From 7e8ee5ed9cad6484e9f13f81731b102ced58402e Mon Sep 17 00:00:00 2001
From: Adam Carpenter <gitlab@53hor.net>
Date: Tue, 9 Jul 2019 15:14:04 -0400
Subject: Init.

---
 meap/meap-code/ch5/ch5-q/src/lib.rs | 76 +++++++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)
 create mode 100755 meap/meap-code/ch5/ch5-q/src/lib.rs

(limited to 'meap/meap-code/ch5/ch5-q/src/lib.rs')

diff --git a/meap/meap-code/ch5/ch5-q/src/lib.rs b/meap/meap-code/ch5/ch5-q/src/lib.rs
new file mode 100755
index 0000000..d05ca3a
--- /dev/null
+++ b/meap/meap-code/ch5/ch5-q/src/lib.rs
@@ -0,0 +1,76 @@
+/// Q1_7 - single byte representation of a fixed point number with range [-1, 1]. 
+/// The name refers to the Texas Instrument representation
+/// 
+/// References:
+///  - English Wikipedia: "Q (number format)" https://en.wikipedia.org/wiki/Q_(number_format)
+#[derive(Debug,Clone,Copy,PartialEq,Eq)]
+pub struct Q7(i8); // tuple struct holding a i8 value
+
+impl From<f64> for Q7 {
+    fn from (n: f64) -> Self {
+        if n >= 1.0 { // out of bounds numbers are coerced to the maximum of the range
+            Q7(127)
+        } else if n <= -1.0 {
+            Q7(-128)
+        } else {
+            Q7((n * 128.0) as i8) // 128 == (2 ** 7) ==  pow(2,7)
+        }
+    }
+}
+
+impl From<Q7> for f64 {
+    fn from(n: Q7) -> f64 {
+        (n.0 as f64) * 2f64.powf(-7.0) // 0.0078125// (2 ** -7) // pow(2, -7)
+    }
+}
+
+impl From<f32> for Q7 {
+    fn from (n: f32) -> Self {
+        Q7::from(n as f64) // conversion from f32 to f64 works perfectly
+    }
+}
+
+impl From<Q7> for f32 {
+    fn from(n: Q7) -> f32 {
+        f64::from(n) as f32 // conversion from f64 to f32 can result in undefined behavior, 
+                            // but not here as f32 can represent all values representable by Q7
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn out_of_bounds() {
+        assert_eq!(Q7::from(10.), Q7::from(1.));
+        assert_eq!(Q7::from(-10.), Q7::from(-1.));
+    }
+
+    #[test]
+    fn f32_to_q7() {
+        let n1: f32 = 0.7;
+        let q1 = Q7::from(n1);
+
+        let n2 = -0.4;
+        let q2 = Q7::from(n2);
+
+        let n3 = 123.0;
+        let q3 = Q7::from(n3);
+
+        assert_eq!(q1, Q7(89));
+        assert_eq!(q2, Q7(-51));
+        assert_eq!(q3, Q7(127));
+    }
+
+    #[test]
+    fn q7_to_f32() {
+        let q1 = Q7::from(0.7);
+        let n1 = f32::from(q1);
+        assert_eq!(n1, 0.6953125);
+
+        let q2 = Q7::from(n1);   // numbers that can be represented exactly by Q7
+        let n2 = f32::from(q2);  // can survive the transition between Q7 and f32
+        assert_eq!(n1, n2);
+    }
+}
-- 
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