Speedup int log10 branchless

library/core/benches/lib.rs

@@ -1,6 +1,7 @@
 // wasm32 does not support benches (no time).
 #![cfg(not(target_arch = "wasm32"))]
 #![feature(flt2dec)]
+#![feature(int_log)]
 #![feature(test)]
 
 extern crate test;

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

@@ -0,0 +1,58 @@
+use rand::Rng;
+use test::{black_box, Bencher};
+
+macro_rules! int_log_bench {
+    ($t:ty, $predictable:ident, $random:ident, $random_small:ident) => {
+        #[bench]
+        fn $predictable(bench: &mut Bencher) {
+            bench.iter(|| {
+                for n in 0..(<$t>::BITS / 8) {
+                    for i in 1..=(100 as $t) {
+                        let x = black_box(i << (n * 8));
+                        black_box(x.log10());
+                    }
+                }
+            });
+        }
+
+        #[bench]
+        fn $random(bench: &mut Bencher) {
+            let mut rng = rand::thread_rng();
+            /* Exponentially distributed random numbers from the whole range of the type.  */
+            let numbers: Vec<$t> = (0..256)
+                .map(|_| {
+                    let x = rng.gen::<$t>() >> rng.gen_range(0, <$t>::BITS);
+                    if x != 0 { x } else { 1 }
+                })
+                .collect();
+            bench.iter(|| {
+                for x in &numbers {
+                    black_box(black_box(x).log10());
+                }
+            });
+        }
+
+        #[bench]
+        fn $random_small(bench: &mut Bencher) {
+            let mut rng = rand::thread_rng();
+            /* Exponentially distributed random numbers from the range 0..256.  */
+            let numbers: Vec<$t> = (0..256)
+                .map(|_| {
+                    let x = (rng.gen::<u8>() >> rng.gen_range(0, u8::BITS)) as $t;
+                    if x != 0 { x } else { 1 }
+                })
+                .collect();
+            bench.iter(|| {
+                for x in &numbers {
+                    black_box(black_box(x).log10());
+                }
+            });
+        }
+    };
+}
+
+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}

library/core/benches/num/mod.rs

@@ -1,5 +1,6 @@
 mod dec2flt;
 mod flt2dec;
+mod int_log;
 
 use std::str::FromStr;
 use test::Bencher;

library/core/src/num/int_log10.rs

@@ -1,76 +1,71 @@
 mod unchecked {
     // 0 < val <= u8::MAX
     pub const fn u8(val: u8) -> u32 {
-        if val >= 100 {
-            2
-        } else if val >= 10 {
-            1
-        } else {
-            0
-        }
+        let val = val as u32;
+
+        // For better performance, avoid branches by assembling the solution
+        // in the bits above the low 8 bits.
+
+        // Adding c1 to val gives 10 in the top bits for val < 10, 11 for val >= 10
+        const C1: u32 = 0b11_00000000 - 10; // 758
+        // Adding c2 to val gives 01 in the top bits for val < 100, 10 for val >= 100
+        const C2: u32 = 0b10_00000000 - 100; // 412
+
+        // Value of top bits:
+        //            +c1  +c2  1&2
+        //     0..=9   10   01   00 = 0
+        //   10..=99   11   01   01 = 1
+        // 100..=255   11   10   10 = 2
+        ((val + C1) & (val + C2)) >> 8
     }
 
-    // 0 < val <= u16::MAX
-    pub const fn u16(val: u16) -> u32 {
-        if val >= 10_000 {
-            4
-        } else if val >= 1000 {
-            3
-        } else if val >= 100 {
-            2
-        } else if val >= 10 {
-            1
-        } else {
-            0
-        }
+    // 0 < val < 100_000
+    const fn less_than_5(val: u32) -> u32 {
+        // Similar to u8, when adding one of these constants to val,
+        // we get two possible bit patterns above the low 17 bits,
+        // depending on whether val is below or above the threshold.
+        const C1: u32 = 0b011_00000000000000000 - 10; // 393206
+        const C2: u32 = 0b100_00000000000000000 - 100; // 524188
+        const C3: u32 = 0b111_00000000000000000 - 1000; // 916504
+        const C4: u32 = 0b100_00000000000000000 - 10000; // 514288
+
+        // Value of top bits:
+        //                +c1  +c2  1&2  +c3  +c4  3&4   ^
+        //         0..=9  010  011  010  110  011  010  000 = 0
+        //       10..=99  011  011  011  110  011  010  001 = 1
+        //     100..=999  011  100  000  110  011  010  010 = 2
+        //   1000..=9999  011  100  000  111  011  011  011 = 3
+        // 10000..=99999  011  100  000  111  100  100  100 = 4
+        (((val + C1) & (val + C2)) ^ ((val + C3) & (val + C4))) >> 17
     }
 
-    // 0 < val < 100_000_000
-    const fn less_than_8(mut val: u32) -> u32 {
-        let mut log = 0;
-        if val >= 10_000 {
-            val /= 10_000;
-            log += 4;
-        }
-        log + if val >= 1000 {
-            3
-        } else if val >= 100 {
-            2
-        } else if val >= 10 {
-            1
-        } else {
-            0
-        }
+    // 0 < val <= u16::MAX
+    pub const fn u16(val: u16) -> u32 {
+        less_than_5(val as u32)
     }
 
     // 0 < val <= u32::MAX
     pub const fn u32(mut val: u32) -> u32 {
         let mut log = 0;
-        if val >= 100_000_000 {
-            val /= 100_000_000;
-            log += 8;
-        }
-        log + less_than_8(val)
-    }
-
-    // 0 < val < 10_000_000_000_000_000
-    const fn less_than_16(mut val: u64) -> u32 {
-        let mut log = 0;
-        if val >= 100_000_000 {
-            val /= 100_000_000;
-            log += 8;
+        if val >= 100_000 {
+            val /= 100_000;
+            log += 5;
         }
-        log + less_than_8(val as u32)
+        log + less_than_5(val)
     }
 
     // 0 < val <= u64::MAX
     pub const fn u64(mut val: u64) -> u32 {
         let mut log = 0;
-        if val >= 10_000_000_000_000_000 {
-            val /= 10_000_000_000_000_000;
-            log += 16;
+        if val >= 10_000_000_000 {
+            val /= 10_000_000_000;
+            log += 10;
+        }
+        if val >= 100_000 {
+            val /= 100_000;
+            log += 5;
         }
-        log + less_than_16(val)
+        log + less_than_5(val as u32)
     }
 
     // 0 < val <= u128::MAX
@@ -79,13 +74,13 @@ mod unchecked {
         if val >= 100_000_000_000_000_000_000_000_000_000_000 {
             val /= 100_000_000_000_000_000_000_000_000_000_000;
             log += 32;
-            return log + less_than_8(val as u32);
+            return log + u32(val as u32);
         }
         if val >= 10_000_000_000_000_000 {
             val /= 10_000_000_000_000_000;
             log += 16;
         }
-        log + less_than_16(val as u64)
+        log + u64(val as u64)
     }
 
     // 0 < val <= i8::MAX

library/core/tests/num/int_log.rs

@@ -96,6 +96,9 @@ fn checked_log10() {
     for i in 1..=u16::MAX {
         assert_eq!(i.checked_log10(), Some((i as f32).log10() as u32));
     }
+    for i in 1..=100_000u32 {
+        assert_eq!(i.checked_log10(), Some((i as f32).log10() as u32));
+    }
 }
 
 macro_rules! log10_loop {