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.
import math from sequtils import map let a = [0.0, PI/6, PI/4, PI/3, PI/2] echo a.map(sin) # @[0.0, 0.499…, 0.707…, 0.866…, 1.0] echo a.map(tan) # @[0.0, 0.577…, 0.999…, 1.732…, 1.633…e+16] echo cos(degToRad(180.0)) # -1.0 echo sqrt(-1.0) # nan (use `complex` module)
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-devide, etc.)
- random module for fast and tiny random number generator
- mersenne module for Mersenne twister random number generator
- stats module for statistical analysis
- strformat module for formatting floats for print
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 classify proc. 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
Procs
proc binom(n, k: int): int {...}{.noSideEffect, raises: [], tags: [].}
-
Computes the binomial coefficient.
Examples:
doAssert binom(6, 2) == binom(6, 4) doAssert binom(6, 2) == 15 doAssert binom(-6, 2) == 1 doAssert binom(6, 0) == 1
Source Edit proc fac(n: int): int {...}{.raises: [], tags: [].}
-
Computes the factorial of a non-negative integer n.
See also:
Examples:
doAssert fac(3) == 6 doAssert fac(4) == 24 doAssert fac(10) == 3628800
Source Edit proc classify(x: float): FloatClass {...}{.raises: [], tags: [].}
-
Classifies a floating point value.
Returns x's class as specified by FloatClass enum.
Examples:
doAssert classify(0.3) == fcNormal doAssert classify(0.0) == fcZero doAssert classify(0.3 / 0.0) == fcInf doAssert classify(-0.3 / 0.0) == fcNegInf
Source Edit proc isPowerOfTwo(x: int): bool {...}{.noSideEffect, 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:
Examples:
doAssert isPowerOfTwo(16) == true doAssert isPowerOfTwo(5) == false doAssert isPowerOfTwo(0) == false doAssert isPowerOfTwo(-16) == false
Source Edit proc nextPowerOfTwo(x: int): int {...}{.noSideEffect, raises: [], tags: [].}
-
Returns x rounded up to the nearest power of two.
Zero and negative numbers get rounded up to 1.
See also:
Examples:
doAssert nextPowerOfTwo(16) == 16 doAssert nextPowerOfTwo(5) == 8 doAssert nextPowerOfTwo(0) == 1 doAssert nextPowerOfTwo(-16) == 1
Source Edit proc countBits32(n: int32): int {...}{.noSideEffect, deprecated: "Deprecated since v0.20.0; use \'bitops.countSetBits\' instead", raises: [], tags: [].}
-
Examples:
doAssert countBits32(7) == 3 doAssert countBits32(8) == 1 doAssert countBits32(15) == 4 doAssert countBits32(16) == 1 doAssert countBits32(17) == 2
Source Edit proc sum[T](x: openArray[T]): T {...}{.noSideEffect.}
-
Computes the sum of the elements in x.
If x is empty, 0 is returned.
See also:
Examples:
doAssert sum([1, 2, 3, 4]) == 10 doAssert sum([-1.5, 2.7, -0.1]) == 1.1
Source Edit proc prod[T](x: openArray[T]): T {...}{.noSideEffect.}
-
Computes the product of the elements in x.
If x is empty, 1 is returned.
See also:
Examples:
doAssert prod([1, 2, 3, 4]) == 24 doAssert prod([-4, 3, 5]) == -60
Source Edit proc cumsummed[T](x: openArray[T]): seq[T]
-
Return cumulative (aka prefix) summation of x.
See also:
- sum proc
- cumsum proc for the in-place version
Examples:
let a = [1, 2, 3, 4] doAssert cumsummed(a) == @[1, 3, 6, 10]
Source Edit proc cumsum[T](x: var openArray[T])
-
Transforms x in-place (must be declared as var) into its cumulative (aka prefix) summation.
See also:
- sum proc
- cumsummed proc for a version which returns cumsummed sequence
Examples:
var a = [1, 2, 3, 4] cumsum(a) doAssert a == @[1, 3, 6, 10]
Source Edit proc sqrt(x: float32): float32 {...}{.importc: "sqrtf", header: "<math.h>", noSideEffect.}
- Source Edit
proc sqrt(x: float64): float64 {...}{.importc: "sqrt", header: "<math.h>", noSideEffect.}
-
Computes the square root of x.
