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ARMath.pas
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ARMath.pas
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{*
ARMath.pas Vector sorting and percentile calculations, significant digit string
formating and useful functions for validating numeric input
----------
Begin: 2005/02/03
Last revision: $Date: 2009-08-11 17:59:07 $ $Author: rhupalo $
Version number: $Revision: 1.22 $
Code Documentation Tags: Begin 2009-04-06, Last Revision: 2009-08-06
Project: APHI General Purpose Delphi Library
Website: http://www.naadsm.org/opensource/delphi
Author: Aaron Reeves <Aaron.Reeves@colostate.edu>
--------------------------------------------------
Copyright (C) 2005 - 2008 Animal Population Health Institute, Colorado State University
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General
Public License as published by the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This unit contains some simple types and useful basic mathematical
functions which do not require external libraries.
Some of these functions may be automatically tested. If the symbol
TESTING is defined in Defs.inc, the appropriate test code is automatically
run when this unit is initialized. Please see the test code and the
initialization section at the end of this unit.
}
(*
Short function descriptions are provided in the interface section. More
detailed comments are provided in the implementation section as needed.
Documentation generation tags begin with {* or ///
Replacing these with (* or // foils the documentation generator
*)
unit ARMath;
interface
uses
Math,
Contnrs,
MyDelphiArrayUtils
;
//--------------------
// Unit self-test
//--------------------
procedure selfTest();
//-------------------------
// Useful types and aliases
//-------------------------
type uint = longword; /// unsigned 32-bit integer
//-------------------------
// Array handling functions
//-------------------------
{ Returns the median (50th percentile) from the raw or sorted array }
function ArrayMedian( arr: TARDoubleArray ): double;
function medianSortedData( sortedData: TARDoubleArray ): double;
{ Returns the specified quantile value from the raw or sorted array }
function arrayQuantile( arr: TARDoubleArray; quantile: double ): double;
function quantileSortedData( sortedData: TARDoubleArray; quantile: double ): double;
//----------------------------
// Number formatting functions
//----------------------------
{ Determines how many significant digits are present in a string representation of a numeric value }
function significantDigits( str: string ): integer;
{ Formats a string representation of the number val with d significant digits }
function showSignificantDigits( val: double; d: integer ): string;
//--------------
// Miscellaneous
//--------------
{ Indicates whether val is not "not a number" (NaN) }
function isNumber( const val: double ): boolean;
{ Indicates whether 0.0 <= val <= 1.0 }
function isProbability( const val: double ): boolean;
function isProportion( const val: double ): boolean;
//------------------
// Testing functions
//------------------
procedure zzTestSignificantDigits();
procedure zzTestShowSignificantDigits();
const
DBARMATH: boolean = false; /// Set to true to enable debugging messages for this unit
implementation
uses
SysUtils,
StrUtils,
MyStrUtils,
DebugWindow,
RoundToXReplacement_3c
;
//-----------------------------------------------------------------------------
// Array handling functions
//-----------------------------------------------------------------------------
{*
Provides the data value for a specified quantile from a sorted array
@param quantile A value between 0 and 1
@param sortedData Sorted (ascending) array of data values
@return Value in the array at the specified quantile
@comment Function is based on code for the GNU Scientific Library, version 1.6
}
function quantileSortedData( sortedData: TARDoubleArray; quantile: double ): double;
var
index: double;
lhs: integer;
delta: double;
n: integer;
begin
n := length( sortedData );
index := quantile * ( n - 1 );
lhs := trunc( index );
delta := index - lhs;
if( 0 = n ) then
result := 0.0
else if( n - 1 = lhs ) then
result := sortedData[n-1]
else
result := ( 1 - delta ) * sortedData[lhs] + delta * sortedData[lhs + 1]
;
end
;
{*
Provides the data value for a specified quantile from an un-sorted array
@param quantile A value between 0 and 1
@param arr Un-sorted array of data values
@return Value in the array at the specified quantile
}
function arrayQuantile( arr: TARDoubleArray; quantile: double ): double;
begin
quickSort( arr );
result := quantileSortedData( arr, quantile );
end
;
{*
Provides the data value for the median of a sorted array
@param sortedData Sorted array of data values
@return Value in the array at the 0.5 quantile
}
function medianSortedData( sortedData: TARDoubleArray ): double;
begin
result := quantileSortedData( sortedData, 0.5 );
end
;
{*
Provides the data value for the median of an un-sorted array
@param arr Un-sorted array of data values
@return Value in the array at the 0.5 quantile
}
function ArrayMedian( arr: TARDoubleArray ): double;
begin
quickSort( arr );
result := quantileSortedData( arr, 0.5 );
end
;
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
// Number formatting functions
//-----------------------------------------------------------------------------
(*
Determines how many significant digits are present in a string representation
of a numeric value. This function is tested by zzTestSignificantDigits().
