Hi Guilers,

It turns out there’s a little blunder in ‘format’ (from ‘ice-9’).  Look
at what happens when using the SCALE argument to format a fixed-point
float (this is Guile from the Git repo at the time of writing):

    GNU Guile 3.0.7.6-22120
    Copyright (C) 1995-2021 Free Software Foundation, Inc.

    Guile comes with ABSOLUTELY NO WARRANTY; for details type `,show w'.
    This program is free software, and you are welcome to redistribute it
    under certain conditions; type `,show c' for details.

    Enter `,help' for help.
    scheme@(guile-user)> (format #t "~,,3f~%" 0.00123)
    0.23
    $3 = #t
    scheme@(guile-user)> (format #t "~,,1f~%" 0.00123)
    ice-9/boot-9.scm:1685:16: In procedure raise-exception:
    Value out of range 0 to 400: -1

    Entering a new prompt.  Type `,bt' for a backtrace or `,q' to continue.

The first example gives the wrong result.  Scaling 0.00123 by 3 should
yield 1.23, not 0.23.  For the second example, instead of 0.0123, we get
an error!  What’s going on here?

Well, our ‘format’ code comes from SLIB and was written in 1998, so it’s
not easy to explain.  There’s so much mutation even a C programmer would
blush!  ;)  The issue happens in the ‘format:parse-float’ procedure
(which is defined inside of ‘format’).  It normalizes the string
representation of a number, and applies the scale argument when needed.
It does this by keeping a string of digits and the location of the
decimal point.  Another thing it keeps track of the leading zeros in a
variable called ‘left-zeros’.  Here’s the code that does the final
shifting and places the decimal point:

    (if (> left-zeros 0)
        (if (<= left-zeros shift) ; shift always > 0 here
            (format:fn-shiftleft shift) ; shift out 0s
            (begin
              (format:fn-shiftleft left-zeros)
              (set! format:fn-dot (- shift left-zeros))))
        (set! format:fn-dot (+ format:fn-dot shift)))

The issue is that the cases in the inner ‘if’ form are reversed.  That
is, if there are MORE leading zeros than we need to shift, we can just
shift.  Otherwise (if there are FEWER leading zeros), we need to shift
out the zeros and then move the decimal point (‘format:fn-dot’).

AFAICS, this bug was in the original SLIB implementation (1998) and has
not been fixed since then.  It’s been in Guile since 1999.

Anyway, that’s more than anyone cares to know....  Here’s a patch with
tests!  :)