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https://github.com/nim-lang/Nim.git
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Documentation improved for math module (#9266)
This commit is contained in:
eqperes
@@ -24,7 +24,10 @@ include "system/inclrtl"
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import bitops
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proc binom*(n, k: int): int {.noSideEffect.} =
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## Computes the binomial coefficient
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## Computes the `binomial coefficient <https://en.wikipedia.org/wiki/Binomial_coefficient>`_.
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##
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## .. code-block:: nim
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## echo binom(6, 2) ## 15
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if k <= 0: return 1
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if 2*k > n: return binom(n, n-k)
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result = n
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@@ -37,7 +40,10 @@ proc createFactTable[N: static[int]]: array[N, int] =
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result[i] = result[i - 1] * i
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proc fac*(n: int): int =
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## Computes the faculty/factorial function.
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## Computes the `factorial <https://en.wikipedia.org/wiki/Factorial>`_ of a non-negative integer ``n``
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##
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## .. code-block:: nim
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## echo fac(4) ## 24
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const factTable =
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when sizeof(int) == 4:
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createFactTable[13]()
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@@ -81,8 +87,13 @@ type
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fcNegInf ## value is negative infinity
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proc classify*(x: float): FloatClass =
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## Classifies a floating point value. Returns `x`'s class as specified by
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## Classifies a floating point value. Returns ``x``'s class as specified by
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## `FloatClass`.
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##
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## .. code-block:: nim
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## echo classify(0.3) ## fcNormal
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## echo classify(0.0) ## fcZero
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## echo classify(0.3/0.0) ## fcInf
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# JavaScript and most C compilers have no classify:
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if x == 0.0:
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@@ -98,13 +109,21 @@ proc classify*(x: float): FloatClass =
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# XXX: fcSubnormal is not detected!
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proc isPowerOfTwo*(x: int): bool {.noSideEffect.} =
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## Returns true, if `x` is a power of two, false otherwise.
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## Returns ``true``, if ``x`` is a power of two, ``false`` otherwise.
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## Zero and negative numbers are not a power of two.
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##
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## .. code-block:: nim
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## echo isPowerOfTwo(5) ## false
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## echo isPowerOfTwo(8) ## true
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return (x > 0) and ((x and (x - 1)) == 0)
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proc nextPowerOfTwo*(x: int): int {.noSideEffect.} =
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## Returns `x` rounded up to the nearest power of two.
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## Returns ``x`` rounded up to the nearest power of two.
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## Zero and negative numbers get rounded up to 1.
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##
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## .. code-block:: nim
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## echo nextPowerOfTwo(8) ## 8
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## echo nextPowerOfTwo(9) ## 16
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result = x - 1
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when defined(cpu64):
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result = result or (result shr 32)
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@@ -118,20 +137,29 @@ proc nextPowerOfTwo*(x: int): int {.noSideEffect.} =
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result += 1 + ord(x<=0)
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proc countBits32*(n: int32): int {.noSideEffect.} =
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## Counts the set bits in `n`.
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## Counts the set bits in ``n``.
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##
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## .. code-block:: nim
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## echo countBits32(13'i32) ## 3
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var v = n
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v = v -% ((v shr 1'i32) and 0x55555555'i32)
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v = (v and 0x33333333'i32) +% ((v shr 2'i32) and 0x33333333'i32)
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result = ((v +% (v shr 4'i32) and 0xF0F0F0F'i32) *% 0x1010101'i32) shr 24'i32
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proc sum*[T](x: openArray[T]): T {.noSideEffect.} =
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## Computes the sum of the elements in `x`.
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## If `x` is empty, 0 is returned.
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## Computes the sum of the elements in ``x``.
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## If ``x`` is empty, 0 is returned.
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##
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## .. code-block:: nim
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## echo sum([1.0, 2.5, -3.0, 4.3]) ## 4.8
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for i in items(x): result = result + i
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proc prod*[T](x: openArray[T]): T {.noSideEffect.} =
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## Computes the product of the elements in ``x``.
