80 lines
1.7 KiB
Nim
80 lines
1.7 KiB
Nim
import std/math
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import std/random
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# randomize()
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## Basic math functions
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proc factorial(n: int): int =
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if n == 0 or n < 0:
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return 1
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else:
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return n * factorial(n - 1)
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proc sine(x: float): float =
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let n = 8
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# ^ Taylor will converge really quickly
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# notice that the factorial of 17 is
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# already pretty gigantic
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var acc = 0.0
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for i in 0..n:
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var k = 2*i + 1
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var taylor = pow(-1, i.float) * pow(x, k.float) / factorial(k).float
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acc = acc + taylor
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return acc
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## Log function
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## Old implementation using Taylor expansion
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proc log_slow(x: float): float =
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var y = x - 1
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let n = 100000000
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var acc = 0.0
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for i in 1..n:
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let taylor = pow(-1.0, float(i+1)) * pow(y, i.float) / i.float
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acc = acc + taylor
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return acc
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## New implementation
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## <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision>
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## Arithmetic-geomtric mean
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proc ag(x: float, y: float): float =
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let n = 128 # just some high number
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var a = (x + y)/2.0
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var b = sqrt(x * y)
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for i in 0..n:
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let temp = a
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a = (a+b)/2.0
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b = sqrt(b*temp)
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return a
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## Find m such that x * 2^m > 2^precision/2
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proc find_m(x:float): float =
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var m = 0.0;
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let precision = 64 # bits
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let c = pow(2.0, precision.float / 2.0)
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while x * pow(2.0, m) < c:
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m = m + 1
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return m
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proc log(x: float): float =
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let m = find_m(x)
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let s = x * pow(2.0, m)
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let ln2 = 0.6931471805599453
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return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2
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## Test these functions
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echo factorial(5)
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echo sine(1.0)
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echo log(1.0)
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echo log(2.0)
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echo log(3.0)
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echo pow(2.0, 32.float)
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## Distribution functions
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proc normal(): float =
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let u1 = rand(1.0)
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let u2 = rand(1.0)
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let z = 1
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# see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form
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