Source Edit

Constructive mathematics is naturally typed. — Simon Thompson

Basic math routines for Nim.

Note that the trigonometric functions naturally operate on radians. The helper functions degToRad and radToDeg provide conversion between radians and degrees.

Example:

import std/math
from std/fenv import epsilon
from std/random import rand
proc generateGaussianNoise(mu: float = 0.0, sigma: float = 1.0): (float, float) =
  # Generates values from a normal distribution.
  # Translated from https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Implementation.
  var u1: float
  var u2: float
  while true:
    u1 = rand(1.0)
    u2 = rand(1.0)
    if u1 > epsilon(float): break
  let mag = sigma * sqrt(-2 * ln(u1))
  let z0 = mag * cos(2 * PI * u2) + mu
  let z1 = mag * sin(2 * PI * u2) + mu
  (z0, z1)
echo generateGaussianNoise()

This module is available for the JavaScript target.

See also

• complex module for complex numbers and their mathematical operations
• rationals module for rational numbers and their mathematical operations
• fenv module for handling of floating-point rounding and exceptions (overflow, zero-divide, etc.)
• random module for a fast and tiny random number generator
• stats module for statistical analysis
• strformat module for formatting floats for printing
• system module for some very basic and trivial math operators (shr, shl, xor, clamp, etc.)

Imports

since, bitops, fenv

Types

FloatClass = enum
  fcNormal,                 ## value is an ordinary nonzero floating point value
  fcSubnormal,              ## value is a subnormal (a very small) floating point value
  fcZero,                   ## value is zero
  fcNegZero,                ## value is the negative zero
  fcNan,                    ## value is Not a Number (NaN)
  fcInf,                    ## value is positive infinity
  fcNegInf                   ## value is negative infinity

Describes the class a floating point value belongs to. This is the type that is returned by the classify func. Source Edit

Consts

E = 2.718281828459045

Euler’s number. Source Edit

MaxFloat32Precision = 8

Maximum number of meaningful digits after the decimal point for Nim’s float32 type. Source Edit

MaxFloat64Precision = 16

Maximum number of meaningful digits after the decimal point for Nim’s float64 type. Source Edit

MaxFloatPrecision = 16

Maximum number of meaningful digits after the decimal point for Nim’s float type. Source Edit

MinFloatNormal = 2.225073858507201e-308

Smallest normal number for Nim’s float type (= 2^-1022). Source Edit

PI = 3.141592653589793

The circle constant PI (Ludolph’s number). Source Edit

TAU = 6.283185307179586

The circle constant TAU (= 2 * PI). Source Edit

Procs

func `^`[T: SomeNumber](x: T; y: Natural): T

Computes x to the power of y.

The exponent y must be non-negative, use pow for negative exponents.

See also:

• pow func for negative exponent or floats
• sqrt func
• cbrt func

Example:

doAssert -3 ^ 0 == 1
doAssert -3 ^ 1 == -3
doAssert -3 ^ 2 == 9

Source Edit

func almostEqual[T: SomeFloat](x, y: T; unitsInLastPlace: Natural = 4): bool {.
    inline.}

Checks if two float values are almost equal, using the machine epsilon.

unitsInLastPlace is the max number of units in the last place difference tolerated when comparing two numbers. The larger the value, the more error is allowed. A 0 value means that two numbers must be exactly the same to be considered equal.

The machine epsilon has to be scaled to the magnitude of the values used and multiplied by the desired precision in ULPs unless the difference is subnormal.

Example:

doAssert almostEqual(PI, 3.14159265358979)
doAssert almostEqual(Inf, Inf)
doAssert not almostEqual(NaN, NaN)

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func arccos(x: float32): float32 {.importc: "acosf", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

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func arccos(x: float64): float64 {.importc: "acos", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Computes the arc cosine of x.

See also:

• cos func

Example:

doAssert almostEqual(radToDeg(arccos(0.0)), 90.0)
doAssert almostEqual(radToDeg(arccos(1.0)), 0.0)

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func arccosh(x: float32): float32 {.importc: "acoshf", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

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func arccosh(x: float64): float64 {.importc: "acosh", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

Computes the inverse hyperbolic cosine of x.

