math¶

Trigonometry, logarithms, roots, rounding, and the constants.

import "std/math" as math;

Every function here takes and returns floats, apart from the three that take or return an int where the underlying operation is integral (ldexp, ilogb, scalbn).

None of them raises. An argument outside a function's domain gives the platform's floating-point answer, so math::sqrt(-1.0) is not-a-number rather than an error. Infinities and not-a-number behave like any other float, and print as inf, -inf and NaN. Unlike the usual floating-point rule, not-a-number compares equal to itself, so test for it with str(x) == "NaN" rather than x != x.

The module binds a small dynamic library that wraps the platform maths library, so it is one of the three std modules that need that library present at run time. A .cdlb built from a program that imports std/math records the binding by name and re-opens it when the artifact runs; see artifacts.

Four common operations are also built-in methods on a number, with no import: x.abs(), x.sqrt(), x.round(), and x.floor().

Trigonometry¶

Function	Returns
`math::sin(x)`	The sine of `x`, in radians
`math::cos(x)`	The cosine of `x`, in radians
`math::tan(x)`	The tangent of `x`, in radians
`math::asin(x)`	The arc sine of `x`, in radians
`math::acos(x)`	The arc cosine of `x`, in radians
`math::atan(x)`	The arc tangent of `x`, in radians
`math::atan2(x, y)`	The arc tangent of `x / y`, using the signs of both to pick the quadrant
`math::sinh(x)`	The hyperbolic sine of `x`
`math::cosh(x)`	The hyperbolic cosine of `x`
`math::tanh(x)`	The hyperbolic tangent of `x`
`math::asinh(x)`	The inverse hyperbolic sine of `x`
`math::acosh(x)`	The inverse hyperbolic cosine of `x`
`math::atanh(x)`	The inverse hyperbolic tangent of `x`

Exponentials and logarithms¶

Function	Returns
`math::exp(x)`	e raised to the power `x`
`math::expm1(x)`	`exp(x) - 1`, accurate for small `x`
`math::log(x)`	The natural logarithm of `x`
`math::log2(x)`	The base-2 logarithm of `x`
`math::log10(x)`	The base-10 logarithm of `x`
`math::log1p(x)`	`log(1 + x)`, accurate for small `x`
`math::logb(x)`	The exponent of `x` in the floating-point radix, as a float
`math::ilogb(x)`	The same exponent, as an int
`math::ldexp(x, n)`	`x` multiplied by 2 raised to the int `n`
`math::scalbn(x, n)`	`x` scaled by the radix raised to the int `n`
`math::pow(x, y)`	`x` raised to the power `y`

Roots and distances¶

Function	Returns
`math::sqrt(x)`	The square root of `x`
`math::cbrt(x)`	The cube root of `x`
`math::hypot(x, y)`	The length of the hypotenuse with sides `x` and `y`, without intermediate overflow
`math::erf(x)`	The error function of `x`
`math::erfc(x)`	The complementary error function, `1 - erf(x)`

Rounding and sign¶

Function	Returns
`math::floor(x)`	The largest whole number not greater than `x`
`math::ceil(x)`	The smallest whole number not less than `x`
`math::round(x)`	`x` rounded to the nearest whole number, halves away from zero
`math::trunc(x)`	`x` with its fractional part discarded, towards zero
`math::fmod(x, y)`	The remainder of `x / y`, with the sign of `x`
`math::copysign(x, y)`	The magnitude of `x` with the sign of `y`

All of these return a float, including floor, ceil, round, and trunc. Convert with int(...) when you want a whole-number type.

Constants¶

Each constant is a function call, so it costs a call and returns a float.

Function	Returns
`math::pi()`	The ratio of a circle's circumference to its diameter
`math::e()`	The base of the natural logarithm
`math::tau()`	The ratio of a circle's circumference to its radius, two pi

import "std/math" as math;

fn main() {
    print(math::sqrt(2.0));
    print(math::round(math::sin(math::pi() / 2.0)));
    print(int(math::floor(7.0 / 2.0)));
}