See also:
- cbrt proc for cubic root
echo sqrt(4.0) ## 2.0 echo sqrt(1.44) ## 1.2 echo sqrt(-4.0) ## nan
Source Edit proc cbrt(x: float32): float32 {...}{.importc: "cbrtf", header: "<math.h>", noSideEffect.}
- Source Edit
proc cbrt(x: float64): float64 {...}{.importc: "cbrt", header: "<math.h>", noSideEffect.}
-
Computes the cubic root of x.
See also:
- sqrt proc for square root
echo cbrt(8.0) ## 2.0 echo cbrt(2.197) ## 1.3 echo cbrt(-27.0) ## -3.0
Source Edit proc ln(x: float32): float32 {...}{.importc: "logf", header: "<math.h>", noSideEffect.}
- Source Edit
proc ln(x: float64): float64 {...}{.importc: "log", header: "<math.h>", noSideEffect.}
-
Computes the natural logarithm of x.
See also:
echo ln(exp(4.0)) ## 4.0 echo ln(1.0)) ## 0.0 echo ln(0.0) ## -inf echo ln(-7.0) ## nan
Source Edit proc log[T: SomeFloat](x, base: T): T {...}{.noSideEffect.}
-
Computes the logarithm of x to base base.
See also:
echo log(9.0, 3.0) ## 2.0 echo log(32.0, 2.0) ## 5.0 echo log(0.0, 2.0) ## -inf echo log(-7.0, 4.0) ## nan echo log(8.0, -2.0) ## nan
Source Edit proc log10(x: float32): float32 {...}{.importc: "log10f", header: "<math.h>", noSideEffect.}
- Source Edit
proc log10(x: float64): float64 {...}{.importc: "log10", header: "<math.h>", noSideEffect.}
-
Computes the common logarithm (base 10) of x.
See also:
echo log10(100.0) ## 2.0 echo log10(0.0) ## nan echo log10(-100.0) ## -inf
Source Edit proc exp(x: float32): float32 {...}{.importc: "expf", header: "<math.h>", noSideEffect.}
- Source Edit
proc exp(x: float64): float64 {...}{.importc: "exp", header: "<math.h>", noSideEffect.}
-
Computes the exponential function of x (e^x).
See also:
echo exp(1.0) ## 2.718281828459045 echo ln(exp(4.0)) ## 4.0 echo exp(0.0) ## 1.0 echo exp(-1.0) ## 0.3678794411714423
Source Edit proc sin(x: float32): float32 {...}{.importc: "sinf", header: "<math.h>", noSideEffect.}
- Source Edit
proc sin(x: float64): float64 {...}{.importc: "sin", header: "<math.h>", noSideEffect.}
-
Computes the sine of x.
See also:
echo sin(PI / 6) ## 0.4999999999999999 echo sin(degToRad(90.0)) ## 1.0
Source Edit proc cos(x: float32): float32 {...}{.importc: "cosf", header: "<math.h>", noSideEffect.}
- Source Edit
proc cos(x: float64): float64 {...}{.importc: "cos", header: "<math.h>", noSideEffect.}
-
Computes the cosine of x.
See also:
echo cos(2 * PI) ## 1.0 echo cos(degToRad(60.0)) ## 0.5000000000000001
Source Edit proc tan(x: float32): float32 {...}{.importc: "tanf", header: "<math.h>", noSideEffect.}
- Source Edit
proc tan(x: float64): float64 {...}{.importc: "tan", header: "<math.h>", noSideEffect.}
-
Computes the tangent of x.
See also:
echo tan(degToRad(45.0)) ## 0.9999999999999999 echo tan(PI / 4) ## 0.9999999999999999
Source Edit proc sinh(x: float32): float32 {...}{.importc: "sinhf", header: "<math.h>", noSideEffect.}
- Source Edit
proc sinh(x: float64): float64 {...}{.importc: "sinh", header: "<math.h>", noSideEffect.}
-
Computes the hyperbolic sine of x.
See also:
echo sinh(0.0) ## 0.0 echo sinh(1.0) ## 1.175201193643801 echo sinh(degToRad(90.0)) ## 2.301298902307295
Source Edit proc cosh(x: float32): float32 {...}{.importc: "coshf", header: "<math.h>", noSideEffect.}
- Source Edit
proc cosh(x: float64): float64 {...}{.importc: "cosh", header: "<math.h>", noSideEffect.}
-
Computes the hyperbolic cosine of x.
See also:
echo cosh(0.0) ## 1.0 echo cosh(1.0) ## 1.543080634815244 echo cosh(degToRad(90.0)) ## 2.509178478658057
Source Edit proc tanh(x: float32): float32 {...}{.importc: "tanhf", header: "<math.h>", noSideEffect.}
- Source Edit
proc tanh(x: float64): float64 {...}{.importc: "tanh", header: "<math.h>", noSideEffect.}
-
Computes the hyperbolic tangent of x.
