[transcendental] sqrt: change error type from () to &'static str. (#7)

* Closes #6: Resolve this by printing an error if an overflow occurs in `sqrt`due to small numbers.
* Add test that shows the approximate lower bound of working values for I32F32
* version bump: v0.5.5

Cargo.toml

@@ -7,7 +7,7 @@
 
 [package]
 name = "substrate-fixed"
-version = "0.5.4"
+version = "0.5.5"
 authors = ["Trevor Spiteri <tspiteri@ieee.org>"]
 description = "Fixed-point numbers"
 documentation = "https://docs.rs/fixed"

src/transcendental.rs

@@ -17,7 +17,7 @@ This module contains transcendental functions.
 */
 use crate::consts;
 use crate::traits::{Fixed, FixedSigned, LossyFrom, ToFixed};
-use crate::types::{I9F23, I9F55, U0F128, U64F64};
+use crate::types::{I9F23, I9F55, U0F128};
 use core::ops::{AddAssign, BitOrAssign, ShlAssign};
 
 type ConstType = I9F23;
@@ -129,14 +129,14 @@ where
 }
 
 /// square root
-pub fn sqrt<S, D>(operand: S) -> Result<D, ()>
+pub fn sqrt<S, D>(operand: S) -> Result<D, &'static str>
 where
     S: Fixed + PartialOrd<ConstType>,
     D: Fixed + PartialOrd<ConstType> + From<S>,
 {
     let mut invert = false;
     if operand < ZERO {
-        return Err(());
+        return Err("Can't calculate sqrt from negative numbers.");
     };
 
     let mut operand = D::from(operand);
@@ -148,7 +148,7 @@ where
         operand = if let Some(r) = D::from_num(1).checked_div(operand) {
             r
         } else {
-            return Err(());
+            return Err("Overflow inverting operand.");
         };
     }
     // Newton iterations
@@ -160,7 +160,7 @@ where
         l = if let Some(r) = D::from_num(1).checked_div(l) {
             r
         } else {
-            return Err(());
+            return Err("Overflow un-inverting operand.");
         };
     }
     Ok(l)
@@ -448,7 +448,7 @@ pub fn asin<T>(angle: T) -> T {
 mod tests {
     use super::*;
     use crate::traits::LossyInto;
-    use crate::types::{I32F32, I64F64};
+    use crate::types::{I32F32, I64F64, U64F64};
 
     #[test]
     fn sqrt_works() {
@@ -475,6 +475,21 @@ mod tests {
         }
     }
 
+    #[test]
+    fn sqrt_check_lower_bound_of_working_values() {
+        // Todo: This could be done for other types too.
+        type S = I32F32;
+        type D = I32F32;
+
+        // this works
+        let result: f64 = sqrt::<S, D>(S::from_num(5.8208e-10)).unwrap().lossy_into();
+        assert_relative_eq!(result, 0.0000261, epsilon = 1.0e-6);
+
+        // slightly below lower bound that produces an overflow
+        let res = sqrt::<S, D>(S::from_num(5.8205e-10));
+        assert_eq!(res.unwrap_err(), "Overflow inverting operand.")
+    }
+
     #[test]
     fn rs_works() {
         let result: f64 = rs(I9F23::from_num(0)).lossy_into();