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## If ``x`` is empty, 1 is returned.
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##
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## .. code-block:: nim
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## echo prod([1.0, 3.0, -0.2]) ## -0.6
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result = 1.T
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for i in items(x): result = result * i
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@@ -139,14 +167,19 @@ proc prod*[T](x: openArray[T]): T {.noSideEffect.} =
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when not defined(JS): # C
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proc sqrt*(x: float32): float32 {.importc: "sqrtf", header: "<math.h>".}
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proc sqrt*(x: float64): float64 {.importc: "sqrt", header: "<math.h>".}
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## Computes the square root of `x`.
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## Computes the square root of ``x``.
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## .. code-block:: nim
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## echo sqrt(1.44) ## 1.2
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proc cbrt*(x: float32): float32 {.importc: "cbrtf", header: "<math.h>".}
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proc cbrt*(x: float64): float64 {.importc: "cbrt", header: "<math.h>".}
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## Computes the cubic root of `x`
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## Computes the cubic root of ``x``.
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## .. code-block:: nim
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## echo cbrt(2.197) ## 1.3
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proc ln*(x: float32): float32 {.importc: "logf", header: "<math.h>".}
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proc ln*(x: float64): float64 {.importc: "log", header: "<math.h>".}
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## Computes the natural log of `x`
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## Computes the `natural logarithm <https://en.wikipedia.org/wiki/Natural_logarithm>`_ of ``x``.
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## .. code-block:: nim
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## echo ln(exp(4.0)) ## 4.0
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else: # JS
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proc sqrt*(x: float32): float32 {.importc: "Math.sqrt", nodecl.}
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proc sqrt*(x: float64): float64 {.importc: "Math.sqrt", nodecl.}
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@@ -155,62 +188,89 @@ else: # JS
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proc ln*(x: float64): float64 {.importc: "Math.log", nodecl.}
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proc log*[T: SomeFloat](x, base: T): T =
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## Computes the logarithm ``base`` of ``x``
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## Computes the logarithm of ``x`` to base ``base``.
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## .. code-block:: nim
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## echo log(9.0, 3.0) ## 2.0
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ln(x) / ln(base)
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when not defined(JS): # C
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proc log10*(x: float32): float32 {.importc: "log10f", header: "<math.h>".}
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proc log10*(x: float64): float64 {.importc: "log10", header: "<math.h>".}
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## Computes the common logarithm (base 10) of `x`
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## Computes the common logarithm (base 10) of ``x``.
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## .. code-block:: nim
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## echo log10(100.0) ## 2.0
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proc exp*(x: float32): float32 {.importc: "expf", header: "<math.h>".}
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proc exp*(x: float64): float64 {.importc: "exp", header: "<math.h>".}
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## Computes the exponential function of `x` (pow(E, x))
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## Computes the exponential function of ``x`` (pow(E, x)).
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## .. code-block:: nim
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## echo exp(1.0) ## 2.718281828459045
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## echo ln(exp(4.0)) ## 4.0
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proc sin*(x: float32): float32 {.importc: "sinf", header: "<math.h>".}
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proc sin*(x: float64): float64 {.importc: "sin", header: "<math.h>".}
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## Computes the sine of `x`
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## Computes the sine of ``x``.
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## .. code-block:: nim
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## echo sin(PI / 6) ## 0.4999999999999999
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## echo sin(degToRad(90.0)) ## 1.0
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proc cos*(x: float32): float32 {.importc: "cosf", header: "<math.h>".}
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proc cos*(x: float64): float64 {.importc: "cos", header: "<math.h>".}
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## Computes the cosine of `x`
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## Computes the cosine of ``x``.
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## .. code-block:: nim
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## echo cos(2 * PI) ## 1.0
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## echo cos(degToRad(60.0)) ## 0.5000000000000001
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proc tan*(x: float32): float32 {.importc: "tanf", header: "<math.h>".}
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proc tan*(x: float64): float64 {.importc: "tan", header: "<math.h>".}
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## Computes the tangent of `x`
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## Computes the tangent of ``x``.