See also:

• cosh func

Source Edit

func arccot[T: float32 | float64](x: T): T

Computes the inverse cotangent of x (arctan(1/x)). Source Edit

func arccoth[T: float32 | float64](x: T): T

Computes the inverse hyperbolic cotangent of x (arctanh(1/x)). Source Edit

func arccsc[T: float32 | float64](x: T): T

Computes the inverse cosecant of x (arcsin(1/x)). Source Edit

func arccsch[T: float32 | float64](x: T): T

Computes the inverse hyperbolic cosecant of x (arcsinh(1/x)). Source Edit

func arcsec[T: float32 | float64](x: T): T

Computes the inverse secant of x (arccos(1/x)). Source Edit

func arcsech[T: float32 | float64](x: T): T

Computes the inverse hyperbolic secant of x (arccosh(1/x)). Source Edit

func arcsin(x: float32): float32 {.importc: "asinf", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

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func arcsin(x: float64): float64 {.importc: "asin", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Computes the arc sine of x.

See also:

• sin func

Example:

doAssert almostEqual(radToDeg(arcsin(0.0)), 0.0)
doAssert almostEqual(radToDeg(arcsin(1.0)), 90.0)

Source Edit

func arcsinh(x: float32): float32 {.importc: "asinhf", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

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func arcsinh(x: float64): float64 {.importc: "asinh", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

Computes the inverse hyperbolic sine of x.

See also:

• sinh func

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func arctan(x: float32): float32 {.importc: "atanf", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

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func arctan(x: float64): float64 {.importc: "atan", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Calculate the arc tangent of x.

See also:

• arctan2 func
• tan func

Example:

doAssert almostEqual(arctan(1.0), 0.7853981633974483)
doAssert almostEqual(radToDeg(arctan(1.0)), 45.0)

Source Edit

func arctan2(y, x: float32): float32 {.importc: "atan2f", header: "<math.h>",
                                       ...raises: [], tags: [], forbids: [].}

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func arctan2(y, x: float64): float64 {.importc: "atan2", header: "<math.h>",
                                       ...raises: [], tags: [], forbids: [].}

Calculate the arc tangent of y/x.

It produces correct results even when the resulting angle is near PI/2 or -PI/2 (x near 0).

See also:

• arctan func

Example:

doAssert almostEqual(arctan2(1.0, 0.0), PI / 2.0)
doAssert almostEqual(radToDeg(arctan2(1.0, 0.0)), 90.0)

Source Edit

func arctanh(x: float32): float32 {.importc: "atanhf", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

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func arctanh(x: float64): float64 {.importc: "atanh", header: "<math.h>",
                                    ...raises: [], tags: [], forbids: [].}

Computes the inverse hyperbolic tangent of x.

See also:

• tanh func

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func binom(n, k: int): int {....raises: [], tags: [], forbids: [].}

Computes the binomial coefficient.

Example:

doAssert binom(6, 2) == 15
doAssert binom(-6, 2) == 1
doAssert binom(6, 0) == 1

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func cbrt(x: float32): float32 {.importc: "cbrtf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func cbrt(x: float64): float64 {.importc: "cbrt", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the cube root of x.

See also:

• sqrt func for the square root

Example:

doAssert almostEqual(cbrt(8.0), 2.0)
doAssert almostEqual(cbrt(2.197), 1.3)
doAssert almostEqual(cbrt(-27.0), -3.0)

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func ceil(x: float32): float32 {.importc: "ceilf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func ceil(x: float64): float64 {.importc: "ceil", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the ceiling function (i.e. the smallest integer not smaller than x).

See also:

• floor func
• round func
• trunc func

Example:

doAssert ceil(2.1)  == 3.0
doAssert ceil(2.9)  == 3.0
doAssert ceil(-2.1) == -2.0

Source Edit

func ceilDiv[T: SomeInteger](x, y: T): T {.inline.}

Ceil division is conceptually defined as ceil(x / y).

Assumes x >= 0 and y > 0 (and x + y - 1 <= high(T) if T is SomeUnsignedInt).

This is different from the system.div operator, which works like trunc(x / y). That is, div rounds towards 0 and ceilDiv rounds up.