For example:
"1" has 1 significant digit.
"-1.00" has 3 significant digits.
"0.004" has 1 significant digit.
"0.0040" has 2 significant digits.
For integers, all digits are currently considered significant:
"1" has 1 significant digit.
"1000" has 4 significant digits.
Scientific notation is not (yet?) supported:
"100" has 3 significant digits.
"1E2" should have 1 significant digit, but this capability is not supported.
*)
{*
Returns the number of significant digits of a numeric value stored as a string
@param str Numeric value represented as a string
@return Number of significant digits
@comment Scientific notation format is not supported
}
function significantDigits( str: string ): integer;
var
dp: integer; // decimal point position
fp: integer; // position of first nonzero digit
flt: double;
charCount: integer;
begin
str := fixup( str );
flt := usStrToFloat( str );
charCount := length( str );
// Was the number negative? If so, subtract 1 from the
// character count so that the minus sign is not counted as a digit.
if( 0 > flt ) then
charCount := charCount - 1
;
// Determine the position of the decimal point.
// Remember: ansiPos is 1-indexed. If '.' is in the
// first position of the string, ansiPos stupidly returns 1.
// Subtract 1 to make this value right with the world.
dp := ansiPos( '.', str );
dp := dp - 1;
if( 0 > dp ) then
begin
// No decimal point was found. Count all digits of the integer as significant.
// (Technically this isn't quite right, but scientific notation is not supported.)
result := charCount;
end
else
begin
// There is a decimal point.
// Is it to the right or left of the first nonzero character?
fp := firstNonZeroChar( str );
// Again, don't forget the minus sign.
if( 0 > flt ) then
fp := fp - 1
;
//dbcout( 'dp: ' + intToStr( dp ) + ', firstNonZeroChar: ' + intToStr( fp ) + ', test: ' + boolToText( dp < fp ) );
if( dp < fp ) then
begin
// The decimal point is to the left of the first nonzero character
// Disregard anything that came before the first actual nonzero character.
result := charCount - fp;
end
else
begin
// The decimal point is "in the middle" of the string.
// Subtract 1, so that it is not counted as a digit.
result := charCount - 1;
end
;
end
;
end
;
{*
Formats a string representation of the number val with d significant digits.
This function is tested by zzTestShowSignificantDigits()
@param val Number to be represented as a string
@param d Desired number of significant digits
@return String representation of input number
}
function showSignificantDigits( val: double; d: integer ): string;
var
str: string;
i: integer;
nextVal: double;
absval: double;
tempStr: string;
fp: integer; // first nonzero position
begin
dbcout( '*** Show ' + intToStr( d ) + ' significant digits of ' + usFloatToStr( val, 15, false ), DBARMATH );
absval := abs( val );
if( d < 1 ) then d := 1;
// If the value is less than 1 but greater than or equal
// to 0.1, just fix at d places.
//------------------------------------------------------
if( ( 0.1 <= absval ) and ( 1 > absval ) ) then
begin
str := format( '%.'+ intToStr(d) + 'f', [val] );
nextVal := usStrToFloat( str );
if( nextVal >= 1 ) then
str := leftStr( str, length(str) - 1 )
;
end
// If abs( value ) is 1 or more, determine how many
// digits are to the left of the decimal point and move
// the fix point to the left.
