complex minor improvement (#16086)

1 files changed, 21 insertions, 129 deletions

diff --git a/lib/pure/complex.nim b/lib/pure/complex.nim
index d57adeb92..d1056e6e8 100644
--- a/lib/pure/complex.nim
+++ b/lib/pure/complex.nim
@@ -42,38 +42,38 @@ 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 =
-  ## Return the distance from (0,0) to ``z``.
+  ## Returns the distance from (0,0) to ``z``.
   result = hypot(z.re, z.im)
 
 proc abs2*[T](z: Complex[T]): T =
-  ## Return 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
 
 proc conjugate*[T](z: Complex[T]): Complex[T] =
-  ## Conjugate of complex number ``z``.
+  ## Conjugates of complex number ``z``.
   result.re = z.re
   result.im = -z.im
 
 proc inv*[T](z: Complex[T]): Complex[T] =
-  ## Multiplicative inverse of complex number ``z``.
+  ## Multiplicatives inverse of complex number ``z``.
   conjugate(z) / abs2(z)
 
 proc `==` *[T](x, y: Complex[T]): bool =
-  ## Compare 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
 
 proc `+` *[T](x: T; y: Complex[T]): Complex[T] =
-  ## Add a real number to a complex number.
+  ## 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] =
-  ## Add a complex number to a real number.
+  ## 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] =
-  ## Add two complex numbers.
+  ## Adds two complex numbers.
   result.re = x.re + y.re
   result.im = x.im + y.im
 
@@ -83,30 +83,30 @@ proc `-` *[T](z: Complex[T]): Complex[T] =
   result.im = -z.im
 
 proc `-` *[T](x: T; y: Complex[T]): Complex[T] =
-  ## Subtract a complex number from a real number.
+  ## Subtracts a complex number from a real number.
   x + (-y)
 
 proc `-` *[T](x: Complex[T]; y: T): Complex[T] =
-  ## Subtract a real number from a complex number.
+  ## 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] =
-  ## Subtract two complex numbers.
+  ## 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] =
-  ## Divide complex number ``x`` by real number ``y``.
+  ## 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] =
-  ## Divide real number ``x`` by complex number ``y``.
+  ## Divides real number ``x`` by complex number ``y``.
   result = x * inv(y)
 
 proc `/` *[T](x, y: Complex[T]): Complex[T] =
-  ## Divide ``x`` by ``y``.
+  ## Divides ``x`` by ``y``.
   var r, den: T
   if abs(y.re) < abs(y.im):
     r = y.re / y.im
@@ -120,39 +120,39 @@ proc `/` *[T](x, y: Complex[T]): Complex[T] =
     result.im = (x.im - r * x.re) / den
 
 proc `*` *[T](x: T; y: Complex[T]): Complex[T] =
-  ## Multiply a real number and a complex number.
+  ## 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] =
-  ## Multiply a complex number with a real number.
+  ## 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] =
-  ## Multiply ``x`` with ``y``.
+  ## 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]) =
-  ## Add ``y`` to ``x``.
+  ## Adds ``y`` to ``x``.
   x.re += y.re
   x.im += y.im
 
 proc `-=` *[T](x: var Complex[T]; y: Complex[T]) =
-  ## Subtract ``y`` from ``x``.
+  ## Subtracts ``y`` from ``x``.
   x.re -= y.re
   x.im -= y.im
 
 proc `*=` *[T](x: var Complex[T]; y: Complex[T]) =
-  ## Multiply ``y`` to ``x``.
+  ## 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]) =
-  ## Divide ``x`` by ``y`` in place.
+  ## Divides ``x`` by ``y`` in place.
   x = x / y
 
 
@@ -346,111 +346,3 @@ proc `$`*(z: Complex): string =
   result = "(" & $z.re & ", " & $z.im & ")"
 
