[jmh530]

Fixes #11114.

The portable exp2 implementation returns zero below the exponent of the smallest normal value, discarding representable subnormal results. For example, exp2(-1023.0) returns zero instead of double.min_normal / 2.

Changes

For inputs in the subnormal-output range, shift the exponent upward by T.mant_dig, evaluate a normal intermediate using the existing approximation, and multiply by 2^(-T.mant_dig) once to round the final result. The exponent shift is exact in this range and requires only one additional evaluation level.

Retain an early zero return below the half-smallest-subnormal boundary. At that boundary and above it, perform the final rounding instead of prematurely returning zero. This avoids relying on ldexp to round subnormal outputs: widening the cutoff alone still failed the nearest-input-above-half test on Windows LDC because its ldexp implementation truncated the result.

The ordinary-input path, approximation coefficients, and existing x87 assembly implementation are unchanged.

Regression tests cover every exactly representable integer power from the smallest normal through the smallest subnormal, public overloads for float, double, and real, and direct portable evaluation at and on either side of the half-smallest-subnormal threshold. Fractional-exponent cases check rounding near the bottom of the range. Boundary expectations use round-to-nearest, ties-to-even.

Validation

• DMD 2.113.0 on Windows: the full std.math.exponential module tests pass in debug and optimized builds, with -preview=dip1000 as required by existing tests.
• LDC 1.43.0 on Windows, --noasm: the full module tests pass in debug and optimized builds, also with DIP1000 enabled.
• GDC 14.2.0 on Ubuntu/WSL: the focused new regressions pass, including portable 80-bit real. The full module suite cannot compile against this installation's older core.int128 API; the same powmod/mul signature error was reproduced with the unchanged source.
• Independent 150-digit Decimal references cover a grid in steps of 1/16 across the subnormal-output interval and the transition to zero. DMD and GDC each pass 2,307 cases across the three types; Windows LDC passes 2,131 cases because its real has double precision. Maximum error is one smallest-subnormal unit. These checks do not establish correct rounding for every input; the existing approximation can still differ by one unit.
• The new regressions fail on the original implementation.
• git diff --check passes.

Performance versus the original

Baseline: upstream commit 1877367354fadf001365292d74e39ffd15c21bbc.

Benchmarks compile the original and fixed portable helper implementations under separate module names and call them through equivalent function pointers. This explicitly measures the portable implementation even where public exp2(real) uses assembly; the assembly path is not changed by this PR.

Each timed sample evaluates 512 inputs over 512 repetitions. Results feed an integer checksum of their bit patterns, avoiding extra floating-point arithmetic on subnormal outputs in the harness. Three process runs alternate baseline/fixed order on a pinned CPU. One warm-up pair is excluded, leaving 24 measured pairs per dataset and type.

The following are median nanoseconds per call, original → fixed. Compiler/environment differences mean these should be compared within each row.

Compiler	Type	Ordinary inputs	Upper subnormal range	Near zero rounding boundary
GDC	float	11.59 → 11.59	1.66 → 56.00	1.67 → 56.35
GDC	double	11.06 → 11.49	1.69 → 58.21	1.70 → 59.53
GDC	real	67.26 → 67.91	8.40 → 223.38	8.41 → 220.43
DMD	float	29.31 → 29.47	1.44 → 60.15	1.46 → 60.33
DMD	double	31.16 → 31.22	1.90 → 65.74	1.90 → 65.66
DMD	real	74.94 → 75.29	14.86 → 224.37	14.98 → 222.19
LDC	float	7.91 → 7.91	1.73 → 53.00	1.73 → 52.68
LDC	double	8.41 → 8.38	1.74 → 53.87	1.76 → 53.73
LDC	real	8.38 → 8.42	1.76 → 53.79	1.74 → 54.10

Ordinary-input paired median changes were approximately +0.1% to +0.2% with DMD and -0.3% to +0.1% with LDC. GDC measured +1.1% to +4.3% in aggregate, but varied substantially by run: float ranged from -3.2% to +7.9%, and double from -1.9% to +13.0%. These small absolute differences are noisy; they do not establish exact equality of performance or a stable GDC regression.

The near-minimum-normal dataset also stayed close: within roughly 1.2% on Windows and 2.9% on GDC. For true-underflow inputs, the additional cutoff check has a small absolute cost in some cases: DMD float changed from about 1.70 to 1.95 ns, DMD portable real from 14.91 to 16.08 ns, and LDC double/real by roughly 0.1–0.2 ns. Overflow-input measurements stayed within about 1.2%.

Subnormal performance tradeoff

The substantial subnormal slowdown is localized to results the original implementation incorrectly replaced with zero. The fixed implementation performs range reduction, approximation, scaling, and subnormal rounding.

For float/double, this changes roughly 1–2 ns into 53–66 ns. Portable 80-bit real changes roughly 8–15 ns into 220–224 ns on this machine. These measurements compare correct computation with the original early zero return. They are whole-call timings, without isolated profiling of the rounding instructions.

Builds use GDC -O2, DMD -O -inline, and LDC -O2 --enable-inlining --noasm, without fast-math. GDC runs under WSL; DMD and LDC run on Windows. IEEE 128-bit real was not available for testing.

This PR was written entirely by an LLM/AI.

AI-Assisted-By: Codex (GPT-6 Astra Medium)

[jmh530]

#11116 is merged, fixing both upstream comment-spacing violations. Could a maintainer rerun Buildkite on this PR against the updated master?

[thewilsonator]

Try rebasing on top of master now that it has that commit.

[0xEAB]

std/internal/math/gammafunction.d(1914:1)[warn]: same visibility attribute used as defined on line 1815.

Looks like a previous commit broke that one.

[jmh530]

std/internal/math/gammafunction.d(1914:1)[warn]: same visibility attribute used as defined on line 1815.

Looks like a previous commit broke that one.

Fixed in commit 26d4c26

[jmh530]

I checked the macOS log: debug64 fails the existing assertion isIdentical(pow(0.0, 6.0), 0.0) at std/math/exponential.d:560. The release64 exponential tests pass.

The assertion and the zero-input path in _powImpl are unchanged by this PR, and that path returns before reaching exp2. The job runs x86-64 DMD through Rosetta on an ARM macOS runner. I haven’t confirmed the cause or reproduced this on the unchanged baseline; is this a known runner/compiler issue?

Separately, Buildkite #10491 fails during installation of pre-commit because pip cannot uninstall Debian’s packaging 24.0 package, before compilation or style checks.

[jmh530]

Rebased to master, prior failing MacOS x64 test no longer failing