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Fix soundness bug in fpa2bv mk_to_real: wrong exponent power for negative exponents (#9513)

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`fpa2bv_converter::mk_to_real` computed `2^(1/|exp|)` instead of
`1/(2^|exp|)` for floats with negative exponents, causing the NRA solver
to reach contradictory conclusions and return spurious `unsat` for
satisfiable QF_FPLRA formulas.

## Root Cause

After the loop that evaluates `exp2 = |unbiased_exp|` as an integer, the
code took `1/exp2` (reciprocal of the integer) before calling
`mk_power`, yielding `2^(1/3)` instead of `2^(-3) = 1/8` for a float
with exponent -3:

```cpp
// Buggy
one_div_exp2 = mk_div(one, exp2);                       // 1/|exp|, not 1/2^|exp|
exp2 = mk_ite(exp_is_neg, one_div_exp2, exp2);
two_exp2 = mk_power(two, exp2);                         // 2^(1/3) ≠ 1/8 for exp=-3
```

## Fix

Compute the power of 2 first, then invert it:

```cpp
// Fixed
two_exp2 = mk_power(two, exp2);                         // 2^|exp|
one_div_two_exp2 = mk_div(one, two_exp2);               // 1/(2^|exp|)
two_exp2 = mk_ite(exp_is_neg, one_div_two_exp2, two_exp2);  // correct 2^exp
```

## Impact

- **QF_FPLRA**: `to_fp(RTZ, r)` with a symbolic real `r` constrained to
an interval containing a float's exact rational value now correctly
returns `sat`.
- **fp.to_real**: Fixes incorrect real-valued encoding for all floats
with negative exponents, including denormals (which adjust the exponent
by subtracting leading-zero count).

A regression test covering the reported case is added to
`src/test/fpa.cpp`.

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: NikolajBjorner <3085284+NikolajBjorner@users.noreply.github.com>
This commit is contained in:
Copilot 2026-05-13 06:11:36 -04:00 • committed by GitHub
parent 6dfb5ab44f
commit 2f7ff62173
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2 changed files with 29 additions and 7 deletions
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23
src/test/fpa.cpp
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@ -60,6 +60,28 @@ static void test_fp_to_real_denormal() {
true);
}
// Regression test for soundness bug in to_fp (from real) with symbolic real interval.
// When the rounding mode is RTZ and the real variable is constrained to an interval
// that includes the exact rational value of a float, Z3 should return SAT.
// This was broken because mk_to_real computed 2^(1/|exp|) instead of 1/(2^|exp|)
// for floats with negative exponents, causing a conflict in the NRA solver.
static void test_to_fp_from_real_interval() {
// The interval (-4127125/16777216, -16508499/67108864] contains -16508499/67108864
// which is the exact rational value of fp #b1 #b01111100 #b11110111110011001010011.
// to_fp(RTZ, r) for r in this closed interval must equal that float.
run_fp_test(
"(set-logic QF_FPLRA)\n"
"(declare-const x Float32)\n"
"(assert (= x (fp #b1 #b01111100 #b11110111110011001010011)))\n"
"(declare-const r Real)\n"
"(assert (and (> r (- (/ 4127125.0 16777216.0))) (<= r (- (/ 16508499.0 67108864.0)))))\n"
"(declare-const w Float32)\n"
"(assert (= w ((_ to_fp 8 24) RTZ r)))\n"
"(assert (= x w))\n"
"(check-sat)\n",
true);
}
static void test_recfun_defined_function_soundness() {
run_fp_test(
"(set-option :model_validate true)\n"
@ -75,5 +97,6 @@ static void test_recfun_defined_function_soundness() {
void tst_fpa() {
test_fp_to_real_denormal();
test_to_fp_from_real_interval();
test_recfun_defined_function_soundness();
}