Summary

Vera has basic math functions (abs, min, max, floor, ceil, round, sqrt, pow) but is missing logarithmic functions, trigonometric functions, mathematical constants, and common numeric utilities.

Proposed API

Logarithmic

• log(@Float64) -> @Float64 — natural logarithm
• log2(@Float64) -> @Float64 — base-2 logarithm
• log10(@Float64) -> @Float64 — base-10 logarithm

Trigonometric

• sin(@Float64) -> @Float64
• cos(@Float64) -> @Float64
• tan(@Float64) -> @Float64
• asin(@Float64) -> @Float64
• acos(@Float64) -> @Float64
• atan(@Float64) -> @Float64
• atan2(@Float64, @Float64) -> @Float64

Constants

• pi() -> @Float64 — 3.14159...
• e() -> @Float64 — 2.71828...

Numeric utilities

• sign(@Int) -> @Int — returns -1, 0, or 1
• clamp(@Int, @Int, @Int) -> @Int — restrict value to [min, max] range
• clamp_float(@Float64, @Float64, @Float64) -> @Float64 — float variant

Implementation

• environment.py: Register as pure functions (no effects)
• codegen/api.py: Host imports delegating to Python math module
• WASM: Most map directly to f64 operations or can use math.log, math.sin, etc.
• Browser runtime: Math.log(), Math.sin(), Math.PI, etc.
• Verification: Standard Z3 real arithmetic axioms where available; trig functions are generally uninterpreted in Z3

Priority

Lower priority than array utilities and sleep/random, but these are standard library functions that every language provides. Useful for scientific computation, graphics, audio, and any problem involving geometry or exponential growth.