std/math

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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

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

PI = 3.141592653589793
The circle constant PI (Ludolph's number).   Source   Edit
TAU = 6.283185307179586
The circle constant TAU (= 2 * PI).   Source   Edit
E = 2.718281828459045
Euler's number.   Source   Edit
MaxFloat64Precision = 16
Maximum number of meaningful digits after the decimal point for Nim's float64 type.   Source   Edit
MaxFloat32Precision = 8
Maximum number of meaningful digits after the decimal point for Nim's float32 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

Procs

func c_frexp(x: cfloat; exponent: var cint): cfloat {.importc: "frexpf",
    header: "<math.h>", deprecated: "Use `frexp` instead".}
Deprecated: Use `frexp` instead
  Source   Edit
func c_frexp(x: cdouble; exponent: var cint): cdouble {.importc: "frexp",
    header: "<math.h>", deprecated: "Use `frexp` instead".}
Deprecated: Use `frexp` instead
  Source   Edit
func binom(n, k: int): int {....raises: [], tags: [].}
Computes the binomial coefficient.

Example:

doAssert binom(6, 2) == 15
doAssert binom(-6, 2) == 1
doAssert binom(6, 0) == 1
  Source   Edit
func fac(n: int): int {....raises: [], tags: [].}

Computes the factorial of a non-negative integer n.

See also:

Example:

doAssert fac(0) == 1
doAssert fac(4) == 24
doAssert fac(10) == 3628800
  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
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)
  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 classify(x: float): FloatClass {....raises: [], tags: [].}

Classifies a floating point value.

Returns x's class as specified by the FloatClass enum. Doesn't work with --passc:-ffast-math.

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

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

Zero and negative numbers are not a power of two.

See also:

Example:

doAssert isPowerOfTwo(16)
doAssert not isPowerOfTwo(5)
doAssert not isPowerOfTwo(0)
doAssert not isPowerOfTwo(-16)
  Source   Edit
func nextPowerOfTwo(x: int): int {....raises: [], tags: [].}

Returns x rounded up to the nearest power of two.

Zero and negative numbers get rounded up to 1.

See also:

Example:

doAssert nextPowerOfTwo(16) == 16
doAssert nextPowerOfTwo(5) == 8
doAssert nextPowerOfTwo(0) == 1
doAssert nextPowerOfTwo(-16) == 1
  Source   Edit
func sum[T](x: openArray[T]): T

Computes the sum of the elements in x.

If x is empty, 0 is returned.

See also:

Example:

doAssert sum([1, 2, 3, 4]) == 10
doAssert sum([-4, 3, 5]) == 4
  Source   Edit
func prod[T](x: openArray[T]): T

Computes the product of the elements in x.

If x is empty, 1 is returned.

See also:

Example:

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

Example:

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

Example:

var a = [1, 2, 3, 4]
cumsum(a)
doAssert a == @[1, 3, 6, 10]
  Source   Edit
func sqrt(x: float32): float32 {.importc: "sqrtf", header: "<math.h>".}
  Source   Edit
func sqrt(x: float64): float64 {.importc: "sqrt", header: "<math.h>".}

Computes the square root of x.

See also:

Example:

doAssert almostEqual(sqrt(4.0), 2.0)
doAssert almostEqual(sqrt(1.44), 1.2)
  Source   Edit
func cbrt(x: float32): float32 {.importc: "cbrtf", header: "<math.h>".}
  Source   Edit
func cbrt(x: float64): float64 {.importc: "cbrt", header: "<math.h>".}

Computes the cube root of x.

See also:

Example:

doAssert almostEqual(cbrt(8.0), 2.0)
doAssert almostEqual(cbrt(2.197), 1.3)
doAssert almostEqual(cbrt(-27.0), -3.0)
  Source   Edit
func ln(x: float32): float32 {.importc: "logf", header: "<math.h>".}
  Source   Edit
func ln(x: float64): float64 {.importc: "log", header: "<math.h>".}

Computes the natural logarithm of x.

See also:

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:

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 log10(x: float32): float32 {.importc: "log10f", header: "<math.h>".}
  Source   Edit
func log10(x: float64): float64 {.importc: "log10", header: "<math.h>".}

Computes the common logarithm (base 10) of x.

See also:

Example:

doAssert almostEqual(log10(100.0) , 2.0)
doAssert almostEqual(log10(0.0), -Inf)
doAssert log10(-100.0).isNaN
  Source   Edit
func exp(x: float32): float32 {.importc: "expf", header: "<math.h>".}
  Source   Edit
func exp(x: float64): float64 {.importc: "exp", header: "<math.h>".}

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

See also:

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 sin(x: float32): float32 {.importc: "sinf", header: "<math.h>".}
  Source   Edit
func sin(x: float64): float64 {.importc: "sin", header: "<math.h>".}

Computes the sine of x.

