Fixtures, Numerical Tolerances, and Property Tests

/**
 * Fintech Math Bootcamp · Lesson 119 of 120
 * Fixtures, Numerical Tolerances, and Property Tests
 * Module 12: Statistical Computing and Reproducibility
 *
 * Scenario: Testing mathematical behavior, not just one screenshot
 * Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
 *
 * Try it:   Why test a shifted dataset as well as the original fixture?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson119() {
  const near=(a:number,b:number)=>Math.abs(a-b)<=1e-12+1e-10*Math.max(Math.abs(a),Math.abs(b));
  const x=[1,2,3,4,5];
  const variance=(a:number[])=>{const m=a.reduce((s,v)=>s+v,0)/a.length;
    return a.reduce((s,v)=>s+(v-m)**2,0)/(a.length-1);};
  const result={decimal:near(.1+.2,.3),fixture:near(variance(x),2.5),
    shift:near(variance(x.map(v=>v+100)),variance(x)),
    scale:near(variance(x.map(v=>2*v)),4*variance(x))};
  return result;
}

export const checkedResult = {"decimal":true,"fixture":true,"shift":true,"scale":true};

// Run this file directly: npx tsx lessons/12-statistical-computing-and-reproducibility/119-fixtures-numerical-tolerances-and-property-tests.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson119(), null, 2));
}

# Fintech Math Bootcamp · Lesson 119 of 120
# Fixtures, Numerical Tolerances, and Property Tests
# Module 12: Statistical Computing and Reproducibility
#
# Scenario: Testing mathematical behavior, not just one screenshot
# Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
#
# Try it:   Why test a shifted dataset as well as the original fixture?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.
#
# Run: python main.py

import json


def lesson_119():
    def near(a, b):
        return abs(a - b) <= 1e-12 + 1e-10 * max(abs(a), abs(b))

    x = [1, 2, 3, 4, 5]

    def variance(a):
        total = 0.0
        for v in a:
            total += v
        m = total / len(a)
        squares = 0.0
        for v in a:
            squares += (v - m) ** 2
        return squares / (len(a) - 1)

    return {
        "decimal": near(0.1 + 0.2, 0.3),
        "fixture": near(variance(x), 2.5),
        "shift": near(variance([v + 100 for v in x]), variance(x)),
        "scale": near(variance([2 * v for v in x]), 4 * variance(x)),
    }


if __name__ == "__main__":
    print(json.dumps(lesson_119(), indent=2))

/*
 * Fintech Math Bootcamp - Lesson 119 of 120
 * Fixtures, Numerical Tolerances, and Property Tests
 * Module 12: Statistical Computing and Reproducibility
 *
 * Scenario: Testing mathematical behavior, not just one screenshot
 * Rule:     |actual-expected| <= absTol + relTol*max(|actual|,|expected|)
 *
 * Try it:   Why test a shifted dataset as well as the original fixture?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run: javac Main.java && java Main
 */

import java.util.*;

public class Main {
    static boolean near(double a, double b) {
        return Math.abs(a - b) <= 1e-12 + 1e-10 * Math.max(Math.abs(a), Math.abs(b));
    }

    static double variance(double[] a) {
        double m = 0;
        for (double v : a) m += v;
        m /= a.length;
        double s = 0;
        for (double v : a) s += Math.pow(v - m, 2);
        return s / (a.length - 1);
    }

    static Map<String, Object> lesson119() {
        double[] x = {1, 2, 3, 4, 5};
        double[] shifted = new double[x.length];
        double[] scaled = new double[x.length];
        for (int i = 0; i < x.length; i++) {
            shifted[i] = x[i] + 100;
            scaled[i] = 2 * x[i];
        }
        return obj("decimal", near(.1 + .2, .3), "fixture", near(variance(x), 2.5),
                "shift", near(variance(shifted), variance(x)), "scale", near(variance(scaled), 4 * variance(x)));
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson119(), ""));
    }

    // Minimal JSON writer: insertion-ordered Map, List, Number, Boolean, String and null.
    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof String) return quote((String) value);
        if (value instanceof Boolean) return value.toString();
        if (value instanceof Double) return formatNumber((Double) value);
        if (value instanceof Number) return value.toString();
        String inner = indent + "  ";
        StringBuilder sb = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            sb.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> e : map.entrySet()) {
                sb.append(inner).append(quote(e.getKey().toString())).append(": ").append(toJson(e.getValue(), inner));
                sb.append(++i < map.size() ? ",\n" : "\n");
            }
            return sb.append(indent).append("}").toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        sb.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            sb.append(inner).append(toJson(list.get(i), inner)).append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return sb.append(indent).append("]").toString();
    }

