(ml5717) Untested impl of more robust index sampling

necsim/core/src/cogs/rng.rs

@@ -1,7 +1,7 @@
 use core::{
     convert::AsMut,
     default::Default,
-    num::{NonZeroU128, NonZeroU32, NonZeroUsize},
+    num::{NonZeroU128, NonZeroU32, NonZeroU64, NonZeroUsize},
     ptr::copy_nonoverlapping,
 };
 
@@ -41,6 +41,7 @@ pub trait SeedableRng<M: MathsCore>: RngCore<M> {
         const INC: u64 = 11_634_580_027_462_260_723_u64;
 
         let mut seed = Self::Seed::default();
+
         for chunk in seed.as_mut().chunks_mut(4) {
             // We advance the state first (to get away from the input value,
             // in case it has low Hamming Weight).
@@ -96,51 +97,112 @@ pub trait RngSampler<M: MathsCore>: RngCore<M> {
     #[inline]
     #[debug_ensures(ret < length.get(), "samples U(0, length - 1)")]
     fn sample_index(&mut self, length: NonZeroUsize) -> usize {
-        // attributes on expressions are experimental
-        // see https://github.com/rust-lang/rust/issues/15701
-        #[allow(
-            clippy::cast_precision_loss,
-            clippy::cast_possible_truncation,
-            clippy::cast_sign_loss
-        )]
-        let index =
-            M::floor(self.sample_uniform_closed_open().get() * (length.get() as f64)) as usize;
-        // Safety in case of f64 rounding errors
-        index.min(length.get() - 1)
+        #[cfg(target_pointer_width = "32")]
+        #[allow(clippy::cast_possible_truncation)]
+        {
+            self.sample_index_u32(unsafe { NonZeroU32::new_unchecked(length.get() as u32) })
+                as usize
+        }
+        #[cfg(target_pointer_width = "64")]
+        #[allow(clippy::cast_possible_truncation)]
+        {
+            self.sample_index_u64(unsafe { NonZeroU64::new_unchecked(length.get() as u64) })
+                as usize
+        }
     }
 
     #[must_use]
     #[inline]
     #[debug_ensures(ret < length.get(), "samples U(0, length - 1)")]
     fn sample_index_u32(&mut self, length: NonZeroU32) -> u32 {
-        // attributes on expressions are experimental
-        // see https://github.com/rust-lang/rust/issues/15701
-        #[allow(
-            clippy::cast_precision_loss,
-            clippy::cast_possible_truncation,
-            clippy::cast_sign_loss
-        )]
-        let index =
-            M::floor(self.sample_uniform_closed_open().get() * f64::from(length.get())) as u32;
-        // Safety in case of f64 rounding errors
-        index.min(length.get() - 1)
+        // TODO: Check if delegation to `sample_index_u64` is faster
+
+        // Adapted from:
+        // https://docs.rs/rand/0.8.4/rand/distributions/uniform/trait.UniformSampler.html#method.sample_single
+
+        const LOWER_MASK: u64 = !0 >> 32;
+
+        // Conservative approximation of the acceptance zone
+        let acceptance_zone = (length.get() << length.leading_zeros()).wrapping_sub(1);
+
+        loop {
+            let raw = self.sample_u64();
+
+            let sample_check_lo = (raw & LOWER_MASK) * u64::from(length.get());
+
+            #[allow(clippy::cast_possible_truncation)]
+            if (sample_check_lo as u32) <= acceptance_zone {
+                return (sample_check_lo >> 32) as u32;
+            }
+
+            let sample_check_hi = (raw >> 32) * u64::from(length.get());
+
+            #[allow(clippy::cast_possible_truncation)]
+            if (sample_check_hi as u32) <= acceptance_zone {
+                return (sample_check_hi >> 32) as u32;
+            }
+        }
+    }
+
+    #[must_use]
+    #[inline]
+    #[debug_ensures(ret < length.get(), "samples U(0, length - 1)")]
+    fn sample_index_u64(&mut self, length: NonZeroU64) -> u64 {
+        // Adapted from:
+        // https://docs.rs/rand/0.8.4/rand/distributions/uniform/trait.UniformSampler.html#method.sample_single
+
+        // Conservative approximation of the acceptance zone
+        let acceptance_zone = (length.get() << length.leading_zeros()).wrapping_sub(1);
+
+        loop {
+            let raw = self.sample_u64();
+
+            let sample_check = u128::from(raw) * u128::from(length.get());
+
+            #[allow(clippy::cast_possible_truncation)]
+            if (sample_check as u64) <= acceptance_zone {
+                return (sample_check >> 64) as u64;
+            }
+        }
     }
 
