Rearrange the pipeline of pow to gain efficiency

The check of the `exp` parameter seems useless if we execute the while-loop more than once.
The original implementation of `pow` function using one more comparison if the `exp==0` and may break the pipeline of the cpu, which may generate a slower code.
The performance gap between the old and the new implementation may be small, but IMO, at least the newer one looks more beautiful.

---

bench prog:
```
extern crate test;
($a:expr)=>{let time=std::time::Instant::now();{$a;}print!("{:?} ",time.elapsed())};
($a:expr,$b:literal)=>{let time=std::time::Instant::now();let mut a=0;for _ in 0..$b{a^=$a;}print!("{:?} {} ",time.elapsed(),a)}
}
pub fn pow_rust(x:i64, mut exp: u32) -> i64 {
    let mut base = x;
    let mut acc = 1;
    while exp > 1 {
        if (exp & 1) == 1 {
            acc = acc * base;
        }
        exp /= 2;
        base = base * base;
    }
    if exp == 1 {
        acc = acc * base;
    }
    acc
}
pub fn pow_new(x:i64, mut exp: u32) -> i64 {
    if exp==0{
        1
    }else{
        let mut base = x;
        let mut acc = 1;
        while exp > 1 {
            if (exp & 1) == 1 {
                acc = acc * base;
            }
            exp >>= 1;
            base = base * base;
        }
        acc * base
    }
}

fn main(){
let a=2i64;
let b=1_u32;
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
timing!(test::black_box(a).pow(test::black_box(b)),100000000);
timing!(pow_new(test::black_box(a),test::black_box(b)),100000000);
timing!(pow_rust(test::black_box(a),test::black_box(b)),100000000);
println!();
}
```
bench in my laptop:
```
neutron@Neutron:/me/rust$ rc commit.rs
rustc commit.rs  && ./commit

3.978419716s 0 4.079765171s 0 3.964630622s 0
3.997127013s 0 4.260304804s 0 3.997638211s 0
3.963195544s 0 4.11657718s 0 4.176054164s 0
3.830128579s 0 3.980396122s 0 3.937258567s 0
3.986055948s 0 4.127804162s 0 4.018943411s 0
4.185568857s 0 4.217512517s 0 3.98313603s 0
3.863018225s 0 4.030447988s 0 3.694878237s 0
4.206987927s 0 4.137608047s 0 4.115564664s 0
neutron@Neutron:/me/rust$ rc commit.rs -O
rustc commit.rs -O && ./commit

162.111993ms 0 165.107125ms 0 166.26924ms 0
175.20479ms 0 205.062565ms 0 176.278791ms 0
174.408975ms 0 166.526899ms 0 201.857604ms 0
146.190062ms 0 168.592821ms 0 154.61411ms 0
199.678912ms 0 168.411598ms 0 162.129996ms 0
147.420765ms 0 209.759326ms 0 154.807907ms 0
165.507134ms 0 188.476239ms 0 157.351524ms 0
121.320123ms 0 126.401229ms 0 114.86428ms 0
```

delete an unnecessary semicolon...

Sorry for the typo.

delete trailing whitespace

Sorry, too..

Sorry for the missing...

I checked all the implementations, and finally found that there is one function that does not check whether `exp == 0`

add extra tests

add extra tests.

finished adding the extra tests to prevent further typo

add pow(2) to negative exp

add whitespace.

add whitespace

add whitespace

delete extra line

src/libcore/num/mod.rs

@@ -1103,6 +1103,9 @@ $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn checked_pow(self, mut exp: u32) -> Option<Self> {
+                if exp == 0 {
+                    return Some(1);
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
 
@@ -1113,15 +1116,11 @@ $EndFeature, "
                     exp /= 2;
                     base = try_opt!(base.checked_mul(base));
                 }
-
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    acc = try_opt!(acc.checked_mul(base));
-                }
-
-                Some(acc)
+                Some(try_opt!(acc.checked_mul(base)))
             }
         }
 
@@ -1631,6 +1630,9 @@ $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn wrapping_pow(self, mut exp: u32) -> Self {
+                if exp == 0 {
+                    return 1;
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
 
@@ -1642,14 +1644,11 @@ $EndFeature, "
                     base = base.wrapping_mul(base);
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    acc = acc.wrapping_mul(base);
-                }
-
-                acc
+                acc.wrapping_mul(base)
             }
         }
 
