diff --git a/rand_distr/src/poisson.rs b/rand_distr/src/poisson.rs
index 96bc8b9b6b4..4f4a0b7a3d9 100644
--- a/rand_distr/src/poisson.rs
+++ b/rand_distr/src/poisson.rs
@@ -10,8 +10,8 @@
 //! The Poisson distribution.
 
 use rand::Rng;
-use crate::{Distribution, Cauchy};
-use crate::utils::log_gamma;
+use crate::{Distribution, Cauchy, Standard};
+use crate::utils::Float;
 
 /// The Poisson distribution `Poisson(lambda)`.
 ///
@@ -24,17 +24,17 @@ use crate::utils::log_gamma;
 /// use rand_distr::{Poisson, Distribution};
 ///
 /// let poi = Poisson::new(2.0).unwrap();
-/// let v = poi.sample(&mut rand::thread_rng());
+/// let v: u64 = poi.sample(&mut rand::thread_rng());
 /// println!("{} is from a Poisson(2) distribution", v);
 /// ```
 #[derive(Clone, Copy, Debug)]
-pub struct Poisson {
-    lambda: f64,
+pub struct Poisson<N> {
+    lambda: N,
     // precalculated values
-    exp_lambda: f64,
-    log_lambda: f64,
-    sqrt_2lambda: f64,
-    magic_val: f64,
+    exp_lambda: N,
+    log_lambda: N,
+    sqrt_2lambda: N,
+    magic_val: N,
 }
 
 /// Error type returned from `Poisson::new`.
@@ -44,11 +44,13 @@ pub enum Error {
     ShapeTooSmall,
 }
 
-impl Poisson {
+impl<N: Float> Poisson<N>
+where Standard: Distribution<N>
+{
     /// Construct a new `Poisson` with the given shape parameter
     /// `lambda`.
-    pub fn new(lambda: f64) -> Result<Poisson, Error> {
-        if !(lambda > 0.0) {
+    pub fn new(lambda: N) -> Result<Poisson<N>, Error> {
+        if !(lambda > N::from(0.0)) {
             return Err(Error::ShapeTooSmall);
         }
         let log_lambda = lambda.ln();
@@ -56,36 +58,37 @@ impl Poisson {
             lambda,
             exp_lambda: (-lambda).exp(),
             log_lambda,
-            sqrt_2lambda: (2.0 * lambda).sqrt(),
-            magic_val: lambda * log_lambda - log_gamma(1.0 + lambda),
+            sqrt_2lambda: (N::from(2.0) * lambda).sqrt(),
+            magic_val: lambda * log_lambda - (N::from(1.0) + lambda).log_gamma(),
         })
     }
 }
 
-impl Distribution<u64> for Poisson {
-    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+impl<N: Float> Distribution<N> for Poisson<N>
+where Standard: Distribution<N>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> N {
         // using the algorithm from Numerical Recipes in C
 
         // for low expected values use the Knuth method
-        if self.lambda < 12.0 {
-            let mut result = 0;
-            let mut p = 1.0;
+        if self.lambda < N::from(12.0) {
+            let mut result = N::from(0.);
+            let mut p = N::from(1.0);
             while p > self.exp_lambda {
-                p *= rng.gen::<f64>();
-                result += 1;
+                p *= rng.gen::<N>();
+                result += N::from(1.);
             }
-            result - 1
+            result - N::from(1.)
         }
         // high expected values - rejection method
         else {
-            let mut int_result: u64;
-
             // we use the Cauchy distribution as the comparison distribution
             // f(x) ~ 1/(1+x^2)
-            let cauchy = Cauchy::new(0.0, 1.0).unwrap();
+            let cauchy = Cauchy::new(N::from(0.0), N::from(1.0)).unwrap();
+            let mut result;
 
             loop {
-                let mut result;
                 let mut comp_dev;
 
                 loop {
@@ -94,32 +97,41 @@ impl Distribution<u64> for Poisson {
                     // shift the peak of the comparison ditribution
                     result = self.sqrt_2lambda * comp_dev + self.lambda;
                     // repeat the drawing until we are in the range of possible values
-                    if result >= 0.0 {
+                    if result >= N::from(0.0) {
                         break;
                     }
                 }
                 // now the result is a random variable greater than 0 with Cauchy distribution
                 // the result should be an integer value
                 result = result.floor();
-                int_result = result as u64;
 
