Greatly sped up checked_isqrt and isqrt methods

* Uses a lookup table for 8-bit integers and then the Karatsuba square root
  algorithm for larger integers.
* Includes optimization hints that give the compiler the exact numeric range
  of results.

Author: ChaiTRex

library/core/src/num/int_macros.rs

@@ -1580,7 +1580,18 @@ macro_rules! int_impl {
             if self < 0 {
                 None
             } else {
-                Some((self as $UnsignedT).isqrt() as Self)
+                let result = crate::num::int_sqrt::$ActualT(self as $ActualT) as $SelfT;
+
+                // SAFETY: Inform the optimizer that square roots of
+                // nonnegative integers are nonnegative and what the maximum
+                // result is.
+                unsafe {
+                    crate::hint::assert_unchecked(result >= 0);
+                    const MAX_RESULT: $SelfT = crate::num::int_sqrt::$ActualT($ActualT::MAX) as $SelfT;
+                    crate::hint::assert_unchecked(result <= MAX_RESULT);
+                }
+
+                Some(result)
             }
         }
 
@@ -2766,14 +2777,21 @@ macro_rules! int_impl {
                       without modifying the original"]
         #[inline]
         pub const fn isqrt(self) -> Self {
-            // I would like to implement it as
-            // ```
-            // self.checked_isqrt().expect("argument of integer square root must be non-negative")
-            // ```
-            // but `expect` is not yet stable as a `const fn`.
-            match self.checked_isqrt() {
-                Some(sqrt) => sqrt,
-                None => panic!("argument of integer square root must be non-negative"),
+            if self < 0 {
+                crate::num::int_sqrt::panic_for_negative_argument();
+            } else {
+                let result = crate::num::int_sqrt::$ActualT(self as $ActualT) as $SelfT;
+
+                // SAFETY: Inform the optimizer that square roots of
+                // nonnegative integers are nonnegative and what the maximum
+                // result is.
+                unsafe {
+                    crate::hint::assert_unchecked(result >= 0);
+                    const MAX_RESULT: $SelfT = crate::num::int_sqrt::$ActualT($ActualT::MAX) as $SelfT;
+                    crate::hint::assert_unchecked(result <= MAX_RESULT);
+                }
+
+                result
             }
         }
 

library/core/src/num/mod.rs

@@ -43,6 +43,7 @@ mod uint_macros; // import uint_impl!
 
 mod error;
 mod int_log10;
+mod int_sqrt;
 mod nonzero;
 mod overflow_panic;
 mod saturating;

library/core/src/num/nonzero.rs

@@ -1247,31 +1247,19 @@ macro_rules! nonzero_integer_signedness_dependent_methods {
                       without modifying the original"]
         #[inline]
         pub const fn isqrt(self) -> Self {
-            // The algorithm is based on the one presented in
-            // <https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Binary_numeral_system_(base_2)>
-            // which cites as source the following C code:
-            // <https://web.archive.org/web/20120306040058/http://medialab.freaknet.org/martin/src/sqrt/sqrt.c>.
-
-            let mut op = self.get();
-            let mut res = 0;
-            let mut one = 1 << (self.ilog2() & !1);
-
-            while one != 0 {
-                if op >= res + one {
-                    op -= res + one;
-                    res = (res >> 1) + one;
-                } else {
-                    res >>= 1;
-                }
-                one >>= 2;
+            let result = super::int_sqrt::$Int(self.get());
+
+            // SAFETY: Inform the optimizer that square roots of positive
+            // integers are positive and what the maximum result is.
+            unsafe {
+                hint::assert_unchecked(result > 0);
+                const MAX_RESULT: $Int = super::int_sqrt::$Int($Int::MAX);
+                hint::assert_unchecked(result <= MAX_RESULT);
             }
 
-            // SAFETY: The result fits in an integer with half as many bits.
-            // Inform the optimizer about it.
-            unsafe { hint::assert_unchecked(res < 1 << (Self::BITS / 2)) };
-
-            // SAFETY: The square root of an integer >= 1 is always >= 1.
-            unsafe { Self::new_unchecked(res) }
+            // SAFETY: The square root of a positive integer is always
+            // positive.
+            unsafe { Self::new_unchecked(result) }
         }
     };
 

library/core/src/num/uint_macros.rs

@@ -2588,10 +2588,15 @@ macro_rules! uint_impl {
                       without modifying the original"]
         #[inline]
         pub const fn isqrt(self) -> Self {
-            match NonZero::new(self) {
-                Some(x) => x.isqrt().get(),
-                None => 0,
+            let result = crate::num::int_sqrt::$ActualT(self as $ActualT) as $SelfT;
+
+            // SAFETY: Inform the optimizer of what the maximum result is.
+            unsafe {
+                const MAX_RESULT: $SelfT = crate::num::int_sqrt::$ActualT($ActualT::MAX) as $SelfT;
+                crate::hint::assert_unchecked(result <= MAX_RESULT);
             }
+
+            result
         }
 
         /// Performs Euclidean division.