latmath.scalar — Scalar Utilities

Mathematical constants, error measures, tolerance-based comparison, and approximate equality for scalar values. Pure stdlib, zero dependencies.

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Constants

from latpy.latmath.scalar import pi, e, tau, inf, nan

Symbol	Value	Description
pi	3.141592653589793	Archimedes’ constant (π)
e	2.718281828459045	Euler’s number
tau	6.283185307179586	τ = 2π
inf	float('inf')	IEEE 754 positive infinity
nan	float('nan')	IEEE 754 Not-a-Number

All constants are Python float values, safe for use in any expression.

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Error Measures

from latpy.latmath.scalar import relative_error, absolute_error

Signature	Description
relative_error(a, b) -> float	|a − b| / |b|; returns 0.0 if both are 0, inf if b = 0 and a ≠ 0
absolute_error(a, b) -> float	|a − b|

Edge cases:

• relative_error(0.0, 0.0) → 0.0 (not undefined)

• relative_error(5.0, 0.0) → inf

• relative_error(0.0, 3.0) → 0.0

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Approximate Equality

from latpy.latmath.scalar import isclose, allclose

Signature	Description
isclose(a, b, rel_tol=1e-9, abs_tol=0.0) -> bool	Delegates to math.isclose
allclose(a, b, rel_tol=1e-9, abs_tol=0.0) -> bool	Pairwise isclose over iterables

Edge cases:

• isclose(nan, nan) → False (IEEE 754 semantics)

• isclose(inf, inf) → True

• allclose stops early on first mismatch

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Robust Comparison

from latpy.latmath.scalar import (
    approx_eq, approx_ne,
    approx_lt, approx_le,
    approx_gt, approx_ge,
)

Signature	Description
approx_eq(a, b, rel_tol, abs_tol) -> bool	True if a ≈ b within tolerance
approx_ne(a, b, rel_tol, abs_tol) -> bool	True if a ≉ b
approx_lt(a, b, rel_tol, abs_tol) -> bool	True if a < b and a ≉ b
approx_le(a, b, rel_tol, abs_tol) -> bool	True if a < b or a ≈ b
approx_gt(a, b, rel_tol, abs_tol) -> bool	True if a > b and a ≉ b
approx_ge(a, b, rel_tol, abs_tol) -> bool	True if a > b or a ≈ b

Rationale: Standard < / > break down when values differ by floating-point rounding. approx_lt(1.0, 1.0 + 1e-16) is False because the two are considered equal within tolerance — avoiding spurious branch misbehavior in numerical algorithms.

Edge cases:

• approx_eq(1.0, 1.0 + 1e-10) → True (default rel_tol=1e-9)

• approx_lt(1.0, 1.0 + 1e-10) → False (within tolerance, so not strictly less)

• approx_ge(1.0 + 1e-10, 1.0) → True (within tolerance, so “greater or equal”)