See also:
echo tanh(0.0) ## 0.0 echo tanh(1.0) ## 0.7615941559557649 echo tanh(degToRad(90.0)) ## 0.9171523356672744
Source Edit proc arccos(x: float32): float32 {...}{.importc: "acosf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arccos(x: float64): float64 {...}{.importc: "acos", header: "<math.h>", noSideEffect.}
-
Computes the arc cosine of x.
See also:
echo radToDeg(arccos(0.0)) ## 90.0 echo radToDeg(arccos(1.0)) ## 0.0
Source Edit proc arcsin(x: float32): float32 {...}{.importc: "asinf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arcsin(x: float64): float64 {...}{.importc: "asin", header: "<math.h>", noSideEffect.}
-
Computes the arc sine of x.
See also:
echo radToDeg(arcsin(0.0)) ## 0.0 echo radToDeg(arcsin(1.0)) ## 90.0
Source Edit proc arctan(x: float32): float32 {...}{.importc: "atanf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arctan(x: float64): float64 {...}{.importc: "atan", header: "<math.h>", noSideEffect.}
-
Calculate the arc tangent of x.
See also:
echo arctan(1.0) ## 0.7853981633974483 echo radToDeg(arctan(1.0)) ## 45.0
Source Edit proc arctan2(y, x: float32): float32 {...}{.importc: "atan2f", header: "<math.h>", noSideEffect.}
- Source Edit
proc arctan2(y, x: float64): float64 {...}{.importc: "atan2", header: "<math.h>", noSideEffect.}
-
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:
echo arctan2(1.0, 0.0) ## 1.570796326794897 echo radToDeg(arctan2(1.0, 0.0)) ## 90.0
Source Edit proc arcsinh(x: float32): float32 {...}{.importc: "asinhf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arcsinh(x: float64): float64 {...}{.importc: "asinh", header: "<math.h>", noSideEffect.}
- Computes the inverse hyperbolic sine of x. Source Edit
proc arccosh(x: float32): float32 {...}{.importc: "acoshf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arccosh(x: float64): float64 {...}{.importc: "acosh", header: "<math.h>", noSideEffect.}
- Computes the inverse hyperbolic cosine of x. Source Edit
proc arctanh(x: float32): float32 {...}{.importc: "atanhf", header: "<math.h>", noSideEffect.}
- Source Edit
proc arctanh(x: float64): float64 {...}{.importc: "atanh", header: "<math.h>", noSideEffect.}
- Computes the inverse hyperbolic tangent of x. Source Edit
proc cot[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the cotangent of x (1 / tan(x)). Source Edit
proc sec[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the secant of x (1 / cos(x)). Source Edit
proc csc[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the cosecant of x (1 / sin(x)). Source Edit
proc coth[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the hyperbolic cotangent of x (1 / tanh(x)). Source Edit
proc sech[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the hyperbolic secant of x (1 / cosh(x)). Source Edit
proc csch[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the hyperbolic cosecant of x (1 / sinh(x)). Source Edit
proc arccot[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse cotangent of x. Source Edit
proc arcsec[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse secant of x. Source Edit
proc arccsc[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse cosecant of x. Source Edit
proc arccoth[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse hyperbolic cotangent of x. Source Edit
proc arcsech[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse hyperbolic secant of x. Source Edit
proc arccsch[T: float32 | float64](x: T): T {...}{.noSideEffect.}
- Computes the inverse hyperbolic cosecant of x. Source Edit
proc hypot(x, y: float32): float32 {...}{.importc: "hypotf", header: "<math.h>", noSideEffect.}
- Source Edit
proc hypot(x, y: float64): float64 {...}{.importc: "hypot", header: "<math.h>", noSideEffect.}
-
Computes the hypotenuse of a right-angle triangle with x and y as its base and height. Equivalent to sqrt(x*x + y*y).
echo hypot(4.0, 3.0) ## 5.0
Source Edit proc pow(x, y: float32): float32 {...}{.importc: "powf", header: "<math.h>", noSideEffect.}
- Source Edit
proc pow(x, y: float64): float64 {...}{.importc: "pow", header: "<math.h>", noSideEffect.}
-
Computes x to power raised of y.
To compute power between integers (e.g. 2^6), use ^ proc.
