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On Mar 12, 2024, at 9:16 AM, Mark Calabretta via fitsbits <fitsbits@listmgr.nrao.edu> wrote:<br>
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<div><span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">For
the benefit of FITS implementors with fewer grey hairs, there is</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">something
that should be pointed out. When FITS was devised in the</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">early
1980s there was no standard floating point format, IEEE 754 came</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">later.
Thus it was not possible to devise a portable image format based</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">on
floating point values. In that era, ALL FITS images were integer-</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">valued;
BSCALE and BZERO were essential to convert them into meaningful</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">physical
values. Your implementation could do the conversion on the fly</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">when
the file was read, or later when the pixel values were used. (If I</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">rememmber
correctly, AIPS allowed you to choose). Later, when IEEE 754</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">was
adopted by FITS, BSCALE and BZERO essentially became redundant for</span><br style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;">
<span style="caret-color: rgb(0, 0, 0); font-family: Menlo-Regular; font-size: 11px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; float: none; display: inline !important;">floating-valued
images, which predominated.</span></div>
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<div>Precisely what I was going to say myself! And I would add that in the early days the presence or not of decimal point in the value for BSCALE or BZERO was not intended to convert any information about how the conversion should be done in code. If BSCALE
or BZERO has an integer value but is being used to convert to a floating-point internal representation, then it should be obvious that floating-point arithmetic should be used (even if the standard implies something different).</div>
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<div>Tim Pearson</div>
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