This function has the above input limitation, because that allows the compiler to generate faster code and it is rarely used with negative values or unsigned integers close to high(T)/2. If you need a ceilDiv that works with any input, see: https://github.com/demotomohiro/divmath.

See also:

• system.div proc for integer division
• floorDiv func for integer division which rounds down.

Example:

assert ceilDiv(12, 3) ==  4
assert ceilDiv(13, 3) ==  5

Source Edit

func clamp[T](val: T; bounds: Slice[T]): T {.inline.}

Like system.clamp, but takes a slice, so you can easily clamp within a range.

Example:

assert clamp(10, 1 .. 5) == 5
assert clamp(1, 1 .. 3) == 1
type A = enum a0, a1, a2, a3, a4, a5
assert a1.clamp(a2..a4) == a2
assert clamp((3, 0), (1, 0) .. (2, 9)) == (2, 9)
doAssertRaises(AssertionDefect): discard clamp(1, 3..2) # invalid bounds

Source Edit

func classify(x: float): FloatClass {....raises: [], tags: [], forbids: [].}

Classifies a floating point value.

Returns x’s class as specified by the FloatClass enum.

Example:

doAssert classify(0.3) == fcNormal
doAssert classify(0.0) == fcZero
doAssert classify(0.3 / 0.0) == fcInf
doAssert classify(-0.3 / 0.0) == fcNegInf
doAssert classify(5.0e-324) == fcSubnormal

Source Edit

func copySign[T: SomeFloat](x, y: T): T {.inline.}

Returns a value with the magnitude of x and the sign of y; this works even if x or y are NaN, infinity or zero, all of which can carry a sign.

Example:

doAssert copySign(10.0, 1.0) == 10.0
doAssert copySign(10.0, -1.0) == -10.0
doAssert copySign(-Inf, -0.0) == -Inf
doAssert copySign(NaN, 1.0).isNaN
doAssert copySign(1.0, copySign(NaN, -1.0)) == -1.0

Source Edit

func cos(x: float32): float32 {.importc: "cosf", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

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func cos(x: float64): float64 {.importc: "cos", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Computes the cosine of x.

See also:

• arccos func

Example:

doAssert almostEqual(cos(2 * PI), 1.0)
doAssert almostEqual(cos(degToRad(60.0)), 0.5)

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func cosh(x: float32): float32 {.importc: "coshf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func cosh(x: float64): float64 {.importc: "cosh", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the hyperbolic cosine of x.

See also:

• arccosh func

Example:

doAssert almostEqual(cosh(0.0), 1.0)
doAssert almostEqual(cosh(1.0), 1.543080634815244)

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func cot[T: float32 | float64](x: T): T

Computes the cotangent of x (1/tan(x)). Source Edit

func coth[T: float32 | float64](x: T): T

Computes the hyperbolic cotangent of x (1/tanh(x)). Source Edit

func csc[T: float32 | float64](x: T): T

Computes the cosecant of x (1/sin(x)). Source Edit

func csch[T: float32 | float64](x: T): T

Computes the hyperbolic cosecant of x (1/sinh(x)). Source Edit

func cumsum[T](x: var openArray[T])

Transforms x in-place (must be declared as var) into its cumulative (aka prefix) summation.

See also:

• sum func
• cumsummed func for a version which returns a cumsummed sequence

Example:

var a = [1, 2, 3, 4]
cumsum(a)
doAssert a == @[1, 3, 6, 10]

Source Edit

func cumsummed[T](x: openArray[T]): seq[T]

Returns the cumulative (aka prefix) summation of x.

If x is empty, @[] is returned.

See also:

• sum func
• cumsum func for the in-place version

Example:

doAssert cumsummed([1, 2, 3, 4]) == @[1, 3, 6, 10]

Source Edit

func degToRad[T: float32 | float64](d: T): T {.inline.}

Converts from degrees to radians.

