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I wondered the same thing. This is exactly how #'%short-float-ratio
works and I assume it was done for speed reasons. The other big
mistake in #'%short-float-ratio is probably that it immediately
checks whether the numerator or denominator is a bignum. That check
might have been sensible in 32-bit implementations since in those
implementations the number of significant bits in a fixnum is
roughly the same as those in a short-float. But such a check doesn't
make sense in 64-bit implementations:<br>
<br>
<font face="monospace">Clozure Common Lisp Version 1.12
(v1.12-2-g5d13fc7d) DarwinX8664<br>
? (integer-length most-positive-fixnum)<br>
60<br>
? (float-digits 1.0s0)<br>
24</font><br>
<br>
Thus by first converting the numerator and denominator to
short-floats, #'%short-float-ratio is losing a great deal of
precision immediately, even when both numerator and denominator are
fixnums.<br>
<br>
Assuming we fixed that, we are left with the monotonicity issue that
Ron points out:<br>
<br>
<font face="monospace">; Here's Ron's original example that uses
rational numbers (more precisely, <i>ratios</i>):<br>
(let ((a 4110710000054) (b 100000000000))<br>
(list (float (/ a b)) (float (/ (+ a 1) b)) (float (/ (+ a 2)
b))))<br>
; (41.1071 41.107098 41.1071) ; weird nonmonotonicity<br>
<br>
<br>
; Reframed to not use any ratios:<br>
(let ((a 4110710000054) (b 100000000000))<br>
(list (float (/ (float a 1.0s0)<br>
(float b 1.0s0)))<br>
(float (/ (float (+ a 1) 1.0s0)<br>
(float b 1.0s0)))<br>
(float (/ (float (+ a 2) 1.0s0)<br>
(float b 1.0s0)))))<br>
; (41.1071 41.1071 41.1071) ; [non-strict] monotonicity returns</font><br>
<br>
This might be what Ron meant when he said "I'm an idiot" but it also
took me a while to figure it out: As Ron demonstrated, ratios are
[effectively] always stored in lowest terms. Because of this, they
bounce around a lot when you increment the numerator. Which in turn
causes unpredictable losses of precision: The variance of said
losses will be large if you always convert numerator and denominator
to short floats before you divide them. But if you force that lowest
terms mechanism not to happen, monotonicity returns (second example
above). So doing ratio conversions with double-floats will be a big
help. It won't make the nonmonotonicity go away entirely -- there's
no way to do that because the lowest terms mechanism will still be
present -- but it will decrease the nonmonotonicity dramatically.<br>
<br>
The obvious next step is to remove the bignum check in
#'%short-float-ratio. I'll try to test that when I have time. The
test is not trivial because it requires a full rebuild of CCL.<br>
<br>
-SS<br>
<br>
<br>
<div class="moz-cite-prefix">On 9/20/21 11:28 AM, Ron Garret wrote:<br>
</div>
<blockquote type="cite"
cite="mid:E745A05B-9B52-472C-8221-2801B1887A85@flownet.com">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
Is there actually a reason, when converting rationals to
single-floats, that the computation is done by converting the
numerator and denominator to single-floats and dividing, rather
than converting them to double-floats, dividing, and then
converting the result to a single-float? The former doesn’t seem
to be appreciably faster on modern hardware:
<div><br>
</div>
<div>
<div>? (time (dotimes (i 1000000)</div>
<div> (let ((x (/ (random 1000000000000) (random
1000000000000))))</div>
<div> (coerce x 'single-float))))</div>
<div>(DOTIMES (I 1000000) (LET ((X (/ (RANDOM 1000000000000)
(RANDOM 1000000000000)))) (COERCE X 'SINGLE-FLOAT)))</div>
<div>took 525,951 microseconds (0.525951 seconds) to run.</div>
<div> 3,967 microseconds (0.003967 seconds, 0.75%) of
which was spent in GC.</div>
