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complex.nim: Use func everywhere (#16294)

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ee7 2020-12-09 10:57:12 +01:00 • committed by GitHub
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lib/pure/complex.nim
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@ -24,15 +24,15 @@ type
Complex32* = Complex[float32] Complex32* = Complex[float32]
## Alias for a pair of 32-bit floats. ## Alias for a pair of 32-bit floats.
proc complex*[T: SomeFloat](re: T; im: T = 0.0): Complex[T] = func complex*[T: SomeFloat](re: T; im: T = 0.0): Complex[T] =
result.re = re result.re = re
result.im = im result.im = im
proc complex32*(re: float32; im: float32 = 0.0): Complex[float32] = func complex32*(re: float32; im: float32 = 0.0): Complex[float32] =
result.re = re result.re = re
result.im = im result.im = im
proc complex64*(re: float64; im: float64 = 0.0): Complex[float64] = func complex64*(re: float64; im: float64 = 0.0): Complex[float64] =
result.re = re result.re = re
result.im = im result.im = im
@ -41,71 +41,71 @@ template im*(arg: typedesc[float64]): Complex64 = complex[float64](0, 1)
template im*(arg: float32): Complex32 = complex[float32](0, arg) template im*(arg: float32): Complex32 = complex[float32](0, arg)
template im*(arg: float64): Complex64 = complex[float64](0, arg) template im*(arg: float64): Complex64 = complex[float64](0, arg)
proc abs*[T](z: Complex[T]): T = func abs*[T](z: Complex[T]): T =
## Returns the distance from (0,0) to ``z``. ## Returns the distance from (0,0) to ``z``.
result = hypot(z.re, z.im) result = hypot(z.re, z.im)
proc abs2*[T](z: Complex[T]): T = func abs2*[T](z: Complex[T]): T =
## Returns the squared distance from (0,0) to ``z``. ## Returns the squared distance from (0,0) to ``z``.
result = z.re*z.re + z.im*z.im result = z.re*z.re + z.im*z.im
proc conjugate*[T](z: Complex[T]): Complex[T] = func conjugate*[T](z: Complex[T]): Complex[T] =
## Conjugates of complex number ``z``. ## Conjugates of complex number ``z``.
result.re = z.re result.re = z.re
result.im = -z.im result.im = -z.im
proc inv*[T](z: Complex[T]): Complex[T] = func inv*[T](z: Complex[T]): Complex[T] =
## Multiplicatives inverse of complex number ``z``. ## Multiplicatives inverse of complex number ``z``.
conjugate(z) / abs2(z) conjugate(z) / abs2(z)
proc `==` *[T](x, y: Complex[T]): bool = func `==` *[T](x, y: Complex[T]): bool =
## Compares two complex numbers ``x`` and ``y`` for equality. ## Compares two complex numbers ``x`` and ``y`` for equality.
result = x.re == y.re and x.im == y.im result = x.re == y.re and x.im == y.im
proc `+` *[T](x: T; y: Complex[T]): Complex[T] = func `+` *[T](x: T; y: Complex[T]): Complex[T] =
## Adds a real number to a complex number. ## Adds a real number to a complex number.
result.re = x + y.re result.re = x + y.re
result.im = y.im result.im = y.im
proc `+` *[T](x: Complex[T]; y: T): Complex[T] = func `+` *[T](x: Complex[T]; y: T): Complex[T] =
## Adds a complex number to a real number. ## Adds a complex number to a real number.
result.re = x.re + y result.re = x.re + y
result.im = x.im result.im = x.im
proc `+` *[T](x, y: Complex[T]): Complex[T] = func `+` *[T](x, y: Complex[T]): Complex[T] =
## Adds two complex numbers. ## Adds two complex numbers.
result.re = x.re + y.re result.re = x.re + y.re
result.im = x.im + y.im result.im = x.im + y.im
proc `-` *[T](z: Complex[T]): Complex[T] = func `-` *[T](z: Complex[T]): Complex[T] =
## Unary minus for complex numbers. ## Unary minus for complex numbers.
result.re = -z.re result.re = -z.re
result.im = -z.im result.im = -z.im
proc `-` *[T](x: T; y: Complex[T]): Complex[T] = func `-` *[T](x: T; y: Complex[T]): Complex[T] =