See also:

Example:

doAssert almostEqual(sin(PI / 6), 0.5)
doAssert almostEqual(sin(degToRad(90.0)), 1.0)
  Source   Edit
func cos(x: float32): float32 {.importc: "cosf", header: "<math.h>".}
  Source   Edit
func cos(x: float64): float64 {.importc: "cos", header: "<math.h>".}

Computes the cosine of x.

See also:

Example:

doAssert almostEqual(cos(2 * PI), 1.0)
doAssert almostEqual(cos(degToRad(60.0)), 0.5)
  Source   Edit
func tan(x: float32): float32 {.importc: "tanf", header: "<math.h>".}
  Source   Edit
func tan(x: float64): float64 {.importc: "tan", header: "<math.h>".}

Computes the tangent of x.

See also:

Example:

doAssert almostEqual(tan(degToRad(45.0)), 1.0)
doAssert almostEqual(tan(PI / 4), 1.0)
  Source   Edit
func sinh(x: float32): float32 {.importc: "sinhf", header: "<math.h>".}
  Source   Edit
func sinh(x: float64): float64 {.importc: "sinh", header: "<math.h>".}

Computes the hyperbolic sine of x.

See also:

Example:

doAssert almostEqual(sinh(0.0), 0.0)
doAssert almostEqual(sinh(1.0), 1.175201193643801)
  Source   Edit
func cosh(x: float32): float32 {.importc: "coshf", header: "<math.h>".}
  Source   Edit
func cosh(x: float64): float64 {.importc: "cosh", header: "<math.h>".}

Computes the hyperbolic cosine of x.

See also:

Example:

doAssert almostEqual(cosh(0.0), 1.0)
doAssert almostEqual(cosh(1.0), 1.543080634815244)
  Source   Edit
func tanh(x: float32): float32 {.importc: "tanhf", header: "<math.h>".}
  Source   Edit
func tanh(x: float64): float64 {.importc: "tanh", header: "<math.h>".}

Computes the hyperbolic tangent of x.

See also:

Example:

doAssert almostEqual(tanh(0.0), 0.0)
doAssert almostEqual(tanh(1.0), 0.7615941559557649)
  Source   Edit
func arcsin(x: float32): float32 {.importc: "asinf", header: "<math.h>".}
  Source   Edit
func arcsin(x: float64): float64 {.importc: "asin", header: "<math.h>".}

Computes the arc sine of x.

See also:

Example:

doAssert almostEqual(radToDeg(arcsin(0.0)), 0.0)
doAssert almostEqual(radToDeg(arcsin(1.0)), 90.0)
  Source   Edit
func arccos(x: float32): float32 {.importc: "acosf", header: "<math.h>".}
  Source   Edit
func arccos(x: float64): float64 {.importc: "acos", header: "<math.h>".}

Computes the arc cosine of x.

See also:

Example:

doAssert almostEqual(radToDeg(arccos(0.0)), 90.0)
doAssert almostEqual(radToDeg(arccos(1.0)), 0.0)
  Source   Edit
func arctan(x: float32): float32 {.importc: "atanf", header: "<math.h>".}
  Source   Edit
func arctan(x: float64): float64 {.importc: "atan", header: "<math.h>".}

Calculate the arc tangent of x.

See also:

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>".}
  Source   Edit
func arctan2(y, x: float64): float64 {.importc: "atan2", header: "<math.h>".}

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:

Example:

doAssert almostEqual(arctan2(1.0, 0.0), PI / 2.0)
doAssert almostEqual(radToDeg(arctan2(1.0, 0.0)), 90.0)
  Source   Edit
func arcsinh(x: float32): float32 {.importc: "asinhf", header: "<math.h>".}
  Source   Edit
func arcsinh(x: float64): float64 {.importc: "asinh", header: "<math.h>".}

Computes the inverse hyperbolic sine of x.

See also:

  Source   Edit
func arccosh(x: float32): float32 {.importc: "acoshf", header: "<math.h>".}
  Source   Edit
func arccosh(x: float64): float64 {.importc: "acosh", header: "<math.h>".}

Computes the inverse hyperbolic cosine of x.

See also:

  Source   Edit
func arctanh(x: float32): float32 {.importc: "atanhf", header: "<math.h>".}
  Source   Edit
func arctanh(x: float64): float64 {.importc: "atanh", header: "<math.h>".}

Computes the inverse hyperbolic tangent of x.