    // Integral doubles print without ".0", as JavaScript does; others use Java's round-trip form.
    static String formatNumber(double x) {
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return Long.toString((long) x);
        return Double.toString(x);
    }

    static String quote(String s) {
        StringBuilder sb = new StringBuilder("\"");
        for (char c : s.toCharArray()) {
            if (c == '"' || c == '\\') sb.append('\\').append(c);
            else if (c < 0x20) sb.append(String.format("\\u%04x", (int) c));
            else sb.append(c);
        }
        return sb.append('"').toString();
    }

    // Builds an insertion-ordered object from alternating keys and values.
    static Map<String, Object> obj(Object... keysAndValues) {
        Map<String, Object> map = new LinkedHashMap<String, Object>();
        for (int i = 0; i < keysAndValues.length; i += 2) map.put((String) keysAndValues[i], keysAndValues[i + 1]);
        return map;
    }

    static List<Object> list(double... values) {
        List<Object> out = new ArrayList<Object>();
        for (double v : values) out.add(v);
        return out;
    }
}

// Fintech Math Bootcamp · Lesson 119 of 120
// Fixtures, Numerical Tolerances, and Property Tests
// Module 12: Statistical Computing and Reproducibility
//
// Scenario: Testing mathematical behavior, not just one screenshot
// Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
//
// Try it:   Why test a shifted dataset as well as the original fixture?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run: go run main.go

package main

import (
	"encoding/json"
	"fmt"
	"math"
)

type Result struct {
	Decimal bool `json:"decimal"`
	Fixture bool `json:"fixture"`
	Shift   bool `json:"shift"`
	Scale   bool `json:"scale"`
}

func near(a, b float64) bool {
	return math.Abs(a-b) <= 1e-12+1e-10*math.Max(math.Abs(a), math.Abs(b))
}

func variance(a []float64) float64 {
	m := 0.0
	for _, v := range a {
		m += v
	}
	m /= float64(len(a))
	s := 0.0
	for _, v := range a {
		s += math.Pow(v-m, 2)
	}
	return s / float64(len(a)-1)
}

func mapValues(a []float64, f func(float64) float64) []float64 {
	out := make([]float64, len(a))
	for i, v := range a {
		out[i] = f(v)
	}
	return out
}

func lesson119() Result {
	x := []float64{1, 2, 3, 4, 5}
	// Variables, not constants: a constant 0.1 + 0.2 would be evaluated exactly in Go.
	a, b, c := 0.1, 0.2, 0.3
	return Result{
		Decimal: near(a+b, c),
		Fixture: near(variance(x), 2.5),
		Shift:   near(variance(mapValues(x, func(v float64) float64 { return v + 100 })), variance(x)),
		Scale:   near(variance(mapValues(x, func(v float64) float64 { return 2 * v })), 4*variance(x)),
	}
}

func main() {
	out, err := json.MarshalIndent(lesson119(), "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

// Fintech Math Bootcamp · Lesson 119 of 120
// Fixtures, Numerical Tolerances, and Property Tests
// Module 12: Statistical Computing and Reproducibility
//
// Scenario: Testing mathematical behavior, not just one screenshot
// Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
//
// Try it:   Why test a shifted dataset as well as the original fixture?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run: g++ -std=c++17 -O1 -o lesson main.cpp && ./lesson

#include <algorithm>
#include <charconv>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <deque>
#include <iostream>
#include <limits>
#include <map>
#include <optional>
#include <stdexcept>
#include <string>
#include <utility>
#include <variant>
#include <vector>

// Minimal JSON value: objects keep insertion order; numbers print in shortest round-trip form.
struct Json {
    enum class Kind { Null, Bool, Number, String, Array, Object };
    Kind kind = Kind::Null;
    bool flag = false;
    double number = 0.0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array items, or object values
};

Json jnull() { return Json{}; }
Json jbool(bool value) { Json j; j.kind = Json::Kind::Bool; j.flag = value; return j; }
Json jnum(double value) { Json j; j.kind = Json::Kind::Number; j.number = value; return j; }
Json jstr(const std::string& value) { Json j; j.kind = Json::Kind::String; j.text = value; return j; }
Json jarr(std::vector<Json> items) { Json j; j.kind = Json::Kind::Array; j.items = std::move(items); return j; }

