Move {widening, carrying}_mul to an intrinsic with fallback MIR

Including implementing it for `u128`, so it can be defined in `uint_impl!`.

This way it works for all backends, including CTFE.

Author: scottmcm

core/src/intrinsics/fallback.rs

@@ -0,0 +1,111 @@
+#![unstable(
+    feature = "core_intrinsics_fallbacks",
+    reason = "The fallbacks will never be stable, as they exist only to be called \
+              by the fallback MIR, but they're exported so they can be tested on \
+              platforms where the fallback MIR isn't actually used",
+    issue = "none"
+)]
+#![allow(missing_docs)]
+
+#[const_trait]
+pub trait CarryingMulAdd: Copy + 'static {
+    type Unsigned: Copy + 'static;
+    fn carrying_mul_add(
+        self,
+        multiplicand: Self,
+        addend: Self,
+        carry: Self,
+    ) -> (Self::Unsigned, Self);
+}
+
+macro_rules! impl_carrying_mul_add_by_widening {
+    ($($t:ident $u:ident $w:ident,)+) => {$(
+        #[rustc_const_unstable(feature = "core_intrinsics_fallbacks", issue = "none")]
+        impl const CarryingMulAdd for $t {
+            type Unsigned = $u;
+            #[inline]
+            fn carrying_mul_add(self, a: Self, b: Self, c: Self) -> ($u, $t) {
+                let wide = (self as $w) * (a as $w) + (b as $w) + (c as $w);
+                (wide as _, (wide >> Self::BITS) as _)
+            }
+        }
+    )+};
+}
+impl_carrying_mul_add_by_widening! {
+    u8 u8 u16,
+    u16 u16 u32,
+    u32 u32 u64,
+    u64 u64 u128,
+    usize usize UDoubleSize,
+    i8 u8 i16,
+    i16 u16 i32,
+    i32 u32 i64,
+    i64 u64 i128,
+    isize usize UDoubleSize,
+}
+
+#[cfg(target_pointer_width = "16")]
+type UDoubleSize = u32;
+#[cfg(target_pointer_width = "32")]
+type UDoubleSize = u64;
+#[cfg(target_pointer_width = "64")]
+type UDoubleSize = u128;
+
+#[inline]
+const fn wide_mul_u128(a: u128, b: u128) -> (u128, u128) {
+    #[inline]
+    const fn to_low_high(x: u128) -> [u128; 2] {
+        const MASK: u128 = u64::MAX as _;
+        [x & MASK, x >> 64]
+    }
+    #[inline]
+    const fn from_low_high(x: [u128; 2]) -> u128 {
+        x[0] | (x[1] << 64)
+    }
+    #[inline]
+    const fn scalar_mul(low_high: [u128; 2], k: u128) -> [u128; 3] {
+        let [x, c] = to_low_high(k * low_high[0]);
+        let [y, z] = to_low_high(k * low_high[1] + c);
+        [x, y, z]
+    }
+    let a = to_low_high(a);
+    let b = to_low_high(b);
+    let low = scalar_mul(a, b[0]);
+    let high = scalar_mul(a, b[1]);
+    let r0 = low[0];
+    let [r1, c] = to_low_high(low[1] + high[0]);
+    let [r2, c] = to_low_high(low[2] + high[1] + c);
+    let r3 = high[2] + c;
+    (from_low_high([r0, r1]), from_low_high([r2, r3]))
+}
+
+#[rustc_const_unstable(feature = "core_intrinsics_fallbacks", issue = "none")]
+impl const CarryingMulAdd for u128 {
+    type Unsigned = u128;
+    #[inline]
+    fn carrying_mul_add(self, b: u128, c: u128, d: u128) -> (u128, u128) {
+        let (low, mut high) = wide_mul_u128(self, b);
+        let (low, carry) = u128::overflowing_add(low, c);
+        high += carry as u128;
+        let (low, carry) = u128::overflowing_add(low, d);
+        high += carry as u128;
+        (low, high)
+    }
+}
+
+#[rustc_const_unstable(feature = "core_intrinsics_fallbacks", issue = "none")]
+impl const CarryingMulAdd for i128 {
+    type Unsigned = u128;
+    #[inline]
+    fn carrying_mul_add(self, b: i128, c: i128, d: i128) -> (u128, i128) {
+        let (low, high) = wide_mul_u128(self as u128, b as u128);
+        let mut high = high as i128;
+        high = high.wrapping_add((self >> 127) * b);
+        high = high.wrapping_add(self * (b >> 127));
+        let (low, carry) = u128::overflowing_add(low, c as u128);
+        high = high.wrapping_add((carry as i128) + (c >> 127));
+        let (low, carry) = u128::overflowing_add(low, d as u128);
+        high = high.wrapping_add((carry as i128) + (d >> 127));
+        (low, high)
+    }
+}

core/src/intrinsics/mod.rs

@@ -68,6 +68,7 @@ use crate::marker::{DiscriminantKind, Tuple};
 use crate::mem::SizedTypeProperties;
 use crate::{ptr, ub_checks};
 
+pub mod fallback;
 pub mod mir;
 pub mod simd;
 
@@ -3305,6 +3306,34 @@ pub const fn mul_with_overflow<T: Copy>(_x: T, _y: T) -> (T, bool) {
     unimplemented!()
 }
 
