vera:math

Mathematical functions for f64 floating-point arithmetic.

import "vera:math"

Overview

Provides constants, utility functions, and transcendental functions for f64 floating-point arithmetic. All functions operate on IEEE 754 double-precision values. Trigonometric functions use Cody-Waite range reduction and minimax polynomial approximations. Exponential and logarithmic functions use Horner-form polynomial evaluation with FMA instructions.

Dependencies: None (pure VERA)

Functions

Constants

math_pi

function math_pi() -> f64

Returns the constant pi (3.14159265358979323846).

math_e

function math_e() -> f64

Returns Euler's number e (2.71828182845904523536).

math_ln2

function math_ln2() -> f64

Returns the natural logarithm of 2 (0.69314718055994530942).

math_ln10

function math_ln10() -> f64

Returns the natural logarithm of 10 (2.30258509299404568402).

Utility

abs_f64

function abs_f64(x: f64) -> f64

Absolute value of a float.

Parameters:

  • x (f64) — input value

Returns: |x|

floor_f64

function floor_f64(x: f64) -> f64

Round toward negative infinity. Returns NaN unchanged. Values with magnitude >= 2^53 are returned unchanged (already integers at f64 precision).

Parameters:

  • x (f64) — input value

Returns: the largest integer value not greater than x

ceil_f64

function ceil_f64(x: f64) -> f64

Round toward positive infinity. Implemented as -floor(-x).

Parameters:

  • x (f64) — input value

Returns: the smallest integer value not less than x

round_f64

function round_f64(x: f64) -> f64

Round to nearest integer (half rounds up). Implemented as floor(x + 0.5).

Parameters:

  • x (f64) — input value

Returns: the nearest integer to x

min_f64

function min_f64(a: f64, b: f64) -> f64

Minimum of two floats.

Parameters:

  • a (f64) — first value
  • b (f64) — second value

Returns: the smaller of a and b

max_f64

function max_f64(a: f64, b: f64) -> f64

Maximum of two floats.

Parameters:

  • a (f64) — first value
  • b (f64) — second value

Returns: the larger of a and b

clamp_f64

function clamp_f64(x: f64, lo: f64, hi: f64) -> f64

Clamp x to the range [lo, hi]. Equivalent to min(max(x, lo), hi).

Parameters:

  • x (f64) — value to clamp
  • lo (f64) — lower bound
  • hi (f64) — upper bound

Returns: x clamped to [lo, hi]

sqrt_f64

function sqrt_f64(x: f64) -> f64

Square root. Wraps the ISA's square_root.f64 instruction.

Parameters:

  • x (f64) — input value (must be >= 0)

Returns: the square root of x

degrees_to_radians

function degrees_to_radians(deg: f64) -> f64

Convert degrees to radians.

Parameters:

  • deg (f64) — angle in degrees

Returns: angle in radians

radians_to_degrees

function radians_to_degrees(rad: f64) -> f64

Convert radians to degrees.

Parameters:

  • rad (f64) — angle in radians

Returns: angle in degrees

Trigonometric

sin_f64

function sin_f64(x: f64) -> f64

Sine of x (radians). Uses Cody-Waite range reduction to [-pi/4, pi/4] and minimax polynomial kernels. Returns NaN unchanged.

Parameters:

  • x (f64) — angle in radians

Returns: sin(x)

cos_f64

function cos_f64(x: f64) -> f64

Cosine of x (radians). Uses the same range reduction as sin_f64. Returns NaN unchanged.

Parameters:

  • x (f64) — angle in radians

Returns: cos(x)

tan_f64

function tan_f64(x: f64) -> f64

Tangent of x (radians). Computed as sin(x) / cos(x).

Parameters:

  • x (f64) — angle in radians

Returns: tan(x)

Exponential / Logarithmic

exp_f64

function exp_f64(x: f64) -> f64

Exponential function e^x. Uses range reduction via x = k * ln2 + r and a minimax polynomial for exp(r). Handles overflow (x > ~709.78 returns +infinity) and underflow (x < ~-745.13 returns 0). Returns NaN unchanged.

Parameters:

  • x (f64) — exponent

Returns: e^x

log_f64

function log_f64(x: f64) -> f64

Natural logarithm of x. Decomposes x into mantissa and exponent, then uses a Horner-form polynomial on s = (m-1)/(m+1). Returns NaN for negative inputs, -infinity for zero, and NaN unchanged.

Parameters:

  • x (f64) — input value (must be > 0 for a meaningful result)

Returns: ln(x)

log2_f64

function log2_f64(x: f64) -> f64

Base-2 logarithm of x. Computed as log(x) * (1/ln2).

Parameters:

  • x (f64) — input value (must be > 0 for a meaningful result)

Returns: log2(x)

log10_f64

function log10_f64(x: f64) -> f64

Base-10 logarithm of x. Computed as log(x) * (1/ln10).

Parameters:

  • x (f64) — input value (must be > 0 for a meaningful result)

Returns: log10(x)

Power

pow_f64

function pow_f64(base: f64, exponent: f64) -> f64

Raise base to the power of exponent. Computed as exp(exponent * log(base)) for positive bases. Handles special cases:

  • Any base raised to 0 returns 1.0 (including NaN^0).
  • 1.0 raised to any exponent returns 1.0.
  • 0.0 raised to a positive exponent returns 0.0; to a negative exponent returns +infinity.
  • Negative bases with integer exponents use sign parity; non-integer exponents return NaN.

Parameters:

  • base (f64) — the base
  • exponent (f64) — the exponent

Returns: base^exponent