std/math

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.

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)
Source Edit
func arccos(x: float32): float32 {.importc: "acosf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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)
Source Edit
func arccosh(x: float32): float32 {.importc: "acoshf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
func arcsinh(x: float64): float64 {.importc: "asinh", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Computes the inverse hyperbolic sine of x.

See also:

sinh func

Source Edit
func arctan(x: float32): float32 {.importc: "atanf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
func arctanh(x: float64): float64 {.importc: "atanh", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Computes the inverse hyperbolic tangent of x.

See also:

tanh func

Source Edit
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
Source Edit
func cbrt(x: float32): float32 {.importc: "cbrtf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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)
Source Edit
func ceil(x: float32): float32 {.importc: "ceilf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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. 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 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: [].}: Source Edit
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)
Source Edit
func cosh(x: float32): float32 {.importc: "coshf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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)
Source Edit
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.
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 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
Source Edit
func pow(x, y: float32): float32 {.importc: "powf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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)
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:

sum func

fac func

Example:

doAssert prod([1, 2, 3, 4]) == 24 doAssert prod([-4, 3, 5]) == -60
Source Edit
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)
Source Edit
func round(x: float32): float32 {.importc: "roundf", header: "<math.h>", ...raises: [], tags: [], forbids: [].}: Source Edit
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
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
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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: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
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: [].}: Source Edit
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
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