See also:

• radToDeg func

Example:

doAssert almostEqual(degToRad(180.0), PI)

Source Edit

func divmod[T: SomeInteger](x, y: T): (T, T) {.inline.}

Specialized instructions for computing both division and modulus. Return structure is: (quotient, remainder)

Example:

doAssert divmod(5, 2) == (2, 1)
doAssert divmod(5, -3) == (-1, 2)

Source Edit

func erf(x: float32): float32 {.importc: "erff", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Source Edit

func erf(x: float64): float64 {.importc: "erf", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Computes the error function for x.

Note: Not available for the JS backend.

Source Edit

func erfc(x: float32): float32 {.importc: "erfcf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Source Edit

func erfc(x: float64): float64 {.importc: "erfc", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the complementary error function for x.

Note: Not available for the JS backend.

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func euclDiv[T: SomeInteger](x, y: T): T

Returns euclidean division of x by y.

Example:

doAssert euclDiv(13, 3) == 4
doAssert euclDiv(-13, 3) == -5
doAssert euclDiv(13, -3) == -4
doAssert euclDiv(-13, -3) == 5

Source Edit

func euclMod[T: SomeNumber](x, y: T): T

Returns euclidean modulo of x by y. euclMod(x, y) is non-negative.

Example:

doAssert euclMod(13, 3) == 1
doAssert euclMod(-13, 3) == 2
doAssert euclMod(13, -3) == 1
doAssert euclMod(-13, -3) == 2

Source Edit

func exp(x: float32): float32 {.importc: "expf", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Source Edit

func exp(x: float64): float64 {.importc: "exp", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Computes the exponential function of x (e^x).

See also:

• ln func

Example:

doAssert almostEqual(exp(1.0), E)
doAssert almostEqual(ln(exp(4.0)), 4.0)
doAssert almostEqual(exp(0.0), 1.0)

Source Edit

func fac(n: int): int {....raises: [], tags: [], forbids: [].}

Computes the factorial of a non-negative integer n.

See also:

• prod func

Example:

doAssert fac(0) == 1
doAssert fac(4) == 24
doAssert fac(10) == 3628800

Source Edit

func floor(x: float32): float32 {.importc: "floorf", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Source Edit

func floor(x: float64): float64 {.importc: "floor", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Computes the floor function (i.e. the largest integer not greater than x).

See also:

• ceil func
• round func
• trunc func

Example:

doAssert floor(2.1)  == 2.0
doAssert floor(2.9)  == 2.0
doAssert floor(-3.5) == -4.0

Source Edit

func floorDiv[T: SomeInteger](x, y: T): T

Floor division is conceptually defined as floor(x / y).

This is different from the system.div operator, which is defined as trunc(x / y). That is, div rounds towards 0 and floorDiv rounds down.

See also:

• system.div proc for integer division
• floorMod func for Python-like (% operator) behavior

Example:

doAssert floorDiv( 13,  3) ==  4
doAssert floorDiv(-13,  3) == -5
doAssert floorDiv( 13, -3) == -5
doAssert floorDiv(-13, -3) ==  4

Source Edit

func floorMod[T: SomeNumber](x, y: T): T

Floor modulo is conceptually defined as x - (floorDiv(x, y) * y).

This func behaves the same as the % operator in Python.

See also:

• mod func
• floorDiv func

Example:

doAssert floorMod( 13,  3) ==  1
doAssert floorMod(-13,  3) ==  2
doAssert floorMod( 13, -3) == -2
doAssert floorMod(-13, -3) == -1

Source Edit

func frexp[T: float32 | float64](x: T): tuple[frac: T, exp: int] {.inline.}

Splits x into a normalized fraction frac and an integral power of 2 exp, such that abs(frac) in 0.5..<1 and x == frac * 2 ^ exp, except for special cases shown below.

Example:

doAssert frexp(8.0) == (0.5, 4)
doAssert frexp(-8.0) == (-0.5, 4)
doAssert frexp(0.0) == (0.0, 0)
# special cases:
when sizeof(int) == 8:
  doAssert frexp(-0.0).frac.signbit # signbit preserved for +-0
  doAssert frexp(Inf).frac == Inf # +- Inf preserved
  doAssert frexp(NaN).frac.isNaN

Source Edit

func frexp[T: float32 | float64](x: T; exponent: var int): T {.inline.}

Overload of frexp that calls (result, exponent) = frexp(x).