## Subtracts a complex number from a real number. ## Subtracts a complex number from a real number.
x + (-y) x + (-y)
proc `-` *[T](x: Complex[T]; y: T): Complex[T] = func `-` *[T](x: Complex[T]; y: T): Complex[T] =
## Subtracts a real number from a complex number. ## Subtracts a real number from a complex number.
result.re = x.re - y result.re = x.re - y
result.im = x.im result.im = x.im
proc `-` *[T](x, y: Complex[T]): Complex[T] = func `-` *[T](x, y: Complex[T]): Complex[T] =
## Subtracts two complex numbers. ## Subtracts two complex numbers.
result.re = x.re - y.re result.re = x.re - y.re
result.im = x.im - y.im result.im = x.im - y.im
proc `/` *[T](x: Complex[T]; y: T): Complex[T] = func `/` *[T](x: Complex[T]; y: T): Complex[T] =
## Divides complex number ``x`` by real number ``y``. ## Divides complex number ``x`` by real number ``y``.
result.re = x.re / y result.re = x.re / y
result.im = x.im / y result.im = x.im / y
proc `/` *[T](x: T; y: Complex[T]): Complex[T] = func `/` *[T](x: T; y: Complex[T]): Complex[T] =
## Divides real number ``x`` by complex number ``y``. ## Divides real number ``x`` by complex number ``y``.
result = x * inv(y) result = x * inv(y)
proc `/` *[T](x, y: Complex[T]): Complex[T] = func `/` *[T](x, y: Complex[T]): Complex[T] =
## Divides ``x`` by ``y``. ## Divides ``x`` by ``y``.
var r, den: T var r, den: T
if abs(y.re) < abs(y.im): if abs(y.re) < abs(y.im):
@ -119,44 +119,44 @@ proc `/` *[T](x, y: Complex[T]): Complex[T] =
result.re = (x.re + r * x.im) / den result.re = (x.re + r * x.im) / den
result.im = (x.im - r * x.re) / den result.im = (x.im - r * x.re) / den
proc `*` *[T](x: T; y: Complex[T]): Complex[T] = func `*` *[T](x: T; y: Complex[T]): Complex[T] =
## Multiplies a real number and a complex number. ## Multiplies a real number and a complex number.
result.re = x * y.re result.re = x * y.re
result.im = x * y.im result.im = x * y.im
proc `*` *[T](x: Complex[T]; y: T): Complex[T] = func `*` *[T](x: Complex[T]; y: T): Complex[T] =
## Multiplies a complex number with a real number. ## Multiplies a complex number with a real number.
result.re = x.re * y result.re = x.re * y
result.im = x.im * y result.im = x.im * y
proc `*` *[T](x, y: Complex[T]): Complex[T] = func `*` *[T](x, y: Complex[T]): Complex[T] =
## Multiplies ``x`` with ``y``. ## Multiplies ``x`` with ``y``.
result.re = x.re * y.re - x.im * y.im result.re = x.re * y.re - x.im * y.im
result.im = x.im * y.re + x.re * y.im result.im = x.im * y.re + x.re * y.im
proc `+=` *[T](x: var Complex[T]; y: Complex[T]) = func `+=` *[T](x: var Complex[T]; y: Complex[T]) =
## Adds ``y`` to ``x``. ## Adds ``y`` to ``x``.
x.re += y.re x.re += y.re
x.im += y.im x.im += y.im
proc `-=` *[T](x: var Complex[T]; y: Complex[T]) = func `-=` *[T](x: var Complex[T]; y: Complex[T]) =
## Subtracts ``y`` from ``x``. ## Subtracts ``y`` from ``x``.
x.re -= y.re x.re -= y.re
x.im -= y.im x.im -= y.im
proc `*=` *[T](x: var Complex[T]; y: Complex[T]) = func `*=` *[T](x: var Complex[T]; y: Complex[T]) =
## Multiplies ``y`` to ``x``. ## Multiplies ``y`` to ``x``.
let im = x.im * y.re + x.re * y.im let im = x.im * y.re + x.re * y.im
x.re = x.re * y.re - x.im * y.im x.re = x.re * y.re - x.im * y.im
x.im = im x.im = im
proc `/=` *[T](x: var Complex[T]; y: Complex[T]) = func `/=` *[T](x: var Complex[T]; y: Complex[T]) =
