make calculations more consistent

parse small "digits"s and "tower"s as integer
calculate more exact termial of "digits"
do not write 1 × in truncate
do not return rough as true in truncate when only zeroes were cut
only turn "approx" and "digits" into integers when below integer_contruction_limit

Author: Aras14HD

Cargo.lock

@@ -1,6 +1,6 @@
 [package]
 name = "factorion-bot-discord"
-version = "2.4.0"
+version = "2.4.1"
 edition = "2024"
 description = "factorion-bot (for factorials and related) on Discord"
 license = "MIT"
@@ -10,7 +10,7 @@ keywords = ["factorial", "termial", "bot", "math", "discord"]
 categories = ["mathematics", "web-programming", "parser-implementations"]
 
 [dependencies]
-factorion-lib = { path = "../factorion-lib", version = "4.4.0", features = ["serde", "influxdb"] }
+factorion-lib = { path = "../factorion-lib", version = "4.4.1", features = ["serde", "influxdb"] }
 serenity = { version = "0.12", default-features = false, features = ["client", "gateway", "rustls_backend", "model", "cache"] }
 tokio = { version = "1.48.0", features = ["macros", "rt-multi-thread", "time"] }
 dotenvy = "^0.15.7"

factorion-bot-discord/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "factorion-bot-reddit"
-version = "5.5.0"
+version = "5.5.1"
 edition = "2024"
 description = "factorion-bot (for factorials and related) on Reddit"
 license = "MIT"
@@ -10,7 +10,7 @@ keywords = ["factorial", "termial", "bot", "math"]
 categories = ["mathematics", "web-programming", "parser-implementations"]
 
 [dependencies]
-factorion-lib = {path = "../factorion-lib", version = "4.4.0", features = ["serde", "influxdb"]}
+factorion-lib = {path = "../factorion-lib", version = "4.4.1", features = ["serde", "influxdb"]}
 reqwest = { version = "0.12.28", features = ["json", "native-tls"], default-features = false }
 serde = { version = "1.0.219", default-features = false, features = ["derive"] }
 serde_json = "1.0.140"

factorion-bot-reddit/Cargo.toml

@@ -1,6 +1,6 @@
 [package]
 name = "factorion-lib"
-version = "4.4.0"
+version = "4.4.1"
 edition = "2024"
 description = "A library used to create bots to recognize and calculate factorials and related concepts"
 license = "MIT"

factorion-lib/Cargo.toml

@@ -1,5 +1,7 @@
 //! This module handles the formatting of the calculations (`The factorial of Subfactorial of 5 is`, etc.)
 
+use factorion_math::rug::Complete;
+use factorion_math::rug::integer::IntegerExt64;
 #[cfg(any(feature = "serde", test))]
 use serde::{Deserialize, Serialize};
 
@@ -583,11 +585,16 @@ fn truncate(number: &Integer, consts: &Consts) -> (String, bool) {
         .to_integer_round(crate::rug::float::Round::Down)
         .unwrap()
         .0;
-    let truncated_number: Integer = &number
-        / (Float::with_val(prec, 10)
-            .pow((length.clone() - consts.number_decimals_scientific - 1u8).max(Integer::ZERO))
-            .to_integer()
-            .unwrap());
+    let ten_exp = Integer::u64_pow_u64(
+        10,
+        (length.clone() - consts.number_decimals_scientific - 1u8)
+            .max(Integer::ZERO)
+            .to_u64()
+            .unwrap(),
+    )
+    .complete();
+    let rough = !number.is_divisible(&ten_exp);
+    let truncated_number: Integer = &number / ten_exp;
     let mut truncated_number = truncated_number.to_string();
     if truncated_number.len() > consts.number_decimals_scientific {
         round(&mut truncated_number);
@@ -609,7 +616,11 @@ fn truncate(number: &Integer, consts: &Consts) -> (String, bool) {
         truncated_number.insert(0, '-');
     }
     if length > consts.number_decimals_scientific + 1 {
-        (format!("{truncated_number} × 10^{length}"), true)
+        if truncated_number == "1" {
+            (format!("10^{length}"), rough)
+        } else {
+            (format!("{truncated_number} × 10^{length}"), rough)
+        }
     } else {
         (orig_number.to_string(), false)
     }
@@ -806,23 +817,39 @@ mod tests {
                 &consts
             )
             .0,
-            "1 × 10^300"
+            "10^300"
+        );
+        assert_eq!(
+            truncate(
+                &Integer::from_str(&format!("1{}", "0".repeat(300))).unwrap(),
+                &consts
+            )
+            .1,
+            false
+        );
+        assert_eq!(
+            truncate(
+                &Integer::from_str(&format!("2{}", "0".repeat(300))).unwrap(),
+                &consts
+            )
+            .0,
+            "2 × 10^300"
         );
         assert_eq!(
             truncate(
-                &-Integer::from_str(&format!("1{}", "0".repeat(300))).unwrap(),
+                &-Integer::from_str(&format!("2{}", "0".repeat(300))).unwrap(),
                 &consts
             )
             .0,
-            "-1 × 10^300"
+            "-2 × 10^300"
         );
         assert_eq!(
             truncate(
-                &Integer::from_str(&format!("1{}", "0".repeat(2000000))).unwrap(),
+                &Integer::from_str(&format!("2{}", "0".repeat(2000000))).unwrap(),
                 &consts
             )
             .0,
-            "1 × 10^2000000"
+            "2 × 10^2000000"
         );
     }
 