                 // this is the ratio of the Poisson distribution to the comparison distribution
                 // the magic value scales the distribution function to a range of approximately 0-1
                 // since it is not exact, we multiply the ratio by 0.9 to avoid ratios greater than 1
                 // this doesn't change the resulting distribution, only increases the rate of failed drawings
-                let check = 0.9 * (1.0 + comp_dev * comp_dev)
-                    * (result * self.log_lambda - log_gamma(1.0 + result) - self.magic_val).exp();
+                let check = N::from(0.9) * (N::from(1.0) + comp_dev * comp_dev)
+                    * (result * self.log_lambda - (N::from(1.0) + result).log_gamma() - self.magic_val).exp();
 
                 // check with uniform random value - if below the threshold, we are within the target distribution
-                if rng.gen::<f64>() <= check {
+                if rng.gen::<N>() <= check {
                     break;
                 }
             }
-            int_result
+            result
         }
     }
 }
 
+impl<N: Float> Distribution<u64> for Poisson<N>
+where Standard: Distribution<N>
+{
+    #[inline]
+    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> u64 {
+        let result: N = self.sample(rng);
+        result.to_u64().unwrap()
+    }
+}
+
 #[cfg(test)]
 mod test {
     use crate::Distribution;
@@ -129,13 +141,20 @@ mod test {
     fn test_poisson_10() {
         let poisson = Poisson::new(10.0).unwrap();
         let mut rng = crate::test::rng(123);
-        let mut sum = 0;
+        let mut sum_u64 = 0;
+        let mut sum_f64 = 0.;
         for _ in 0..1000 {
-            sum += poisson.sample(&mut rng);
+            let s_u64: u64 = poisson.sample(&mut rng);
+            let s_f64: f64 = poisson.sample(&mut rng);
+            sum_u64 += s_u64;
+            sum_f64 += s_f64;
+        }
+        let avg_u64 = (sum_u64 as f64) / 1000.0;
+        let avg_f64 = sum_f64 / 1000.0;
+        println!("Poisson averages: {} (u64)  {} (f64)", avg_u64, avg_f64);
+        for &avg in &[avg_u64, avg_f64] {
+            assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
         }
-        let avg = (sum as f64) / 1000.0;
-        println!("Poisson average: {}", avg);
-        assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
     }
 
     #[test]
@@ -143,13 +162,61 @@ mod test {
         // Take the 'high expected values' path
         let poisson = Poisson::new(15.0).unwrap();
         let mut rng = crate::test::rng(123);
-        let mut sum = 0;
+        let mut sum_u64 = 0;
+        let mut sum_f64 = 0.;
         for _ in 0..1000 {
-            sum += poisson.sample(&mut rng);
+            let s_u64: u64 = poisson.sample(&mut rng);
+            let s_f64: f64 = poisson.sample(&mut rng);
+            sum_u64 += s_u64;
+            sum_f64 += s_f64;
+        }
+        let avg_u64 = (sum_u64 as f64) / 1000.0;
+        let avg_f64 = sum_f64 / 1000.0;
+        println!("Poisson average: {} (u64)  {} (f64)", avg_u64, avg_f64);
+        for &avg in &[avg_u64, avg_f64] {
+            assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
+        }
+    }
+
+    #[test]
+    fn test_poisson_10_f32() {
+        let poisson = Poisson::new(10.0f32).unwrap();
+        let mut rng = crate::test::rng(123);
+        let mut sum_u64 = 0;
+        let mut sum_f32 = 0.;
+        for _ in 0..1000 {
+            let s_u64: u64 = poisson.sample(&mut rng);
+            let s_f32: f32 = poisson.sample(&mut rng);
+            sum_u64 += s_u64;
+            sum_f32 += s_f32;
+        }
+        let avg_u64 = (sum_u64 as f32) / 1000.0;
+        let avg_f32 = sum_f32 / 1000.0;
+        println!("Poisson averages: {} (u64)  {} (f32)", avg_u64, avg_f32);
+        for &avg in &[avg_u64, avg_f32] {
+            assert!((avg - 10.0).abs() < 0.5); // not 100% certain, but probable enough
+        }
+    }
+
+    #[test]
+    fn test_poisson_15_f32() {
+        // Take the 'high expected values' path
+        let poisson = Poisson::new(15.0f32).unwrap();
+        let mut rng = crate::test::rng(123);
+        let mut sum_u64 = 0;
+        let mut sum_f32 = 0.;
+        for _ in 0..1000 {
+            let s_u64: u64 = poisson.sample(&mut rng);
+            let s_f32: f32 = poisson.sample(&mut rng);
+            sum_u64 += s_u64;
+            sum_f32 += s_f32;
+        }
+        let avg_u64 = (sum_u64 as f32) / 1000.0;
+        let avg_f32 = sum_f32 / 1000.0;
+        println!("Poisson average: {} (u64)  {} (f32)", avg_u64, avg_f32);
+        for &avg in &[avg_u64, avg_f32] {
+            assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
         }
-        let avg = (sum as f64) / 1000.0;
-        println!("Poisson average: {}", avg);
-        assert!((avg - 15.0).abs() < 0.5); // not 100% certain, but probable enough
     }
 