//------------------------------------------------------
else if ( 1 <= absval ) then
begin
i := length( intToStr( trunc( absval ) ) );
d := d - i;
if( d < 0 ) then
begin
val := roundDblTo( val, -1 * d );
str := format( '%.0f', [val] );
end
else
begin
str := format( '%.'+ intToStr(d) + 'f', [val] );
nextVal := usStrToFloat( str );
if( ( d > 0 ) and ( nextVal / power( 10, i ) >= 1 ) ) then
str := leftStr( str, length(str) - 1 )
;
end
;
end
// If abs( value ) is less than 0.1, determine how many
// leading zeros there are, and move the fix point to the right.
//---------------------------------------------------------------
else if( absVal < 0.1 ) then
begin
tempStr := usFloatToStr( val, 15, false );
fp := firstNonZeroChar( tempStr ) - 2;
dbcout( '--- fp is ' + intToStr( fp ), DBARMATH );
if( fp = -3 ) then // All digits are zeroes
begin
str := leftStr( tempStr, d+1 ); // Show the right number of zeroes
if( rightStr( str, 1 ) = '.' ) then str := leftStr( str, length( str ) - 1 );
end
else
begin
d := d + fp;
str := format( '%.'+ intToStr(d) + 'f', [val] );
nextVal := usStrToFloat( str );
if( nextVal / power( 10, -1 * fp ) >= 1 ) then
str := leftStr( str, length(str) - 1 )
;
end
;
end
// If all else fails...
//----------------------
else
str := usFloatToStr( val )
;
if( charAt( str, length(str) - 1 ) = '.' ) then
str := leftStr( str, length(str) - 1 )
;
result := str;
end
;
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
// Miscellaneous
//-----------------------------------------------------------------------------
{*
Indicates whether val is a number
@param val Numeric value
@return True if input value is a valid number
}
function isNumber( const val: double ): boolean;
begin
result := not( isNaN( val ) );
end
;
{*
Indicates whether val is a probability
@param val Numeric value
@return True if input is a proportion between 0 and 1
}
function isProbability( const val: double ): boolean;
begin
result := isProportion( val );
end
;
{*
Helper function to isProbability
indicates whether val is a proportion
@param val Numeric value
@return True if input is a proportion between 0 and 1
}
function isProportion( const val: double ): boolean;
begin
if( not( isNumber( val ) ) ) then
result := false
else
result := ( ( 0.0 <= val ) and ( 1.0 >= val ) )
;
end
;
//-----------------------------------------------------------------------------
//-----------------------------------------------------------------------------
// Automated testing code.
//-----------------------------------------------------------------------------
{*
Automated testing of the function showSignificantDigits()
}
procedure zzTestShowSignificantDigits();
var
f: double;
str: string;
begin
f := strToFloat( '0.3003875015456' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 0.3003875015456, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '0.3' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.2958593758176' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.2958593758176, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.30' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.3258246410987' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.3258246410987, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.32582' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.24801144096091' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.24801144096091, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.2480' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.6759830991468' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.6759830991468, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.676' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.5380395114935' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.5380395114935, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.53804' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.1179284519676' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.1179284519676, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.1179' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.680139982358' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.680139982358, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.68' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.1978594317807' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.1978594317807, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.20' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.2647016599567' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.2647016599567, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.2647' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.35298496805171' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.35298496805171, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.35' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.186325644464' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.186325644464, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.1863' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.3558299148126' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.3558299148126, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.3558' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.2449393445395' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.2449393445395, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.245' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.5355320225017' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.5355320225017, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.536' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.9319234922332' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.9319234922332, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.93192' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.280229251739' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.280229251739, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.2802' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.8069872427731' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 0.8069872427731, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '0.8' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.2695979772288' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 0.2695979772288, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '0.3' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.16355094406481' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.16355094406481, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.16' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.7433988411894' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.7433988411894, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.74340' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.35093833928931' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.35093833928931, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.35094' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.25923126600446' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.25923126600446, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.259' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.88646482457989' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.88646482457989, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.8865' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '0.03003875015456' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 0.03003875015456, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '0.03' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.002958593758176' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.002958593758176, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.0030' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0003258246410987' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.0003258246410987, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.00032582' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.024801144096091' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.024801144096091, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.02480' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0000006759830991468' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.0000006759830991468, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.000000676' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0163216931387' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.0163216931387, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.0163' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0127056465717' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.0127056465717, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.013' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '10.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '9.997' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '9.9970' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 6 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 6 ) + ' sig digits is ' + str );
