mirror of
https://github.com/PaddiM8/kalker.git
synced 2024-12-13 18:10:42 +01:00
Estimation for any fractions with a denominator < 100
This commit is contained in:
bakk
parent
39587bd30e
commit
d1806f27df
@ -1326,78 +1326,4 @@ mod tests {
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assert_eq!(output, result);
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}
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}
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#[test]
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fn test_estimate() {
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let in_out = vec![
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(0.99999999, Some(String::from("1"))),
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(-0.9999999, Some(String::from("-1"))),
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(0.0000000001, Some(String::from("0"))),
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(-0.000000001, Some(String::from("0"))),
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(1.99999999, Some(String::from("2"))),
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(-1.9999999, Some(String::from("-2"))),
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(1.000000001, Some(String::from("1"))),
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(-1.000001, Some(String::from("-1"))),
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(0.5, Some(String::from("1/2"))),
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(-0.5, Some(String::from("-1/2"))),
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(0.3333333333, Some(String::from("1/3"))),
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(1.3333333333, Some(String::from("1 + 1/3"))),
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(-0.666666666, Some(String::from("-2/3"))),
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(-1.666666666, Some(String::from("-1 - 2/3"))),
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(-1.666666666, Some(String::from("-1 - 2/3"))),
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(100.33333333, Some(String::from("100 + 1/3"))),
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(-100.6666666, Some(String::from("-100 - 2/3"))),
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(0.9932611, None),
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(-0.9932611, None),
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(-0.00001, None),
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(1.9932611, None),
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(-1.9932611, None),
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(24f64, None),
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(-24f64, None),
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(1.23456f64, None),
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(-1.23456f64, None),
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(1.98, None),
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(-1.98, None),
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(9999999999f64, None),
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(-9999999999f64, None),
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(1000000001f64, None),
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(-1000000001f64, None),
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(0.53f64, None),
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(-0.53f64, None),
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(-1.51f64, None),
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(0.335f64, None),
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(-0.335f64, None),
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(0.665f64, None),
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(-0.665f64, None),
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(100f64, None),
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(-100f64, None),
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(1f64, None),
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(0.12f64, None),
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(0.1f64, None),
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(1.2f64, None),
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(1.23f64, None),
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(1.234f64, None),
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(1.2345f64, None),
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(1.23456f64, None),
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(1.234567f64, None),
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(1.2345678f64, None),
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(1.23456789f64, None),
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(-0.12f64, None),
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(-0.1f64, None),
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(-1.2f64, None),
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(-1.23f64, None),
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(-1.234f64, None),
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(-1.2345f64, None),
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(-1.23456f64, None),
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(-1.234567f64, None),
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(-1.2345678f64, None),
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(-1.23456789f64, None),
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];
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for (input, output) in in_out {
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let result = KalkValue::from(input).estimate();
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println!("{}", input);
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assert_eq!(output, result);
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}
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}
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}
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@ -1,4 +1,4 @@
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use std::{collections::HashMap};
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use std::collections::HashMap;
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use crate::{float, primitive};
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use lazy_static::lazy_static;
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@ -42,7 +42,6 @@ lazy_static! {
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};
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}
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pub(super) fn estimate(
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input: &KalkValue,
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complex_number_type: ComplexNumberType,
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@ -53,76 +52,37 @@ pub(super) fn estimate(
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return None;
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};
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let (value, value_string) = match complex_number_type {
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ComplexNumberType::Real => (real, input.to_string_real(10)),
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ComplexNumberType::Imaginary => (imaginary, input.to_string_imaginary(10, true)),
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let value = match complex_number_type {
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ComplexNumberType::Real => real,
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ComplexNumberType::Imaginary => imaginary,
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};
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let fract = value.clone().fract().abs();
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let integer = value.clone().trunc();
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#[cfg(feature = "rug")]
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let fract_as_string = fract.to_f64().to_string();
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#[cfg(not(feature = "rug"))]
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let fract_as_string = fract.to_string();
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// If it's an integer, there's nothing that would be done to it.
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if fract == 0f64 {
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if value > &f64::MAX {
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return None;
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}
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// Eg. 0.5 to 1/2
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let as_abs_string = value_string.trim_start_matches('-').to_string();
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let sign = if value < &0f64 { "-" } else { "" };
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if as_abs_string.starts_with("0.5")
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&& (as_abs_string.len() == 3 || (as_abs_string.len() > 6 && &as_abs_string[3..5] == "00"))
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{
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return Some(format!("{}1/2", sign));
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let value = primitive!(value);
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// If it's an integer, there's nothing that would be done to it.
