ESBMaths(TM) v3.1 17 April 2000

by ESB Consultancy (Glenn Crouch) mailto:info@esbconsult.com.au

(c) 1997-2001 ESB Consultancy
PO Box 2259
Boulder WA 6449
AUSTRALIA
http://www.esbconsult.com.au/

Includes over 150 Routines!

The aim of this code is to provide miscellaneous Mathematical and
Statistical Routines both for Integers and Floating Point Values.

The Delphi Math unit is not required so this can safely be used
by owners of the Standard versions.

Code is Delphi 4 & 5 but should also work fine in Delphi 2 and 3 due
to conditional compiler instructions. ESBMaths2 unit is Delphi 4 & 5
specific as it contains routines for Dynamic Arrays.

You are free to use the code as you see fit, however an
Email or Postcard would be nice, as would a reference to
our web site included on our web site or in your docs.
Though none of this is obligatory.

ESB Consultancy makes no guarantees regarding the capabilities
nor the "Safeness" of this code. It is free after all,
so you take all the risks :-)

ESB Consultancy makes no promise of support for this code,
however we are happy to receive Email comments

There is a support Conference available at:
http://e-fora.net:8080/~ESB

This allows access via Web Board, Mailing List and/or News Reader.
If you have trouble accessing, then email us and we will happily
add you to Mailing List Access.

Latest version always at http://www.esbconsult.com.au

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If you want even more Math & Stats watch checkout ESBPCS -
ESB Professional Computation Suite - with 3000+ routines
and 80+ components to make Data Entry and Manipulation
Easier in Delphi 4 & 5 and C++ Builder 4 & 5.

http://www.esbconsult.com.au/esbpcs.html

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Special thanks to Marcel Martin who donated some optimised
code. Marcel's excellent product HIT - Huge Integer Tools -
can be downloaded from:

http://www.esbconsult.com.au/esbpcs-hit.html

Special thanks to Rory Daulton who also donated optimised
code to make things even better.

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Version History:

v3.1 17 April 2001
- Added Rory Daulton's LongWord Routines
- Added Rory Daulton's IGreatestPowerOf2 Routine
- Added Gamma Function Calculation
- Added Inverse Gamma Function Calculation
- Added LnGamma (Natural Log of Gamma) Function Calculation
- Added Beta Function Calculation
- Added Incomplete Beta Function Calculation

v3.0 8 October 2000
- Many improvements to Optimisation.
- Improved and Added Constants.
- Michael Schnell developed BitsHighest that makes BitsNeeded much
	more efficient.
- Set Default ESBTolerance much smaller.
- Added FloatIsNegative & FloatIsPositive.
- Swaps changed back to Pascal since for D4 and above it optimises to
	better code.
- Added Swaps for the Floats and Int64.
- Improved ISqrt from Rory Daulton.
- Added ILog2 from Rory Daulton.
- Factorial, Permutations & Binomial Coefficients now correctly handle
	up to N = 1754.
- Added ESBArcSec and ESBArcCosec.
- Power & Log Routines completely overhauled - many thanks to Rory Daulton.

v2.3 13 November 1999
- very nice GCD Routine donated by Marcel Martin.
- LCM and Relative Prime Routines to go with above added.
- InPlace Addition & Subtraction of Matrices added.
- Multiplication of Matrices added.
- Transposing Matrices added.

v2.2 18 September 1999
- Now over 130 Routines
- Added Delphi 5 Support
- All Optional Dependence on Math Unit removed by our own routines
- Added a collection of Constants for faster calculations
- Added several Trigonometric Routines
- Added Hyperbolic Routines
- Added Various Logarithm and Power Routines

v2.1 13 July 1999
- Now with over 110 Routines!
- Added ESBDigits and ESBBitsNeeded for Cardinals to ESBMaths
- Added ESBMagnitude for Reals to ESBMaths
- Added GrandMean to ESBMath2
- Added Matrix Operations to ESBMath2, just the start

v2.0 16 Apr 1999
- Delphi 4 specific routines moved to ESBMaths2
- Added Vector operations to ESBMath2

v1.1 22 Jan 1999
- Improved Delphi 4 support
- Added: SumLWArray, SumSqEArray, SumSqDiffEArray, SumXYEArray
- Added: IsPositiveEArray
- Added: Geometric and Harmonic Means
- Added ESBMean, Median and Mode
- Added Routines for Variances and Means for Populations & Samples
- Added Quartile Calculations
- Fixed a couple of minor bugs
- Fixed bug in XY2Polar reported by Wolfgang Werner
- Added Help File

v1.01 17 July 1998
- Added some improvements suggested by Rory Daulton
- Added Factorials using Extendeds
- Added Permutations using Extendeds
- Added Combinations using Extendeds
- Added SwapI32 to Swap Integers
- Added SwapC to Swap Cardinals
- Added Factorials computed using Extendeds
- Added Permutations computed using Extendeds
- Added Binomial Coefficients (Combinations) computed using Extendeds

1.0 17 Apr 1997
- First Public Freeware Release