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## .. code-block:: nim
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## echo tan(degToRad(45.0)) ## 0.9999999999999999
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## echo tan(PI / 4) ## 0.9999999999999999
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proc sinh*(x: float32): float32 {.importc: "sinhf", header: "<math.h>".}
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proc sinh*(x: float64): float64 {.importc: "sinh", header: "<math.h>".}
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## Computes the hyperbolic sine of `x`
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## Computes the `hyperbolic sine <https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions>`_ of ``x``.
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## .. code-block:: nim
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## echo sinh(1.0) ## 1.175201193643801
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proc cosh*(x: float32): float32 {.importc: "coshf", header: "<math.h>".}
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proc cosh*(x: float64): float64 {.importc: "cosh", header: "<math.h>".}
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## Computes the hyperbolic cosine of `x`
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## Computes the `hyperbolic cosine <https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions>`_ of ``x``.
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## .. code-block:: nim
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## echo cosh(1.0) ## 1.543080634815244
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proc tanh*(x: float32): float32 {.importc: "tanhf", header: "<math.h>".}
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proc tanh*(x: float64): float64 {.importc: "tanh", header: "<math.h>".}
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## Computes the hyperbolic tangent of `x`
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## Computes the `hyperbolic tangent <https://en.wikipedia.org/wiki/Hyperbolic_function#Definitions>`_ of ``x``.
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## .. code-block:: nim
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## echo tanh(1.0) ## 0.7615941559557649
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proc arccos*(x: float32): float32 {.importc: "acosf", header: "<math.h>".}
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proc arccos*(x: float64): float64 {.importc: "acos", header: "<math.h>".}
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## Computes the arc cosine of `x`
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## Computes the arc cosine of ``x``.
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## .. code-block:: nim
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## echo arccos(1.0) ## 0.0
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proc arcsin*(x: float32): float32 {.importc: "asinf", header: "<math.h>".}
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proc arcsin*(x: float64): float64 {.importc: "asin", header: "<math.h>".}
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## Computes the arc sine of `x`
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## Computes the arc sine of ``x``.
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proc arctan*(x: float32): float32 {.importc: "atanf", header: "<math.h>".}
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proc arctan*(x: float64): float64 {.importc: "atan", header: "<math.h>".}
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## Calculate the arc tangent of `y` / `x`
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## Calculate the arc tangent of ``x``.
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## .. code-block:: nim
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## echo arctan(1.0) ## 0.7853981633974483
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## echo radToDeg(arctan(1.0)) ## 45.0
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proc arctan2*(y, x: float32): float32 {.importc: "atan2f", header: "<math.h>".}
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proc arctan2*(y, x: float64): float64 {.importc: "atan2", header: "<math.h>".}
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## Calculate the arc tangent of `y` / `x`.
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## `atan2` returns the arc tangent of `y` / `x`; it produces correct
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## Calculate the arc tangent of ``y`` / ``x``.
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## `arctan2` returns the arc tangent of ``y`` / ``x``; it produces correct
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## results even when the resulting angle is near pi/2 or -pi/2
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## (`x` near 0).
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## (``x`` near 0).
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## .. code-block:: nim
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## echo arctan2(1.0, 0.0) ## 1.570796326794897
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## echo radToDeg(arctan2(1.0, 0.0)) ## 90.0
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proc arcsinh*(x: float32): float32 {.importc: "asinhf", header: "<math.h>".}
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proc arcsinh*(x: float64): float64 {.importc: "asinh", header: "<math.h>".}
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## Computes the inverse hyperbolic sine of `x`
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## Computes the inverse hyperbolic sine of ``x``.