factorion-lib/src/calculation_results.rs

@@ -132,9 +132,9 @@ impl CalculationJob {
         let prec = consts.float_precision;
         let calc_num = match num {
             CalculationResult::Approximate(base, exponent) => {
-                let res = base.as_float() * Float::with_val(prec, 10).pow(&exponent);
-                if Float::is_finite(&(res.clone() * math::APPROX_FACT_SAFE_UPPER_BOUND_FACTOR)) {
-                    res.to_integer().unwrap()
+                if exponent <= consts.integer_construction_limit {
+                    let x: Float = base.as_float() * Float::with_val(prec, 10).pow(&exponent);
+                    x.to_integer().unwrap()
                 } else {
                     return Some(if base.as_float() < &0.0 {
                         CalculationResult::ComplexInfinity
@@ -143,7 +143,11 @@ impl CalculationJob {
                             (Float::from(base), exponent),
                             -level as u32,
                         );
-                        CalculationResult::Approximate(termial.0.into(), termial.1)
+                        if termial.0 == 1 {
+                            CalculationResult::ApproximateDigits(false, termial.1)
+                        } else {
+                            CalculationResult::Approximate(termial.0.into(), termial.1)
+                        }
                     } else {
                         let mut exponent = exponent;
                         exponent.add_from(math::length(&exponent, prec));
@@ -152,17 +156,32 @@ impl CalculationJob {
                 }
             }
             CalculationResult::ApproximateDigits(was_neg, digits) => {
-                return Some(if digits.is_negative() {
-                    CalculationResult::Float(Float::new(prec).into())
-                } else if was_neg {
-                    CalculationResult::ComplexInfinity
-                } else if level < 0 {
-                    CalculationResult::ApproximateDigits(false, (digits - 1) * 2 + 1)
+                if digits <= consts.integer_construction_limit {
+                    let x: Float = Float::with_val(prec, 10).pow(digits.clone() - 1);
+                    x.to_integer().unwrap()
                 } else {
-                    let mut digits = digits;
-                    digits.add_from(math::length(&digits, prec));
-                    CalculationResult::ApproximateDigitsTower(false, false, 1.into(), digits)
-                });
+                    return Some(if digits.is_negative() {
+                        CalculationResult::Float(Float::new(prec).into())
+                    } else if was_neg {
+                        CalculationResult::ComplexInfinity
+                    } else if level < 0 {
+                        let mut one = Float::with_val(consts.float_precision, 1);
+                        if was_neg {
+                            one *= -1;
+                        }
+                        let termial =
+                            math::approximate_approx_termial((one, digits), -level as u32);
+                        if termial.0 == 1 {
+                            CalculationResult::ApproximateDigits(false, termial.1)
+                        } else {
+                            CalculationResult::Approximate(termial.0.into(), termial.1)
+                        }
+                    } else {
+                        let mut digits = digits;
+                        digits.add_from(math::length(&digits, prec));
+                        CalculationResult::ApproximateDigitsTower(false, false, 1.into(), digits)
+                    });
+                }
             }
             CalculationResult::ApproximateDigitsTower(was_neg, neg, depth, exponent) => {
                 return Some(if neg {

factorion-lib/src/calculation_tasks.rs

@@ -12,7 +12,7 @@ use crate::{
 pub mod recommended {
     use factorion_math::rug::Integer;
 
-    pub static INTEGER_CONSTRUCTION_LIMIT: fn() -> Integer = || 10_000_000u128.into();
+    pub static INTEGER_CONSTRUCTION_LIMIT: fn() -> Integer = || 200_000_000u128.into();
 }
 
 const POI_STARTS: &[char] = &[
@@ -579,12 +579,19 @@ fn parse_num(
             *text = &text[3..];
             let part = part.replace(SEPARATORS, "");
             let n = part.parse::<Integer>().ok()?;
-            return Some(Number::ApproximateDigitsTower(
-                false,
-                false,
-                n - 1,
-                1.into(),
-            ));
+            match n.to_usize() {
+                Some(0) => return Some(1.into()),
+                Some(1) => return Some(10.into()),
+                Some(2) => return Some(Number::Exact(10_000_000_000u64.into())),
+                _ => {
+                    return Some(Number::ApproximateDigitsTower(
+                        false,
+                        false,
+                        n - 1,
+                        1.into(),
+                    ));
+                }
+            }
         } else {
             // Skip ^ only (because ret None)
             *text = orig_text;
@@ -666,6 +673,11 @@ fn parse_num(
         }
 
         if depth == 1 {
+            if top < consts.integer_construction_limit {
+                return Some(Number::Exact(
+                    Integer::u64_pow_u64(10, top.to_u64().unwrap()).complete(),
+                ));
+            }
             return Some(Number::ApproximateDigits(false, top));
         } else {
             return Some(Number::ApproximateDigitsTower(
@@ -1846,6 +1858,17 @@ mod test {
                 5.into()
             ))
         );
+        let num = parse_num(
+            &mut "10^50000000000",
+            false,
+            false,
+            &consts,
+            &NumFormat::V1(&locale::v1::NumFormat { decimal: '.' }),
+        );
+        assert_eq!(
+            num,
+            Some(Number::ApproximateDigits(false, 50000000000u64.into()))
+        );
         let num = parse_num(
             &mut "10^5!",
             false,
@@ -1861,7 +1884,7 @@ mod test {
             &consts,
             &NumFormat::V1(&locale::v1::NumFormat { decimal: '.' }),
         );
-        assert_eq!(num, Some(Number::ApproximateDigits(false, 5.into())));
+        assert_eq!(num, Some(Number::Exact(100000.into())));
         let num = parse_num(
             &mut "10^5",
             false,