diff options
Diffstat (limited to 'lib/pure/complex.nim')
| -rw-r--r-- | lib/pure/complex.nim | 94 |
1 files changed, 48 insertions, 46 deletions
diff --git a/lib/pure/complex.nim b/lib/pure/complex.nim index 1392b73aa..a8709e098 100644 --- a/lib/pure/complex.nim +++ b/lib/pure/complex.nim @@ -1,6 +1,6 @@ # # -# Nimrod's Runtime Library +# Nim's Runtime Library # (c) Copyright 2010 Andreas Rumpf # # See the file "copying.txt", included in this @@ -25,53 +25,55 @@ const type - TComplex* = tuple[re, im: float] + Complex* = tuple[re, im: float] ## a complex number, consisting of a real and an imaginary part -proc `==` *(x, y: TComplex): bool = +{.deprecated: [TComplex: Complex].} + +proc `==` *(x, y: Complex): bool = ## Compare two complex numbers `x` and `y` for equality. result = x.re == y.re and x.im == y.im -proc `=~` *(x, y: TComplex): bool = +proc `=~` *(x, y: Complex): bool = ## Compare two complex numbers `x` and `y` approximately. result = abs(x.re-y.re)<EPS and abs(x.im-y.im)<EPS -proc `+` *(x, y: TComplex): TComplex = +proc `+` *(x, y: Complex): Complex = ## Add two complex numbers. result.re = x.re + y.re result.im = x.im + y.im -proc `+` *(x: TComplex, y: float): TComplex = +proc `+` *(x: Complex, y: float): Complex = ## Add complex `x` to float `y`. result.re = x.re + y result.im = x.im -proc `+` *(x: float, y: TComplex): TComplex = +proc `+` *(x: float, y: Complex): Complex = ## Add float `x` to complex `y`. result.re = x + y.re result.im = y.im -proc `-` *(z: TComplex): TComplex = +proc `-` *(z: Complex): Complex = ## Unary minus for complex numbers. result.re = -z.re result.im = -z.im -proc `-` *(x, y: TComplex): TComplex = +proc `-` *(x, y: Complex): Complex = ## Subtract two complex numbers. result.re = x.re - y.re result.im = x.im - y.im -proc `-` *(x: TComplex, y: float): TComplex = +proc `-` *(x: Complex, y: float): Complex = ## Subtracts float `y` from complex `x`. result = x + (-y) -proc `-` *(x: float, y: TComplex): TComplex = +proc `-` *(x: float, y: Complex): Complex = ## Subtracts complex `y` from float `x`. result = x + (-y) -proc `/` *(x, y: TComplex): TComplex = +proc `/` *(x, y: Complex): Complex = ## Divide `x` by `y`. var r, den: float @@ -86,73 +88,73 @@ proc `/` *(x, y: TComplex): TComplex = result.re = (x.re + r * x.im) / den result.im = (x.im - r * x.re) / den -proc `/` *(x : TComplex, y: float ): TComplex = +proc `/` *(x : Complex, y: float ): Complex = ## Divide complex `x` by float `y`. result.re = x.re/y result.im = x.im/y -proc `/` *(x : float, y: TComplex ): TComplex = +proc `/` *(x : float, y: Complex ): Complex = ## Divide float `x` by complex `y`. - var num : TComplex = (x, 0.0) + var num : Complex = (x, 0.0) result = num/y -proc `*` *(x, y: TComplex): TComplex = +proc `*` *(x, y: Complex): Complex = ## Multiply `x` with `y`. result.re = x.re * y.re - x.im * y.im result.im = x.im * y.re + x.re * y.im -proc `*` *(x: float, y: TComplex): TComplex = +proc `*` *(x: float, y: Complex): Complex = ## Multiply float `x` with complex `y`. result.re = x * y.re result.im = x * y.im -proc `*` *(x: TComplex, y: float): TComplex = +proc `*` *(x: Complex, y: float): Complex = ## Multiply complex `x` with float `y`. result.re = x.re * y result.im = x.im * y -proc `+=` *(x: var TComplex, y: TComplex) = +proc `+=` *(x: var Complex, y: Complex) = ## Add `y` to `x`. x.re += y.re x.im += y.im -proc `+=` *(x: var TComplex, y: float) = +proc `+=` *(x: var Complex, y: float) = ## Add `y` to the complex number `x`. x.re += y -proc `-=` *(x: var TComplex, y: TComplex) = +proc `-=` *(x: var Complex, y: Complex) = ## Subtract `y` from `x`. x.re -= y.re x.im -= y.im -proc `-=` *(x: var TComplex, y: float) = +proc `-=` *(x: var Complex, y: float) = ## Subtract `y` from the complex number `x`. x.re -= y -proc `*=` *(x: var TComplex, y: TComplex) = +proc `*=` *(x: var Complex, y: Complex) = ## Multiply `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 `*=` *(x: var TComplex, y: float) = +proc `*=` *(x: var Complex, y: float) = ## Multiply `y` to the complex number `x`. x.re *= y x.im *= y -proc `/=` *(x: var TComplex, y: TComplex) = +proc `/=` *(x: var Complex, y: Complex) = ## Divide `x` by `y` in place. x = x / y -proc `/=` *(x : var TComplex, y: float) = +proc `/=` *(x : var Complex, y: float) = ## Divide complex `x` by float `y` in place. x.re /= y x.im /= y -proc abs*(z: TComplex): float = +proc abs*(z: Complex): float = ## Return the distance from (0,0) to `z`. # optimized by checking special cases (sqrt is expensive) @@ -172,7 +174,7 @@ proc abs*(z: TComplex): float = result = y * sqrt(1.0 + temp * temp) -proc sqrt*(z: TComplex): TComplex = +proc sqrt*(z: Complex): Complex = ## Square root for a complex number `z`. var x, y, w, r: float @@ -196,7 +198,7 @@ proc sqrt*(z: TComplex): TComplex = result.re = z.im / (result.im + result.im) -proc exp*(z: TComplex): TComplex = +proc exp*(z: Complex): Complex = ## e raised to the power `z`. var rho = exp(z.re) var theta = z.im @@ -204,21 +206,21 @@ proc exp*(z: TComplex): TComplex = result.im = rho*sin(theta) -proc ln*(z: TComplex): TComplex = +proc ln*(z: Complex): Complex = ## Returns the natural log of `z`. result.re = ln(abs(z)) result.im = arctan2(z.im,z.re) -proc log10*(z: TComplex): TComplex = +proc log10*(z: Complex): Complex = ## Returns the log base 10 of `z`. result = ln(z)/ln(10.0) -proc log2*(z: TComplex): TComplex = +proc log2*(z: Complex): Complex = ## Returns the log base 2 of `z`. result = ln(z)/ln(2.0) -proc pow*(x, y: TComplex): TComplex = +proc pow*(x, y: Complex): Complex = ## `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: @@ -240,53 +242,53 @@ proc pow*(x, y: TComplex): TComplex = result.im = s*sin(r) -proc sin*(z: TComplex): TComplex = +proc sin*(z: Complex): Complex = ## Returns the sine of `z`. result.re = sin(z.re)*cosh(z.im) result.im = cos(z.re)*sinh(z.im) -proc arcsin*(z: TComplex): TComplex = +proc arcsin*(z: Complex): Complex = ## Returns the inverse sine of `z`. - var i: TComplex = (0.0,1.0) + var i: Complex = (0.0,1.0) result = -i*ln(i*z + sqrt(1.0-z*z)) -proc cos*(z: TComplex): TComplex = +proc cos*(z: Complex): Complex = ## Returns the cosine of `z`. result.re = cos(z.re)*cosh(z.im) result.im = -sin(z.re)*sinh(z.im) -proc arccos*(z: TComplex): TComplex = +proc arccos*(z: Complex): Complex = ## Returns the inverse cosine of `z`. - var i: TComplex = (0.0,1.0) + var i: Complex = (0.0,1.0) result = -i*ln(z + sqrt(z*z-1.0)) -proc tan*(z: TComplex): TComplex = +proc tan*(z: Complex): Complex = ## Returns the tangent of `z`. result = sin(z)/cos(z) -proc cot*(z: TComplex): TComplex = +proc cot*(z: Complex): Complex = ## Returns the cotangent of `z`. result = cos(z)/sin(z) -proc sec*(z: TComplex): TComplex = +proc sec*(z: Complex): Complex = ## Returns the secant of `z`. result = 1.0/cos(z) -proc csc*(z: TComplex): TComplex = +proc csc*(z: Complex): Complex = ## Returns the cosecant of `z`. result = 1.0/sin(z) -proc sinh*(z: TComplex): TComplex = +proc sinh*(z: Complex): Complex = ## Returns the hyperbolic sine of `z`. result = 0.5*(exp(z)-exp(-z)) -proc cosh*(z: TComplex): TComplex = +proc cosh*(z: Complex): Complex = ## Returns the hyperbolic cosine of `z`. result = 0.5*(exp(z)+exp(-z)) -proc `$`*(z: TComplex): string = +proc `$`*(z: Complex): string = ## Returns `z`'s string representation as ``"(re, im)"``. result = "(" & $z.re & ", " & $z.im & ")" |