<div>During that period, and with 4 available CPU cores,</div>
<div> 534,009 microseconds (0.534009 seconds) were spent in
user mode</div>
<div> 6,094 microseconds (0.006094 seconds) were spent in
system mode</div>
<div> 32,000,000 bytes of memory allocated.</div>
<div> 42 minor page faults, 0 major page faults, 0 swaps.</div>
<div>NIL</div>
<div>? (time (dotimes (i 1000000)</div>
<div> (let ((x (/ (random 1000000000000) (random
1000000000000))))</div>
<div> (coerce (the double-float</div>
<div> (/ (the doble-float (coerce
(numerator x) 'double-float))</div>
<div> (the double-float (coerce
(denominator x) 'double-float))))</div>
<div> 'single-float))))</div>
<div>;Compiler warnings :</div>
<div>; In an anonymous lambda form at position 158: Unknown
type DOBLE-FLOAT, declaration ignored</div>
<div>(DOTIMES (I 1000000) (LET ((X (/ (RANDOM 1000000000000)
(RANDOM 1000000000000)))) (COERCE (THE DOUBLE-FLOAT (/ (THE
DOBLE-FLOAT (COERCE (NUMERATOR X) 'DOUBLE-FLOAT)) (THE
DOUBLE-FLOAT (COERCE (DENOMINATOR X) 'DOUBLE-FLOAT))))
'SINGLE-FLOAT)))</div>
<div>took 542,226 microseconds (0.542226 seconds) to run.</div>
<div> 8,720 microseconds (0.008720 seconds, 1.61%) of
which was spent in GC.</div>
<div>During that period, and with 4 available CPU cores,</div>
<div> 548,880 microseconds (0.548880 seconds) were spent in
user mode</div>
<div> 14,421 microseconds (0.014421 seconds) were spent in
system mode</div>
<div> 64,000,000 bytes of memory allocated.</div>
<div> 2,926 minor page faults, 0 major page faults, 0 swaps.</div>
</div>
<div><br>
</div>
<div><br>
<div>
<div>On Sep 20, 2021, at 10:16 AM, Ron Garret <<a
href="mailto:ron@flownet.com" moz-do-not-send="true"
class="moz-txt-link-freetext">ron@flownet.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<meta http-equiv="Content-Type" content="text/html;
charset=UTF-8">
<div style="word-wrap: break-word; -webkit-nbsp-mode: space;
-webkit-line-break: after-white-space;">Oh never mind, I’m
an idiot.
<div><br>
</div>
<div>
<div>? 4110710000054/100000000000</div>
<div>2055355000027/50000000000</div>
<div>? 4110710000055/100000000000</div>
<div>822142000011/20000000000</div>
<div>? 4110710000056/100000000000</div>
<div>513838750007/12500000000</div>
<div><br>
</div>
<div>
<div>On Sep 20, 2021, at 9:53 AM, Ron Garret <<a
href="mailto:ron@flownet.com"
moz-do-not-send="true"
class="moz-txt-link-freetext">ron@flownet.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<meta http-equiv="Content-Type" content="text/html;
charset=UTF-8">
<div style="word-wrap: break-word;
-webkit-nbsp-mode: space; -webkit-line-break:
after-white-space;">All this is true, but it does
not account for the anomaly. This appears to be a
legitimate bug:
<div><br>
</div>
<div>
<div>? (let ((a 4110710000054) (b 100000000000))</div>
<div> (list (float (/ a b)) (float (/ (+ a
1) b)) (float (/ (+ a 2) b))))</div>
<div>(41.1071 41.107098 41.1071)</div>
</div>
<div>
<div>? (mapcar 'decode-float *)</div>
<div>(0.64229846 0.6422984 0.64229846)</div>
<div><br>
</div>
<div>It is very data dependent, only manifesting
itself for very particular values of A. I
have not yet been able to discern any pattern,
but here are a few interesting edge cases:</div>
<div><br>
</div>
<div>
<div>? (let ((a 7110710000054) (b
100000000000))</div>
<div> (list (float (/ a b)) (float (/ (+ a
1) b)) (float (/ (+ a 2) b))))</div>
<div>(71.1071 71.10709 71.1071)</div>
</div>
<div><br>
</div>
<div>
<div>? (let ((a 7110720000054) (b
100000000000))</div>
<div> (list (float (/ a b)) (float (/ (+ a
1) b)) (float (/ (+ a 2) b))))</div>
<div>(71.1072 71.1072 71.1072)</div>
</div>
<div><br>
</div>
<div>
<div>? (let ((a 4110709000054) (b
100000000000))</div>
<div> (list (float (/ a b)) (float (/ (+ a
1) b)) (float (/ (+ a 2) b))))</div>
