polar_to_cartesian

std.geometry.polar_to_cartesian · Level L5

From polar coordinates (r, θ) to Cartesian ones: x = r·cos θ, y = r·sin θ.

(x, y) = (r cos θ, r sin θ)

Signature

polar_to_cartesian(r: f64[n], theta: f64[n]) → f64[n], f64[n]

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.
Agrees with the reference r * np.cos(theta), r * np.sin(theta) to 80 digits (100-digit arithmetic), on all 40 test cases.
All 306 float64 results inside the running error bound; the closest uses 15% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 20% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 86%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 1.05

Identity

Calls

—

Called by

—

sha256:aca376d8d3f89d7dc4d918fd8db6f5e0adb37545f3cd2cfb2cc6c0255cec23aa

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.polar_to_cartesian · Ω:polar_to_cartesian
Pins: sha256:f9973fea4096c0dc5f25042f344f5fe4654e52c0046b079ed8a45b7ff3e477b6this graph alone
Evidence: sha256:4c7354971be28c88e320016218d92ab1e6b53f7bcee887af2deedce9a1c10578the 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.