floats_equal.pro
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;+
; NAME:
; FLOATS_EQUAL
;
; PURPOSE:
;
; The purpose of this function is to compare two floating-point values or
; arrays to determine if the values or arrays are equal. Arrays are equal
; if they have the same number of elements, and each element is equal.
;
; To learn why determing if floats are equal is hard (and probably not done
; correctly in this program), please read the following article::
;
; http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
;
; AUTHOR:
;
; FANNING SOFTWARE CONSULTING
; David Fanning, Ph.D.
; 1645 Sheely Drive
; Fort Collins, CO 80526 USA
; Phone: 970-221-0438
; E-mail: david@idlcoyote.com
; Coyote's Guide to IDL Programming: http://www.idlcoyote.com
;
; CATEGORY:
;
; Utilities
;
; CALLING SEQUENCE:
;
; result = FLOATS_EQUAL(array_1, array_2)
;
; ARGUMENTS:
;
; array_1 Any single or double precision value or array. Required parameter.
;
; array_2 Any single or double precision value or array. Required parameter.
;
; KEYWORDS:
;
; ULP UNIT in the LAST PLACE. It is the gap or difference between two
; floating point numbers in the last digit that can distinguish the
; two numbers. Must be a positive integer. Set to 1 by default. Set
; to a larger value if you suspect accumulative round-off errors
; in your arrays.
;
; RETURN VALUE:
;
; result Set to 1 if the arrays are equal, which means that the arrays have
; the same number of elements and each element is equal to the same
; element in the other array. Set to 0 if the arrays are not equal.
; COMMON BLOCKS:
; None.
;
; EXAMPLE:
;
; IDL> a = Findgen(11)
; IDL> b = Findgen(11)
; IDL> Print, Floats_Equal(a,b)
; 1
; IDL> b[4] = b[4] + 0.0001
; IDL> Print, Floats_Equal(a,b)
; 0
;
; RESTRICTIONS:
;
; None.
;
; MODIFICATION HISTORY:
;
; Written by: David W. Fanning, 29 August 2007.
; Fixed a problem when using large numbers with the TOTAL command
; by setting the INTEGER keyword. 22 June 2011. DWF.
;-
;******************************************************************************************;
; Copyright (c) 2008, by Fanning Software Consulting, Inc. ;
; All rights reserved. ;
; ;
; Redistribution and use in source and binary forms, with or without ;
; modification, are permitted provided that the following conditions are met: ;
; ;
; * Redistributions of source code must retain the above copyright ;
; notice, this list of conditions and the following disclaimer. ;
; * Redistributions in binary form must reproduce the above copyright ;
; notice, this list of conditions and the following disclaimer in the ;
; documentation and/or other materials provided with the distribution. ;
; * Neither the name of Fanning Software Consulting, Inc. nor the names of its ;
; contributors may be used to endorse or promote products derived from this ;
; software without specific prior written permission. ;
; ;
; THIS SOFTWARE IS PROVIDED BY FANNING SOFTWARE CONSULTING, INC. ''AS IS'' AND ANY ;
; EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES ;
; OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT ;
; SHALL FANNING SOFTWARE CONSULTING, INC. BE LIABLE FOR ANY DIRECT, INDIRECT, ;
; INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED ;
; TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; ;
; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ;
; ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT ;
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ;
; SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ;
;******************************************************************************************;
FUNCTION FLOATS_EQUAL, array_1, array_2, ULP=ulp
; Error handling. Return to caller on error.
ON_ERROR, 2
IF N_Params() NE 2 THEN Message, 'Must pass two arrays or values to compare.'
; Are we comparing double precision values?
IF Size(array_1, /TNAME) EQ 'DOUBLE' OR Size(array_2, /TNAME) EQ 'DOUBLE' THEN $
double = 1 ELSE double = 0
; Check keyword.
IF N_Elements(ulp) EQ 0 THEN ulp = 1.0D ELSE ulp = ROUND(ABS(ulp))
; Arrays not equal if they are not the same length.
IF N_Elements(array_1) NE N_Elements(array_2) THEN RETURN, 0
; Choose a number "sufficiently close" to zero for comparison.
epsilon = (MACHAR(DOUBLE=double)).eps
NUMBER = (Abs(array_1) > Abs(array_2)) * epsilon * ulp
; Compare the arrays.
IF Total(Abs(array_1 - array_2) LE NUMBER, /INTEGER) EQ N_Elements(array_1) THEN $
RETURN, 1 ELSE RETURN, 0
END