Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!news.glorb.com!npeer03.iad.highwinds-media.com!news.highwinds-media.com!feed-me.highwinds-media.com!border3.nntp.dca.giganews.com!Xl.tags.giganews.com!border1.nntp.dca.giganews.com!nntp.giganews.com!local2.nntp.dca.giganews.com!nntp.earthlink.com!news.earthlink.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 15 Apr 2012 00:26:08 -0500
Message-ID: <4F8A5BF2.17C5@mindspring.com>
Date: Sun, 15 Apr 2012 01:26:10 -0400
From: pete <pfiland@mindspring.com>
Reply-To: pfiland@mindspring.com
Organization: PF
X-Mailer: Mozilla 3.04Gold (WinNT; I)
MIME-Version: 1.0
Newsgroups: sci.math.num-analysis,alt.lang.asm,comp.programming
Subject: Re: Exp() function reloaded
References: <jmdbuh$fql$1@dont-email.me>
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Lines: 88
X-Usenet-Provider: http://www.giganews.com
NNTP-Posting-Host: 4.154.218.101
X-Trace: sv3-qybtIzi5SFenPLDSCvnBs+QlDG8CasO5HvIoSrsSsamHJ0XpIFVb42YOWIir6jV0mgkdns4FKvJT9de!GhR9MbWNOvsE8XKgtUasmw4xNi8H6yvTr61ovLrNM7YdI0lwxxgD4q/Jexe7D/GH0egHQxQoNRuE!IaXVk+FnzCA=
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 2983
X-Received-Bytes: 3124
Xref: csiph.com comp.programming:1470

hopcode wrote:
> 
> Hi,
> here my method for the exponentianal function e^x .
> it is a mix of 2 fundamentals:
> - Taylor series running at a 10 steps for decimals -1.0 < x < +1.0
> - a couple of basic rules of the logarithms.
 
> it is ~40 lines of code (my Taylors's exp() code + main routine)
> it accepts only +numbers for now, and makes no exaustive check
> on the floats. for those and negative values i leave it to the
> reader's creativity ( being e^-x essentially 1 / e^x ).

I've code Taylors's exp(x) for both positive and negative x in C,
using -1.0 < x < +1.0,
but without making use of e^-x being essentially 1 / e^x.

/* BEGIN new.c output */

fs_expl(20.3) is 654904512.153239
fs_expl(20.3)  - 654904512.153230 is 8.583069e-006

fs_expl(-20.3) is 1.526940e-009
fs_expl(-20.3)  - 1.526940e-009   is 1.591266e-016

/* END new.c output */






/* BEGIN new.c */

#include <stdio.h>

long double fs_expl(long double x)
{
    long unsigned n, square; 
    long double b, e, old;
    
    for (square = 0; x > 1; x /= 2) {
        ++square;
    }
    while (-1 > x) {
        ++square;
        x /= 2;
    }
    e = b = n = 1;
    do {
        b /= n++;
        b *= x;
        e += b;
        b /= n++;
        b *= x;
        old = e;
        e += b;
    } while (e > old);
    while (square-- != 0) {
        e *= e;
    }
    return e;
}

int 
main(void)
{
    puts("/* BEGIN new.c output */\n");
    printf("fs_expl(20.3) is %lf\n", 
            fs_expl(20.3));
    printf("fs_expl(20.3)  - 654904512.153230 is %le\n\n", 
            fs_expl(20.3)  - 654904512.153230);


    printf("fs_expl(-20.3) is %le\n", 
            fs_expl(-20.3));
    printf("fs_expl(-20.3)  - 1.526940e-009   is %le\n\n", 
            fs_expl(-20.3)  - 1.526940e-009);

    puts("/* END new.c output */");
    return 0;
}

/* END new.c */


-- 
pete