## Divides ``x`` by ``y`` in place. ## Divides ``x`` by ``y`` in place.
x = x / y x = x / y
proc sqrt*[T](z: Complex[T]): Complex[T] = func sqrt*[T](z: Complex[T]): Complex[T] =
## Square root for a complex number ``z``. ## Square root for a complex number ``z``.
var x, y, w, r: T var x, y, w, r: T
@ -179,7 +179,7 @@ proc sqrt*[T](z: Complex[T]): Complex[T] =
result.im = if z.im >= 0.0: w else: -w result.im = if z.im >= 0.0: w else: -w
result.re = z.im / (result.im + result.im) result.re = z.im / (result.im + result.im)
proc exp*[T](z: Complex[T]): Complex[T] = func exp*[T](z: Complex[T]): Complex[T] =
## ``e`` raised to the power ``z``. ## ``e`` raised to the power ``z``.
var var
rho = exp(z.re) rho = exp(z.re)
@ -187,20 +187,20 @@ proc exp*[T](z: Complex[T]): Complex[T] =
result.re = rho * cos(theta) result.re = rho * cos(theta)
result.im = rho * sin(theta) result.im = rho * sin(theta)
proc ln*[T](z: Complex[T]): Complex[T] = func ln*[T](z: Complex[T]): Complex[T] =
## Returns the natural log of ``z``. ## Returns the natural log of ``z``.
result.re = ln(abs(z)) result.re = ln(abs(z))
result.im = arctan2(z.im, z.re) result.im = arctan2(z.im, z.re)
proc log10*[T](z: Complex[T]): Complex[T] = func log10*[T](z: Complex[T]): Complex[T] =
## Returns the log base 10 of ``z``. ## Returns the log base 10 of ``z``.
result = ln(z) / ln(10.0) result = ln(z) / ln(10.0)
proc log2*[T](z: Complex[T]): Complex[T] = func log2*[T](z: Complex[T]): Complex[T] =
## Returns the log base 2 of ``z``. ## Returns the log base 2 of ``z``.
result = ln(z) / ln(2.0) result = ln(z) / ln(2.0)
proc pow*[T](x, y: Complex[T]): Complex[T] = func pow*[T](x, y: Complex[T]): Complex[T] =
## ``x`` raised to the power ``y``. ## ``x`` raised to the power ``y``.
if x.re == 0.0 and x.im == 0.0: if x.re == 0.0 and x.im == 0.0:
if y.re == 0.0 and y.im == 0.0: if y.re == 0.0 and y.im == 0.0:
@ -222,118 +222,118 @@ proc pow*[T](x, y: Complex[T]): Complex[T] =
result.re = s * cos(r) result.re = s * cos(r)
result.im = s * sin(r) result.im = s * sin(r)
proc pow*[T](x: Complex[T]; y: T): Complex[T] = func pow*[T](x: Complex[T]; y: T): Complex[T] =
## Complex number ``x`` raised to the power ``y``. ## Complex number ``x`` raised to the power ``y``.
pow(x, complex[T](y)) pow(x, complex[T](y))
proc sin*[T](z: Complex[T]): Complex[T] = func sin*[T](z: Complex[T]): Complex[T] =
## Returns the sine of ``z``. ## Returns the sine of ``z``.
result.re = sin(z.re) * cosh(z.im) result.re = sin(z.re) * cosh(z.im)
result.im = cos(z.re) * sinh(z.im) result.im = cos(z.re) * sinh(z.im)
proc arcsin*[T](z: Complex[T]): Complex[T] = func arcsin*[T](z: Complex[T]): Complex[T] =
## Returns the inverse sine of ``z``. ## Returns the inverse sine of ``z``.
result = -im(T) * ln(im(T) * z + sqrt(T(1.0) - z*z)) result = -im(T) * ln(im(T) * z + sqrt(T(1.0) - z*z))
proc cos*[T](z: Complex[T]): Complex[T] = func cos*[T](z: Complex[T]): Complex[T] =
## Returns the cosine of ``z``. ## Returns the cosine of ``z``.
result.re = cos(z.re) * cosh(z.im) result.re = cos(z.re) * cosh(z.im)
result.im = -sin(z.re) * sinh(z.im) result.im = -sin(z.re) * sinh(z.im)
proc arccos*[T](z: Complex[T]): Complex[T] = func arccos*[T](z: Complex[T]): Complex[T] =