See also:

  Source   Edit
func cot[T: float32 | float64](x: T): T
Computes the cotangent of x (1/tan(x)).   Source   Edit
func sec[T: float32 | float64](x: T): T
Computes the secant of x (1/cos(x)).   Source   Edit
func csc[T: float32 | float64](x: T): T
Computes the cosecant of x (1/sin(x)).   Source   Edit
func coth[T: float32 | float64](x: T): T
Computes the hyperbolic cotangent of x (1/tanh(x)).   Source   Edit
func sech[T: float32 | float64](x: T): T
Computes the hyperbolic secant of x (1/cosh(x)).   Source   Edit
func csch[T: float32 | float64](x: T): T
Computes the hyperbolic cosecant of x (1/sinh(x)).   Source   Edit
func arccot[T: float32 | float64](x: T): T
Computes the inverse cotangent of x (arctan(1/x)).   Source   Edit
func arcsec[T: float32 | float64](x: T): T
Computes the inverse secant of x (arccos(1/x)).   Source   Edit
func arccsc[T: float32 | float64](x: T): T
Computes the inverse cosecant of x (arcsin(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 arcsech[T: float32 | float64](x: T): T
Computes the inverse hyperbolic secant of x (arccosh(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 hypot(x, y: float32): float32 {.importc: "hypotf", header: "<math.h>".}
  Source   Edit
func hypot(x, y: float64): float64 {.importc: "hypot", header: "<math.h>".}
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 pow(x, y: float32): float32 {.importc: "powf", header: "<math.h>".}
  Source   Edit
func pow(x, y: float64): float64 {.importc: "pow", header: "<math.h>".}

Computes x raised to the power of y.

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

See also:

Example:

doAssert almostEqual(pow(100, 1.5), 1000.0)
doAssert almostEqual(pow(16.0, 0.5), 4.0)
  Source   Edit
func erf(x: float32): float32 {.importc: "erff", header: "<math.h>".}
  Source   Edit
func erf(x: float64): float64 {.importc: "erf", header: "<math.h>".}

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>".}
  Source   Edit
func erfc(x: float64): float64 {.importc: "erfc", header: "<math.h>".}

Computes the complementary error function for x.

Note: Not available for the JS backend.

  Source   Edit
func gamma(x: float32): float32 {.importc: "tgammaf", header: "<math.h>".}
  Source   Edit
func gamma(x: float64): float64 {.importc: "tgamma", header: "<math.h>".}

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 lgamma(x: float32): float32 {.importc: "lgammaf", header: "<math.h>".}
  Source   Edit
func lgamma(x: float64): float64 {.importc: "lgamma", header: "<math.h>".}

Computes the natural logarithm of the gamma function for x.

Note: Not available for the JS backend.

See also:

  Source   Edit
func floor(x: float32): float32 {.importc: "floorf", header: "<math.h>".}
  Source   Edit
func floor(x: float64): float64 {.importc: "floor", header: "<math.h>".}

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

See also:

Example:

doAssert floor(2.1)  == 2.0
doAssert floor(2.9)  == 2.0
doAssert floor(-3.5) == -4.0
  Source   Edit
func ceil(x: float32): float32 {.importc: "ceilf", header: "<math.h>".}
  Source   Edit
func ceil(x: float64): float64 {.importc: "ceil", header: "<math.h>".}

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

See also:

Example:

doAssert ceil(2.1)  == 3.0
doAssert ceil(2.9)  == 3.0
doAssert ceil(-2.1) == -2.0
  Source   Edit
func round(x: float32): float32 {.importc: "roundf", header: "<math.h>".}
  Source   Edit
func round(x: float64): float64 {.importc: "round", header: "<math.h>".}

Rounds a float to zero decimal places.

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

See also:

Example:

doAssert round(3.4) == 3.0
doAssert round(3.5) == 4.0
doAssert round(4.5) == 5.0
  Source   Edit
func trunc(x: float32): float32 {.importc: "truncf", header: "<math.h>".}
  Source   Edit
func trunc(x: float64): float64 {.importc: "trunc", header: "<math.h>".}

Truncates x to the decimal point.

See also:

Example:

doAssert trunc(PI) == 3.0
doAssert trunc(-1.85) == -1.0
  Source   Edit
func `mod`(x, y: float32): float32 {.importc: "fmodf", header: "<math.h>".}
  Source   Edit
func `mod`(x, y: float64): float64 {.importc: "fmod", header: "<math.h>".}

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

See also:

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 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
  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:

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:

Example:

doAssert floorMod( 13,  3) ==  1
doAssert floorMod(-13,  3) ==  2
doAssert floorMod( 13, -3) == -2
doAssert floorMod(-13, -3) == -1
  Source   Edit
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 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 log2(x: float32): float32 {.importc: "log2f", header: "<math.h>".}
  Source   Edit
func log2(x: float64): float64 {.importc: "log2", header: "<math.h>".}

Computes the binary logarithm (base 2) of x.

See also:

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

Converts from degrees to radians.

See also:

Example:

doAssert almostEqual(degToRad(180.0), PI)
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func radToDeg[T: float32 | float64](d: T): T {.inline.}

Converts from radians to degrees.

See also:

Example:

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

Example:

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

Example:

doAssert gcd(13.5, 9.0) == 4.5
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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:

Example:

doAssert gcd(12, 8) == 4
doAssert gcd(17, 63) == 1
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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
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func lcm[T](x, y: T): T

Computes the least common multiple of x and y.

See also:

Example:

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