     #[test]
diff --git a/rand_distr/src/utils.rs b/rand_distr/src/utils.rs
index e5f107f23e5..c275d0e5cba 100644
--- a/rand_distr/src/utils.rs
+++ b/rand_distr/src/utils.rs
@@ -33,9 +33,13 @@ pub trait Float: Copy + Sized + cmp::PartialOrd
     fn pi() -> Self;
     /// Support approximate representation of a f64 value
     fn from(x: f64) -> Self;
+    /// Support converting to an unsigned integer.
+    fn to_u64(self) -> Option<u64>;
     
     /// Take the absolute value of self
     fn abs(self) -> Self;
+    /// Take the largest integer less than or equal to self
+    fn floor(self) -> Self;
     
     /// Take the exponential of self
     fn exp(self) -> Self;
@@ -48,34 +52,81 @@ pub trait Float: Copy + Sized + cmp::PartialOrd
     
     /// Take the tangent of self
     fn tan(self) -> Self;
+    /// Take the logarithm of the gamma function of self
+    fn log_gamma(self) -> Self;
 }
 
 impl Float for f32 {
+    #[inline]
     fn pi() -> Self { core::f32::consts::PI }
+    #[inline]
     fn from(x: f64) -> Self { x as f32 }
+    #[inline]
+    fn to_u64(self) -> Option<u64> {
+        if self >= 0. && self <= ::core::u64::MAX as f32 {
+            Some(self as u64)
+        } else {
+            None
+        }
+    }
     
+    #[inline]
     fn abs(self) -> Self { self.abs() }
+    #[inline]
+    fn floor(self) -> Self { self.floor() }
     
+    #[inline]
     fn exp(self) -> Self { self.exp() }
+    #[inline]
     fn ln(self) -> Self { self.ln() }
+    #[inline]
     fn sqrt(self) -> Self { self.sqrt() }
+    #[inline]
     fn powf(self, power: Self) -> Self { self.powf(power) }
     
+    #[inline]
     fn tan(self) -> Self { self.tan() }
+    #[inline]
+    fn log_gamma(self) -> Self {
+        let result = log_gamma(self as f64);
+        assert!(result <= ::core::f32::MAX as f64);
+        assert!(result >= ::core::f32::MIN as f64);
+        result as f32
+    }
 }
 
 impl Float for f64 {
+    #[inline]
     fn pi() -> Self { core::f64::consts::PI }
+    #[inline]
     fn from(x: f64) -> Self { x }
+    #[inline]
+    fn to_u64(self) -> Option<u64> {
+        if self >= 0. && self <= ::core::u64::MAX as f64 {
+            Some(self as u64)
+        } else {
+            None
+        }
+    }
     
+    #[inline]
     fn abs(self) -> Self { self.abs() }
+    #[inline]
+    fn floor(self) -> Self { self.floor() }
     
+    #[inline]
     fn exp(self) -> Self { self.exp() }
+    #[inline]
     fn ln(self) -> Self { self.ln() }
+    #[inline]
     fn sqrt(self) -> Self { self.sqrt() }
+    #[inline]
     fn powf(self, power: Self) -> Self { self.powf(power) }
     
+    #[inline]
     fn tan(self) -> Self { self.tan() }
+    #[inline]
+    fn log_gamma(self) -> Self { log_gamma(self) }
 }
 
 /// Calculates ln(gamma(x)) (natural logarithm of the gamma
@@ -109,7 +160,7 @@ pub(crate) fn log_gamma(x: f64) -> f64 {
     // the first few terms of the series for Ag(x)
     let mut a = 1.000000000190015;
     let mut denom = x;
-    for coeff in &coefficients {
+    for &coeff in &coefficients {
         denom += 1.0;
         a += coeff / denom;
     }