diff options
Diffstat (limited to 'lib/pure/math.nim')
| -rw-r--r-- | lib/pure/math.nim | 206 |
1 files changed, 135 insertions, 71 deletions
diff --git a/lib/pure/math.nim b/lib/pure/math.nim index 49d87f007..6be19a339 100644 --- a/lib/pure/math.nim +++ b/lib/pure/math.nim @@ -130,7 +130,7 @@ proc sum*[T](x: openArray[T]): T {.noSideEffect.} = for i in items(x): result = result + i {.push noSideEffect.} -when not defined(JS): +when not defined(JS): # C proc sqrt*(x: float32): float32 {.importc: "sqrtf", header: "<math.h>".} proc sqrt*(x: float64): float64 {.importc: "sqrt", header: "<math.h>".} ## Computes the square root of `x`. @@ -144,12 +144,33 @@ when not defined(JS): proc log10*(x: float32): float32 {.importc: "log10f", header: "<math.h>".} proc log10*(x: float64): float64 {.importc: "log10", header: "<math.h>".} ## Computes the common logarithm (base 10) of `x` - proc log2*[T: float32|float64](x: T): T = return ln(x) / ln(2.0) + proc log2*(x: float32): float32 {.importc: "log2f", header: "<math.h>".} + proc log2*(x: float64): float64 {.importc: "log2", header: "<math.h>".} ## Computes the binary logarithm (base 2) of `x` proc exp*(x: float32): float32 {.importc: "expf", header: "<math.h>".} proc exp*(x: float64): float64 {.importc: "exp", header: "<math.h>".} ## Computes the exponential function of `x` (pow(E, x)) + proc sin*(x: float32): float32 {.importc: "sinf", header: "<math.h>".} + proc sin*(x: float64): float64 {.importc: "sin", header: "<math.h>".} + ## Computes the sine of `x` + proc cos*(x: float32): float32 {.importc: "cosf", header: "<math.h>".} + proc cos*(x: float64): float64 {.importc: "cos", header: "<math.h>".} + ## Computes the cosine of `x` + proc tan*(x: float32): float32 {.importc: "tanf", header: "<math.h>".} + proc tan*(x: float64): float64 {.importc: "tan", header: "<math.h>".} + ## Computes the tangent of `x` + + proc sinh*(x: float32): float32 {.importc: "sinhf", header: "<math.h>".} + proc sinh*(x: float64): float64 {.importc: "sinh", header: "<math.h>".} + ## Computes the hyperbolic sine of `x` + proc cosh*(x: float32): float32 {.importc: "coshf", header: "<math.h>".} + proc cosh*(x: float64): float64 {.importc: "cosh", header: "<math.h>".} + ## Computes the hyperbolic cosine of `x` + proc tanh*(x: float32): float32 {.importc: "tanhf", header: "<math.h>".} + proc tanh*(x: float64): float64 {.importc: "tanh", header: "<math.h>".} + ## Computes the hyperbolic tangent of `x` + proc arccos*(x: float32): float32 {.importc: "acosf", header: "<math.h>".} proc arccos*(x: float64): float64 {.importc: "acos", header: "<math.h>".} ## Computes the arc cosine of `x` @@ -166,33 +187,80 @@ when not defined(JS): ## results even when the resulting angle is near pi/2 or -pi/2 ## (`x` near 0). - proc cos*(x: float32): float32 {.importc: "cosf", header: "<math.h>".} - proc cos*(x: float64): float64 {.importc: "cos", header: "<math.h>".} - ## Computes the cosine of `x` + proc arcsinh*(x: float32): float32 {.importc: "asinhf", header: "<math.h>".} + proc arcsinh*(x: float64): float64 {.importc: "asinh", header: "<math.h>".} + ## Computes the inverse hyperbolic sine of `x` + proc arccosh*(x: float32): float32 {.importc: "acoshf", header: "<math.h>".} + proc arccosh*(x: float64): float64 {.importc: "acosh", header: "<math.h>".} + ## Computes the inverse hyperbolic cosine of `x` + proc arctanh*(x: float32): float32 {.importc: "atanhf", header: "<math.h>".