more modules updated
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Araq
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3 changed files with 70 additions and 70 deletions
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@ -30,50 +30,50 @@ type
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{.deprecated: [TComplex: Complex].}
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proc `==` *(x, y: TComplex): bool =
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proc `==` *(x, y: Complex): bool =
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## Compare two complex numbers `x` and `y` for equality.
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result = x.re == y.re and x.im == y.im
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proc `=~` *(x, y: TComplex): bool =
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proc `=~` *(x, y: Complex): bool =
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## Compare two complex numbers `x` and `y` approximately.
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result = abs(x.re-y.re)<EPS and abs(x.im-y.im)<EPS
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proc `+` *(x, y: TComplex): TComplex =
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proc `+` *(x, y: Complex): Complex =
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## Add two complex numbers.
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result.re = x.re + y.re
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result.im = x.im + y.im
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proc `+` *(x: TComplex, y: float): TComplex =
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proc `+` *(x: Complex, y: float): Complex =
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## Add complex `x` to float `y`.
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result.re = x.re + y
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result.im = x.im
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proc `+` *(x: float, y: TComplex): TComplex =
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proc `+` *(x: float, y: Complex): Complex =
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## Add float `x` to complex `y`.
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result.re = x + y.re
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result.im = y.im
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proc `-` *(z: TComplex): TComplex =
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proc `-` *(z: Complex): Complex =
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## Unary minus for complex numbers.
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result.re = -z.re
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result.im = -z.im
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proc `-` *(x, y: TComplex): TComplex =
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proc `-` *(x, y: Complex): Complex =
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## Subtract two complex numbers.
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result.re = x.re - y.re
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result.im = x.im - y.im
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proc `-` *(x: TComplex, y: float): TComplex =
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proc `-` *(x: Complex, y: float): Complex =
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## Subtracts float `y` from complex `x`.
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result = x + (-y)
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proc `-` *(x: float, y: TComplex): TComplex =
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proc `-` *(x: float, y: Complex): Complex =
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## Subtracts complex `y` from float `x`.
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result = x + (-y)
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proc `/` *(x, y: TComplex): TComplex =
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proc `/` *(x, y: Complex): Complex =
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## Divide `x` by `y`.
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var
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r, den: float
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@ -88,73 +88,73 @@ proc `/` *(x, y: TComplex): TComplex =
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result.re = (x.re + r * x.im) / den
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result.im = (x.im - r * x.re) / den
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proc `/` *(x : TComplex, y: float ): TComplex =
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proc `/` *(x : Complex, y: float ): Complex =
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## Divide complex `x` by float `y`.
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result.re = x.re/y
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result.im = x.im/y
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proc `/` *(x : float, y: TComplex ): TComplex =
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proc `/` *(x : float, y: Complex ): Complex =
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## Divide float `x` by complex `y`.
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var num : TComplex = (x, 0.0)
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var num : Complex = (x, 0.0)
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result = num/y
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proc `*` *(x, y: TComplex): TComplex =
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proc `*` *(x, y: Complex): Complex =
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## Multiply `x` with `y`.
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result.re = x.re * y.re - x.im * y.im
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result.im = x.im * y.re + x.re * y.im
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proc `*` *(x: float, y: TComplex): TComplex =
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proc `*` *(x: float, y: Complex): Complex =
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## Multiply float `x` with complex `y`.
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result.re = x * y.re
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result.im = x * y.im
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proc `*` *(x: TComplex, y: float): TComplex =
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proc `*` *(x: Complex, y: float): Complex =
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## Multiply complex `x` with float `y`.
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result.re = x.re * y
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result.im = x.im * y
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proc `+=` *(x: var TComplex, y: TComplex) =
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proc `+=` *(x: var Complex, y: Complex) =
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## Add `y` to `x`.
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x.re += y.re
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x.im += y.im
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proc `+=` *(x: var TComplex, y: float) =
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proc `+=` *(x: var Complex, y: float) =
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## Add `y` to the complex number `x`.
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x.re += y
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proc `-=` *(x: var TComplex, y: TComplex) =
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proc `-=` *(x: var Complex, y: Complex) =
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## Subtract `y` from `x`.
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x.re -= y.re
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x.im -= y.im
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proc `-=` *(x: var TComplex, y: float) =
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proc `-=` *(x: var Complex, y: float) =
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## Subtract `y` from the complex number `x`.
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x.re -= y
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proc `*=` *(x: var TComplex, y: TComplex) =
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proc `*=` *(x: var Complex, y: Complex) =
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## Multiply `y` to `x`.
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let im = x.im * y.re + x.re * y.im
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x.re = x.re * y.re - x.im * y.im
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x.im = im
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proc `*=` *(x: var TComplex, y: float) =
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proc `*=` *(x: var Complex, y: float) =
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## Multiply `y` to the complex number `x`.