Example:

var x: int
doAssert frexp(5.0, x) == 0.625
doAssert x == 3

Source Edit

func gamma(x: float32): float32 {.importc: "tgammaf", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Source Edit

func gamma(x: float64): float64 {.importc: "tgamma", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Computes the gamma function for x.

Note: Not available for the JS backend.

See also:

• lgamma func for the natural logarithm of the gamma function

Example:

doAssert almostEqual(gamma(1.0), 1.0)
doAssert almostEqual(gamma(4.0), 6.0)
doAssert almostEqual(gamma(11.0), 3628800.0)

Source Edit

func gcd(x, y: SomeInteger): SomeInteger

Computes the greatest common (positive) divisor of x and y, using the binary GCD (aka Stein’s) algorithm.

See also:

• gcd func for a float version
• lcm func

Example:

doAssert gcd(12, 8) == 4
doAssert gcd(17, 63) == 1

Source Edit

func gcd[T](x, y: T): T

Computes the greatest common (positive) divisor of x and y.

Note that for floats, the result cannot always be interpreted as “greatest decimal z such that z*N == x and z*M == y where N and M are positive integers”.

See also:

• gcd func for an integer version
• lcm func

Example:

doAssert gcd(13.5, 9.0) == 4.5

Source Edit

func gcd[T](x: openArray[T]): T

Computes the greatest common (positive) divisor of the elements of x.

See also:

• gcd func for a version with two arguments

Example:

doAssert gcd(@[13.5, 9.0]) == 4.5

Source Edit

func hypot(x, y: float32): float32 {.importc: "hypotf", header: "<math.h>",
                                     ...raises: [], tags: [], forbids: [].}

Source Edit

func hypot(x, y: float64): float64 {.importc: "hypot", header: "<math.h>",
                                     ...raises: [], tags: [], forbids: [].}

Computes the length of the hypotenuse of a right-angle triangle with x as its base and y as its height. Equivalent to sqrt(x*x + y*y).

Example:

doAssert almostEqual(hypot(3.0, 4.0), 5.0)

Source Edit

func isNaN(x: SomeFloat): bool {.inline.}

Returns whether x is a NaN, more efficiently than via classify(x) == fcNan. Works even with --passc:-ffast-math.

Example:

doAssert NaN.isNaN
doAssert not Inf.isNaN
doAssert not isNaN(3.1415926)

Source Edit

func isPowerOfTwo(x: int): bool {....raises: [], tags: [], forbids: [].}

Returns true, if x is a power of two, false otherwise.

Zero and negative numbers are not a power of two.

See also:

• nextPowerOfTwo func

Example:

doAssert isPowerOfTwo(16)
doAssert not isPowerOfTwo(5)
doAssert not isPowerOfTwo(0)
doAssert not isPowerOfTwo(-16)

Source Edit

func lcm[T](x, y: T): T

Computes the least common multiple of x and y.

See also:

• gcd func

Example:

doAssert lcm(24, 30) == 120
doAssert lcm(13, 39) == 39

Source Edit

func lcm[T](x: openArray[T]): T

Computes the least common multiple of the elements of x.

See also:

• lcm func for a version with two arguments

Example:

doAssert lcm(@[24, 30]) == 120

Source Edit

func lgamma(x: float32): float32 {.importc: "lgammaf", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Source Edit

func lgamma(x: float64): float64 {.importc: "lgamma", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Computes the natural logarithm of the gamma function for x.

Note: Not available for the JS backend.

See also:

• gamma func for gamma function

Source Edit

func ln(x: float32): float32 {.importc: "logf", header: "<math.h>", ...raises: [],
                               tags: [], forbids: [].}

Source Edit

func ln(x: float64): float64 {.importc: "log", header: "<math.h>", ...raises: [],
                               tags: [], forbids: [].}

Computes the natural logarithm of x.

See also:

• log func
• log10 func
• log2 func
• exp func

Example:

doAssert almostEqual(ln(exp(4.0)), 4.0)
doAssert almostEqual(ln(1.0), 0.0)
doAssert almostEqual(ln(0.0), -Inf)
doAssert ln(-7.0).isNaN

Source Edit

func log[T: SomeFloat](x, base: T): T

Computes the logarithm of x to base base.

