#5354 bfloat of a float at fpprec below 16 truncates instead of rounding, and differently for negative values

[David Scherfgen]

This bug was discovered by Claude Opus 5.5 and reproduced on Maxima Git commit c62924c (2026-09-26) with SBCL 2.2.9. It supersedes [#4853], which reported the same bug. Related: [#4738].

Where: src/float.lisp, FLOATTOFP

When fpprec has fewer bits than the float, the mantissa is shifted with ASH, which floors: positive floats are truncated toward zero and negative ones rounded away from zero, giving up to 1 ulp error and bfloat(-x) # -bfloat(x). The fix rounds with FPROUND and takes the shift from *M; for fpprec >= 16 the result is unchanged.

Steps

1. Verify that the existing behavior is incorrect: run the reproducer below; it gives the result under "Before the fix". Judge for yourself that this is wrong instead of relying on the ticket: where the bug allows it, try some related inputs of your own, or check the result another way, for example numerically or against the documentation.
2. Edit the file src/float.lisp as described under "Fix".
3. Rebuild Maxima.
4. Verify that the behavior is now correct: the reproducer gives the result under "Correct result". Judge for yourself that this is right, not only that it matches: where the bug allows it, try some related inputs of your own, including some that the fix should leave unchanged.
5. Add the test case(s) under "Test cases" to tests/ulp_tests.mac, at the end of the file.
6. Add the line * \#5354 bfloat of a float at fpprec below 16 truncates instead of rounding, and differently for negative values to ChangeLog, under "Bug fixes for numbered bugs:".
7. Commit the fix; a proposed Git commit message is under "Commit message".
8. Push the commit. Then set this ticket's status to "closed" and add a comment naming the commit, for example Fixed by commit [1a2b3c]., with the first six characters of the commit's SHA in the brackets (git rev-parse HEAD | cut -c1-6 prints them). SourceForge links this to the commit.

Reproducer

block([fpprec:5], bfloat(0.7) + bfloat(-0.7));

Before the fix:

-1.9073b-6

Correct result:

0.0b0

Fix

In src/float.lisp (FLOATTOFP, snippet "(let ((scale (- fpprec (integer-length frac))))"), replace

        ;; Scale frac to the desired number of bits, and adjust the
        ;; exponent accordingly.
        (let ((scale (- fpprec (integer-length frac))))
          (list (ash (* sign frac) scale)
                (+ fpprec (- exp scale)))))))

with

        ;; Round frac to the desired number of bits, and adjust the
        ;; exponent by the shift FPROUND reports in *M.
        (let ((man (fpround (* sign frac))))
          (list man (+ fpprec exp *m))))))

The source file indents with tabs (8 columns); the code above shows them as spaces.

Test cases

Add to tests/ulp_tests.mac:

/* FLOATTOFP: at fpprec below 16, bfloat of a float rounds to nearest,
   the same for both signs */
block([fpprec: 5],
  [is(bfloat(-0.7) = -bfloat(0.7)), is(bfloat(0.7) = bfloat(7/10))]);
[true, true]$

Commit message

bfloat(): round a float to nearest at low fpprec

When fpprec has fewer bits than the float, FLOATTOFP shifted the
mantissa with ASH, which floors: positive floats were truncated and
negative ones rounded away from zero, so bfloat(-0.7) was not
-bfloat(0.7) at fpprec 5. The mantissa is now rounded with FPROUND and
the exponent adjusted by the shift it leaves in *M; for fpprec >= 16
nothing changes.

This fixes bug #5354.

Found and fixed by Claude Opus 5.5.