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feat: remove odd log implementation, get normal, lognormal & to

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NunoSempere 2023-05-20 23:06:34 -04:00
parent 6e22e78d4f
commit ccdeb77f3f
2 changed files with 34 additions and 23 deletions
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@ -1,7 +1,7 @@
import std/math import std/math
import std/random import std/random
# randomize() randomize()
## Basic math functions ## Basic math functions
proc factorial(n: int): int = proc factorial(n: int): int =
@ -23,18 +23,6 @@ proc sine(x: float): float =
return acc return acc
## Log function ## Log function
## Old implementation using Taylor expansion
proc log_slow(x: float): float =
var y = x - 1
let n = 100000000
var acc = 0.0
for i in 1..n:
let taylor = pow(-1.0, float(i+1)) * pow(y, i.float) / i.float
acc = acc + taylor
return acc
## New implementation
## <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision> ## <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision>
## Arithmetic-geomtric mean ## Arithmetic-geomtric mean
@ -64,16 +52,39 @@ proc log(x: float): float =
return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2 return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2
## Test these functions ## Test these functions
echo factorial(5) ## echo factorial(5)
echo sine(1.0) ## echo sine(1.0)
echo log(1.0) ## echo log(0.1)
echo log(2.0) ## echo log(2.0)
echo log(3.0) ## echo log(3.0)
echo pow(2.0, 32.float) ## echo pow(2.0, 32.float)
## Distribution functions ## Distribution functions
proc normal(): float =
## Normal
## <https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form>
proc ur_normal(): float =
let u1 = rand(1.0) let u1 = rand(1.0)
let u2 = rand(1.0) let u2 = rand(1.0)
let z = 1 let z = sqrt(-2.0 * log(u1)) * sine(2 * PI * u2)
# see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form return z
proc normal(mean: float, sigma: float): float =
return (mean + sigma * ur_normal())
proc lognormal(logmean: float, logsigma: float): float =
let answer = pow(E, normal(logmean, logsigma))
return answer
proc to(low: float, high: float): float =
let normal95confidencePoint = 1.6448536269514722
let loglow = log(low)
let loghigh = log(high)
let logmean = (loglow + loghigh)/2
let logsigma = (loghigh - loglow) / (2.0 * normal95confidencePoint);
return lognormal(logmean, logsigma)
echo ur_normal()
echo normal(10, 20)
echo lognormal(2, 4)
echo to(10, 90)