See also:

• ln func
• log10 func
• log2 func

Example:

doAssert almostEqual(log(9.0, 3.0), 2.0)
doAssert almostEqual(log(0.0, 2.0), -Inf)
doAssert log(-7.0, 4.0).isNaN
doAssert log(8.0, -2.0).isNaN

Source Edit

func log2(x: float32): float32 {.importc: "log2f", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Source Edit

func log2(x: float64): float64 {.importc: "log2", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the binary logarithm (base 2) of x.

See also:

• log func
• log10 func
• ln func

Example:

doAssert almostEqual(log2(8.0), 3.0)
doAssert almostEqual(log2(1.0), 0.0)
doAssert almostEqual(log2(0.0), -Inf)
doAssert log2(-2.0).isNaN

Source Edit

func log10(x: float32): float32 {.importc: "log10f", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Source Edit

func log10(x: float64): float64 {.importc: "log10", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Computes the common logarithm (base 10) of x.

See also:

• ln func
• log func
• log2 func

Example:

doAssert almostEqual(log10(100.0) , 2.0)
doAssert almostEqual(log10(0.0), -Inf)
doAssert log10(-100.0).isNaN

Source Edit

func `mod`(x, y: float32): float32 {.importc: "fmodf", header: "<math.h>",
                                     ...raises: [], tags: [], forbids: [].}

Source Edit

func `mod`(x, y: float64): float64 {.importc: "fmod", header: "<math.h>",
                                     ...raises: [], tags: [], forbids: [].}

Computes the modulo operation for float values (the remainder of x divided by y).

See also:

• floorMod func for Python-like (% operator) behavior

Example:

doAssert  6.5 mod  2.5 ==  1.5
doAssert -6.5 mod  2.5 == -1.5
doAssert  6.5 mod -2.5 ==  1.5
doAssert -6.5 mod -2.5 == -1.5

Source Edit

func nextPowerOfTwo(x: int): int {....raises: [], tags: [], forbids: [].}

Returns x rounded up to the nearest power of two.

Zero and negative numbers get rounded up to 1.

See also:

• isPowerOfTwo func

Example:

doAssert nextPowerOfTwo(16) == 16
doAssert nextPowerOfTwo(5) == 8
doAssert nextPowerOfTwo(0) == 1
doAssert nextPowerOfTwo(-16) == 1

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func pow(x, y: float32): float32 {.importc: "powf", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

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func pow(x, y: float64): float64 {.importc: "pow", header: "<math.h>",
                                   ...raises: [], tags: [], forbids: [].}

Computes x raised to the power of y.

To compute the power between integers (e.g. 2^6), use the ^ func.

See also:

• ^ func
• sqrt func
• cbrt func

Example:

doAssert almostEqual(pow(100, 1.5), 1000.0)
doAssert almostEqual(pow(16.0, 0.5), 4.0)

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func prod[T](x: openArray[T]): T

Computes the product of the elements in x.

If x is empty, 1 is returned.

See also:

• sum func
• fac func

Example:

doAssert prod([1, 2, 3, 4]) == 24
doAssert prod([-4, 3, 5]) == -60

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func radToDeg[T: float32 | float64](d: T): T {.inline.}

Converts from radians to degrees.

See also:

• degToRad func

Example:

doAssert almostEqual(radToDeg(2 * PI), 360.0)

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func round(x: float32): float32 {.importc: "roundf", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

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func round(x: float64): float64 {.importc: "round", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Rounds a float to zero decimal places.

Used internally by the round func when the specified number of places is 0.

See also:

• round func for rounding to the specific number of decimal places
• floor func
• ceil func
• trunc func

Example:

doAssert round(3.4) == 3.0
doAssert round(3.5) == 4.0
doAssert round(4.5) == 5.0

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func round[T: float32 | float64](x: T; places: int): T

Decimal rounding on a binary floating point number.

