The right formula for rounding

Developers,

Many of Ghostscript's quirks happen due to an inaccurate rounding.
The correct rounding formula from math is

       i =  (int)(x + 0.5)

rather than

       i = (int)x

The constant 0.5 is not a "minor detail".
Missing it, the result is biased in average.
This is especially danger with iterations,
for example with a subdivision of a curve while flattening.

With HWResolution an iteration is rare
but it is still possible if an user iteratively runs Photoshop
and Ghostscript multiple times while designing a document.
He'll wonder why the document page becomes smaller
and smaller in each next revision.

Please be accurate developing Ghostscript.
Save our time from maintenance of a poor code.

Igor.


----- Original Message ----- 
From: "Dan Coby" <[email protected]>
To: "Igor V. Melichev" <[email protected]>
Cc: <[email protected]>
Sent: Sunday, February 15, 2004 12:34 AM
Subject: RE: [gs-code-review] Fix for 687294 psdcmyk device does not
writeresolution correctly to PSD files


>
> Igor,
>
> >I can't review your algorithm because I have no knowledge about the  PSD
> >format.
> >The syntax looks perfect.
>
> If you are really interested, I can send you a copy of the specifications.
> My copy of Photoshop includes a copy of the Photoshop SDK.  The SDK
> includes the specifications.  If you have Photoshop then you probably
> also have the specifications.
>
>
> >Don't know where it's fine to assume that HWResolution is an integer.
> >I would code
> >
> >    (int) (pdev->HWResolution[0] * 0x10000 + 0.5);
>
> There is no assumption that HWResolution is an integer.  It is defined
> as a 'float'.  The value is cast to an integer only after multiplying
> by 0x10000.  The cast is needed because Photoshop uses a 'fixed' format
> for storing resolution.  The 'fixed' format consists of a 16 bit integer
> and a 16 bit fraction.  The addition of 0.5 for rounding is minor but I
> have added it to the code.
>
>
> Dan