A lot of progress.

src/utils.rs

@@ -0,0 +1,113 @@
+use std::f64::consts::PI;
+
+const CS: [f64; 14] = [
+    0.00048204,
+    -0.00142906,
+    0.0013200243174,
+    0.0009461589032,
+    -0.0045563339802,
+    0.00556964649138,
+    0.00125993961762116,
+    -0.01621575378835404,
+    0.02629651521057465,
+    -0.001829764677455021,
+    2.0 * (1.0 - PI / 3.0),
+    (4.0 - PI) / 3.0,
+    1.0,
+    1.0,
+];
+
+const RS: [f64; 5] = [
+    1.2753666447299659525,
+    5.019049726784267463450,
+    6.1602098531096305441,
+    7.409740605964741794425,
+    2.9788656263939928886,
+];
+
+const QS: [f64; 6] = [
+    2.260528520767326969592,
+    9.3960340162350541504,
+    12.048951927855129036034,
+    17.081440747466004316,
+    9.608965327192787870698,
+    3.3690752069827527677,
+];
+
+/// Normal cumulative density function.
+fn normcdf(x: f64) -> f64 {
+    // If X ~ N(0,1), returns P(X < x).
+    // erfc(-x / SQRT2) / 2.0
+
+    todo!();
+}
+
+/// Compute the log of the normal cumulative density function.
+pub fn logphi(z: f64) -> (f64, f64) {
+    // Adapted from the GPML function `logphi.m`.
+    let SQRT2: f64 = 2.0f64.sqrt();
+    let SQRT2PI: f64 = (2.0 * PI).sqrt();
+
+    if z * z < 0.0492 {
+        // First case: z close to zero.
+        let coef = -z / SQRT2PI;
+        let mut val = 0.0;
+
+        for c in &CS {
+            val = coef * (c + val);
+        }
+
+        let res = -2.0 * val - 2.0f64.ln();
+        let dres = (-(z * z) / 2.0 - res).exp() / SQRT2PI;
+
+        (res, dres)
+    } else if z < -11.3137 {
+        // Second case: z very small.
+        let mut num = 0.5641895835477550741;
+
+        for r in &RS {
+            num = -z * num / SQRT2 + r;
+        }
+
+        let mut den = 1.0;
+
+        for q in &QS {
+            den = -z * den / SQRT2 + q;
+        }
+
+        let res = (num / (2.0 * den)).ln() - (z * z) / 2.0;
+        let dres = (den / num).abs() * (2.0 / PI).sqrt();
+
+        (res, dres)
+    } else {
+        let res = normcdf(z).ln();
+        let dres = (-(z * z) / 2.0 - res).exp() / SQRT2PI;
+
+        (res, dres)
+    }
+
+    /*
+    if z * z < 0.0492:
+        # First case: z close to zero.
+        coef = -z / SQRT2PI
+        val = 0
+        for c in CS:
+            val = coef * (c + val)
+        res = -2 * val - log(2)
+        dres = exp(-(z * z) / 2 - res) / SQRT2PI
+    elif z < -11.3137:
+        # Second case: z very small.
+        num = 0.5641895835477550741
+        for r in RS:
+            num = -z * num / SQRT2 + r
+        den = 1.0
+        for q in QS:
+            den = -z * den / SQRT2 + q
+        res = log(num / (2 * den)) - (z * z) / 2
+        dres = abs(den / num) * sqrt(2.0 / pi)
+    else:
+        res = log(normcdf(z))
+        dres = exp(-(z * z) / 2 - res) / SQRT2PI
+    return res, dres
+    */
+}