sss_similar

std.geometry.sss_similar · Level L3

Whether triangle B is similar to triangle A with ratio k = p/q > 0 under the given correspondence Aᵢ ↔ Bᵢ (rows of A and B), as 1 or 0, by side-side-side: every corresponding side has |BᵢBⱼ| = k·|AᵢAⱼ|, checked exactly as q²·|BᵢBⱼ|² = p²·|AᵢAⱼ|² for integer coordinates. A reflection keeps the ratio. A failure rules out this ratio and correspondence only, not similarity by another.

q²|BᵢBⱼ|² = p²|AᵢAⱼ|²

Signature

sss_similar(A: f64[3, 2], B: f64[3, 2], p: f64[], q: f64[]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference squared side lengths in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 40 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:c2d1f8bbeacb4618c711ca3cb530122c7ab98b003516c3d190a8ce20aa371f4a

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.geometry.sss_similar · Ω:sss_similar
Pins: sha256:6f07cc1f51217da7f55989190ed4040f1b723af1edce1b4689e114139c861384this graph alone
Evidence: sha256:12591c565057c3bd4dc68c77a3464078359bcbd75ec215a69d8edafd82b906a3the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.