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Optimize integer pow by removing exit branch
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The branch at the end of the `pow` implementations is redundant
with multiplication code already present in the loop. By rotating
the exit check, this branch can be largely removed, improving code size
and instruction cache coherence.
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@mzabaluev
mzabaluev committed Jul 11, 2024
1 parent a18fbd0 commit 4cfe24a
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Showing 2 changed files with 52 additions and 73 deletions.
61 changes: 26 additions & 35 deletions core/src/num/int_macros.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1495,18 +1495,17 @@ macro_rules! int_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = try_opt!(acc.checked_mul(base));
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return Some(acc);
}
}
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.
acc.checked_mul(base)
}

/// Strict exponentiation. Computes `self.pow(exp)`, panicking if
Expand Down Expand Up @@ -1546,18 +1545,17 @@ macro_rules! int_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc.strict_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
base = base.strict_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.
acc.strict_mul(base)
}

/// Returns the square root of the number, rounded down.
Expand Down Expand Up @@ -2181,19 +2179,17 @@ macro_rules! int_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc.wrapping_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
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.
acc.wrapping_mul(base)
}

/// Calculates `self` + `rhs`
Expand Down Expand Up @@ -2687,9 +2683,14 @@ macro_rules! int_impl {
// Scratch space for storing results of overflowing_mul.
let mut r;

while exp > 1 {
loop {
if (exp & 1) == 1 {
r = acc.overflowing_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
r.1 |= overflown;
return r;
}
acc = r.0;
overflown |= r.1;
}
Expand All @@ -2698,14 +2699,6 @@ macro_rules! int_impl {
base = r.0;
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.
r = acc.overflowing_mul(base);
r.1 |= overflown;
r
}

/// Raises self to the power of `exp`, using exponentiation by squaring.
Expand All @@ -2732,19 +2725,17 @@ macro_rules! int_impl {
let mut base = self;
let mut acc = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc * base;
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
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.
acc * base
}

/// Returns the square root of the number, rounded down.
Expand Down
64 changes: 26 additions & 38 deletions core/src/num/uint_macros.rs
View file
Original file line number Diff line number Diff line change
Expand Up @@ -1534,20 +1534,17 @@ macro_rules! uint_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = try_opt!(acc.checked_mul(base));
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return Some(acc);
}
}
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.

acc.checked_mul(base)
}

/// Strict exponentiation. Computes `self.pow(exp)`, panicking if
Expand Down Expand Up @@ -1587,18 +1584,17 @@ macro_rules! uint_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc.strict_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
base = base.strict_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.
acc.strict_mul(base)
}

/// Saturating integer addition. Computes `self + rhs`, saturating at
Expand Down Expand Up @@ -2059,19 +2055,17 @@ macro_rules! uint_impl {
let mut base = self;
let mut acc: Self = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc.wrapping_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
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.
acc.wrapping_mul(base)
}

/// Calculates `self` + `rhs`
Expand Down Expand Up @@ -2516,9 +2510,14 @@ macro_rules! uint_impl {
// Scratch space for storing results of overflowing_mul.
let mut r;

while exp > 1 {
loop {
if (exp & 1) == 1 {
r = acc.overflowing_mul(base);
// since exp!=0, finally the exp must be 1.
if exp == 1 {
r.1 |= overflown;
return r;
}
acc = r.0;
overflown |= r.1;
}
Expand All @@ -2527,15 +2526,6 @@ macro_rules! uint_impl {
base = r.0;
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.
r = acc.overflowing_mul(base);
r.1 |= overflown;

r
}

/// Raises self to the power of `exp`, using exponentiation by squaring.
Expand All @@ -2560,19 +2550,17 @@ macro_rules! uint_impl {
let mut base = self;
let mut acc = 1;

while exp > 1 {
loop {
if (exp & 1) == 1 {
acc = acc * base;
// since exp!=0, finally the exp must be 1.
if exp == 1 {
return acc;
}
}
exp /= 2;
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.
acc * base
}

/// Returns the square root of the number, rounded down.
Expand Down

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