complex.nim: Use `func` everywhere (#16294)

1 files changed, 60 insertions, 60 deletions

diff --git a/lib/pure/complex.nim b/lib/pure/complex.nim
index d1056e6e8..04e5e8e56 100644
--- a/lib/pure/complex.nim
+++ b/lib/pure/complex.nim
@@ -24,15 +24,15 @@ type
   Complex32* = Complex[float32]
     ## 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.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.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.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: 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``.
   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``.
   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``.
   result.re = z.re
   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``.
   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.
   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.
   result.re = x + y.re
   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.
   result.re = x.re + y
   result.im = x.im
 
-proc `+` *[T](x, y: Complex[T]): Complex[T] =
+func `+` *[T](x, y: Complex[T]): Complex[T] =
   ## Adds two complex numbers.
   result.re = x.re + y.re
   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.
   result.re = -z.re
   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.
   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.
   result.re = x.re - y
   result.im = x.im
 
-proc `-` *[T](x, y: Complex[T]): Complex[T] =
+func `-` *[T](x, y: Complex[T]): Complex[T] =
   ## Subtracts two complex numbers.
   result.re = x.re - y.re
   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``.
   result.re = x.re / 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``.
   result = x * inv(y)
 
-proc `/` *[T](x, y: Complex[T]): Complex[T] =
+func `/` *[T](x, y: Complex[T]): Complex[T] =
   ## Divides ``x`` by ``y``.
   var r, den: T
   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.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.
   result.re = x * y.re
   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.
   result.re = x.re * 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``.
   result.re = x.re * y.re - x.im * 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``.
   x.re += y.re
   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``.
   x.re -= y.re
   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``.
   let im = x.im * y.re + x.re * y.im
   x.re = x.re * y.re - x.im * y.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.
   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``.
   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.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``.
   var
     rho = exp(z.re)
@@ -187,20 +187,20 @@ proc exp*[T](z: Complex[T]): Complex[T] =
   result.re = rho * cos(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``.
   result.re = ln(abs(z))
   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``.
   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``.
   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``.
   if x.re == 0.0 and x.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.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``.
   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``.
   result.re = sin(z.re) * cosh(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``.
   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``.
   result.re = cos(z.re) * cosh(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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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``.
   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.
   (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``.
   ##
   ## | ``result.re = r * cos(phi)``
@@ -341,7 +341,7 @@ proc rect*[T](r, phi: T): Complex[T] =
   complex(r * cos(phi), r * sin(phi))
 
 
-proc `$`*(z: Complex): string =
+func `$`*(z: Complex): string =
   ## Returns ``z``'s string representation as ``"(re, im)"``.
   result = "(" & $z.re & ", " & $z.im & ")"