checked_ilog: improve performance

library/core/benches/num/int_log/mod.rs

@@ -1,7 +1,7 @@
 use rand::Rng;
 use test::{black_box, Bencher};
 
-macro_rules! int_log_bench {
+macro_rules! int_log10_bench {
     ($t:ty, $predictable:ident, $random:ident, $random_small:ident) => {
         #[bench]
         fn $predictable(bench: &mut Bencher) {
@@ -51,8 +51,75 @@ macro_rules! int_log_bench {
     };
 }
 
-int_log_bench! {u8, u8_log10_predictable, u8_log10_random, u8_log10_random_small}
-int_log_bench! {u16, u16_log10_predictable, u16_log10_random, u16_log10_random_small}
-int_log_bench! {u32, u32_log10_predictable, u32_log10_random, u32_log10_random_small}
-int_log_bench! {u64, u64_log10_predictable, u64_log10_random, u64_log10_random_small}
-int_log_bench! {u128, u128_log10_predictable, u128_log10_random, u128_log10_random_small}
+int_log10_bench! {u8, u8_log10_predictable, u8_log10_random, u8_log10_random_small}
+int_log10_bench! {u16, u16_log10_predictable, u16_log10_random, u16_log10_random_small}
+int_log10_bench! {u32, u32_log10_predictable, u32_log10_random, u32_log10_random_small}
+int_log10_bench! {u64, u64_log10_predictable, u64_log10_random, u64_log10_random_small}
+int_log10_bench! {u128, u128_log10_predictable, u128_log10_random, u128_log10_random_small}
+
+macro_rules! int_log_bench {
+    ($t:ty, $random:ident, $random_small:ident, $geometric:ident) => {
+        #[bench]
+        fn $random(bench: &mut Bencher) {
+            let mut rng = crate::bench_rng();
+            /* Exponentially distributed random numbers from the whole range of the type.  */
+            let numbers: Vec<$t> = (0..256)
+                .map(|_| {
+                    let x = rng.gen::<$t>() >> rng.gen_range(0..<$t>::BITS);
+                    if x >= 2 { x } else { 2 }
+                })
+                .collect();
+            bench.iter(|| {
+                for &b in &numbers {
+                    for &x in &numbers {
+                        black_box(black_box(x).ilog(b));
+                    }
+                }
+            });
+        }
+
+        #[bench]
+        fn $random_small(bench: &mut Bencher) {
+            let mut rng = crate::bench_rng();
+            /* Exponentially distributed random numbers from the range 0..256.  */
+            let numbers: Vec<$t> = (0..256)
+                .map(|_| {
+                    let x = (rng.gen::<u8>() >> rng.gen_range(0..u8::BITS)) as $t;
+                    if x >= 2 { x } else { 2 }
+                })
+                .collect();
+            bench.iter(|| {
+                for &b in &numbers {
+                    for &x in &numbers {
+                        black_box(black_box(x).ilog(b));
+                    }
+                }
+            });
+        }
+
+        #[bench]
+        fn $geometric(bench: &mut Bencher) {
+            let bases: [$t; 16] = [2, 3, 4, 5, 7, 8, 9, 15, 16, 17, 31, 32, 33, 63, 64, 65];
+            let base_and_numbers: Vec<($t, Vec<$t>)> = bases
+                .iter()
+                .map(|&b| {
+                    let numbers = (0..=<$t>::MAX.ilog(b)).map(|exp| b.pow(exp)).collect();
+                    (b, numbers)
+                })
+                .collect();
+            bench.iter(|| {
+                for (b, numbers) in &base_and_numbers {
+                    for &x in numbers {
+                        black_box(black_box(x).ilog(black_box(*b)));
+                    }
+                }
+            });
+        }
+    };
+}
+
+int_log_bench! {u8, u8_log_random, u8_log_random_small, u8_log_geometric}
+int_log_bench! {u16, u16_log_random, u16_log_random_small, u16_log_geometric}
+int_log_bench! {u32, u32_log_random, u32_log_random_small, u32_log_geometric}
+int_log_bench! {u64, u64_log_random, u64_log_random_small, u64_log_geometric}
+int_log_bench! {u128, u128_log_random, u128_log_random_small, u128_log_geometric}

library/core/src/num/int_macros.rs

@@ -2476,21 +2476,9 @@ macro_rules! int_impl {
             if self <= 0 || base <= 1 {
                 None
             } else {
-                let mut n = 0;
-                let mut r = self;
-
-                // Optimization for 128 bit wide integers.
-                if Self::BITS == 128 {
-                    let b = Self::ilog2(self) / (Self::ilog2(base) + 1);
-                    n += b;
-                    r /= base.pow(b as u32);
-                }
-
-                while r >= base {
-                    r /= base;
-                    n += 1;
-                }
-                Some(n)
+                // Delegate to the unsigned implementation.
+                // The condition makes sure that both casts are exact.
+                (self as $UnsignedT).checked_ilog(base as $UnsignedT)
             }
         }
 

library/core/src/num/uint_macros.rs

@@ -810,18 +810,25 @@ macro_rules! uint_impl {
                 None
             } else {
                 let mut n = 0;
-                let mut r = self;
+                let mut r = 1;
 
                 // Optimization for 128 bit wide integers.
                 if Self::BITS == 128 {
-                    let b = Self::ilog2(self) / (Self::ilog2(base) + 1);
-                    n += b;
-                    r /= base.pow(b as u32);
+                    // The following is a correct lower bound for ⌊log(base,self)⌋ because
+                    //
+                    // log(base,self) = log(2,self) / log(2,base)
+                    //                ≥ ⌊log(2,self)⌋ / (⌊log(2,base)⌋ + 1)
+                    //
+                    // hence
+                    //
+                    // ⌊log(base,self)⌋ ≥ ⌊ ⌊log(2,self)⌋ / (⌊log(2,base)⌋ + 1) ⌋ .
+                    n = self.ilog2() / (base.ilog2() + 1);
+                    r = base.pow(n);
                 }
 
-                while r >= base {
-                    r /= base;
+                while r <= self / base {
                     n += 1;
+                    r *= base;
                 }
                 Some(n)
             }