This function is NOT reliable. Floating point numbers cannot hold non integer decimals precisely. If places is 0 (or omitted), round to the nearest integral value following normal mathematical rounding rules (e.g. round(54.5) -> 55.0). If places is greater than 0, round to the given number of decimal places, e.g. round(54.346, 2) -> 54.350000000000001421…. If places is negative, round to the left of the decimal place, e.g. round(537.345, -1) -> 540.0.

Example:

doAssert round(PI, 2) == 3.14
doAssert round(PI, 4) == 3.1416

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func sec[T: float32 | float64](x: T): T

Computes the secant of x (1/cos(x)). Source Edit

func sech[T: float32 | float64](x: T): T

Computes the hyperbolic secant of x (1/cosh(x)). Source Edit

func sgn[T: SomeNumber](x: T): int {.inline.}

Sign function.

Returns:

• -1 for negative numbers and NegInf,
• 1 for positive numbers and Inf,
• 0 for positive zero, negative zero and NaN

Example:

doAssert sgn(5) == 1
doAssert sgn(0) == 0
doAssert sgn(-4.1) == -1

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proc signbit(x: SomeFloat): bool {.inline.}

Returns true if x is negative, false otherwise.

Example:

doAssert not signbit(0.0)
doAssert signbit(-0.0)
doAssert signbit(-0.1)
doAssert not signbit(0.1)

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func sin(x: float32): float32 {.importc: "sinf", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

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func sin(x: float64): float64 {.importc: "sin", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Computes the sine of x.

See also:

• arcsin func

Example:

doAssert almostEqual(sin(PI / 6), 0.5)
doAssert almostEqual(sin(degToRad(90.0)), 1.0)

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func sinh(x: float32): float32 {.importc: "sinhf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func sinh(x: float64): float64 {.importc: "sinh", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the hyperbolic sine of x.

See also:

• arcsinh func

Example:

doAssert almostEqual(sinh(0.0), 0.0)
doAssert almostEqual(sinh(1.0), 1.175201193643801)

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func splitDecimal[T: float32 | float64](x: T): tuple[intpart: T, floatpart: T]

Breaks x into an integer and a fractional part.

Returns a tuple containing intpart and floatpart, representing the integer part and the fractional part, respectively.

Both parts have the same sign as x. Analogous to the modf function in C.

Example:

doAssert splitDecimal(5.25) == (intpart: 5.0, floatpart: 0.25)
doAssert splitDecimal(-2.73) == (intpart: -2.0, floatpart: -0.73)

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func sqrt(x: float32): float32 {.importc: "sqrtf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func sqrt(x: float64): float64 {.importc: "sqrt", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the square root of x.

See also:

• cbrt func for the cube root

Example:

doAssert almostEqual(sqrt(4.0), 2.0)
doAssert almostEqual(sqrt(1.44), 1.2)

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func sum[T](x: openArray[T]): T

Computes the sum of the elements in x.

If x is empty, 0 is returned.

See also:

• prod func
• cumsum func
• cumsummed func

Example:

doAssert sum([1, 2, 3, 4]) == 10
doAssert sum([-4, 3, 5]) == 4

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func tan(x: float32): float32 {.importc: "tanf", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

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func tan(x: float64): float64 {.importc: "tan", header: "<math.h>", ...raises: [],
                                tags: [], forbids: [].}

Computes the tangent of x.

See also:

• arctan func

Example:

doAssert almostEqual(tan(degToRad(45.0)), 1.0)
doAssert almostEqual(tan(PI / 4), 1.0)

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func tanh(x: float32): float32 {.importc: "tanhf", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

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func tanh(x: float64): float64 {.importc: "tanh", header: "<math.h>",
                                 ...raises: [], tags: [], forbids: [].}

Computes the hyperbolic tangent of x.

See also:

• arctanh func

Example:

doAssert almostEqual(tanh(0.0), 0.0)
doAssert almostEqual(tanh(1.0), 0.7615941559557649)

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func trunc(x: float32): float32 {.importc: "truncf", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

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func trunc(x: float64): float64 {.importc: "trunc", header: "<math.h>",
                                  ...raises: [], tags: [], forbids: [].}

Truncates x to the decimal point.

See also:

• floor func
• ceil func
• round func

Example:

doAssert trunc(PI) == 3.0
doAssert trunc(-1.85) == -1.0

Source Edit