} + proc arctanh*(x: float64): float64 {.importc: "atanh", header: "<math.h>".} + ## Computes the inverse hyperbolic tangent of `x` + +else: # JS + proc sqrt*(x: float32): float32 {.importc: "Math.sqrt", nodecl.} + proc sqrt*(x: float64): float64 {.importc: "Math.sqrt", nodecl.} - proc cosh*(x: float32): float32 {.importc: "coshf", header: "<math.h>".} - proc cosh*(x: float64): float64 {.importc: "cosh", header: "<math.h>".} - ## Computes the hyperbolic cosine of `x` + proc ln*(x: float32): float32 {.importc: "Math.log", nodecl.} + proc ln*(x: float64): float64 {.importc: "Math.log", nodecl.} + proc log10*(x: float32): float32 {.importc: "Math.log10", nodecl.} + proc log10*(x: float64): float64 {.importc: "Math.log10", nodecl.} + proc log2*(x: float32): float32 {.importc: "Math.log2", nodecl.} + proc log2*(x: float64): float64 {.importc: "Math.log2", nodecl.} + proc exp*(x: float32): float32 {.importc: "Math.exp", nodecl.} + proc exp*(x: float64): float64 {.importc: "Math.exp", nodecl.} + proc sin*[T: float32|float64](x: T): T {.importc: "Math.sin", nodecl.} + proc cos*[T: float32|float64](x: T): T {.importc: "Math.cos", nodecl.} + proc tan*[T: float32|float64](x: T): T {.importc: "Math.tan", nodecl.} + + proc sinh*[T: float32|float64](x: T): T {.importc: "Math.sinh", nodecl.} + proc cosh*[T: float32|float64](x: T): T {.importc: "Math.cosh", nodecl.} + proc tanh*[T: float32|float64](x: T): T {.importc: "Math.tanh", nodecl.} + + proc arcsin*[T: float32|float64](x: T): T {.importc: "Math.asin", nodecl.} + proc arccos*[T: float32|float64](x: T): T {.importc: "Math.acos", nodecl.} + proc arctan*[T: float32|float64](x: T): T {.importc: "Math.atan", nodecl.} + proc arctan2*[T: float32|float64](y, x: T): T {.importC: "Math.atan2", nodecl.} + + proc arcsinh*[T: float32|float64](x: T): T {.importc: "Math.asinh", nodecl.} + proc arccosh*[T: float32|float64](x: T): T {.importc: "Math.acosh", nodecl.} + proc arctanh*[T: float32|float64](x: T): T {.importc: "Math.atanh", nodecl.} + +proc cot*[T: float32|float64](x: T): T = 1.0 / tan(x) + ## Computes the cotangent of `x` +proc sec*[T: float32|float64](x: T): T = 1.0 / cos(x) + ## Computes the secant of `x`. +proc csc*[T: float32|float64](x: T): T = 1.0 / sin(x) + ## Computes the cosecant of `x` + +proc coth*[T: float32|float64](x: T): T = 1.0 / tanh(x) + ## Computes the hyperbolic cotangent of `x` +proc sech*[T: float32|float64](x: T): T = 1.0 / cosh(x) + ## Computes the hyperbolic secant of `x` +proc csch*[T: float32|float64](x: T): T = 1.0 / sinh(x) + ## Computes the hyperbolic cosecant of `x` + +proc arccot*[T: float32|float64](x: T): T = arctan(1.0 / x) + ## Computes the inverse cotangent of `x` +proc arcsec*[T: float32|float64](x: T): T = arccos(1.0 / x) + ## Computes the inverse secant of `x` +proc arccsc*[T: float32|float64](x: T): T = arcsin(1.0 / x) + ## Computes the inverse cosecant of `x` + +proc arccoth*[T: float32|float64](x: T): T = arctanh(1.0 / x) + ## Computes the inverse hyperbolic cotangent of `x` +proc arcsech*[T: float32|float64](x: T): T = arccosh(1.0 / x) + ## Computes the inverse hyperbolic secant of `x` +proc arccsch*[T: float32|float64](x: T): T = arcsinh(1.0 / x) + ## Computes the inverse hyperbolic cosecant of `x` + +when not defined(JS): # C proc hypot*(x, y: float32): float32 {.importc: "hypotf", header: "<math.h>".