Orkuncakilkaya
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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>
22 lines
895 B
Markdown
22 lines
895 B
Markdown
---
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id: math-log
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name: Math.log
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category: math
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kind: namespace-method
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tokens: Math.log
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sig: Math.log(x) -> fixed
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tip: The natural logarithm of x.
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order: 30
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ns: Math
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member: log
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---
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Returns the natural logarithm <code>ln(x)</code> for <code>x > 0</code>, computed in Q16.16 from a deterministic integer <code>log₂</code> (bit-scan for the exponent, a short series for the mantissa) scaled by <code>ln 2</code> — bit-identical on every platform. It is the inverse of <code>Math.exp</code>: reach for it to turn multiplicative growth into a straight line — score-to-level curves, logarithmic difficulty, decibel-style volume. Non-positive inputs are out of domain and saturate to a large negative value rather than returning a meaningful number.
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```ludic
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program Demo {
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handler Step phase Update {
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let level = Math.floor(Math.log(score)) # diminishing returns on score
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}
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}
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```
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