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Andreas Rumpf
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200 changed files with 24344 additions and 17809 deletions
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lib/math.nim
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lib/math.nim
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#
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#
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# Nimrod's Runtime Library
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# (c) Copyright 2006 Andreas Rumpf
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# (c) Copyright 2008 Andreas Rumpf
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#
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# See the file "copying.txt", included in this
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# distribution, for details about the copyright.
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#
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# math routines
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# interface
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## Basic math routines for Nimrod.
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## This module is available for the ECMAScript target.
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{.push debugger:off .} # the user does not want to trace a part
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# of the standard library!
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{.push checks:off, line_dir:off, stack_trace:off.}
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proc nextPowerOfTwo*(x: int): int
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## returns the nearest power of two, so that
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## result**2 >= x > (result-1)**2.
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proc isPowerOfTwo*(x: int): bool {.noSideEffect.}
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## returns true, if x is a power of two, false otherwise.
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## Negative numbers are not a power of two.
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proc countBits*(n: int32): int {.noSideEffect.}
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## counts the set bits in `n`.
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proc random*(max: int): int
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## returns a random number in the range 0..max-1. The sequence of
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## random number is always the same, unless `randomize` is called
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## which initializes the random number generator with a "random"
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## number, i.e. a tickcount.
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proc randomize*()
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## initializes the random number generator with a "random"
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## number, i.e. a tickcount.
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proc sqrt*(x: float): float {.importc: "sqrt", header: "<math.h>".}
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## computes the square root of `x`.
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proc ln*(x: float): float {.importc: "log", header: "<math.h>".}
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## computes ln(x).
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proc exp*(x: float): float {.importc: "exp", header: "<math.h>".}
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## computes e**x.
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proc frexp*(x: float, exponent: var int): float {.
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importc: "frexp", header: "<math.h>".}
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## Split a number into mantissa and exponent.
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## `frexp` calculates the mantissa m (a float greater than or equal to 0.5
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## and less than 1) and the integer value n such that `x` (the original
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## float value) equals m * 2**n. frexp stores n in `exponent` and returns
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## m.
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proc arccos*(x: float): float {.importc: "acos", header: "<math.h>".}
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proc arcsin*(x: float): float {.importc: "asin", header: "<math.h>".}
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proc arctan*(x: float): float {.importc: "atan", header: "<math.h>".}
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proc arctan2*(y, x: float): float {.importc: "atan2", header: "<math.h>".}
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## Calculate the arc tangent of `y` / `x`.
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## `atan2` returns the arc tangent of `y` / `x`; it produces correct
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## results even when the resulting angle is near pi/2 or -pi/2
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## (`x` near 0).
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proc cos*(x: float): float {.importc: "cos", header: "<math.h>".}
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proc cosh*(x: float): float {.importc: "cosh", header: "<math.h>".}
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proc hypot*(x: float): float {.importc: "hypot", header: "<math.h>".}
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proc log10*(x: float): float {.importc: "log10", header: "<math.h>".}
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proc sinh*(x: float): float {.importc: "sinh", header: "<math.h>".}
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proc tan*(x: float): float {.importc: "tan", header: "<math.h>".}
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proc tanh*(x: float): float {.importc: "tanh", header: "<math.h>".}
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proc pow*(x, y: float): float {.importc: "pos", header: "<math.h>".}
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## computes x to power raised of y.
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when defined(Posix):
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{.passl: "-lm".}
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type
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TFloatClass* = enum ## describes the class a floating point value belongs to.
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@ -82,34 +29,11 @@ type
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fcInf, ## value is positive infinity
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fcNegInf ## value is negative infinity
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proc classify*(x: float): TFloatClass
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proc classify*(x: float): TFloatClass =
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## classifies a floating point value. Returns `x`'s class as specified by
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## `TFloatClass`
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# implementation
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include cntbits
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proc nextPowerOfTwo(x: int): int =
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result = x - 1
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when defined(cpu64):
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result = result or (result shr 32)
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result = result or (result shr 16)
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result = result or (result shr 8)
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result = result or (result shr 4)
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result = result or (result shr 2)
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result = result or (result shr 1)
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Inc(result)
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# C procs:
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proc gettime(dummy: ptr cint): cint {.
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importc: "time", header: "<time.h>".}
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proc srand(seed: cint) {.
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importc: "srand", nodecl.}
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proc rand(): cint {.importc: "rand", nodecl.}
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# most C compilers have no classify:
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proc classify(x: float): TFloatClass =
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## `TFloatClass`.
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# ECMAScript and most C compilers have no classify:
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if x == 0.0:
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if 1.0/x == 1.0/0.0:
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return fcZero
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@ -122,10 +46,130 @@ proc classify(x: float): TFloatClass =
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return fcNormal
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# XXX: fcSubnormal is not detected!
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proc randomize() = srand(gettime(nil))
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proc random(max: int): int = return rand() mod max
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proc isPowerOfTwo(x: int): bool = return (x and -x) == x
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proc isPowerOfTwo*(x: int): bool {.noSideEffect.} =
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## returns true, if x is a power of two, false otherwise.
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## Negative numbers are not a power of two.
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return (x and -x) == x
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proc nextPowerOfTwo*(x: int): int =
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## returns the nearest power of two, so that
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## result**2 >= x > (result-1)**2.