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if value.fract() == 0f64 {
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return None;
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}
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// Eg. 1.33333333 to 1 + 1/3
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if fract_as_string.len() >= 7 {
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let first_five_decimals = &fract_as_string[2..7];
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if first_five_decimals == "33333" || first_five_decimals == "66666" {
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let fraction = match first_five_decimals {
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"33333" => "1/3",
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"66666" => "2/3",
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_ => "?",
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};
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if integer == 0f64 {
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return Some(format!("{}{}", sign, fraction));
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} else {
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let explicit_sign = if sign.is_empty() { "+" } else { "-" };
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return Some(format!(
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"{} {} {}",
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trim_zeroes(&integer.to_string()),
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explicit_sign,
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fraction
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));
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}
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}
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if let Some(equivalent_fraction) = equivalent_fraction(value) {
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return Some(equivalent_fraction);
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}
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// Match with common numbers, eg. π, 2π/3, √2
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if as_abs_string.len() >= 8 {
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if let Some(constant) = CONSTANTS.get(&as_abs_string[0..8]) {
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return Some(format!("{}{}", sign, constant));
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}
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if let Some(equivalent_constant) = equivalent_constant(&value.to_string()) {
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return Some(equivalent_constant);
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}
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// If the value squared (and rounded) is an integer,
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// eg. x² is an integer,
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// then it can be expressed as sqrt(x²).
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// Ignore it if the square root of the result is an integer.
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if fract != 0f64 {
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let squared = KalkValue::Number(value.clone() * value, float!(0), String::new())
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.round_if_needed()
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.values()
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.0;
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if squared.clone().sqrt().fract() != 0f64 && squared.clone().fract() == 0f64 {
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return Some(format!("√{}", primitive!(squared) as i32));
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}
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if let Some(equivalent_root) = equivalent_root(value) {
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return Some(equivalent_root);
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}
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// If nothing above was relevant, simply round it off a bit, eg. from 0.99999 to 1
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@ -138,6 +98,145 @@ pub(super) fn estimate(
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}))
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}
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fn equivalent_fraction(value: f64) -> Option<String> {
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fn gcd(mut a: i64, mut b: i64) -> i64 {
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while a != 0 {
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let old_a = a;
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a = b % a;
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b = old_a;
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}
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b.abs()
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}
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let original_sign = value.signum();
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let value = value.abs();
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let abs_value_str = value.to_string();
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// https://goodcalculators.com/repeating-decimal-to-fraction-conversion-calculator/
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let (mut numer, mut denom) = if let Some(repeatend_str) = find_repeatend(&abs_value_str) {
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let repeatend_pos = abs_value_str.find(&repeatend_str)?;
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let non_repeating_str = &abs_value_str[..repeatend_pos];
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// non-repeating
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let non_repeating = non_repeating_str.parse::<f64>().unwrap_or(0f64);
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let non_repeating_dec_count =
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non_repeating_str.len() - non_repeating_str.find('.').unwrap_or(0) - 1;
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let a = non_repeating.fract();
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// repeatend
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let b = match repeatend_str.parse::<i64>() {
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Ok(b) => b,
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Err(_) => return None,
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};
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let factor = 10i64.pow(non_repeating_dec_count as u32) as f64;
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let nines = (10i64.pow(repeatend_str.len() as u32) - 1) as f64;
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let a_numer = a as f64 * factor * nines;
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let b_numer = b as f64;
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let ab_denom = nines * factor;
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let integer_part_as_numer = non_repeating.trunc() * ab_denom;
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(a_numer + b_numer + integer_part_as_numer, ab_denom)
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} else {
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const PREC: f64 = 10e10f64;
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(value * PREC, PREC)
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};
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let gcd = gcd(numer as i64, denom as i64) as f64;
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numer /= gcd;
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denom /= gcd;
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if denom <= 1f64 || denom >= 100f64 || denom == 10f64 {
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return None;
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}
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let integer_part = (numer / denom).trunc();
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if integer_part > 1f64 {
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numer -= integer_part * denom;
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let sign = if original_sign.is_sign_positive() {
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"+"
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} else {
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"-"
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};
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Some(format!(
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"{} {} {}/{}",
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integer_part * original_sign,
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sign,
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numer.abs(),
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denom.abs()
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))
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} else {
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Some(format!("{}/{}", numer * original_sign, denom))
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}
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}
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fn find_repeatend(input: &str) -> Option<String> {
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if input.len() < 10 {
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return None;
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}
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for len in 1..=9 {
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for offset in 1..=len {
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let chars: Vec<char> = input[..input.len() - offset].chars().rev().collect();
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let mut chunks = chars.chunks(len);
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let mut repeats = 1;
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let mut prev: &[char] = chunks.next()?;
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for chunk in chunks {