See also:
echo pow(100, 1.5) ## 1000.0 echo pow(16.0, 0.5) ## 4.0
Source Edit proc erf(x: float32): float32 {...}{.importc: "erff", header: "<math.h>", noSideEffect.}
- Source Edit
proc erf(x: float64): float64 {...}{.importc: "erf", header: "<math.h>", noSideEffect.}
- Computes the error function for x. Source Edit
proc erfc(x: float32): float32 {...}{.importc: "erfcf", header: "<math.h>", noSideEffect.}
- Source Edit
proc erfc(x: float64): float64 {...}{.importc: "erfc", header: "<math.h>", noSideEffect.}
- Computes the complementary error function for x. Source Edit
proc gamma(x: float32): float32 {...}{.importc: "tgammaf", header: "<math.h>", noSideEffect.}
- Source Edit
proc gamma(x: float64): float64 {...}{.importc: "tgamma", header: "<math.h>", noSideEffect.}
-
Computes the the gamma function for x.
See also:
- lgamma proc for a natural log of gamma function
echo gamma(1.0) # 1.0 echo gamma(4.0) # 6.0 echo gamma(11.0) # 3628800.0 echo gamma(-1.0) # nan
Source Edit proc tgamma(x: float32): float32 {...}{.deprecated: "Deprecated since v0.19.0; use \'gamma\' instead", importc: "tgammaf", header: "<math.h>", noSideEffect.}
- Source Edit
proc tgamma(x: float64): float64 {...}{.deprecated: "Deprecated since v0.19.0; use \'gamma\' instead", importc: "tgamma", header: "<math.h>", noSideEffect.}
- The gamma function Source Edit
proc lgamma(x: float32): float32 {...}{.importc: "lgammaf", header: "<math.h>", noSideEffect.}
- Source Edit
proc lgamma(x: float64): float64 {...}{.importc: "lgamma", header: "<math.h>", noSideEffect.}
-
Computes the natural log of the gamma function for x.
See also:
- gamma proc for gamma function
echo lgamma(1.0) # 1.0 echo lgamma(4.0) # 1.791759469228055 echo lgamma(11.0) # 15.10441257307552 echo lgamma(-1.0) # inf
Source Edit proc floor(x: float32): float32 {...}{.importc: "floorf", header: "<math.h>", noSideEffect.}
- Source Edit
proc floor(x: float64): float64 {...}{.importc: "floor", header: "<math.h>", noSideEffect.}
-
Computes the floor function (i.e., the largest integer not greater than x).
See also:
echo floor(2.1) ## 2.0 echo floor(2.9) ## 2.0 echo floor(-3.5) ## -4.0
Source Edit proc ceil(x: float32): float32 {...}{.importc: "ceilf", header: "<math.h>", noSideEffect.}
- Source Edit
proc ceil(x: float64): float64 {...}{.importc: "ceil", header: "<math.h>", noSideEffect.}
-
Computes the ceiling function (i.e., the smallest integer not smaller than x).
See also:
echo ceil(2.1) ## 3.0 echo ceil(2.9) ## 3.0 echo ceil(-2.1) ## -2.0
Source Edit proc round(x: float32): float32 {...}{.importc: "roundf", header: "<math.h>", noSideEffect.}
- Source Edit
proc round(x: float64): float64 {...}{.importc: "round", header: "<math.h>", noSideEffect.}
-
Rounds a float to zero decimal places.
Used internally by the round proc when the specified number of places is 0.
See also:
- round proc for rounding to the specific number of decimal places
- floor proc
- ceil proc
- trunc proc
echo round(3.4) ## 3.0 echo round(3.5) ## 4.0 echo round(4.5) ## 5.0
Source Edit proc trunc(x: float32): float32 {...}{.importc: "truncf", header: "<math.h>", noSideEffect.}
- Source Edit
proc trunc(x: float64): float64 {...}{.importc: "trunc", header: "<math.h>", noSideEffect.}
-
Truncates x to the decimal point.
See also:
echo trunc(PI) # 3.0 echo trunc(-1.85) # -1.0
Source Edit proc fmod(x, y: float32): float32 {...}{.deprecated: "Deprecated since v0.19.0; use \'mod\' instead", importc: "fmodf", header: "<math.h>", noSideEffect.}
- Source Edit
proc fmod(x, y: float64): float64 {...}{.deprecated: "Deprecated since v0.19.0; use \'mod\' instead", importc: "fmod", header: "<math.h>", noSideEffect.}
- Computes the remainder of x divided by y. Source Edit
proc `mod`(x, y: float32): float32 {...}{.importc: "fmodf", header: "<math.h>", noSideEffect.}
- Source Edit
proc `mod`(x, y: float64): float64 {...}{.importc: "fmod", header: "<math.h>", noSideEffect.}
-
Computes the modulo operation for float values (the remainder of x divided by y).
