  * CODED IN C BY K.C. NG, 1/19/85;
22:  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 3/24/85, 4/16/85.
23:  *
24:  * Required system supported functions:
25:  *	scalb(x,n)
26:  *	copysign(x,y)
27:  *	logb(x)
28:  *	finite(x)
29:  *
30:  * Required kernel function:
31:  *	log__L(z)
32:  *
33:  * Method :
34:  *	1. Argument Reduction: find k and f such that
35:  *			x = 2^k * (1+f),
36:  *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
37:  *
38:  *	2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
39:  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
40:  *	   log(1+f) is computed by
41:  *
42:  *	     		log(1+f) = 2s + s*log__L(s*s)
43:  *	   where
44:  *		log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
45:  *
46:  *	   See log__L() for the values of the coefficients.
47:  *
48:  *	3. Finally,  log(x) = k*ln2 + log(1+f).  (Here n*ln2 will be stored
49:  *	   in two floating point number: n*ln2hi + n*ln2lo, n*ln2hi is exact
50:  *	   since the last 20 bits of ln2hi is 0.)
51:  *
52:  * Special cases:
53:  *	log(x) is NaN with signal if x < 0 (including -INF) ;
54:  *	log(+INF) is +INF; log(0) is -INF with signal;
55:  *	log(NaN) is that NaN with no signal.
56:  *
57:  * Accuracy:
58:  *	log(x) returns the exact log(x) nearly rounded. In a test run with
59:  *	1,536,000 random arguments on a VAX, the maximum observed error was
60:  *	.826 ulps (units in the last place).
61:  *
62:  * Constants:
63:  * The hexadecimal values are the intended ones for the following constants.
64:  * The decimal values may be used, provided that the compiler will convert
65:  * from decimal to binary accurately enough to produce the hexadecimal values
66:  * shown.
67:  */
68:
69: #ifdef VAX  /* VAX D format */
70: #include <errno.h>
71:
72: /* double static */
73: /* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 */
74: /* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC */
75: /* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */
76: static long     ln2hix[] = { 0x72174031, 0x0000f7d0};
77: static long     ln2lox[] = { 0xbcd52ce7, 0xd9cce4f1};
78: static long     sqrt2x[] = { 0x04f340b5, 0xde6533f9};
79: #define    ln2hi    (*(double*)ln2hix)
80: #define    ln2lo    (*(double*)ln2lox)
81: #define    sqrt2    (*(double*)sqrt2x)
82: #else   /* IEEE double */
83: double static
84: ln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */
85: ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */
86: sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */
87: #endif
88:
89: double log(x)
90: double x;
91: {
92:     static double zero=0.0, negone= -1.0, half=1.0/2.0;
93:     double logb(),scalb(),copysign(),log__L(),s,z,t;
94:     int k,n,finite();
95:
96: #ifndef VAX
97:     if(x!=x) return(x); /* x is NaN */
98: #endif
99:     if(finite(x)) {
100:        if( x > zero ) {
101:
102:        /* argument reduction */
103:           k=logb(x);   x=scalb(x,-k);
104:           if(k == -1022) /* subnormal no. */
105:            {n=logb(x); x=scalb(x,-n); k+=n;}
106:           if(x >= sqrt2 ) {k += 1; x *= half;}
107:           x += negone ;
108:
109:        /* compute log(1+x)  */
110:               s=x/(2+x); t=x*x*half;
111:           z=k*ln2lo+s*(t+log__L(s*s));
112:           x += (z - t) ;
113:
114:           return(k*ln2hi+x);
115:        }
116:     /* end of if (x > zero) */
117:
118:        else {
119: #ifdef VAX
120:         extern double infnan();
121:         if ( x == zero )
122:             return (infnan(-ERANGE));   /* -INF */
123:         else
124:             return (infnan(EDOM));  /* NaN */
125: #else   /* IEEE double */
126:         /* zero argument, return -INF with signal */
127:         if ( x == zero )
128:             return( negone/zero );
129:
130:         /* negative argument, return NaN with signal */
131:         else
132:             return ( zero / zero );
133: #endif
134:         }
135:     }
136:     /* end of if (finite(x)) */
137:     /* NOT REACHED ifdef VAX */
138:
139:     /* log(-INF) is NaN with signal */
140:     else if (x<0)
141:         return(zero/zero);
142:
143:     /* log(+INF) is +INF */
144:     else return(x);
145:
146: }
```

#### Defined variables

ln2hi defined in line 84; never used
ln2hix defined in line 76; used 1 times
• in line 79
ln2lox defined in line 77; used 1 times
• in line 80
sccsid defined in line 15; never used
sqrt2x defined in line 78; used 1 times
• in line 81

#### Defined macros

ln2hi defined in line 79; used 1 times
ln2lo defined in line 80; used 2 times
sqrt2 defined in line 81; used 2 times
 Last modified: 1985-08-21 Generated: 2016-12-26 Generated by src2html V0.67 page hit count: 1217