Message-Id: <9805110742.AA14523@axe.bre.da>
Subject: Re: Code to Fix sinh() in libm.a
To: Kbwms AT aol DOT com (Kbwms)
Date: Mon, 11 May 1998 9:42:23 METDST
Cc: djgpp AT delorie DOT com
In-Reply-To: <5bc654c6.3551fb66@aol.com>; from "Kbwms" at May 7, 98 2:20 pm
From: Jens Bischoff <j DOT bischoff AT airbus DOT dasa DOT de>
Precedence: bulk

Hi!

Thank you for your work! 
However, I believe that the coefficients are slightly inexact.
The correct values should be:

long double C[] = { 1.L, 
                    1/6.L,
                    1/120.L,
                    1/5040.L,
                    1/362880.L,
                    1/39916800.L,
                    1/6227020800.L};

if they are derived from the series for sinhx(x):

sinh(x) = 1 + x^3/3! + x^5/5! + x^7/7! + ...

Besides, this approximation (that uses 7 coefficients) is only
accurate with 64bit (double) arithmetic.
With long doubles a 8th coefficient should be added:

C[7] = 1/1307674368000.L

Jens 
---
|      |      | Jens Bischoff   |   Daimler-Benz Aerospace Airbus |
|   --<O>--   +-----------------+---------------------------------+
|      |      | Aerodynamic Data Department (EFD)                 |
| Dasa Airbus | Huenefeldstrasse 1-5     D-28199 Bremen (Germany) |