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proc arccosh*(x: float32): float32 {.importc: "acoshf", header: "<math.h>".}
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proc arccosh*(x: float64): float64 {.importc: "acosh", header: "<math.h>".}
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## Computes the inverse hyperbolic cosine of `x`
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## Computes the inverse hyperbolic cosine of ``x``.
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proc arctanh*(x: float32): float32 {.importc: "atanhf", header: "<math.h>".}
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proc arctanh*(x: float64): float64 {.importc: "atanh", header: "<math.h>".}
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## Computes the inverse hyperbolic tangent of `x`
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## Computes the inverse hyperbolic tangent of ``x``.
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else: # JS
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proc log10*(x: float32): float32 {.importc: "Math.log10", nodecl.}
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@@ -238,59 +298,61 @@ else: # JS
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proc arctanh*[T: float32|float64](x: T): T {.importc: "Math.atanh", nodecl.}
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proc cot*[T: float32|float64](x: T): T = 1.0 / tan(x)
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## Computes the cotangent of `x`
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## Computes the cotangent of ``x``.
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proc sec*[T: float32|float64](x: T): T = 1.0 / cos(x)
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## Computes the secant of `x`.
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## Computes the secant of ``x``.
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proc csc*[T: float32|float64](x: T): T = 1.0 / sin(x)
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## Computes the cosecant of `x`
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## Computes the cosecant of ``x``.
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proc coth*[T: float32|float64](x: T): T = 1.0 / tanh(x)
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## Computes the hyperbolic cotangent of `x`
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## Computes the hyperbolic cotangent of ``x``.
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proc sech*[T: float32|float64](x: T): T = 1.0 / cosh(x)
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## Computes the hyperbolic secant of `x`
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## Computes the hyperbolic secant of ``x``.
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proc csch*[T: float32|float64](x: T): T = 1.0 / sinh(x)
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## Computes the hyperbolic cosecant of `x`
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## Computes the hyperbolic cosecant of ``x``.
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proc arccot*[T: float32|float64](x: T): T = arctan(1.0 / x)
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## Computes the inverse cotangent of `x`
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## Computes the inverse cotangent of ``x``.
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proc arcsec*[T: float32|float64](x: T): T = arccos(1.0 / x)
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## Computes the inverse secant of `x`
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## Computes the inverse secant of ``x``.
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proc arccsc*[T: float32|float64](x: T): T = arcsin(1.0 / x)
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## Computes the inverse cosecant of `x`
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## Computes the inverse cosecant of ``x``.
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proc arccoth*[T: float32|float64](x: T): T = arctanh(1.0 / x)
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## Computes the inverse hyperbolic cotangent of `x`
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## Computes the inverse hyperbolic cotangent of ``x``.
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proc arcsech*[T: float32|float64](x: T): T = arccosh(1.0 / x)
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## Computes the inverse hyperbolic secant of `x`
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## Computes the inverse hyperbolic secant of ``x``.
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proc arccsch*[T: float32|float64](x: T): T = arcsinh(1.0 / x)
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## Computes the inverse hyperbolic cosecant of `x`
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## Computes the inverse hyperbolic cosecant of ``x``.
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const windowsCC89 = defined(windows) and defined(bcc)
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when not defined(JS): # C
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proc hypot*(x, y: float32): float32 {.importc: "hypotf", header: "<math.h>".}
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proc hypot*(x, y: float64): float64 {.importc: "hypot", header: "<math.h>".}
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## Computes the hypotenuse of a right-angle triangle with `x` and
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## `y` as its base and height. Equivalent to ``sqrt(x*x + y*y)``.
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## Computes the hypotenuse of a right-angle triangle with ``x`` and
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## ``y`` as its base and height. Equivalent to ``sqrt(x*x + y*y)``.
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## .. code-block:: nim
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## echo hypot(4.0, 3.0) ## 5.0
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proc pow*(x, y: float32): float32 {.importc: "powf", header: "<math.h>".}
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proc pow*(x, y: float64): float64 {.importc: "pow", header: "<math.h>".}
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## computes x to power raised of y.
