www.pudn.com > CRGAB.zip > LNX.C

/* 
HEADER:		; 
TITLE:		Series approximation of ln(x); 
VERSION:	1.0; 
 
DESCRIPTION:	Function to perform a Taylor series approximation of the 
		function ln(x).  Large arguments are easily handled and 
		convergence is rapid; 
 
KEYWORDS:	log(x), math functions, approximations; 
SYSTEM:		MSDOS; 
FILENAME:	LNX; 
WARNINGS:       Domain errors; 
 
SEE-ALSO:	LNX, SINX, EXP, MATHCLUD.FUN, XPON; 
AUTHORS:	Dr. Ronald J. Terry; 
COMPILERS:	Turbo C, will also compile under QC, MS-C, power C; 
*/ 
/*  Natural logarithm of x */ 
#include "mathclud.fun" 
 
double lnx(double x) 
{ 
     double sum=0,sum1=0,logtoln=2.30258509299404568402; 
     int i=1,basecount; 
     if(x<=0) 
     { 
     printf("Lnx is undefined at %lf\n",x); 
     return(-1e710); 
     } 
/* Caculate ln(x) as ln(x1) + ln(x2) where x = x1*x2 and x1 is a power of */ 
/* 10 and ln(x1) = x1*ln(10) = x1*2.302... and x2 lies between 1 and 10   */ 
     if(x<1) 
     {              /* Do if x is a fractional number smaller than 1 */ 
       for(basecount=0;x<1;basecount--) 
	 x = x*10.0; 
       if(x>3) 
       { 
	 x = x/10.0; 
	 basecount++; 
       } 
     } 
     else 
     {               /* Do if x is a number greater than or equal to 1 */ 
       for(basecount=0;x>1;basecount++) 
	 x = x/10.0; 
       if(x<=0.3) 
       { 
	 x = x*10.0; 
	 basecount--; 
       } 
     } 
     logtoln = logtoln*basecount; 
     x = (x-1)/(x+1);  /* Series expansion of lnx for x>0 */ 
     for(;;) 
     { 
       sum = sum + Intpwr(x,i)/i; 
       i += 2; 
       if(Abs_val(sum - sum1)<=1e-15) 
	 break; 
       sum1 = sum; 
     } 
     sum = 2*sum + logtoln; 
     return (sum); 
}