commit ccdeb77f3fc2e48f876483d722a037cedf3f2167
parent 6e22e78d4fd70b9e38542d7cd8c2ba931a571801
Author: NunoSempere <nuno.sempere@protonmail.com>
Date: Sat, 20 May 2023 23:06:34 -0400
feat: remove odd log implementation, get normal, lognormal & to
Diffstat:
2 files changed, 34 insertions(+), 23 deletions(-)
diff --git a/wip/nim/samples b/wip/nim/samples
Binary files differ.
diff --git a/wip/nim/samples.nim b/wip/nim/samples.nim
@@ -1,7 +1,7 @@
import std/math
import std/random
-# randomize()
+randomize()
## Basic math functions
proc factorial(n: int): int =
@@ -23,18 +23,6 @@ proc sine(x: float): float =
return acc
## 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>
## Arithmetic-geomtric mean
@@ -64,16 +52,39 @@ proc log(x: float): float =
return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2
## Test these functions
-echo factorial(5)
-echo sine(1.0)
-echo log(1.0)
-echo log(2.0)
-echo log(3.0)
-echo pow(2.0, 32.float)
-
+## echo factorial(5)
+## echo sine(1.0)
+## echo log(0.1)
+## echo log(2.0)
+## echo log(3.0)
+## echo pow(2.0, 32.float)
+
## 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 u2 = rand(1.0)
- let z = 1
- # see https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform#Basic_form
+ let z = sqrt(-2.0 * log(u1)) * sine(2 * PI * u2)
+ 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)