Json jobj(std::vector<std::pair<std::string, Json>> fields) {
    Json j;
    j.kind = Json::Kind::Object;
    for (auto& field : fields) {
        j.keys.push_back(field.first);
        j.items.push_back(std::move(field.second));
    }
    return j;
}

Json jnums(const std::vector<double>& values) {
    std::vector<Json> items;
    for (double v : values) items.push_back(jnum(v));
    return jarr(std::move(items));
}

Json jnums(const std::vector<std::optional<double>>& values) {
    std::vector<Json> items;
    for (const auto& v : values) items.push_back(v ? jnum(*v) : jnull());
    return jarr(std::move(items));
}

std::string formatNumber(double value) {
    char buffer[64];
    auto result = std::to_chars(buffer, buffer + sizeof buffer, value);  // shortest round-trip form
    return std::string(buffer, result.ptr);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') {
            out += '\\';
            out += c;
        } else if (static_cast<unsigned char>(c) < 0x20) {
            char buffer[8];
            std::snprintf(buffer, sizeof buffer, "\\u%04x", static_cast<unsigned>(c));
            out += buffer;
        } else {
            out += c;
        }
    }
    return out + "\"";
}

void writeJson(std::ostream& out, const Json& value, const std::string& indent = "") {
    const std::string inner = indent + "  ";
    switch (value.kind) {
        case Json::Kind::Null: out << "null"; return;
        case Json::Kind::Bool: out << (value.flag ? "true" : "false"); return;
        case Json::Kind::Number: out << formatNumber(value.number); return;
        case Json::Kind::String: out << quote(value.text); return;
        case Json::Kind::Array:
        case Json::Kind::Object: {
            const bool isObject = value.kind == Json::Kind::Object;
            if (value.items.empty()) {
                out << (isObject ? "{}" : "[]");
                return;
            }
            out << (isObject ? "{\n" : "[\n");
            for (std::size_t i = 0; i < value.items.size(); ++i) {
                out << inner;
                if (isObject) out << quote(value.keys[i]) << ": ";
                writeJson(out, value.items[i], inner);
                out << (i + 1 < value.items.size() ? ",\n" : "\n");
            }
            out << indent << (isObject ? "}" : "]");
        }
    }
}

bool near(double a, double b) {
    return std::abs(a - b) <= 1e-12 + 1e-10 * std::max(std::abs(a), std::abs(b));
}

double variance(const std::vector<double>& a) {
    double m = 0;
    for (double v : a) m += v;
    m /= static_cast<double>(a.size());
    double s = 0;
    for (double v : a) s += std::pow(v - m, 2);
    return s / static_cast<double>(a.size() - 1);
}

Json lesson119() {
    const std::vector<double> x{1, 2, 3, 4, 5};
    std::vector<double> shifted, scaled;
    for (double v : x) {
        shifted.push_back(v + 100);
        scaled.push_back(2 * v);
    }
    return jobj({{"decimal", jbool(near(.1 + .2, .3))},
                 {"fixture", jbool(near(variance(x), 2.5))},
                 {"shift", jbool(near(variance(shifted), variance(x)))},
                 {"scale", jbool(near(variance(scaled), 4 * variance(x)))}});
}

int main() {
    writeJson(std::cout, lesson119());
    std::cout << "\n";
    return 0;
}

// Fintech Math Bootcamp · Lesson 119 of 120
// Fixtures, Numerical Tolerances, and Property Tests
// Module 12: Statistical Computing and Reproducibility
//
// Scenario: Testing mathematical behavior, not just one screenshot
// Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
//
// Try it:   Why test a shifted dataset as well as the original fixture?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run: rustc -O main.rs && ./main

#![allow(dead_code)]

/// Minimal JSON value; objects keep insertion order.
enum Json {
    Null,
    Bool(bool),
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

fn obj(fields: Vec<(&str, Json)>) -> Json {
    Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
}

fn nums(values: &[f64]) -> Json {
    Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
}

fn optional_nums(values: &[Option<f64>]) -> Json {
    Json::Arr(values.iter().map(|v| v.map_or(Json::Null, Json::Num)).collect())
}

fn quote(text: &str) -> String {
    let mut out = String::from("\"");
    for c in text.chars() {
        match c {
            '"' => out.push_str("\\\""),
            '\\' => out.push_str("\\\\"),
            c if (c as u32) < 0x20 => out.push_str(&format!("\\u{:04x}", c as u32)),
            c => out.push(c),
        }
    }
    out.push('"');
    out
}