     #[must_use]
     #[inline]
     #[debug_ensures(ret < length.get(), "samples U(0, length - 1)")]
     fn sample_index_u128(&mut self, length: NonZeroU128) -> u128 {
-        // attributes on expressions are experimental
-        // see https://github.com/rust-lang/rust/issues/15701
-        #[allow(
-            clippy::cast_precision_loss,
-            clippy::cast_possible_truncation,
-            clippy::cast_sign_loss
-        )]
-        let index =
-            M::floor(self.sample_uniform_closed_open().get() * (length.get() as f64)) as u128;
-        // Safety in case of f64 rounding errors
-        index.min(length.get() - 1)
+        // Adapted from:
+        // https://docs.rs/rand/0.8.4/rand/distributions/uniform/trait.UniformSampler.html#method.sample_single
+
+        const LOWER_MASK: u128 = !0 >> 64;
+
+        // Conservative approximation of the acceptance zone
+        let acceptance_zone = (length.get() << length.leading_zeros()).wrapping_sub(1);
+
+        loop {
+            let raw_hi = u128::from(self.sample_u64());
+            let raw_lo = u128::from(self.sample_u64());
+
+            // 256-bit multiplication (hi, lo) = (raw_hi, raw_lo) * length
+            let mut low = raw_lo * (length.get() & LOWER_MASK);
+            let mut t = low >> 64;
+            low &= LOWER_MASK;
+            t += raw_hi * (length.get() & LOWER_MASK);
+            low += (t & LOWER_MASK) << 64;
+            let mut high = t >> 64;
+            t = low >> 64;
+            low &= LOWER_MASK;
+            t += (length.get() >> 64) * raw_lo;
+            low += (t & LOWER_MASK) << 64;
+            high += t >> 64;
+            high += raw_hi * (length.get() >> 64);
+
+            let sample = high;
+            let check = low;
+
+            if check <= acceptance_zone {
+                return sample;
+            }
+        }
     }
 
     #[must_use]

necsim/impls/no-std/src/cogs/active_lineage_sampler/alias/dynamic/indexed/mod.rs

@@ -1,9 +1,10 @@
 use alloc::{vec, vec::Vec};
 use core::{
     cmp::Ordering,
+    convert::TryFrom,
     fmt,
     hash::Hash,
-    num::{NonZeroU128, NonZeroUsize},
+    num::{NonZeroU128, NonZeroU64, NonZeroUsize},
 };
 use fnv::FnvBuildHasher;
 
@@ -191,6 +192,8 @@ impl<E: Eq + Hash + Clone> DynamicAliasMethodIndexedSampler<E> {
         if let Some(total_weight) = NonZeroU128::new(self.total_weight) {
             let cdf_sample = if let [_group] = &self.groups[..] {
                 0_u128
+            } else if let Ok(total_weight) = NonZeroU64::try_from(total_weight) {
+                u128::from(rng.sample_index_u64(total_weight))
             } else {
                 rng.sample_index_u128(total_weight)
             };

necsim/impls/no-std/src/cogs/active_lineage_sampler/alias/dynamic/stack/mod.rs

@@ -1,9 +1,10 @@
 use alloc::{vec, vec::Vec};
 use core::{
     cmp::Ordering,
+    convert::TryFrom,
     fmt,
     hash::Hash,
-    num::{NonZeroU128, NonZeroUsize},
+    num::{NonZeroU128, NonZeroU64, NonZeroUsize},
 };
 
 use necsim_core::cogs::{MathsCore, RngCore, RngSampler};
@@ -125,6 +126,8 @@ impl<E: Eq + Hash + Clone> DynamicAliasMethodStackSampler<E> {
         if let Some(total_weight) = NonZeroU128::new(self.total_weight) {
             let cdf_sample = if let [_group] = &self.groups[..] {
                 0_u128
+            } else if let Ok(total_weight) = NonZeroU64::try_from(total_weight) {
+                u128::from(rng.sample_index_u64(total_weight))
             } else {
                 rng.sample_index_u128(total_weight)
             };