<div>(41.10709 41.10709 41.10709)</div>
</div>
<div><br>
</div>
<div>AFAICT the bug is in
<a class="moz-txt-link-freetext" href="ccl::%short-float-ratio">ccl::%short-float-ratio</a>. I’ll track it down
when I have time, but with the above test
cases it should not be too hard to figure it
out.</div>
<div><br>
</div>
<div>rg</div>
<div><br>
</div>
<div>
<div>On Sep 19, 2021, at 10:56 PM, Raymond
Wiker <<a href="mailto:rwiker@gmail.com"
moz-do-not-send="true"
class="moz-txt-link-freetext">rwiker@gmail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<blockquote type="cite">
<meta http-equiv="Content-Type"
content="text/html; charset=UTF-8">
<div style="word-wrap: break-word;
-webkit-nbsp-mode: space; line-break:
after-white-space;" class="">
<meta http-equiv="Content-Type"
content="text/html; charset=UTF-8"
class="">
<div style="word-wrap: break-word;
-webkit-nbsp-mode: space; line-break:
after-white-space;" class="">For
IEEE-754 single-precision
floating-point, the mantissa is held in
23 bits. log10 of 2^23 is about 6.9237,
so you should expect less than 7 decimal
digits of accuracy. 411071.0 is 7
digits, so anything after that can (and
should) be ignored. The difference
between 411071.0 and 411071.03 expressed
as a float32 is a single bit: the least
significant bit of the mantissa.
<div class=""><br class="">
</div>
<div class="">The reason that coerce
gives a slightly worse result is that
you compute the value as float32, then
convert to float64, and when you print
the number, more digits will be
printed.</div>
<div class=""><br class="">
</div>
<div class="">
<div class=""><br class="">
<blockquote type="cite" class="">
<div class="">On 19 Sep 2021, at
15:05, Steven Nunez <<a
href="mailto:steve_nunez@yahoo.com"
class="moz-txt-link-freetext"
moz-do-not-send="true">steve_nunez@yahoo.com</a>>
wrote:</div>
<br
class="Apple-interchange-newline">
<div class="">
<div class="">
<div class="yahoo-style-wrap"
style="font-family:Helvetica
Neue, Helvetica, Arial,
sans-serif;font-size:13px;">
<div dir="ltr"
data-setdir="false"
class="">Hi folks,</div>
<div dir="ltr"
data-setdir="false"
class=""><br class="">
</div>
<div dir="ltr"
data-setdir="false"
class="">I just posted an
issue regarding what looks
like a <a
href="https://github.com/Clozure/ccl/issues/390"
class=""
moz-do-not-send="true">bug
in rational->float
conversion</a>, and I'm
hoping someone here can
try this on 1.12
(preferably on MS
Windows), or perhaps
provide some insight as to
what might be going on
here for a quick fix.<br
class="">
</div>
<div class=""><br class="">
</div>
<div dir="ltr"
data-setdir="false"
class="">
<div class=""><font
class=""
face=""courier
new", courier,
monaco, monospace,
sans-serif">CL-USER>
(lisp-implementation-version)<br class="">
"Version 1.11.8
(v1.11.8-2-gd411e378)
WindowsX8664"<br
class="">
CL-USER> (float
41107100000541273/100000000000)<br
class="">
411071.03<br class="">
<br class="">
<font class=""
face=""Helvetica
Neue",
Helvetica, Arial,
sans-serif">Hmm. If
you work out the
decimal points, the
float is:
411071.00000541273,
that's a long way
from .03. Maybe <font
class=""
face=""courier
new",
courier, monaco,
monospace,
sans-serif">coerce</font>?
Nope, that's even
worse:</font><br
class="">
<br class="">
CL-USER> (coerce
41107100000541273/100000000000
'double-float)<br
class="">
411071.03125D0</font><br
class="">
<br class="">
</div>
<div dir="ltr"
data-setdir="false"
class="">Any ideas?
That's not a small
rounding error.<br
class="">
</div>
<div dir="ltr"
data-setdir="false"
class=""><br class="">
</div>
<div dir="ltr"
data-setdir="false"
class="">Regards,</div>
<div dir="ltr"
data-setdir="false"
class=""> Steve<br
class="">
</div>
</div>
</div>
</div>
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