From 4548408393c31d016370e2f0acd1e220ab74bc59 Mon Sep 17 00:00:00 2001
From: Markus Mayer <widemeadows@gmail.com>
Date: Thu, 25 Jul 2024 22:11:19 +0200
Subject: [PATCH] Add approximation for hyperbolic cosine (cosh) (#113)

---
 src/float.rs      |  1 +
 src/float/cosh.rs | 95 +++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 96 insertions(+)
 create mode 100644 src/float/cosh.rs

diff --git a/src/float.rs b/src/float.rs
index 34377a3..706df65 100644
--- a/src/float.rs
+++ b/src/float.rs
@@ -8,6 +8,7 @@ pub(crate) mod atan2;
 pub(crate) mod ceil;
 pub(crate) mod copysign;
 pub(crate) mod cos;
+pub(crate) mod cosh;
 pub(crate) mod div_euclid;
 pub(crate) mod exp;
 pub(crate) mod floor;
diff --git a/src/float/cosh.rs b/src/float/cosh.rs
new file mode 100644
index 0000000..4bcf7bc
--- /dev/null
+++ b/src/float/cosh.rs
@@ -0,0 +1,95 @@
+//! Hyperbolic cosine function
+
+use super::F32;
+
+impl F32 {
+    /// Approximates `cosh(x)` with a maximum error of `0.003` in the range 0...π,
+    /// and a maximum error of `0.1` in the range `π...τ`.
+    ///
+    /// ## Arguments
+    /// * `self` - The angle in radians.
+    pub fn cosh(self) -> Self {
+        let exp_x = self.exp();
+        let exp_neg_x = (-self).exp();
+        (exp_x + exp_neg_x) / 2.0
+    }
+}
+
+#[cfg(test)]
+pub(crate) mod tests {
+    use super::F32;
+
+    /// Maximum error in radians
+    pub(crate) const MAX_ERROR_1: f32 = 0.001;
+    pub(crate) const MAX_ERROR_2: f32 = 0.002;
+    pub(crate) const MAX_ERROR_3: f32 = 0.003;
+    pub(crate) const MAX_ERROR_4: f32 = 0.005;
+    pub(crate) const MAX_ERROR_5: f32 = 0.02;
+    pub(crate) const MAX_ERROR: f32 = 0.092;
+
+    /// Cosine test vectors - `(input, output)`
+    const TEST_VECTORS: &[(f32, f32, f32)] = &[
+        (0.000, 1.000, MAX_ERROR_1),
+        (0.140, 1.010, MAX_ERROR_1),
+        (0.279, 1.039, MAX_ERROR_1),
+        (0.419, 1.089, MAX_ERROR_1),
+        (0.559, 1.160, MAX_ERROR_1),
+        (0.698, 1.254, MAX_ERROR_1),
+        (0.838, 1.372, MAX_ERROR_1),
+        (0.977, 1.516, MAX_ERROR_1),
+        (1.117, 1.691, MAX_ERROR_1),
+        (1.257, 1.900, MAX_ERROR_1),
+        (1.396, 2.143, MAX_ERROR_1),
+        (1.536, 2.431, MAX_ERROR_1),
+        (1.676, 2.766, MAX_ERROR_1),
+        (1.815, 3.152, MAX_ERROR_1),
+        (1.955, 3.603, MAX_ERROR_2),
+        (2.094, 4.120, MAX_ERROR_2),
+        (2.234, 4.722, MAX_ERROR_2),
+        (2.374, 5.417, MAX_ERROR_2),
+        (2.513, 6.211, MAX_ERROR_2),
+        (2.653, 7.134, MAX_ERROR_3),
+        (2.793, 8.196, MAX_ERROR_3),
+        (2.932, 9.409, MAX_ERROR_3),
+        (3.072, 10.816, MAX_ERROR_3),
+        (3.211, 12.422, MAX_ERROR_3),
+        (3.351, 14.283, MAX_ERROR_4),
+        (3.491, 16.425, MAX_ERROR_4),
+        (3.630, 18.870, MAX_ERROR_4),
+        (3.770, 21.702, MAX_ERROR_4),
+        (3.910, 24.959, MAX_ERROR_4),
+        (4.049, 28.679, MAX_ERROR_5),
+        (4.189, 32.986, MAX_ERROR_5),
+        (4.328, 37.903, MAX_ERROR_5),
+        (4.468, 43.597, MAX_ERROR_5),
+        (4.608, 50.147, MAX_ERROR_5),
+        (4.747, 57.623, MAX_ERROR),
+        (4.887, 66.281, MAX_ERROR),
+        (5.027, 76.241, MAX_ERROR),
+        (5.166, 87.609, MAX_ERROR),
+        (5.306, 100.774, MAX_ERROR),
+        (5.445, 115.801, MAX_ERROR),
+        (5.585, 133.202, MAX_ERROR),
+        (5.725, 153.218, MAX_ERROR),
+        (5.864, 176.066, MAX_ERROR),
+        (6.004, 202.524, MAX_ERROR),
+        (6.144, 232.958, MAX_ERROR),
+        (6.283, 267.697, MAX_ERROR),
+    ];
+
+    #[test]
+    fn sanity_check() {
+        for &(x, expected, max_error) in TEST_VECTORS {
+            let cosh_x = F32(x).cosh();
+            let delta = (cosh_x - expected).abs();
+
+            assert!(
+                delta <= max_error,
+                "delta {} too large: {} vs {}",
+                delta,
+                cosh_x,
+                expected
+            );
+        }
+    }
+}