} proc hypot*(x, y: float64): float64 {.importc: "hypot", header: "<math.h>".} ## Computes the hypotenuse of a right-angle triangle with `x` and ## `y` as its base and height. Equivalent to ``sqrt(x*x + y*y)``. - proc sinh*(x: float32): float32 {.importc: "sinhf", header: "<math.h>".} - proc sinh*(x: float64): float64 {.importc: "sinh", header: "<math.h>".} - ## Computes the hyperbolic sine of `x` - proc sin*(x: float32): float32 {.importc: "sinf", header: "<math.h>".} - proc sin*(x: float64): float64 {.importc: "sin", header: "<math.h>".} - ## Computes the sine of `x` - - proc tan*(x: float32): float32 {.importc: "tanf", header: "<math.h>".} - proc tan*(x: float64): float64 {.importc: "tan", header: "<math.h>".} - ## Computes the tangent of `x` - proc tanh*(x: float32): float32 {.importc: "tanhf", header: "<math.h>".} - proc tanh*(x: float64): float64 {.importc: "tanh", header: "<math.h>".} - ## Computes the hyperbolic tangent of `x` - proc pow*(x, y: float32): float32 {.importc: "powf", header: "<math.h>".} proc pow*(x, y: float64): float64 {.importc: "pow", header: "<math.h>".} ## computes x to power raised of y. @@ -295,57 +363,31 @@ when not defined(JS): ## .. code-block:: nim ## echo trunc(PI) # 3.0 - proc fmod*(x, y: float32): float32 {.importc: "fmodf", header: "<math.h>".} - proc fmod*(x, y: float64): float64 {.importc: "fmod", header: "<math.h>".} + proc fmod*(x, y: float32): float32 {.deprecated, importc: "fmodf", header: "<math.h>".} + proc fmod*(x, y: float64): float64 {.deprecated, importc: "fmod", header: "<math.h>".} ## Computes the remainder of `x` divided by `y` ## ## .. code-block:: nim ## echo fmod(-2.5, 0.3) ## -0.1 -else: - proc trunc*(x: float32): float32 {.importc: "Math.trunc", nodecl.} - proc trunc*(x: float64): float64 {.importc: "Math.trunc", nodecl.} + proc `mod`*(x, y: float32): float32 {.importc: "fmodf", header: "<math.h>".} + proc `mod`*(x, y: float64): float64 {.importc: "fmod", header: "<math.h>".} + ## Computes the modulo operation for float operators. +else: # JS + proc hypot*[T: float32|float64](x, y: T): T = return sqrt(x*x + y*y) + proc pow*(x, y: float32): float32 {.importC: "Math.pow", nodecl.} + proc pow*(x, y: float64): float64 {.importc: "Math.pow", nodecl.} proc floor*(x: float32): float32 {.importc: "Math.floor", nodecl.} proc floor*(x: float64): float64 {.importc: "Math.floor", nodecl.} proc ceil*(x: float32): float32 {.importc: "Math.ceil", nodecl.} proc ceil*(x: float64): float64 {.importc: "Math.ceil", nodecl.} - - proc sqrt*(x: float32): float32 {.importc: "Math.sqrt", nodecl.} - proc sqrt*(x: float64): float64 {.importc: "Math.sqrt", nodecl.} - proc ln*(x: float32): float32 {.importc: "Math.log", nodecl.} - proc ln*(x: float64): float64 {.importc: "Math.log", nodecl.} - proc log10*[T: float32|float64](x: T): T = return ln(x) / ln(10.0) - proc log2*[T: float32|float64](x: T): T = return ln(x) / ln(2.0) - - proc exp*(x: float32): float32 {.importc: "Math.exp", nodecl.} - proc exp*(x: float64): float64 {.importc: "Math.exp", nodecl.} proc round0(x: float): float {.importc: "Math.round", nodecl.} + proc trunc*(x: float32): float32 {.importc: "Math.trunc", nodecl.} + proc trunc*(x: float64): float64 {.importc: "Math.trunc", nodecl.} - proc pow*(x, y: float32): float32 {.importC: "Math.pow", nodecl.} - proc pow*(x, y: float64): float64 {.importc: "Math.pow", nodecl.} - - proc arccos*(x: float32): float32 {.importc: "Math.acos", nodecl.