// Display for f64 prints the shortest string that round-trips, as JavaScript does.
fn write_json(value: &Json, indent: &str, out: &mut String) {
    let inner = format!("{}  ", indent);
    match value {
        Json::Null => out.push_str("null"),
        Json::Bool(b) => out.push_str(if *b { "true" } else { "false" }),
        Json::Num(n) => out.push_str(&format!("{}", n)),
        Json::Str(s) => out.push_str(&quote(s)),
        Json::Arr(items) if items.is_empty() => out.push_str("[]"),
        Json::Obj(fields) if fields.is_empty() => out.push_str("{}"),
        Json::Arr(items) => {
            out.push_str("[\n");
            for (i, item) in items.iter().enumerate() {
                out.push_str(&inner);
                write_json(item, &inner, out);
                out.push_str(if i + 1 < items.len() { ",\n" } else { "\n" });
            }
            out.push_str(indent);
            out.push(']');
        }
        Json::Obj(fields) => {
            out.push_str("{\n");
            for (i, (key, item)) in fields.iter().enumerate() {
                out.push_str(&inner);
                out.push_str(&quote(key));
                out.push_str(": ");
                write_json(item, &inner, out);
                out.push_str(if i + 1 < fields.len() { ",\n" } else { "\n" });
            }
            out.push_str(indent);
            out.push('}');
        }
    }
}

fn near(a: f64, b: f64) -> bool {
    (a - b).abs() <= 1e-12 + 1e-10 * a.abs().max(b.abs())
}

fn variance(a: &[f64]) -> f64 {
    let n = a.len() as f64;
    let m = a.iter().fold(0.0, |s, v| s + v) / n;
    a.iter().fold(0.0, |s, v| s + (v - m).powi(2)) / (n - 1.0)
}

fn lesson_119() -> Json {
    let x: [f64; 5] = [1.0, 2.0, 3.0, 4.0, 5.0];
    let shifted: Vec<f64> = x.iter().map(|v| v + 100.0).collect();
    let scaled: Vec<f64> = x.iter().map(|v| 2.0 * v).collect();
    obj(vec![
        ("decimal", Json::Bool(near(0.1 + 0.2, 0.3))),
        ("fixture", Json::Bool(near(variance(&x), 2.5))),
        ("shift", Json::Bool(near(variance(&shifted), variance(&x)))),
        ("scale", Json::Bool(near(variance(&scaled), 4.0 * variance(&x)))),
    ])
}

fn main() {
    let mut out = String::new();
    write_json(&lesson_119(), "", &mut out);
    println!("{}", out);
}

// Fintech Math Bootcamp · Lesson 119 of 120
// Fixtures, Numerical Tolerances, and Property Tests
// Module 12: Statistical Computing and Reproducibility
//
// Scenario: Testing mathematical behavior, not just one screenshot
// Rule:     |actual−expected| ≤ absTol + relTol·max(|actual|,|expected|)
//
// Try it:   Why test a shifted dataset as well as the original fixture?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/statistical-computing-and-reproducibility/fixtures-numerical-tolerances-and-property-tests/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run: dotnet run

using System;
using System.Collections.Generic;
using System.Globalization;
using System.Linq;
using System.Text.Encodings.Web;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true, Encoder = JavaScriptEncoder.UnsafeRelaxedJsonEscaping };
Console.WriteLine(JsonSerializer.Serialize(Lesson119(), options));

static object Lesson119()
{
    static bool Near(double a, double b) => Math.Abs(a - b) <= 1e-12 + 1e-10 * Math.Max(Math.Abs(a), Math.Abs(b));
    static double Variance(double[] a)
    {
        double m = a.Aggregate(0.0, (s, v) => s + v) / a.Length;
        return a.Aggregate(0.0, (s, v) => s + Math.Pow(v - m, 2)) / (a.Length - 1);
    }
    double[] x = { 1, 2, 3, 4, 5 };
    return new
    {
        @decimal = Near(.1 + .2, .3),
        fixture = Near(Variance(x), 2.5),
        shift = Near(Variance(x.Select(v => v + 100).ToArray()), Variance(x)),
        scale = Near(Variance(x.Select(v => 2 * v).ToArray()), 4 * Variance(x)),
    };
}