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if chunk == prev {
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repeats += 1;
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} else {
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repeats = 0;
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prev = chunk;
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}
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let required_repeats = match len {
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1..=3 => 4,
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_ => 2,
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};
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if repeats >= required_repeats && !prev.iter().all(|x| x == &'0') {
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return Some(prev.iter().rev().cloned().collect::<String>());
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}
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}
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}
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}
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None
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}
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fn equivalent_constant(value_str: &str) -> Option<String> {
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if value_str.trim_start_matches('-').len() < 8 {
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return None;
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}
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let (abs_value_str, sign) = if let Some(abs_value_str) = value_str.strip_prefix('-') {
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(abs_value_str, "-")
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} else {
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(value_str, "")
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};
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CONSTANTS
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.get(&abs_value_str[..8])
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.map(|constant| format!("{}{}", sign, constant))
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}
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fn equivalent_root(value: f64) -> Option<String> {
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if value.fract() != 0f64 {
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let squared = KalkValue::Number(float!(value * value), float!(0), String::new())
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.round_if_needed()
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.values()
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.0;
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if squared.clone().sqrt().fract() != 0f64 && squared.clone().fract() == 0f64 {
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return Some(format!("√{}", primitive!(squared) as i32));
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}
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}
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None
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}
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pub(super) fn round(
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input: &KalkValue,
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complex_number_type: ComplexNumberType,
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@ -205,3 +304,92 @@ pub(super) fn trim_zeroes(input: &str) -> String {
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input.into()
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_estimate() {
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let in_out = vec![
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(0.99999999, Some(String::from("1"))),
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(-0.9999999, Some(String::from("-1"))),
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(0.0000000001, Some(String::from("0"))),
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(-0.000000001, Some(String::from("0"))),
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(1.99999999, Some(String::from("2"))),
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(-1.9999999, Some(String::from("-2"))),
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(1.000000001, Some(String::from("1"))),
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(-1.000001, Some(String::from("-1"))),
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(0.5, Some(String::from("1/2"))),
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(-0.5, Some(String::from("-1/2"))),
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(0.3333333333, Some(String::from("1/3"))),
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(1.3333333333, Some(String::from("4/3"))),
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(-0.666666666, Some(String::from("-2/3"))),
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(-1.666666666, Some(String::from("-5/3"))),
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(100.33333333, Some(String::from("100 + 1/3"))),
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(-100.6666666, Some(String::from("-100 - 2/3"))),
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(0.9932611, None),
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(-0.9932611, None),
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(-0.00001, None),
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(1.9932611, None),
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(-1.9932611, None),
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(24f64, None),
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(-24f64, None),
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(1.23456f64, None),
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(-1.23456f64, None),
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(9999999999f64, None),
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(-9999999999f64, None),
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(1000000001f64, None),
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(-1000000001f64, None),
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(0.53f64, None),
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(-0.53f64, None),
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(-1.51f64, None),
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(0.335f64, None),
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(-0.335f64, None),
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(0.665f64, None),
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(-0.665f64, None),
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(100f64, None),
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(-100f64, None),
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(1f64, None),
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(0.1f64, None),
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(1.23f64, None),
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(1.234f64, None),
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(1.2345f64, None),
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(1.23456f64, None),
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(1.234567f64, None),
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(1.2345678f64, None),
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(1.23456789f64, None),
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(-0.1f64, None),
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(-1.23f64, None),
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(-1.234f64, None),
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(-1.2345f64, None),
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(-1.23456f64, None),
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(-1.234567f64, None),
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(-1.2345678f64, None),
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(-1.23456789f64, None),
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];
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for (input, output) in in_out {
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let result = KalkValue::from(input).estimate();
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println!("{}", input);
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assert_eq!(output, result);
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}
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}
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#[test]
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fn test_equivalent_fraction() {
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assert_eq!(equivalent_fraction(0.5f64).unwrap(), "1/2");
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assert_eq!(equivalent_fraction(-0.5f64).unwrap(), "-1/2");
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assert_eq!(equivalent_fraction(1f64 / 3f64).unwrap(), "1/3");
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assert_eq!(equivalent_fraction(4f64 / 3f64).unwrap(), "4/3");
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assert_eq!(equivalent_fraction(7f64 / 3f64).unwrap(), "2 + 1/3");
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assert_eq!(equivalent_fraction(-1f64 / 12f64).unwrap(), "-1/12");
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assert_eq!(equivalent_fraction(-16f64 / -7f64).unwrap(), "2 + 2/7");
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assert!(equivalent_fraction(0.123f64).is_none());
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assert!(equivalent_fraction(1f64).is_none());
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assert!(equivalent_fraction(0.01f64).is_none());
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assert!(equivalent_fraction(-0.9999999f64).is_none());
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assert!(equivalent_fraction(0.9999999f64).is_none());
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assert!(equivalent_fraction(1.9999999f64).is_none());
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}
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}
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