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##
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## To compute power between integers, use `^` e.g. 2 ^ 6
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## To compute power between integers, use ``^`` e.g. 2 ^ 6
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## .. code-block:: nim
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## echo pow(16.0, 0.5) ## 4.0
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# TODO: add C89 version on windows
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when not windowsCC89:
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proc erf*(x: float32): float32 {.importc: "erff", header: "<math.h>".}
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proc erf*(x: float64): float64 {.importc: "erf", header: "<math.h>".}
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## The error function
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## Computes the `error function <https://en.wikipedia.org/wiki/Error_function>`_ for ``x``.
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proc erfc*(x: float32): float32 {.importc: "erfcf", header: "<math.h>".}
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proc erfc*(x: float64): float64 {.importc: "erfc", header: "<math.h>".}
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## The complementary error function
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## Computes the `complementary error function <https://en.wikipedia.org/wiki/Error_function#Complementary_error_function>`_ for ``x``.
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proc gamma*(x: float32): float32 {.importc: "tgammaf", header: "<math.h>".}
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proc gamma*(x: float64): float64 {.importc: "tgamma", header: "<math.h>".}
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## The gamma function
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## Computes the the `gamma function <https://en.wikipedia.org/wiki/Gamma_function>`_ for ``x``.
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proc tgamma*(x: float32): float32
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{.deprecated: "use gamma instead", importc: "tgammaf", header: "<math.h>".}
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proc tgamma*(x: float64): float64
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@@ -299,18 +361,18 @@ when not defined(JS): # C
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## **Deprecated since version 0.19.0**: Use ``gamma`` instead.
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proc lgamma*(x: float32): float32 {.importc: "lgammaf", header: "<math.h>".}
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proc lgamma*(x: float64): float64 {.importc: "lgamma", header: "<math.h>".}
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## Natural log of the gamma function
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## Computes the natural log of the gamma function for ``x``.
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proc floor*(x: float32): float32 {.importc: "floorf", header: "<math.h>".}
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proc floor*(x: float64): float64 {.importc: "floor", header: "<math.h>".}
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## Computes the floor function (i.e., the largest integer not greater than `x`)
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## Computes the floor function (i.e., the largest integer not greater than ``x``).
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##
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## .. code-block:: nim
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## echo floor(-3.5) ## -4.0
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proc ceil*(x: float32): float32 {.importc: "ceilf", header: "<math.h>".}
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proc ceil*(x: float64): float64 {.importc: "ceil", header: "<math.h>".}
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## Computes the ceiling function (i.e., the smallest integer not less than `x`)
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## Computes the ceiling function (i.e., the smallest integer not less than ``x``).
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##
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## .. code-block:: nim
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## echo ceil(-2.1) ## -2.0
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@@ -378,21 +440,23 @@ when not defined(JS): # C
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proc trunc*(x: float32): float32 {.importc: "truncf", header: "<math.h>".}
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proc trunc*(x: float64): float64 {.importc: "trunc", header: "<math.h>".}
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||||
## Truncates `x` to the decimal point
|
||||
## Truncates ``x`` to the decimal point.
|
||||
##
|
||||
## .. code-block:: nim
|
||||
## echo trunc(PI) # 3.0
|
||||
## echo trunc(-1.85) # -1.0
|
||||
|
||||
proc fmod*(x, y: float32): float32 {.deprecated: "use mod instead", importc: "fmodf", header: "<math.h>".}
|
||||
proc fmod*(x, y: float64): float64 {.deprecated: "use mod instead", importc: "fmod", header: "<math.h>".}