@@ -1999,6 +1998,9 @@ $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn overflowing_pow(self, mut exp: u32) -> (Self, bool) {
+                if exp == 0 {
+                    return (1,false);
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
                 let mut overflown = false;
@@ -2017,16 +2019,13 @@ $EndFeature, "
                     overflown |= r.1;
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    r = acc.overflowing_mul(base);
-                    acc = r.0;
-                    overflown |= r.1;
-                }
-
-                (acc, overflown)
+                r = acc.overflowing_mul(base);
+                r.1 |= overflown;
+                r
             }
         }
 
@@ -2050,6 +2049,9 @@ $EndFeature, "
             #[inline]
             #[rustc_inherit_overflow_checks]
             pub const fn pow(self, mut exp: u32) -> Self {
+                if exp == 0 {
+                    return 1;
+                }
                 let mut base = self;
                 let mut acc = 1;
 
@@ -2061,14 +2063,11 @@ $EndFeature, "
                     base = base * base;
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    acc = acc * base;
-                }
-
-                acc
+                acc * base
             }
         }
 
@@ -3306,6 +3305,9 @@ assert_eq!(", stringify!($SelfT), "::MAX.checked_pow(2), None);", $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn checked_pow(self, mut exp: u32) -> Option<Self> {
+                if exp == 0 {
+                    return Some(1);
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
 
@@ -3317,14 +3319,12 @@ assert_eq!(", stringify!($SelfT), "::MAX.checked_pow(2), None);", $EndFeature, "
                     base = try_opt!(base.checked_mul(base));
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    acc = try_opt!(acc.checked_mul(base));
-                }
 
-                Some(acc)
+                Some(try_opt!(acc.checked_mul(base)))
             }
         }
 
@@ -3715,6 +3715,9 @@ assert_eq!(3u8.wrapping_pow(6), 217);", $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn wrapping_pow(self, mut exp: u32) -> Self {
+                if exp == 0 {
+                    return 1;
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
 
@@ -3726,14 +3729,11 @@ assert_eq!(3u8.wrapping_pow(6), 217);", $EndFeature, "
                     base = base.wrapping_mul(base);
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    acc = acc.wrapping_mul(base);
-                }
-
-                acc
+                acc.wrapping_mul(base)
             }
         }
 
@@ -4040,6 +4040,9 @@ assert_eq!(3u8.overflowing_pow(6), (217, true));", $EndFeature, "
                           without modifying the original"]
             #[inline]
             pub const fn overflowing_pow(self, mut exp: u32) -> (Self, bool) {
+                if exp == 0{
+                    return (1,false);
+                }
                 let mut base = self;
                 let mut acc: Self = 1;
                 let mut overflown = false;
@@ -4058,16 +4061,14 @@ assert_eq!(3u8.overflowing_pow(6), (217, true));", $EndFeature, "
                     overflown |= r.1;
                 }
 
+                // since exp!=0, finally the exp must be 1.
                 // Deal with the final bit of the exponent separately, since
                 // squaring the base afterwards is not necessary and may cause a
                 // needless overflow.
-                if exp == 1 {
-                    r = acc.overflowing_mul(base);
-                    acc = r.0;
-                    overflown |= r.1;
-                }
+                r = acc.overflowing_mul(base);
+                r.1 |= overflown;
 
-                (acc, overflown)
+                r
             }
         }
 
@@ -4088,6 +4089,9 @@ Basic usage:
         #[inline]
         #[rustc_inherit_overflow_checks]
         pub const fn pow(self, mut exp: u32) -> Self {
+            if exp == 0 {
+                return 1;
+            }
             let mut base = self;
             let mut acc = 1;
 
@@ -4099,14 +4103,11 @@ Basic usage:
                 base = base * base;
             }
 