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result = x - 1
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when defined(cpu64):
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result = result or (result shr 32)
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result = result or (result shr 16)
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result = result or (result shr 8)
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result = result or (result shr 4)
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result = result or (result shr 2)
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result = result or (result shr 1)
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Inc(result)
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proc countBits*(n: int32): int {.noSideEffect.}
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## counts the set bits in `n`.
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include cntbits
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when not defined(ECMAScript):
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proc random*(max: int): int
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## returns a random number in the range 0..max-1. The sequence of
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## random number is always the same, unless `randomize` is called
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## which initializes the random number generator with a "random"
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## number, i.e. a tickcount.
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proc randomize*()
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## initializes the random number generator with a "random"
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## number, i.e. a tickcount. Note: Does nothing for the ECMAScript target,
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## as ECMAScript does not support this.
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proc sqrt*(x: float): float {.importc: "sqrt", header: "<math.h>".}
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## computes the square root of `x`.
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proc ln*(x: float): float {.importc: "log", header: "<math.h>".}
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## computes ln(x).
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proc log10*(x: float): float {.importc: "log10", header: "<math.h>".}
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proc log2*(x: float): float = return ln(x) / ln(2.0)
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proc exp*(x: float): float {.importc: "exp", header: "<math.h>".}
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## computes e**x.
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proc frexp*(x: float, exponent: var int): float {.
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importc: "frexp", header: "<math.h>".}
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## Split a number into mantissa and exponent.
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## `frexp` calculates the mantissa m (a float greater than or equal to 0.5
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## and less than 1) and the integer value n such that `x` (the original
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## float value) equals m * 2**n. frexp stores n in `exponent` and returns
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## m.
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proc round*(x: float): int {.importc: "lrint", nodecl.}
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## converts a float to an int by rounding.
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proc arccos*(x: float): float {.importc: "acos", header: "<math.h>".}
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proc arcsin*(x: float): float {.importc: "asin", header: "<math.h>".}
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proc arctan*(x: float): float {.importc: "atan", header: "<math.h>".}
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proc arctan2*(y, x: float): float {.importc: "atan2", header: "<math.h>".}
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## Calculate the arc tangent of `y` / `x`.
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## `atan2` returns the arc tangent of `y` / `x`; it produces correct
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## results even when the resulting angle is near pi/2 or -pi/2
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## (`x` near 0).
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proc cos*(x: float): float {.importc: "cos", header: "<math.h>".}
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proc cosh*(x: float): float {.importc: "cosh", header: "<math.h>".}
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proc hypot*(x, y: float): float {.importc: "hypot", header: "<math.h>".}
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## same as ``sqrt(x*x + y*y)``.
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proc sinh*(x: float): float {.importc: "sinh", header: "<math.h>".}
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proc tan*(x: float): float {.importc: "tan", header: "<math.h>".}
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proc tanh*(x: float): float {.importc: "tanh", header: "<math.h>".}
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proc pow*(x, y: float): float {.importc: "pow", header: "<math.h>".}
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## computes x to power raised of y.
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# C procs:
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proc gettime(dummy: ptr cint): cint {.importc: "time", header: "<time.h>".}
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proc srand(seed: cint) {.importc: "srand", nodecl.}
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proc rand(): cint {.importc: "rand", nodecl.}
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proc randomize() = srand(gettime(nil))
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proc random(max: int): int = return rand() mod max
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else:
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proc mathrandom(): float {.importc: "Math.random", nodecl.}
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proc mathfloor(x: float): float {.importc: "Math.floor", nodecl.}
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proc random*(max: int): int = return mathfloor(mathrandom() * max)
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proc randomize*() = nil
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proc sqrt*(x: float): float {.importc: "Math.sqrt", nodecl.}
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proc ln*(x: float): float {.importc: "Math.log", nodecl.}
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proc log10*(x: float): float = return ln(x) / ln(10.0)
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proc log2*(x: float): float = return ln(x) / ln(2.0)
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proc exp*(x: float): float {.importc: "Math.exp", nodecl.}
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proc round*(x: float): int {.importc: "Math.round", nodecl.}
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proc pow*(x, y: float): float {.importc: "Math.pow", nodecl.}
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proc frexp*(x: float, exponent: var int): float =
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if x == 0.0:
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exponent = 0.0
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result = 0.0
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elif x < 0.0:
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result = -frexp(-x, exponent)
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else:
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var ex = mathfloor(log2(x))
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exponent = round(ex)
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result = x / pow(2.0, ex)
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proc arccos*(x: float): float {.importc: "Math.acos", nodecl.}
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proc arcsin*(x: float): float {.importc: "Math.asin", nodecl.}
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proc arctan*(x: float): float {.importc: "Math.atan", nodecl.}
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proc arctan2*(y, x: float): float {.importc: "Math.atan2", nodecl.}
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proc cos*(x: float): float {.importc: "Math.cos", nodecl.}
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proc cosh*(x: float): float = return (exp(x)+exp(-x))*0.5
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proc hypot*(x, y: float): float = return sqrt(x*x + y*y)
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proc sinh*(x: float): float = return (exp(x)-exp(-x))*0.5
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proc tan*(x: float): float {.importc: "Math.tan", nodecl.}
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proc tanh*(x: float): float =
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var y = exp(2.0*x)
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return (y-1.0)/(y+1.0)
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{.pop.}
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{.pop.}
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