|
||||
## Computes the remainder of `x` divided by `y`
|
||||
##
|
||||
## .. code-block:: nim
|
||||
## echo fmod(-2.5, 0.3) ## -0.1
|
||||
## Computes the remainder of ``x`` divided by ``y``.
|
||||
## **Deprecated since version 0.19.0**: Use the ``mod`` operator instead.
|
||||
|
||||
proc `mod`*(x, y: float32): float32 {.importc: "fmodf", header: "<math.h>".}
|
||||
proc `mod`*(x, y: float64): float64 {.importc: "fmod", header: "<math.h>".}
|
||||
## Computes the modulo operation for float operators.
|
||||
## Computes the modulo operation for float values (the remainder of ``x`` divided by ``y``).
|
||||
##
|
||||
## .. code-block:: nim
|
||||
## echo 2.5 mod 0.3 ## 0.1
|
||||
else: # JS
|
||||
proc hypot*[T: float32|float64](x, y: T): T = return sqrt(x*x + y*y)
|
||||
proc pow*(x, y: float32): float32 {.importC: "Math.pow", nodecl.}
|
||||
@@ -407,19 +471,22 @@ else: # JS
|
||||
|
||||
proc `mod`*(x, y: float32): float32 {.importcpp: "# % #".}
|
||||
proc `mod`*(x, y: float64): float64 {.importcpp: "# % #".}
|
||||
## Computes the modulo operation for float operators.
|
||||
## Computes the modulo operation for float values (the remainder of ``x`` divided by ``y``).
|
||||
##
|
||||
## .. code-block:: nim
|
||||
## echo 2.5 mod 0.3 ## 0.1
|
||||
|
||||
proc round*[T: float32|float64](x: T, places: int): T {.deprecated: "use format instead".} =
|
||||
## 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),
|
||||
## 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
|
||||
## 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`
|
||||
## 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``
|
||||
if places == 0:
|
||||
result = round(x)
|
||||
else:
|
||||
@@ -431,13 +498,19 @@ proc floorDiv*[T: SomeInteger](x, y: T): T =
|
||||
## This is different from the ``div`` operator, which is defined
|
||||
## as ``trunc(x / y)``. That is, ``div`` rounds towards ``0`` and ``floorDiv``
|
||||
## rounds down.
|
||||
## .. code-block:: nim
|
||||
## echo floorDiv(13, 3) # 4
|
||||
## echo floorDiv(-13, 3) # -5
|
||||
result = x div y
|
||||
let r = x mod y
|
||||
if (r > 0 and y < 0) or (r < 0 and y > 0): result.dec 1
|
||||
|
||||
proc floorMod*[T: SomeNumber](x, y: T): T =
|
||||
## Floor modulus is conceptually defined as ``x - (floorDiv(x, y) * y).
|
||||
## This proc behaves the same as the ``%`` operator in python.
|
||||
## This proc behaves the same as the ``%`` operator in Python.
|
||||
## .. code-block:: nim
|
||||
## echo floorMod(13, 3) # 1
|
||||
## echo floorMod(-13, 3) # 2
|
||||
result = x mod y
|
||||
if (result > 0 and y < 0) or (result < 0 and y > 0): result += y
|
||||
|
||||
@@ -448,10 +521,14 @@ when not defined(JS):
|
||||
importc: "frexp", header: "<math.h>".}
|
||||
proc frexp*[T, U](x: T, exponent: var U): T =
|
||||
## 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
|
||||
## ``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.
|
||||
## .. code-block:: nim
|
||||
## var x : int
|
||||
## echo frexp(5.0, x) # 0.625
|
||||
## echo x # 3
|
||||
var exp: int32
|
||||
result = c_frexp(x, exp)
|
||||
exponent = exp
|
||||
@@ -475,7 +552,7 @@ when not defined(JS):
|
||||
else:
|
||||
proc log2*(x: float32): float32 {.importc: "log2f", header: "<math.h>".}
|
||||
proc log2*(x: float64): float64 {.importc: "log2", header: "<math.h>".}
|
||||
## Computes the binary logarithm (base 2) of `x`
|
||||
## Computes the binary logarithm (base 2) of ``x``
|
||||
|
||||
else:
|
||||
proc frexp*[T: float32|float64](x: T, exponent: var int): T =
|
||||
@@ -495,13 +572,15 @@ else:
|
||||
result = 0.99999999999999988898
|
||||
|
||||
proc splitDecimal*[T: float32|float64](x: T): tuple[intpart: T, floatpart: T] =
|
||||
## Breaks `x` into an integral and a fractional part.
|
||||
## Breaks ``x`` into an integer and a fractional part.
|
||||
##
|
||||
## Returns a tuple containing intpart and floatpart representing
|
||||
## 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`
|
||||
## Both parts have the same sign as ``x``. Analogous to the ``modf``
|
||||
## function in C.
|
||||
## .. code-block:: nim
|
||||
## echo splitDecimal(5.25) # (intpart: 5.0, floatpart: 0.25)
|
||||
var
|
||||
absolute: T
|
||||
absolute = abs(x)
|
||||
@@ -515,16 +594,23 @@ proc splitDecimal*[T: float32|float64](x: T): tuple[intpart: T, floatpart: T] =
|
||||
|
||||
proc degToRad*[T: float32|float64](d: T): T {.inline.} =
|
||||
## Convert from degrees to radians
|
||||
## .. code-block:: nim
|
||||
## echo degToRad(180.0) # 3.141592653589793
|
||||
result = T(d) * RadPerDeg
|
||||
|
||||
proc radToDeg*[T: float32|float64](d: T): T {.inline.} =
|
||||
## Convert from radians to degrees
|
||||
## .. code-block:: nim
|
||||
## echo degToRad(2 * PI) # 360.0
|
||||
result = T(d) / RadPerDeg
|
||||
|
||||
proc sgn*[T: SomeNumber](x: T): int {.inline.} =
|
||||
## Sign function. Returns -1 for negative numbers and `NegInf`, 1 for
|
||||
## positive numbers and `Inf`, and 0 for positive zero, negative zero and
|
||||
## `NaN`.
|
||||
## Sign function. Returns -1 for negative numbers and ``NegInf``, 1 for
|
||||
## positive numbers and ``Inf``, and 0 for positive zero, negative zero and
|
||||
## ``NaN``.
|
||||
## .. code-block:: nim
|
||||
## echo sgn(-5) # 1
|
||||
## echo sgn(-4.1) # -1
|
||||
ord(T(0) < x) - ord(x < T(0))
|
||||
|
||||
{.pop.}
|
||||
@@ -533,6 +619,8 @@ proc sgn*[T: SomeNumber](x: T): int {.inline.} =
|
||||
proc `^`*[T](x: T, y: Natural): T =
|
||||
## Computes ``x`` to the power ``y``. ``x`` must be non-negative, use
|
||||
## `pow <#pow,float,float>`_ for negative exponents.
|
||||
## .. code-block:: nim
|
||||
## echo 2 ^ 3 # 8
|
||||
when compiles(y >= T(0)):
|
||||
assert y >= T(0)
|
||||
else:
|
||||
@@ -562,6 +650,8 @@ proc gcd*[T](x, y: T): T =
|
||||
proc gcd*(x, y: SomeInteger): SomeInteger =
|
||||
## Computes the greatest common (positive) divisor of ``x`` and ``y``.
|
||||
## Using binary GCD (aka Stein's) algorithm.
|
||||
## .. code-block:: nim
|
||||
## echo gcd(24, 30) # 6
|
||||
when x is SomeSignedInt:
|
||||
var x = abs(x)
|
||||
else:
|
||||
@@ -587,6 +677,8 @@ proc gcd*(x, y: SomeInteger): SomeInteger =
|
||||
|
||||
proc lcm*[T](x, y: T): T =
|
||||
## Computes the least common multiple of ``x`` and ``y``.
|
||||
## .. code-block:: nim
|
||||
## echo lcm(24, 30) # 120
|
||||
x div gcd(x, y) * y
|
||||
|
||||
when isMainModule and not defined(JS) and not windowsCC89:
|
||||
|
||||
Reference in New Issue
Block a user