commit 1ebc3ce7b9f0373a56387f730fb7147a8e8616aa
parent 6454b2eeabdf28d85fc67b459e92f85297abfc6a
Author: NunoSempere <nuno.sempere@protonmail.com>
Date: Sun, 21 May 2023 01:29:57 -0400
move hardcore defs to a different folder, use stdlib math
Makes this way faster. Don't roll your stdlib, Nuño
Diffstat:
6 files changed, 18 insertions(+), 59 deletions(-)
diff --git a/wip/nim/hardcore/README.md b/wip/nim/hardcore/README.md
@@ -0,0 +1,4 @@
+This is a version of time-to-botec for nim for which I define logarithms, normals & lognormals pretty much
+from scratch, without relying on libraries except for random numbers, sqrts, or taking a to the power of b.
+
+This is interesting because it leads to better understanding. But it doesn't help compare the efficiency of various languages. So I'm setting it aside for now, even though I think it was really interesting.
diff --git a/wip/nim/hardcore/makefile b/wip/nim/hardcore/makefile
@@ -0,0 +1,11 @@
+SHELL := /bin/bash
+
+build: samples.nim
+ nim c --verbosity:0 samples.nim
+
+run: samples
+ ./samples --verbosity:0
+
+examine: samples
+ # nim c --verbosity:0 --opt:speed -d:release -d:danger --checks:off samples.nim && time ./samples --verbosity:0 --checks:off
+ nim c -d:release samples.nim && time ./samples
diff --git a/wip/nim/samples b/wip/nim/hardcore/samples
Binary files differ.
diff --git a/wip/nim/samples.nim b/wip/nim/hardcore/samples.nim
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
@@ -5,62 +5,6 @@ import std/sequtils
randomize()
-## Basic math functions
-proc factorial(n: int): int =
- if n == 0 or n < 0:
- return 1
- else:
- return n * factorial(n - 1)
-
-proc sine(x: float): float =
- let n = 8
- # ^ Taylor will converge really quickly
- # notice that the factorial of 17 is
- # already pretty gigantic
- var acc = 0.0
- for i in 0..n:
- var k = 2*i + 1
- var taylor = pow(-1, i.float) * pow(x, k.float) / factorial(k).float
- acc = acc + taylor
- return acc
-
-## Log function
-## <https://en.wikipedia.org/wiki/Natural_logarithm#High_precision>
-
-## Arithmetic-geomtric mean
-proc ag(x: float, y: float): float =
- let n = 16 # just some high number
- var a = (x + y)/2.0
- var b = sqrt(x * y)
- for i in 0..n:
- let temp = a
- a = (a+b)/2.0
- b = sqrt(b*temp)
- return a
-
-## Find m such that x * 2^m > 2^precision/2
-proc find_m(x:float): float =
- var m = 0.0;
- let precision = 32 # bits
- let c = pow(2.0, precision.float / 2.0)
- while x * pow(2.0, m) < c:
- m = m + 1
- return m
-
-proc log(x: float): float =
- let m = find_m(x)
- let s = x * pow(2.0, m)
- let ln2 = 0.6931471805599453
- return ( PI / (2.0 * ag(1, 4.0/s)) ) - m * ln2
-
-## Test these functions
-## 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
## Normal
@@ -68,7 +12,7 @@ proc log(x: float): float =
proc ur_normal(): float =
let u1 = rand(1.0)
let u2 = rand(1.0)
- let z = sqrt(-2.0 * log(u1)) * sine(2 * PI * u2)
+ let z = sqrt(-2.0 * ln(u1)) * sin(2 * PI * u2)
return z
proc normal(mean: float, sigma: float): float =
@@ -80,8 +24,8 @@ proc lognormal(logmean: float, logsigma: float): float =
proc to(low: float, high: float): float =
let normal95confidencePoint = 1.6448536269514722
- let loglow = log(low)
- let loghigh = log(high)
+ let loglow = ln(low)
+ let loghigh = ln(high)
let logmean = (loglow + loghigh)/2
let logsigma = (loghigh - loglow) / (2.0 * normal95confidencePoint);
return lognormal(logmean, logsigma)
