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complex minor improvement (#16086)

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flywind 2020-11-22 04:20:33 +08:00 • committed by GitHub
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2 changed files with 129 additions and 129 deletions
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150
lib/pure/complex.nim
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@ -42,38 +42,38 @@ 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 = 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) result = hypot(z.re, z.im)
proc abs2*[T](z: Complex[T]): T = 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 result = z.re*z.re + z.im*z.im
proc conjugate*[T](z: Complex[T]): Complex[T] = proc conjugate*[T](z: Complex[T]): Complex[T] =
## Conjugate 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] = proc inv*[T](z: Complex[T]): Complex[T] =
## Multiplicative 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 = 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 result = x.re == y.re and x.im == y.im
proc `+` *[T](x: T; y: Complex[T]): Complex[T] = 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.re = x + y.re
result.im = y.im result.im = y.im
proc `+` *[T](x: Complex[T]; y: T): Complex[T] = 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.re = x.re + y
result.im = x.im result.im = x.im
proc `+` *[T](x, y: Complex[T]): Complex[T] = proc `+` *[T](x, y: Complex[T]): Complex[T] =
## Add 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
@ -83,30 +83,30 @@ proc `-` *[T](z: Complex[T]): Complex[T] =
result.im = -z.im result.im = -z.im
proc `-` *[T](x: T; y: Complex[T]): Complex[T] = 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) x + (-y)
proc `-` *[T](x: Complex[T]; y: T): Complex[T] = 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.re = x.re - y
result.im = x.im result.im = x.im
proc `-` *[T](x, y: Complex[T]): Complex[T] = proc `-` *[T](x, y: Complex[T]): Complex[T] =
## Subtract 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] = 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.re = x.re / y
result.im = x.im / y result.im = x.im / y
proc `/` *[T](x: T; y: Complex[T]): Complex[T] = 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) result = x * inv(y)
proc `/` *[T](x, y: Complex[T]): Complex[T] = proc `/` *[T](x, y: Complex[T]): Complex[T] =
## Divide ``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):
r = y.re / 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 result.im = (x.im - r * x.re) / den
proc `*` *[T](x: T; y: Complex[T]): Complex[T] = 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.re = x * y.re
result.im = x * y.im result.im = x * y.im
proc `*` *[T](x: Complex[T]; y: T): Complex[T] = 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.re = x.re * y
result.im = x.im * y result.im = x.im * y
proc `*` *[T](x, y: Complex[T]): Complex[T] = 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.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]) = proc `+=` *[T](x: var Complex[T]; y: Complex[T]) =
## Add ``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]) = proc `-=` *[T](x: var Complex[T]; y: Complex[T]) =
## Subtract ``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]) = 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 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]) = proc `/=` *[T](x: var Complex[T]; y: Complex[T]) =
## Divide ``x`` by ``y`` in place. ## Divides ``x`` by ``y`` in place.
x = x / y x = x / y
@ -346,111 +346,3 @@ proc `$`*(z: Complex): string =
result = "(" & $z.re & ", " & $z.im & ")" result = "(" & $z.re & ", " & $z.im & ")"
{.pop.} {.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

108
tests/stdlib/tcomplex.nim Normal file
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@ -0,0 +1,108 @@
import complex, math
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