[php-src] PR #23581: Fix expm1() losing precision on 32-bit x86

From: Date: Sat, 05 Sep 2026 09:46:39 +0000
Subject: [php-src] PR #23581: Fix expm1() losing precision on 32-bit x86
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Pull Request: https://github.com/php/php-src/pull/23581 Author: marc-mabe ### Problem On 32-bit x86, expm1() returns results that are off by many ULP compared to other platforms, and that are not correctly rounded: ```php var_dump(expm1(3)); // i386: float(19.08553692318767) // other: float(19.085536923187668) var_dump(expm1(10)); // i386: float(22025.465794806725) // other: float(22025.465794806718) ``` Measured against e**x - 1 evaluated to 80 decimal digits and rounded to nearest double, over 720 sampled inputs, the i386 result is correctly rounded in only 81 cases (11.2%), with a mean error of ~12 ULP and a worst case in the hundreds of ULP. This makes expm1() silently architecture-dependent, so comparisons against precomputed constants fail, cached or serialized values differ between machines, and the error propagates into anything built on expm1(). ### Cause init_executor() calls zend_init_fpu(), which clamps the x87 FPU to double precision (a 53-bit mantissa) for the whole request so that PHP's own double arithmetic behaves like IEEE-754 binary64 rather than carrying x87's 64-bit excess precision. libm's expm1(), however, computes on that same x87 unit and relies on the extended range internally in order to round correctly to double. While the clamp is in place it loses that headroom, so expm1() inside PHP is markedly less accurate than the very same libm expm1() is outside PHP. ### Fix zend_expm1() in Zend/zend_float.h restores extended precision for the duration of the libm call and truncates the result back to double on return, using the XPFPA macros already in that header. PHP_FUNCTION(expm1) calls it. Wherever XPFPA_HAVE_CW is 0 — x86-64, arm64, and every other target without x87 precision control — zend_expm1() compiles down to a plain expm1() call, so no other platform is affected in behaviour or code generation. Result on i386, same 720 inputs and same reference: | build | correctly rounded | | --- | --- | | i386, before | 81/720 (11.2%) | | i386, after | 714/720 (99.2%) | The accuracy figures here are stated against a high-precision reference rather than against another platform, because for expm1() no mainstream platform is a correct baseline: glibc on arm64 is itself only correctly rounded for 641/720 (89.0%) of the same inputs. Comparing i386 against arm64 would therefore understate the improvement and mislabel some fixed cases as regressions. ### Known limitations This is a large improvement, not a guarantee. expm1(67) regresses by 1 ULP, because the clamped result there is genuinely the correctly rounded one. It is the only regression in the sample, and the test asserts only inputs that this change fixes. ### Tests ext/standard/tests/math/expm1_fpu_precision.phpt. All arguments are exact binary fractions and every expected value is the correctly rounded double, written as the shortest decimal that round-trips back to it. Inputs were chosen from the intersection of cases that are wrong on clamped i386, correct on i386 with this change, and correct on x86-64/arm64. Verified locally with a full make clean + ./configure + make per configuration, on i386 and arm64: | | without fix | with fix | | --- | --- | --- | | arm64 | pass | pass | | i386 | **fail** | pass | ### Relationship to the other XPFPA PRs This is the same class of bug as the pow()/fpow() and exp() fixes and adds a helper to the same part of Zend/zend_float.h. ### Notes * This is the same class of bug as #23578 and #23579 fix and adds a helper to the same part of Zend/zend_float.h * This PR is mostly LLM work - I manually verified * Failing tests of phpt-only commit is visible here TODO * This is the third PR - PR for sinh will follow

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