if( '9.99700' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '100.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '99.996' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 6 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 6 ) + ' sig digits is ' + str );
if( '99.9960' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 7 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 7 ) + ' sig digits is ' + str );
if( '99.99600' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '1000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '1000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '1000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '1000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '1000.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 6 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 6 ) + ' sig digits is ' + str );
if( '999.996' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 7 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 7 ) + ' sig digits is ' + str );
if( '999.9960' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '999.996' );
str := showSignificantDigits( f, 8 );
dbtest( usFloatToStr( 999.996, 15 ) + ' to ' + intToStr( 8 ) + ' sig digits is ' + str );
if( '999.99600' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '0.1' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '0.10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.1000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.10000' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 6 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 6 ) + ' sig digits is ' + str );
if( '0.0999996' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 7 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 7 ) + ' sig digits is ' + str );
if( '0.09999960' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.0999996' );
str := showSignificantDigits( f, 8 );
dbtest( usFloatToStr( 0.0999996, 15 ) + ' to ' + intToStr( 8 ) + ' sig digits is ' + str );
if( '0.099999600' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '43.3003875015456' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 43.3003875015456, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '40' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '6.2958593758176' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 6.2958593758176, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '6.3' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '47.3258246410987' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 47.3258246410987, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '47.326' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '2.24801144096091' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 2.24801144096091, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '2.248' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '15.6759830991468' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 15.6759830991468, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '15.7' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '19.5380395114935' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 19.5380395114935, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '19.538' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '44.1179284519676' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 44.1179284519676, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '44.12' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '19.680139982358' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 19.680139982358, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '20' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '50.1978594317807' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 50.1978594317807, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '50' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '43.0127056465717' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 43.0127056465717, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '43' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '44.2647016599567' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 44.2647016599567, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '44.26' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '5.35298496805171' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 5.35298496805171, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '5.4' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '41.186325644464' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 41.186325644464, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '41.19' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '38.3558299148126' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 38.3558299148126, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '38.36' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '34.2449393445395' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 34.2449393445395, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '34.2' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '32.5355320225017' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 32.5355320225017, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '32.5' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '17.9319234922332' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 17.9319234922332, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '17.932' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '32.280229251739' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 32.280229251739, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '32.28' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '47.8069872427731' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 47.8069872427731, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '50' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '25.2695979772288' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 25.2695979772288, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '30' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '22.0163216931387' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 22.0163216931387, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '22.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '6.16355094406481' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 6.16355094406481, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '6.2' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '39.7433988411894' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 39.7433988411894, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '39.743' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '6.35093833928931' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 6.35093833928931, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '6.3509' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.25923126600446' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 9.25923126600446, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '9.26' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '5.88646482457989' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 5.88646482457989, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '5.886' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '100.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '10' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '9.997' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 9.997, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '10.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '100.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '100.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 0 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 0 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '99.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 99.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '100' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
f := strToFloat( '0.996' );
str := showSignificantDigits( f, 1 );
dbtest( usFloatToStr( 0.996, 15 ) + ' to ' + intToStr( 1 ) + ' sig digits is ' + str );
if( '1' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.996' );
str := showSignificantDigits( f, 2 );
dbtest( usFloatToStr( 0.996, 15 ) + ' to ' + intToStr( 2 ) + ' sig digits is ' + str );
if( '1.0' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.996' );
str := showSignificantDigits( f, 3 );
dbtest( usFloatToStr( 0.996, 15 ) + ' to ' + intToStr( 3 ) + ' sig digits is ' + str );
if( '0.996' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.996' );
str := showSignificantDigits( f, 4 );
dbtest( usFloatToStr( 0.996, 15 ) + ' to ' + intToStr( 4 ) + ' sig digits is ' + str );
if( '0.9960' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
f := strToFloat( '0.996' );
str := showSignificantDigits( f, 5 );
dbtest( usFloatToStr( 0.996, 15 ) + ' to ' + intToStr( 5 ) + ' sig digits is ' + str );
if( '0.99600' <> str ) then raise exception.create( 'ARMath.zzTestShowSignificantDigits failed' );
dbtest( endl );
end