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Diffstat (limited to 'lib/libm/common_source/log1p.c')
| -rw-r--r-- | lib/libm/common_source/log1p.c | 170 |
1 files changed, 170 insertions, 0 deletions
diff --git a/lib/libm/common_source/log1p.c b/lib/libm/common_source/log1p.c new file mode 100644 index 000000000000..cbf9fcd895e2 --- /dev/null +++ b/lib/libm/common_source/log1p.c @@ -0,0 +1,170 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* LOG1P(x) + * RETURN THE LOGARITHM OF 1+x + * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * logb(x) + * finite(x) + * + * Required kernel function: + * log__L(z) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * log(1+f) is computed by + * + * log(1+f) = 2s + s*log__L(s*s) + * where + * log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...))) + * + * See log__L() for the values of the coefficients. + * + * 3. Finally, log(1+x) = k*ln2 + log(1+f). + * + * Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers + * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last + * 20 bits (for VAX D format), or the last 21 bits ( for IEEE + * double) is 0. This ensures n*ln2hi is exactly representable. + * 2. In step 1, f may not be representable. A correction term c + * for f is computed. It follows that the correction term for + * f - t (the leading term of log(1+f) in step 2) is c-c*x. We + * add this correction term to n*ln2lo to attenuate the error. + * + * + * Special cases: + * log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal; + * log1p(INF) is +INF; log1p(-1) is -INF with signal; + * only log1p(0)=0 is exact for finite argument. + * + * Accuracy: + * log1p(x) returns the exact log(1+x) nearly rounded. In a test run + * with 1,536,000 random arguments on a VAX, the maximum observed + * error was .846 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include <errno.h> +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) +vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) +ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#define sqrt2 vccast(sqrt2) +#endif + +double log1p(x) +double x; +{ + const static double zero=0.0, negone= -1.0, one=1.0, + half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */ + double z,s,t,c; + int k; + +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + + if(finite(x)) { + if( x > negone ) { + + /* argument reduction */ + if(copysign(x,one)<small) return(x); + k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k); + if(z+t >= sqrt2 ) + { k += 1 ; z *= half; t *= half; } + t += negone; x = z + t; + c = (t-x)+z ; /* correction term for x */ + + /* compute log(1+x) */ + s = x/(2+x); t = x*x*half; + c += (k*ln2lo-c*x); + z = c+s*(t+__log__L(s*s)); + x += (z - t) ; + + return(k*ln2hi+x); + } + /* end of if (x > negone) */ + + else { +#if defined(vax)||defined(tahoe) + if ( x == negone ) + return (infnan(-ERANGE)); /* -INF */ + else + return (infnan(EDOM)); /* NaN */ +#else /* defined(vax)||defined(tahoe) */ + /* x = -1, return -INF with signal */ + if ( x == negone ) return( negone/zero ); + + /* negative argument for log, return NaN with signal */ + else return ( zero / zero ); +#endif /* defined(vax)||defined(tahoe) */ + } + } + /* end of if (finite(x)) */ + + /* log(-INF) is NaN */ + else if(x<0) + return(zero/zero); + + /* log(+INF) is INF */ + else return(x); +} |