## Returns the inverse cosine of ``z``. ## Returns the inverse cosine of ``z``.
result = -im(T) * ln(z + sqrt(z*z - T(1.0))) result = -im(T) * ln(z + sqrt(z*z - T(1.0)))
proc tan*[T](z: Complex[T]): Complex[T] = func tan*[T](z: Complex[T]): Complex[T] =
## Returns the tangent of ``z``. ## Returns the tangent of ``z``.
result = sin(z) / cos(z) result = sin(z) / cos(z)
proc arctan*[T](z: Complex[T]): Complex[T] = func arctan*[T](z: Complex[T]): Complex[T] =
## Returns the inverse tangent of ``z``. ## Returns the inverse tangent of ``z``.
result = T(0.5)*im(T) * (ln(T(1.0) - im(T)*z) - ln(T(1.0) + im(T)*z)) result = T(0.5)*im(T) * (ln(T(1.0) - im(T)*z) - ln(T(1.0) + im(T)*z))
proc cot*[T](z: Complex[T]): Complex[T] = func cot*[T](z: Complex[T]): Complex[T] =
## Returns the cotangent of ``z``. ## Returns the cotangent of ``z``.
result = cos(z)/sin(z) result = cos(z)/sin(z)
proc arccot*[T](z: Complex[T]): Complex[T] = func arccot*[T](z: Complex[T]): Complex[T] =
## Returns the inverse cotangent of ``z``. ## Returns the inverse cotangent of ``z``.
result = T(0.5)*im(T) * (ln(T(1.0) - im(T)/z) - ln(T(1.0) + im(T)/z)) result = T(0.5)*im(T) * (ln(T(1.0) - im(T)/z) - ln(T(1.0) + im(T)/z))
proc sec*[T](z: Complex[T]): Complex[T] = func sec*[T](z: Complex[T]): Complex[T] =
## Returns the secant of ``z``. ## Returns the secant of ``z``.
result = T(1.0) / cos(z) result = T(1.0) / cos(z)
proc arcsec*[T](z: Complex[T]): Complex[T] = func arcsec*[T](z: Complex[T]): Complex[T] =
## Returns the inverse secant of ``z``. ## Returns the inverse secant of ``z``.
result = -im(T) * ln(im(T) * sqrt(1.0 - 1.0/(z*z)) + T(1.0)/z) result = -im(T) * ln(im(T) * sqrt(1.0 - 1.0/(z*z)) + T(1.0)/z)
proc csc*[T](z: Complex[T]): Complex[T] = func csc*[T](z: Complex[T]): Complex[T] =
## Returns the cosecant of ``z``. ## Returns the cosecant of ``z``.
result = T(1.0) / sin(z) result = T(1.0) / sin(z)
proc arccsc*[T](z: Complex[T]): Complex[T] = func arccsc*[T](z: Complex[T]): Complex[T] =
## Returns the inverse cosecant of ``z``. ## Returns the inverse cosecant of ``z``.
result = -im(T) * ln(sqrt(T(1.0) - T(1.0)/(z*z)) + im(T)/z) result = -im(T) * ln(sqrt(T(1.0) - T(1.0)/(z*z)) + im(T)/z)
proc sinh*[T](z: Complex[T]): Complex[T] = func sinh*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic sine of ``z``. ## Returns the hyperbolic sine of ``z``.
result = T(0.5) * (exp(z) - exp(-z)) result = T(0.5) * (exp(z) - exp(-z))
proc arcsinh*[T](z: Complex[T]): Complex[T] = func arcsinh*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic sine of ``z``. ## Returns the inverse hyperbolic sine of ``z``.
result = ln(z + sqrt(z*z + 1.0)) result = ln(z + sqrt(z*z + 1.0))
proc cosh*[T](z: Complex[T]): Complex[T] = func cosh*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic cosine of ``z``. ## Returns the hyperbolic cosine of ``z``.
result = T(0.5) * (exp(z) + exp(-z)) result = T(0.5) * (exp(z) + exp(-z))
proc arccosh*[T](z: Complex[T]): Complex[T] = func arccosh*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic cosine of ``z``. ## Returns the inverse hyperbolic cosine of ``z``.
result = ln(z + sqrt(z*z - T(1.0))) result = ln(z + sqrt(z*z - T(1.0)))
proc tanh*[T](z: Complex[T]): Complex[T] = func tanh*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic tangent of ``z``. ## Returns the hyperbolic tangent of ``z``.