See also:
- floorMod proc for Python-like (% operator) behavior
( 6.5 mod 2.5) == 1.5 (-6.5 mod 2.5) == -1.5 ( 6.5 mod -2.5) == 1.5 (-6.5 mod -2.5) == -1.5
Source Edit proc round[T: float32 | float64](x: T; places: int): T {...}{. deprecated: "use strformat module instead", noSideEffect.}
-
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
echo round(PI, 2) ## 3.14 echo round(PI, 4) ## 3.1416
Source Edit proc floorDiv[T: SomeInteger](x, y: T): T {...}{.noSideEffect.}
-
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 proc for Python-like (% operator) behavior
echo floorDiv( 13, 3) # 4 echo floorDiv(-13, 3) # -5 echo floorDiv( 13, -3) # -5 echo floorDiv(-13, -3) # 4
Source Edit proc floorMod[T: SomeNumber](x, y: T): T {...}{.noSideEffect.}
-
Floor modulus is conceptually defined as x - (floorDiv(x, y) * y).
This proc behaves the same as the % operator in Python.
See also:
echo floorMod( 13, 3) # 1 echo floorMod(-13, 3) # 2 echo floorMod( 13, -3) # -2 echo floorMod(-13, -3) # -1
Source Edit proc c_frexp(x: float32; exponent: var int32): float32 {...}{.importc: "frexp", header: "<math.h>", noSideEffect.}
- Source Edit
proc c_frexp(x: float64; exponent: var int32): float64 {...}{.importc: "frexp", header: "<math.h>", noSideEffect.}
- Source Edit
proc frexp[T, U](x: T; exponent: var U): T {...}{.noSideEffect.}
-
Split a number into mantissa and exponent.
frexp calculates the mantissa m (a float greater than or equal to 0.5 and less than 1) and the integer value n such that x (the original float value) equals m * 2**n. frexp stores n in exponent and returns m.
var x: int echo frexp(5.0, x) # 0.625 echo x # 3
Source Edit proc log2(x: float32): float32 {...}{.importc: "log2f", header: "<math.h>", noSideEffect.}
- Source Edit
proc log2(x: float64): float64 {...}{.importc: "log2", header: "<math.h>", noSideEffect.}
-
Computes the binary logarithm (base 2) of x.
See also:
echo log2(8.0) # 3.0 echo log2(1.0) # 0.0 echo log2(0.0) # -inf echo log2(-2.0) # nan
Source Edit proc splitDecimal[T: float32 | float64](x: T): tuple[intpart: T, floatpart: T] {...}{. noSideEffect.}
-
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.
echo splitDecimal(5.25) # (intpart: 5.0, floatpart: 0.25) echo splitDecimal(-2.73) # (intpart: -2.0, floatpart: -0.73)
Source Edit proc degToRad[T: float32 | float64](d: T): T {...}{.inline.}
-
Convert from degrees to radians.
See also:
echo degToRad(180.0) # 3.141592653589793
Source Edit proc radToDeg[T: float32 | float64](d: T): T {...}{.inline.}
-
Convert from radians to degrees.
See also:
echo degToRad(2 * PI) # 360.0
Source Edit proc 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
echo sgn(5) # 1 echo sgn(0) # 0 echo sgn(-4.1) # -1
Source Edit proc `^`[T](x: T; y: Natural): T
-
Computes x to the power y.
Exponent y must be non-negative, use pow proc for negative exponents.
See also:
Examples:
assert -3.0 ^ 0 == 1.0 assert -3 ^ 1 == -3 assert -3 ^ 2 == 9 assert -3.0 ^ 3 == -27.0 assert -3.0 ^ 4 == 81.0
Source Edit proc 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:
Examples:
doAssert gcd(13.5, 9.0) == 4.5
Source Edit proc gcd(x, y: SomeInteger): SomeInteger
-
Computes the greatest common (positive) divisor of x and y, using binary GCD (aka Stein's) algorithm.
See also:
Examples:
doAssert gcd(12, 8) == 4 doAssert gcd(17, 63) == 1
Source Edit proc lcm[T](x, y: T): T
-
Computes the least common multiple of x and y.
See also:
Examples:
doAssert lcm(24, 30) == 120 doAssert lcm(13, 39) == 39
Source Edit