 {.pop.}
-
-
-when isMainModule:
-  proc `=~`[T](x, y: Complex[T]): bool =
-    result = abs(x.re-y.re) < 1e-6 and abs(x.im-y.im) < 1e-6
-
-  proc `=~`[T](x: Complex[T]; y: T): bool =
-    result = abs(x.re-y) < 1e-6 and abs(x.im) < 1e-6
-
-  var
-    z: Complex64 = complex(0.0, 0.0)
-    oo: Complex64 = complex(1.0, 1.0)
-    a: Complex64 = complex(1.0, 2.0)
-    b: Complex64 = complex(-1.0, -2.0)
-    m1: Complex64 = complex(-1.0, 0.0)
-    i: Complex64 = complex(0.0, 1.0)
-    one: Complex64 = complex(1.0, 0.0)
-    tt: Complex64 = complex(10.0, 20.0)
-    ipi: Complex64 = complex(0.0, -PI)
-
-  doAssert(a/2.0 =~ complex(0.5, 1.0))
-  doAssert(a == a)
-  doAssert((a-a) == z)
-  doAssert((a+b) == z)
-  doAssert((a+b) =~ 0.0)
-  doAssert((a/b) == m1)
-  doAssert((1.0/a) =~ complex(0.2, -0.4))
-  doAssert((a*b) == complex(3.0, -4.0))
-  doAssert(10.0*a == tt)
-  doAssert(a*10.0 == tt)
-  doAssert(tt/10.0 == a)
-  doAssert(oo+(-1.0) == i)
-  doAssert( (-1.0)+oo == i)
-  doAssert(abs(oo) == sqrt(2.0))
-  doAssert(conjugate(a) == complex(1.0, -2.0))
-  doAssert(sqrt(m1) == i)
-  doAssert(exp(ipi) =~ m1)
-
-  doAssert(pow(a, b) =~ complex(-3.72999124927876, -1.68815826725068))
-  doAssert(pow(z, a) =~ complex(0.0, 0.0))
-  doAssert(pow(z, z) =~ complex(1.0, 0.0))
-  doAssert(pow(a, one) =~ a)
-  doAssert(pow(a, m1) =~ complex(0.2, -0.4))
-  doAssert(pow(a, 2.0) =~ complex(-3.0, 4.0))
-  doAssert(pow(a, 2) =~ complex(-3.0, 4.0))
-  doAssert(not(pow(a, 2.0) =~ a))
-
-  doAssert(ln(a) =~ complex(0.804718956217050, 1.107148717794090))
-  doAssert(log10(a) =~ complex(0.349485002168009, 0.480828578784234))
-  doAssert(log2(a) =~ complex(1.16096404744368, 1.59727796468811))
-
-  doAssert(sin(a) =~ complex(3.16577851321617, 1.95960104142161))
-  doAssert(cos(a) =~ complex(2.03272300701967, -3.05189779915180))
-  doAssert(tan(a) =~ complex(0.0338128260798967, 1.0147936161466335))
-  doAssert(cot(a) =~ 1.0 / tan(a))
-  doAssert(sec(a) =~ 1.0 / cos(a))
-  doAssert(csc(a) =~ 1.0 / sin(a))
-  doAssert(arcsin(a) =~ complex(0.427078586392476, 1.528570919480998))
-  doAssert(arccos(a) =~ complex(1.14371774040242, -1.52857091948100))
-  doAssert(arctan(a) =~ complex(1.338972522294494, 0.402359478108525))
-  doAssert(arccot(a) =~ complex(0.2318238045004031, -0.402359478108525))
-  doAssert(arcsec(a) =~ complex(1.384478272687081, 0.3965682301123288))
-  doAssert(arccsc(a) =~ complex(0.1863180541078155, -0.3965682301123291))
-
-  doAssert(cosh(a) =~ complex(-0.642148124715520, 1.068607421382778))
-  doAssert(sinh(a) =~ complex(-0.489056259041294, 1.403119250622040))
-  doAssert(tanh(a) =~ complex(1.1667362572409199, -0.243458201185725))
-  doAssert(sech(a) =~ 1.0 / cosh(a))
-  doAssert(csch(a) =~ 1.0 / sinh(a))
-  doAssert(coth(a) =~ 1.0 / tanh(a))
-  doAssert(arccosh(a) =~ complex(1.528570919480998, 1.14371774040242))
-  doAssert(arcsinh(a) =~ complex(1.469351744368185, 1.06344002357775))
-  doAssert(arctanh(a) =~ complex(0.173286795139986, 1.17809724509617))
-  doAssert(arcsech(a) =~ arccosh(1.0/a))
-  doAssert(arccsch(a) =~ arcsinh(1.0/a))
-  doAssert(arccoth(a) =~ arctanh(1.0/a))
-
-  doAssert(phase(a) == 1.1071487177940904)
-  var t = polar(a)
-  doAssert(rect(t.r, t.phi) =~ a)
-  doAssert(rect(1.0, 2.0) =~ complex(-0.4161468365471424, 0.9092974268256817))
-
-
-  var
-    i64: Complex32 = complex(0.0f, 1.0f)
-    a64: Complex32 = 2.0f*i64 + 1.0.float32
-    b64: Complex32 = complex(-1.0'f32, -2.0'f32)
-
-  doAssert(a64 == a64)
-  doAssert(a64 == -b64)
-  doAssert(a64 + b64 =~ 0.0'f32)
-  doAssert(not(pow(a64, b64) =~ a64))
-  doAssert(pow(a64, 0.5f) =~ sqrt(a64))
-  doAssert(pow(a64, 2) =~ complex(-3.0'f32, 4.0'f32))
-  doAssert(sin(arcsin(b64)) =~ b64)
-  doAssert(cosh(arccosh(a64)) =~ a64)
-
-  doAssert(phase(a64) - 1.107149f < 1e-6)
-  var t64 = polar(a64)
-  doAssert(rect(t64.r, t64.phi) =~ a64)
-  doAssert(rect(1.0f, 2.0f) =~ complex(-0.4161468f, 0.90929742f))
-  doAssert(sizeof(a64) == 8)
-  doAssert(sizeof(a) == 16)
-
-  doAssert 123.0.im + 456.0 == complex64(456, 123)
-
-  var localA = complex(0.1'f32)
-  doAssert localA.im is float32