result = sinh(z) / cosh(z) result = sinh(z) / cosh(z)
proc arctanh*[T](z: Complex[T]): Complex[T] = func arctanh*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic tangent of ``z``. ## Returns the inverse hyperbolic tangent of ``z``.
result = T(0.5) * (ln((T(1.0)+z) / (T(1.0)-z))) result = T(0.5) * (ln((T(1.0)+z) / (T(1.0)-z)))
proc sech*[T](z: Complex[T]): Complex[T] = func sech*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic secant of ``z``. ## Returns the hyperbolic secant of ``z``.
result = T(2.0) / (exp(z) + exp(-z)) result = T(2.0) / (exp(z) + exp(-z))
proc arcsech*[T](z: Complex[T]): Complex[T] = func arcsech*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic secant of ``z``. ## Returns the inverse hyperbolic secant of ``z``.
result = ln(1.0/z + sqrt(T(1.0)/z+T(1.0)) * sqrt(T(1.0)/z-T(1.0))) result = ln(1.0/z + sqrt(T(1.0)/z+T(1.0)) * sqrt(T(1.0)/z-T(1.0)))
proc csch*[T](z: Complex[T]): Complex[T] = func csch*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic cosecant of ``z``. ## Returns the hyperbolic cosecant of ``z``.
result = T(2.0) / (exp(z) - exp(-z)) result = T(2.0) / (exp(z) - exp(-z))
proc arccsch*[T](z: Complex[T]): Complex[T] = func arccsch*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic cosecant of ``z``. ## Returns the inverse hyperbolic cosecant of ``z``.
result = ln(T(1.0)/z + sqrt(T(1.0)/(z*z) + T(1.0))) result = ln(T(1.0)/z + sqrt(T(1.0)/(z*z) + T(1.0)))
proc coth*[T](z: Complex[T]): Complex[T] = func coth*[T](z: Complex[T]): Complex[T] =
## Returns the hyperbolic cotangent of ``z``. ## Returns the hyperbolic cotangent of ``z``.
result = cosh(z) / sinh(z) result = cosh(z) / sinh(z)
proc arccoth*[T](z: Complex[T]): Complex[T] = func arccoth*[T](z: Complex[T]): Complex[T] =
## Returns the inverse hyperbolic cotangent of ``z``. ## Returns the inverse hyperbolic cotangent of ``z``.
result = T(0.5) * (ln(T(1.0) + T(1.0)/z) - ln(T(1.0) - T(1.0)/z)) result = T(0.5) * (ln(T(1.0) + T(1.0)/z) - ln(T(1.0) - T(1.0)/z))
proc phase*[T](z: Complex[T]): T = func phase*[T](z: Complex[T]): T =
## Returns the phase of ``z``. ## Returns the phase of ``z``.
arctan2(z.im, z.re) arctan2(z.im, z.re)
proc polar*[T](z: Complex[T]): tuple[r, phi: T] = func polar*[T](z: Complex[T]): tuple[r, phi: T] =
## Returns ``z`` in polar coordinates. ## Returns ``z`` in polar coordinates.
(r: abs(z), phi: phase(z)) (r: abs(z), phi: phase(z))
proc rect*[T](r, phi: T): Complex[T] = func rect*[T](r, phi: T): Complex[T] =
## Returns the complex number with polar coordinates ``r`` and ``phi``. ## Returns the complex number with polar coordinates ``r`` and ``phi``.
## ##
## | ``result.re = r * cos(phi)`` ## | ``result.re = r * cos(phi)``
@ -341,7 +341,7 @@ proc rect*[T](r, phi: T): Complex[T] =
complex(r * cos(phi), r * sin(phi)) complex(r * cos(phi), r * sin(phi))
proc `$`*(z: Complex): string = func `$`*(z: Complex): string =
## Returns ``z``'s string representation as ``"(re, im)"``. ## Returns ``z``'s string representation as ``"(re, im)"``.
result = "(" & $z.re & ", " & $z.im & ")" result = "(" & $z.re & ", " & $z.im & ")"

1
tests/effects/tstrict_funcs.nim
View file

@ -6,6 +6,7 @@ import tables, streams, parsecsv
# We import the below modules to check that they compile with `strictFuncs`. # We import the below modules to check that they compile with `strictFuncs`.
# They are otherwise unused in this file. # They are otherwise unused in this file.
import import
complex,
httpcore, httpcore,
math, math,
nre, nre,