1 files changed, 209 insertions, 0 deletions
diff --git a/library/compiler-builtins/libm/src/math/tgamma.rs b/library/compiler-builtins/libm/src/math/tgamma.rs
new file mode 100644
index 00000000000..3059860646a
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+++ b/library/compiler-builtins/libm/src/math/tgamma.rs
@@ -0,0 +1,209 @@
+/*
+"A Precision Approximation of the Gamma Function" - Cornelius Lanczos (1964)
+"Lanczos Implementation of the Gamma Function" - Paul Godfrey (2001)
+"An Analysis of the Lanczos Gamma Approximation" - Glendon Ralph Pugh (2004)
+
+approximation method:
+
+                        (x - 0.5)         S(x)
+Gamma(x) = (x + g - 0.5)         *  ----------------
+                                    exp(x + g - 0.5)
+
+with
+                 a1      a2      a3            aN
+S(x) ~= [ a0 + ----- + ----- + ----- + ... + ----- ]
+               x + 1   x + 2   x + 3         x + N
+
+with a0, a1, a2, a3,.. aN constants which depend on g.
+
+for x < 0 the following reflection formula is used:
+
+Gamma(x)*Gamma(-x) = -pi/(x sin(pi x))
+
+most ideas and constants are from boost and python
+*/
+use super::{exp, floor, k_cos, k_sin, pow};
+
+const PI: f64 = 3.141592653589793238462643383279502884;
+
+/* sin(pi x) with x > 0x1p-100, if sin(pi*x)==0 the sign is arbitrary */
+fn sinpi(mut x: f64) -> f64 {
+    let mut n: isize;
+
+    /* argument reduction: x = |x| mod 2 */
+    /* spurious inexact when x is odd int */
+    x = x * 0.5;
+    x = 2.0 * (x - floor(x));
+
+    /* reduce x into [-.25,.25] */
+    n = (4.0 * x) as isize;
+    n = div!(n + 1, 2);
+    x -= (n as f64) * 0.5;
+
+    x *= PI;
+    match n {
+        1 => k_cos(x, 0.0),
+        2 => k_sin(-x, 0.0, 0),
+        3 => -k_cos(x, 0.0),
+        // 0
+        _ => k_sin(x, 0.0, 0),
+    }
+}
+
+const N: usize = 12;
+//static const double g = 6.024680040776729583740234375;
+const GMHALF: f64 = 5.524680040776729583740234375;
+const SNUM: [f64; N + 1] = [
+    23531376880.410759688572007674451636754734846804940,
+    42919803642.649098768957899047001988850926355848959,
+    35711959237.355668049440185451547166705960488635843,
+    17921034426.037209699919755754458931112671403265390,
+    6039542586.3520280050642916443072979210699388420708,
+    1439720407.3117216736632230727949123939715485786772,
+    248874557.86205415651146038641322942321632125127801,
+    31426415.585400194380614231628318205362874684987640,
+    2876370.6289353724412254090516208496135991145378768,
+    186056.26539522349504029498971604569928220784236328,
+    8071.6720023658162106380029022722506138218516325024,
+    210.82427775157934587250973392071336271166969580291,
+    2.5066282746310002701649081771338373386264310793408,
+];
+const SDEN: [f64; N + 1] = [
+    0.0,
+    39916800.0,
+    120543840.0,
+    150917976.0,
+    105258076.0,
+    45995730.0,
+    13339535.0,
+    2637558.0,
+    357423.0,
+    32670.0,
+    1925.0,
+    66.0,
+    1.0,
+];
+/* n! for small integer n */
+const FACT: [f64; 23] = [
+    1.0,
+    1.0,
+    2.0,
+    6.0,
+    24.0,
+    120.0,
+    720.0,
+    5040.0,
+    40320.0,
+    362880.0,
+    3628800.0,
+    39916800.0,
+    479001600.0,
+    6227020800.0,
+    87178291200.0,
+    1307674368000.0,
+    20922789888000.0,
+    355687428096000.0,
+    6402373705728000.0,
+    121645100408832000.0,
+    2432902008176640000.0,
+    51090942171709440000.0,
+    1124000727777607680000.0,
+];
+
+/* S(x) rational function for positive x */
+fn s(x: f64) -> f64 {
+    let mut num: f64 = 0.0;
+    let mut den: f64 = 0.0;
+
+    /* to avoid overflow handle large x differently */
+    if x < 8.0 {
+        for i in (0..=N).rev() {
+            num = num * x + i!(SNUM, i);
+            den = den * x + i!(SDEN, i);
+        }
+    } else {
+        for i in 0..=N {
+            num = num / x + i!(SNUM, i);
+            den = den / x + i!(SDEN, i);
+        }
+    }
+    return num / den;
+}
+
+/// The [Gamma function](https://en.wikipedia.org/wiki/Gamma_function) (f64).
+#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
+pub fn tgamma(mut x: f64) -> f64 {
+    let u: u64 = x.to_bits();
+    let absx: f64;
+    let mut y: f64;
+    let mut dy: f64;
+    let mut z: f64;
+    let mut r: f64;
+    let ix: u32 = ((u >> 32) as u32) & 0x7fffffff;
+    let sign: bool = (u >> 63) != 0;
+
+    /* special cases */
+    if ix >= 0x7ff00000 {
+        /* tgamma(nan)=nan, tgamma(inf)=inf, tgamma(-inf)=nan with invalid */
+        return x + f64::INFINITY;
+    }
+    if ix < ((0x3ff - 54) << 20) {
+        /* |x| < 2^-54: tgamma(x) ~ 1/x, +-0 raises div-by-zero */
+        return 1.0 / x;
+    }
+
+    /* integer arguments */
+    /* raise inexact when non-integer */
+    if x == floor(x) {
+        if sign {
+            return 0.0 / 0.0;
+        }
+        if x <= FACT.len() as f64 {
+            return i!(FACT, (x as usize) - 1);
+        }
+    }
+
+    /* x >= 172: tgamma(x)=inf with overflow */
+    /* x =< -184: tgamma(x)=+-0 with underflow */
+    if ix >= 0x40670000 {
+        /* |x| >= 184 */
+        if sign {
+            let x1p_126 = f64::from_bits(0x3810000000000000); // 0x1p-126 == 2^-126
+            force_eval!((x1p_126 / x) as f32);
+            if floor(x) * 0.5 == floor(x * 0.5) {
+                return 0.0;
+            } else {
+                return -0.0;
+            }
+        }
+        let x1p1023 = f64::from_bits(0x7fe0000000000000); // 0x1p1023 == 2^1023
+        x *= x1p1023;
+        return x;
+    }
+
+    absx = if sign { -x } else { x };
+
+    /* handle the error of x + g - 0.5 */
+    y = absx + GMHALF;
+    if absx > GMHALF {
+        dy = y - absx;
+        dy -= GMHALF;
+    } else {
+        dy = y - GMHALF;
+        dy -= absx;
+    }
+
+    z = absx - 0.5;
+    r = s(absx) * exp(-y);
+    if x < 0.0 {
+        /* reflection formula for negative x */
+        /* sinpi(absx) is not 0, integers are already handled */
+        r = -PI / (sinpi(absx) * absx * r);
+        dy = -dy;
+        z = -z;
+    }
+    r += dy * (GMHALF + 0.5) * r / y;
+    z = pow(y, 0.5 * z);
+    y = r * z * z;
+    return y;
+}