From ebe3f8597672f873c144e67810797015c0017a9f Mon Sep 17 00:00:00 2001
From: Vinzent Steinberg <Vinzent.Steinberg@gmail.com>
Date: Fri, 17 Mar 2017 17:25:26 +0100
Subject: [PATCH 1/3] Implement multinomial

---
 integer/src/lib.rs | 91 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 91 insertions(+)

diff --git a/integer/src/lib.rs b/integer/src/lib.rs
index b84b7af..6230c84 100644
--- a/integer/src/lib.rs
+++ b/integer/src/lib.rs
@@ -16,6 +16,8 @@
 
 extern crate num_traits as traits;
 
+use std::ops::Add;
+
 use traits::{Num, Signed};
 
 pub trait Integer: Sized + Num + PartialOrd + Ord + Eq {
@@ -694,6 +696,22 @@ pub fn binomial<T: Integer + Clone>(mut n: T, k: T) -> T {
     r
 }
 
+/// Calculate the multinomial coefficient.
+///
+/// Panics if no integers are specified.
+pub fn multinomial<T: Integer + Clone>(k: &[T]) -> T
+    where for<'a> T: Add<&'a T, Output = T>
+{
+    assert!(k.len() > 0, "need at least one integer");
+    let mut r = T::one();
+    let mut p = T::zero();
+    for i in k {
+        p = p + i;
+        r = r * binomial(p.clone(), i.clone());
+    }
+    r
+}
+
 #[test]
 fn test_lcm_overflow() {
     macro_rules! check {
@@ -777,3 +795,76 @@ fn test_binomial() {
     check!(i64, 0, 0, 1);
     check!(i64, 2, 3, 0);
 }
+
+#[test]
+fn test_multinomial() {
+    macro_rules! check_binomial {
+        ($t:ty, $k:expr) => { {
+            let n: $t = $k.iter().sum();
+            let k: &[$t] = $k;
+            assert_eq!(k.len(), 2);
+            assert_eq!(multinomial(k), binomial(n, k[0]));
+        } }
+    }
+
+    check_binomial!(u8, &[4, 5]);
+
+    check_binomial!(i8, &[4, 5]);
+
+    check_binomial!(u16, &[2, 98]);
+    check_binomial!(u16, &[4, 10]);
+
+    check_binomial!(i16, &[2, 98]);
+    check_binomial!(i16, &[4, 10]);
+
+    check_binomial!(u32, &[2, 98]);
+    check_binomial!(u32, &[11, 24]);
+    check_binomial!(u32, &[4, 10]);
+
+    check_binomial!(i32, &[2, 98]);
+    check_binomial!(i32, &[11, 24]);
+    check_binomial!(i32, &[4, 10]);
+
+    check_binomial!(u64, &[2, 98]);
+    check_binomial!(u64, &[11, 24]);
+    check_binomial!(u64, &[4, 10]);
+
+    check_binomial!(i64, &[2, 98]);
+    check_binomial!(i64, &[11, 24]);
+    check_binomial!(i64, &[4, 10]);
+
+    macro_rules! check_multinomial {
+        ($t:ty, $k:expr, $r:expr) => { {
+            let k: &[$t] = $k;
+            let expected: $t = $r;
+            assert_eq!(multinomial(k), expected);
+        } }
+    }
+
+    check_multinomial!(u8, &[2, 1, 2], 30);
+    check_multinomial!(u8, &[2, 3, 0], 10);
+
+    check_multinomial!(i8, &[2, 1, 2], 30);
+    check_multinomial!(i8, &[2, 3, 0], 10);
+
+    check_multinomial!(u16, &[2, 1, 2], 30);
+    check_multinomial!(u16, &[2, 3, 0], 10);
+
+    check_multinomial!(i16, &[2, 1, 2], 30);
+    check_multinomial!(i16, &[2, 3, 0], 10);
+
+    check_multinomial!(u32, &[2, 1, 2], 30);
+    check_multinomial!(u32, &[2, 3, 0], 10);
+
+    check_multinomial!(i32, &[2, 1, 2], 30);
+    check_multinomial!(i32, &[2, 3, 0], 10);
+
+    check_multinomial!(u64, &[2, 1, 2], 30);
+    check_multinomial!(u64, &[2, 3, 0], 10);
+
+    check_multinomial!(i64, &[2, 1, 2], 30);
+    check_multinomial!(i64, &[2, 3, 0], 10);
+
+    check_multinomial!(u64, &[0], 1);
+    check_multinomial!(u64, &[12345], 1);
+}

From c408bd66052fafb55500a77a640ff39c034b2083 Mon Sep 17 00:00:00 2001
From: Vinzent Steinberg <Vinzent.Steinberg@gmail.com>
Date: Fri, 17 Mar 2017 18:21:06 +0100
Subject: [PATCH 2/3] Try to fix build on Rust 1.8

---
 integer/src/lib.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/integer/src/lib.rs b/integer/src/lib.rs
index 6230c84..dedbd94 100644
--- a/integer/src/lib.rs
+++ b/integer/src/lib.rs
@@ -800,7 +800,7 @@ fn test_binomial() {
 fn test_multinomial() {
     macro_rules! check_binomial {
         ($t:ty, $k:expr) => { {
-            let n: $t = $k.iter().sum();
+            let n: $t = $k.iter().fold(0, |acc, &x| acc + x);
             let k: &[$t] = $k;
             assert_eq!(k.len(), 2);
             assert_eq!(multinomial(k), binomial(n, k[0]));

From 3de345f91298def0e2499019cf3160caacb5fe72 Mon Sep 17 00:00:00 2001
From: Vinzent Steinberg <Vinzent.Steinberg@gmail.com>
Date: Mon, 20 Mar 2017 09:43:01 +0100
Subject: [PATCH 3/3] Don't panic when calculating multinomial

---
 integer/src/lib.rs | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/integer/src/lib.rs b/integer/src/lib.rs
index dedbd94..0273641 100644
--- a/integer/src/lib.rs
+++ b/integer/src/lib.rs
@@ -697,12 +697,9 @@ pub fn binomial<T: Integer + Clone>(mut n: T, k: T) -> T {
 }
 
 /// Calculate the multinomial coefficient.
-///
-/// Panics if no integers are specified.
 pub fn multinomial<T: Integer + Clone>(k: &[T]) -> T
     where for<'a> T: Add<&'a T, Output = T>
 {
-    assert!(k.len() > 0, "need at least one integer");
     let mut r = T::one();
     let mut p = T::zero();
     for i in k {
@@ -865,6 +862,7 @@ fn test_multinomial() {
     check_multinomial!(i64, &[2, 1, 2], 30);
     check_multinomial!(i64, &[2, 3, 0], 10);
 
+    check_multinomial!(u64, &[], 1);
     check_multinomial!(u64, &[0], 1);
     check_multinomial!(u64, &[12345], 1);
 }