ludic/docs/language/math/math-exp.md
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feat(stdlib): Math.exp/log/pow + Ease.elastic transcendentals (issue #25)
Finish the unblocked "Math / Ease" half of #25: the fixed-point
transcendentals deferred from #2. Vec.* stays blocked on the vec2 type
in #1.

- Math.exp, Math.log (natural), Math.pow — deterministic Q16.16 via two
  new prelude fns in emit_math_prelude: @fn_fx_exp2 (range-reduced 5th-order
  Taylor 2^f, then a clamped shift by the integer part) and @fn_fx_log2
  (llvm.ctlz for the exponent + an atanh series on (m-1)/(m+1) for the
  mantissa). exp=2^(x·log2 e), log=log2(x)·ln2, pow=2^(b·log2 a).
- Ease.elastic — ease-out elastic 2^(-10t)·sin((10t-0.75)·2pi/3)+1.
- Pure integer IR, so bit-identical on every platform. Results must fit the
  Q16.16 range (|x| < 32768); larger magnitudes saturate (documented).

Test selfhost/tests/transcend.ludic (registered in the self-host suite) +
docs for all four. Reseeded; the C-free bootstrap fixpoint holds. All suites
green (24 self-host, 45 regression, 29 tool).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-08-30 01:19:44 +03:00

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Markdown

---
id: math-exp
name: Math.exp
category: math
kind: namespace-method
tokens: Math.exp
sig: Math.exp(x) -> fixed
tip: e raised to the power x.
order: 29
ns: Math
member: exp
---
Returns <code>e<sup>x</sup></code> (the natural exponential), computed in Q16.16 as <code>2<sup>x·log₂e</sup></code> through a range-reduced integer polynomial — so it is bit-identical on every platform, the same guarantee the rest of the runtime gives. Pair it with <code>Math.log</code> for exponential decay and growth: cooldowns that ease off, difficulty ramps, or a value that relaxes toward a target. The result must land inside the fixed-point range (magnitudes below <code>32768</code>), so keep <code>x</code> under about <code>10</code>; larger exponents saturate.
```ludic
program Demo {
handler Step phase Update {
let remaining = Math.exp(0.0 - decay * elapsed) # smooth decay 1 -> 0
}
}
```