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x.re *= y
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x.im *= y
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proc `/=` *(x: var TComplex, y: TComplex) =
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proc `/=` *(x: var Complex, y: Complex) =
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## Divide `x` by `y` in place.
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x = x / y
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proc `/=` *(x : var TComplex, y: float) =
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proc `/=` *(x : var Complex, y: float) =
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## Divide complex `x` by float `y` in place.
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x.re /= y
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x.im /= y
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proc abs*(z: TComplex): float =
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proc abs*(z: Complex): float =
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## Return the distance from (0,0) to `z`.
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# optimized by checking special cases (sqrt is expensive)
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@ -174,7 +174,7 @@ proc abs*(z: TComplex): float =
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result = y * sqrt(1.0 + temp * temp)
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proc sqrt*(z: TComplex): TComplex =
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proc sqrt*(z: Complex): Complex =
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## Square root for a complex number `z`.
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var x, y, w, r: float
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@ -198,7 +198,7 @@ proc sqrt*(z: TComplex): TComplex =
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result.re = z.im / (result.im + result.im)
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proc exp*(z: TComplex): TComplex =
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proc exp*(z: Complex): Complex =
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## e raised to the power `z`.
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var rho = exp(z.re)
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var theta = z.im
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@ -206,21 +206,21 @@ proc exp*(z: TComplex): TComplex =
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result.im = rho*sin(theta)
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proc ln*(z: TComplex): TComplex =
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proc ln*(z: Complex): Complex =
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## Returns the natural log of `z`.
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result.re = ln(abs(z))
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result.im = arctan2(z.im,z.re)
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proc log10*(z: TComplex): TComplex =
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proc log10*(z: Complex): Complex =
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## Returns the log base 10 of `z`.
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result = ln(z)/ln(10.0)
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proc log2*(z: TComplex): TComplex =
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proc log2*(z: Complex): Complex =
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## Returns the log base 2 of `z`.
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result = ln(z)/ln(2.0)
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proc pow*(x, y: TComplex): TComplex =
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proc pow*(x, y: Complex): Complex =
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## `x` raised to the power `y`.
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if x.re == 0.0 and x.im == 0.0:
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if y.re == 0.0 and y.im == 0.0:
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@ -242,53 +242,53 @@ proc pow*(x, y: TComplex): TComplex =
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result.im = s*sin(r)
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proc sin*(z: TComplex): TComplex =
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proc sin*(z: Complex): Complex =
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## Returns the sine of `z`.
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result.re = sin(z.re)*cosh(z.im)
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result.im = cos(z.re)*sinh(z.im)
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proc arcsin*(z: TComplex): TComplex =
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proc arcsin*(z: Complex): Complex =
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## Returns the inverse sine of `z`.
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var i: TComplex = (0.0,1.0)
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var i: Complex = (0.0,1.0)
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result = -i*ln(i*z + sqrt(1.0-z*z))
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proc cos*(z: TComplex): TComplex =
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proc cos*(z: Complex): Complex =
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## Returns the cosine of `z`.
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result.re = cos(z.re)*cosh(z.im)
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result.im = -sin(z.re)*sinh(z.im)
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proc arccos*(z: TComplex): TComplex =
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proc arccos*(z: Complex): Complex =
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## Returns the inverse cosine of `z`.
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var i: TComplex = (0.0,1.0)
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var i: Complex = (0.0,1.0)
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result = -i*ln(z + sqrt(z*z-1.0))
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proc tan*(z: TComplex): TComplex =
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proc tan*(z: Complex): Complex =
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## Returns the tangent of `z`.
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result = sin(z)/cos(z)
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proc cot*(z: TComplex): TComplex =
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proc cot*(z: Complex): Complex =
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## Returns the cotangent of `z`.
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result = cos(z)/sin(z)
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proc sec*(z: TComplex): TComplex =
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proc sec*(z: Complex): Complex =
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## Returns the secant of `z`.
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result = 1.0/cos(z)
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proc csc*(z: TComplex): TComplex =
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proc csc*(z: Complex): Complex =
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## Returns the cosecant of `z`.
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result = 1.0/sin(z)
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proc sinh*(z: TComplex): TComplex =
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proc sinh*(z: Complex): Complex =
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## Returns the hyperbolic sine of `z`.
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result = 0.5*(exp(z)-exp(-z))
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proc cosh*(z: TComplex): TComplex =
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proc cosh*(z: Complex): Complex =
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## Returns the hyperbolic cosine of `z`.
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result = 0.5*(exp(z)+exp(-z))
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proc `$`*(z: TComplex): string =
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proc `$`*(z: Complex): string =
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## Returns `z`'s string representation as ``"(re, im)"``.
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result = "(" & $z.re & ", " & $z.im & ")"
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