calculation error

[Xerix]

Hello

 

In a program, I have to do the addition of several numbers.

 

But instead of getting 32.04, I get 32.0400000000001

 

I can reduce this result to 2 digits after the decimal point but why this result, while there are always 2 digits after the decimal point ?

 

I do not know from where comes the problem, so I've put all the numbers in addition to test.

 

Thank you

 

$cal = 0.19+0.11+0.4+0.35+0.43+0.27+1.22+0.07+0.04+0.2+6.8+0.04+0.03+0.24+0.62+0.75+0.77+0.18+0.77+0.1+1.35+1.05+0.01+0.01+2.46+5.94+0.19+0.04+2.27+0.02+0.03+0.03+0.03+0.03+0.02+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.02+0.03+0.03+0.03+0.03+0.03+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.04+0.03+0.03+0.03+0.03+0.03+0.02+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.32+0.17+1.35+0.45+1.05
MsgBox(4096,"",$cal)

 

[Danyfirex]

Hi. use StringFormat

$cal = 0.19+0.11+0.4+0.35+0.43+0.27+1.22+0.07+0.04+0.2+6.8+0.04+0.03+0.24+0.62+0.75+0.77+0.18+0.77+0.1+1.35+1.05+0.01+0.01+2.46+5.94+0.19+0.04+2.27+0.02+0.03+0.03+0.03+0.03+0.02+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.02+0.03+0.03+0.03+0.03+0.03+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.04+0.03+0.03+0.03+0.03+0.03+0.02+0.02+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.03+0.32+0.17+1.35+0.45+1.05
MsgBox(4096,"",StringFormat("%.2f",$cal))

Saludos

[jchd]

Floating-point uses binary representation internally, not decimal. Hence rounding errors can accumulate very easily.

This is inherent to IEEE754 floating-point, so AutoIt by itself can do nothing to help. Use Round(), StringFormat() or shift all all your inputs by 10ⁿ and perform calculation in integers.

[Xerix]

Thank you Danyfirex

 

Yes it works, we can also use ROUND but that I wanted to know is if it was normal or if it was a bug.

 

Jchd

 

Thank you for the explanation

Edited February 18, 2014 by Xerix

[jchd]

You can see the phenomenom by yourself by running this simple script:

ConsoleWrite(Hex(0.75) & @LF)    ; 3FE8000000000000
ConsoleWrite(Hex(0.3) & @LF)      ; 3FD3333333333333

Point your browser to this page to better see the breakout of those values and see that 0.3 has an infinite fractional binary expansion which can only be approximated within a 64-bit FP value.

EDIT: while I'm at it, keep in mind that FP has two distinct representations of zero: +0.0 and -0.0

Fortunately AutoIt compares them equal, despite their hex representation differ:

ConsoleWrite("0.0 = " & Hex(0.0) & @LF)
ConsoleWrite("-0.0 = " & Hex(-0.0) & @LF)
ConsoleWrite("0.0 = -0.0 " & (0.0 = -0.0) & @LF)
ConsoleWrite("-0.0 > 0 " & (-0.0 > 0) & @LF)
ConsoleWrite("-0.0 < 0 " & (-0.0 < 0) & @LF)

Edited February 18, 2014 by jchd