} - proc arccos*(x: float64): float64 {.importc: "Math.acos", nodecl.} - proc arcsin*(x: float32): float32 {.importc: "Math.asin", nodecl.} - proc arcsin*(x: float64): float64 {.importc: "Math.asin", nodecl.} - proc arctan*(x: float32): float32 {.importc: "Math.atan", nodecl.} - proc arctan*(x: float64): float64 {.importc: "Math.atan", nodecl.} - proc arctan2*(y, x: float32): float32 {.importC: "Math.atan2", nodecl.} - proc arctan2*(y, x: float64): float64 {.importc: "Math.atan2", nodecl.} - - proc cos*(x: float32): float32 {.importc: "Math.cos", nodecl.} - proc cos*(x: float64): float64 {.importc: "Math.cos", nodecl.} - proc cosh*(x: float32): float32 = return (exp(x)+exp(-x))*0.5 - proc cosh*(x: float64): float64 = return (exp(x)+exp(-x))*0.5 - proc hypot*[T: float32|float64](x, y: T): T = return sqrt(x*x + y*y) - proc sinh*[T: float32|float64](x: T): T = return (exp(x)-exp(-x))*0.5 - proc sin*(x: float32): float32 {.importc: "Math.sin", nodecl.} - proc sin*(x: float64): float64 {.importc: "Math.sin", nodecl.} - proc tan*(x: float32): float32 {.importc: "Math.tan", nodecl.} - proc tan*(x: float64): float64 {.importc: "Math.tan", nodecl.} - proc tanh*[T: float32|float64](x: T): T = - var y = exp(2.0*x) - return (y-1.0)/(y+1.0) + proc `mod`*(x, y: float32): float32 {.importcpp: "# % #".} + proc `mod`*(x, y: float64): float64 {.importcpp: "# % #".} + ## Computes the modulo operation for float operators. proc round*[T: float32|float64](x: T, places: int = 0): T = ## Round a floating point number. @@ -362,6 +404,21 @@ proc round*[T: float32|float64](x: T, places: int = 0): T = var mult = pow(10.0, places.T) result = round0(x*mult)/mult +proc floorDiv*[T: SomeInteger](x, y: T): T = + ## Floor division is conceptually defined as ``floor(x / y)``. + ## This is different from the ``div`` operator, which is defined + ## as ``trunc(x / y)``. That is, ``div`` rounds towards ``0`` and ``floorDiv`` + ## rounds down. + result = x div y + let r = x mod y + if (r > 0 and y < 0) or (r < 0 and y > 0): result.dec 1 + +proc floorMod*[T: SomeNumber](x, y: T): T = + ## Floor modulus is conceptually defined as ``x - (floorDiv(x, y) * y). + ## This proc behaves the same as the ``%`` operator in python. + result = x mod y + if (result > 0 and y < 0) or (result < 0 and y > 0): result += y + when not defined(JS): proc c_frexp*(x: float32, exponent: var int32): float32 {. importc: "frexp", header: "<math.h>".} @@ -426,15 +483,6 @@ proc sgn*[T: SomeNumber](x: T): int {.inline.} = ## `NaN`. ord(T(0) < x) - ord(x < T(0)) -proc `mod`*[T: float32|float64](x, y: T): T = - ## Computes the modulo operation for float operators. Equivalent - ## to ``x - y * floor(x/y)``. Note that the remainder will always - ## have the same sign as the divisor. - ## - ## .. code-block:: nim - ## echo (4.0 mod -3.1) # -2.2 - result = if y == 0.0: x else: x - y * (x/y).floor - {.pop.} {.pop.} @@ -599,3 +647,19 @@ when isMainModule: doAssert fac(2) == 2 doAssert fac(3) == 6 doAssert fac(4) == 24 + + block: # floorMod/floorDiv + doAssert floorDiv(8, 3) == 2 + doAssert floorMod(8, 3) == 2 + + doAssert floorDiv(8, -3) == -3 + doAssert floorMod(8, -3) == -1 + + doAssert floorDiv(-8, 3) == -3 + doAssert floorMod(-8, 3) == 1 + + doAssert floorDiv(-8, -3) == 2 + doAssert floorMod(-8, -3) == -2 + + doAssert floorMod(8.0, -3.0) ==~ -1.0 + doAssert floorMod(-8.5, 3.0) ==~ 0.5 |