Hoopoe

@/math: numeric functions and constants ​

The math module is ambient: its methods and constants are available without an import. Floating-point operations use IEEE-754 double-precision semantics, including JavaScript's NaN and positive or negative infinity results for out-of-domain and overflow cases.

Float methods ​

float provides the trigonometric methods sin, cos, tan, asin, acos, and atan; the hyperbolic methods sinh, cosh, tanh, asinh, acosh, and atanh; and floor, ceil, and round. exp() computes (e^x), while ln() computes the natural logarithm. log(base) is defined in Hoopoe as:

hoopoe
func log(base: float): float = this.ln() / base.ln()

atan2(y, x) is a top-level function whose operands are interpreted in that order. Integer trigonometric and hyperbolic convenience methods convert their receiver to float and return a float.

The host implementations receive canonical boxed Hoopoe values and return canonical float or int boxes. Raw JavaScript numbers exist only while a host math primitive is being called; source operands are evaluated once in source order.

Constants ​

  • pi, tau, e, and phi are the usual mathematical constants.
  • max_float is the largest finite positive float (Number.MAX_VALUE).
  • min_float is the most negative finite float (-Number.MAX_VALUE).
  • min_positive_float is the smallest positive representable float (Number.MIN_VALUE, including subnormal values).
  • max_int and min_int are the language's nominal signed integer bounds.

The external float constants are immutable boxed values initialized once per generated program and shared by every reference.

Complex numbers and powers ​

import std/math/complex with (Complex) provides the canonical Complex.new(real: float, imaginary: float) constructs a complex number. It supports addition, subtraction, multiplication, division, negation, conjugation, magnitude, and the exact scalar exponentiation matrix documented under Operators. The same import supplies the real base/float exponent rows because those rows return Complex.

Integer and integral-valued float powers use exponentiation by squaring. Non-integral powers use a positive-real fast path where valid and otherwise the principal branch

[ z^x = \exp!\left(x\operatorname{Log}(z)\right), ]

where Log uses ln(abs(z)) and atan2(imaginary, real). Thus, for example, (-4) ** 0.5 has a positive imaginary component on the principal branch. 0 ** 0 is one, zero to a positive exponent is zero, and zero to a negative exponent raises a runtime domain error.