+            // since exp!=0, finally the exp must be 1.
             // Deal with the final bit of the exponent separately, since
             // squaring the base afterwards is not necessary and may cause a
             // needless overflow.
-            if exp == 1 {
-                acc = acc * base;
-            }
-
-            acc
+            acc * base
         }
     }
 

src/libcore/tests/num/int_macros.rs

@@ -255,12 +255,43 @@ macro_rules! int_module {
             #[test]
             fn test_pow() {
                 let mut r = 2 as $T;
-
                 assert_eq!(r.pow(2), 4 as $T);
                 assert_eq!(r.pow(0), 1 as $T);
+                assert_eq!(r.wrapping_pow(2), 4 as $T);
+                assert_eq!(r.wrapping_pow(0), 1 as $T);
+                assert_eq!(r.checked_pow(2), Some(4 as $T));
+                assert_eq!(r.checked_pow(0), Some(1 as $T));
+                assert_eq!(r.overflowing_pow(2), (4 as $T, false));
+                assert_eq!(r.overflowing_pow(0), (1 as $T, false));
+                assert_eq!(r.saturating_pow(2), 4 as $T);
+                assert_eq!(r.saturating_pow(0), 1 as $T);
+
+                r = MAX;
+                // use `^` to represent .pow() with no overflow.
+                // if itest::MAX == 2^j-1, then itest is a `j` bit int,
+                // so that `itest::MAX*itest::MAX == 2^(2*j)-2^(j+1)+1`,
+                // thussaturating_pow the overflowing result is exactly 1.
+                assert_eq!(r.wrapping_pow(2), 1 as $T);
+                assert_eq!(r.checked_pow(2), None);
+                assert_eq!(r.overflowing_pow(2), (1 as $T, true));
+                assert_eq!(r.saturating_pow(2), MAX);
+                //test for negative exponent.
                 r = -2 as $T;
                 assert_eq!(r.pow(2), 4 as $T);
                 assert_eq!(r.pow(3), -8 as $T);
+                assert_eq!(r.pow(0), 1 as $T);
+                assert_eq!(r.wrapping_pow(2), 4 as $T);
+                assert_eq!(r.wrapping_pow(3), -8 as $T);
+                assert_eq!(r.wrapping_pow(0), 1 as $T);
+                assert_eq!(r.checked_pow(2), Some(4 as $T));
+                assert_eq!(r.checked_pow(3), Some(-8 as $T));
+                assert_eq!(r.checked_pow(0), Some(1 as $T));
+                assert_eq!(r.overflowing_pow(2), (4 as $T, false));
+                assert_eq!(r.overflowing_pow(3), (-8 as $T, false));
+                assert_eq!(r.overflowing_pow(0), (1 as $T, false));
+                assert_eq!(r.saturating_pow(2), 4 as $T);
+                assert_eq!(r.saturating_pow(3), -8 as $T);
+                assert_eq!(r.saturating_pow(0), 1 as $T);
             }
         }
     };

src/libcore/tests/num/uint_macros.rs

@@ -184,6 +184,31 @@ macro_rules! uint_module {
                 assert_eq!($T::from_str_radix("Z", 10).ok(), None::<$T>);
                 assert_eq!($T::from_str_radix("_", 2).ok(), None::<$T>);
             }
+
+            #[test]
+            fn test_pow() {
+                let mut r = 2 as $T;
+                assert_eq!(r.pow(2), 4 as $T);
+                assert_eq!(r.pow(0), 1 as $T);
+                assert_eq!(r.wrapping_pow(2), 4 as $T);
+                assert_eq!(r.wrapping_pow(0), 1 as $T);
+                assert_eq!(r.checked_pow(2), Some(4 as $T));
+                assert_eq!(r.checked_pow(0), Some(1 as $T));
+                assert_eq!(r.overflowing_pow(2), (4 as $T, false));
+                assert_eq!(r.overflowing_pow(0), (1 as $T, false));
+                assert_eq!(r.saturating_pow(2), 4 as $T);
+                assert_eq!(r.saturating_pow(0), 1 as $T);
+
+                r = MAX;
+                // use `^` to represent .pow() with no overflow.
+                // if itest::MAX == 2^j-1, then itest is a `j` bit int,
+                // so that `itest::MAX*itest::MAX == 2^(2*j)-2^(j+1)+1`,
+                // thussaturating_pow the overflowing result is exactly 1.
+                assert_eq!(r.wrapping_pow(2), 1 as $T);
+                assert_eq!(r.checked_pow(2), None);
+                assert_eq!(r.overflowing_pow(2), (1 as $T, true));
+                assert_eq!(r.saturating_pow(2), MAX);
+            }
         }
     };
 }