+/// Performs full-width multiplication and addition with a carry:
+/// `multiplier * multiplicand + addend + carry`.
+///
+/// This is possible without any overflow.  For `uN`:
+///    MAX * MAX + MAX + MAX
+/// => (2ⁿ-1) × (2ⁿ-1) + (2ⁿ-1) + (2ⁿ-1)
+/// => (2²ⁿ - 2ⁿ⁺¹ + 1) + (2ⁿ⁺¹ - 2)
+/// => 2²ⁿ - 1
+///
+/// For `iN`, the upper bound is MIN * MIN + MAX + MAX => 2²ⁿ⁻² + 2ⁿ - 2,
+/// and the lower bound is MAX * MIN + MIN + MIN => -2²ⁿ⁻² - 2ⁿ + 2ⁿ⁺¹.
+///
+/// This currently supports unsigned integers *only*, no signed ones.
+/// The stabilized versions of this intrinsic are available on integers.
+#[unstable(feature = "core_intrinsics", issue = "none")]
+#[rustc_const_unstable(feature = "const_carrying_mul_add", issue = "85532")]
+#[rustc_nounwind]
+#[cfg_attr(not(bootstrap), rustc_intrinsic)]
+#[cfg_attr(not(bootstrap), miri::intrinsic_fallback_is_spec)]
+pub const fn carrying_mul_add<T: ~const fallback::CarryingMulAdd<Unsigned = U>, U>(
+    multiplier: T,
+    multiplicand: T,
+    addend: T,
+    carry: T,
+) -> (U, T) {
+    multiplier.carrying_mul_add(multiplicand, addend, carry)
+}
+
 /// Performs an exact division, resulting in undefined behavior where
 /// `x % y != 0` or `y == 0` or `x == T::MIN && y == -1`
 ///

core/src/lib.rs

@@ -110,6 +110,7 @@
 #![cfg_attr(bootstrap, feature(do_not_recommend))]
 #![feature(array_ptr_get)]
 #![feature(asm_experimental_arch)]
+#![feature(const_carrying_mul_add)]
 #![feature(const_eval_select)]
 #![feature(const_typed_swap)]
 #![feature(core_intrinsics)]

core/src/num/mod.rs

@@ -228,134 +228,6 @@ macro_rules! midpoint_impl {
     };
 }
 
-macro_rules! widening_impl {
-    ($SelfT:ty, $WideT:ty, $BITS:literal, unsigned) => {
-        /// Calculates the complete product `self * rhs` without the possibility to overflow.
-        ///
-        /// This returns the low-order (wrapping) bits and the high-order (overflow) bits
-        /// of the result as two separate values, in that order.
-        ///
-        /// If you also need to add a carry to the wide result, then you want
-        /// [`Self::carrying_mul`] instead.
-        ///
-        /// # Examples
-        ///
-        /// Basic usage:
-        ///
-        /// Please note that this example is shared between integer types.
-        /// Which explains why `u32` is used here.
-        ///
-        /// ```
-        /// #![feature(bigint_helper_methods)]
-        /// assert_eq!(5u32.widening_mul(2), (10, 0));
-        /// assert_eq!(1_000_000_000u32.widening_mul(10), (1410065408, 2));
-        /// ```
-        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
-        #[must_use = "this returns the result of the operation, \
-                      without modifying the original"]
-        #[inline]
-        pub const fn widening_mul(self, rhs: Self) -> (Self, Self) {
-            // note: longer-term this should be done via an intrinsic,
-            //   but for now we can deal without an impl for u128/i128
-            // SAFETY: overflow will be contained within the wider types
-            let wide = unsafe { (self as $WideT).unchecked_mul(rhs as $WideT) };
-            (wide as $SelfT, (wide >> $BITS) as $SelfT)
-        }
-
-        /// Calculates the "full multiplication" `self * rhs + carry`
-        /// without the possibility to overflow.
-        ///
-        /// This returns the low-order (wrapping) bits and the high-order (overflow) bits
-        /// of the result as two separate values, in that order.
-        ///
-        /// Performs "long multiplication" which takes in an extra amount to add, and may return an
-        /// additional amount of overflow. This allows for chaining together multiple
-        /// multiplications to create "big integers" which represent larger values.
-        ///
-        /// If you don't need the `carry`, then you can use [`Self::widening_mul`] instead.
-        ///
-        /// # Examples
-        ///
-        /// Basic usage:
-        ///
-        /// Please note that this example is shared between integer types.
-        /// Which explains why `u32` is used here.
-        ///
-        /// ```
-        /// #![feature(bigint_helper_methods)]
-        /// assert_eq!(5u32.carrying_mul(2, 0), (10, 0));
-        /// assert_eq!(5u32.carrying_mul(2, 10), (20, 0));
-        /// assert_eq!(1_000_000_000u32.carrying_mul(10, 0), (1410065408, 2));
-        /// assert_eq!(1_000_000_000u32.carrying_mul(10, 10), (1410065418, 2));
-        #[doc = concat!("assert_eq!(",
-            stringify!($SelfT), "::MAX.carrying_mul(", stringify!($SelfT), "::MAX, ", stringify!($SelfT), "::MAX), ",
-            "(0, ", stringify!($SelfT), "::MAX));"
-        )]
-        /// ```
-        ///
-        /// This is the core operation needed for scalar multiplication when
-        /// implementing it for wider-than-native types.
-        ///
-        /// ```
-        /// #![feature(bigint_helper_methods)]
-        /// fn scalar_mul_eq(little_endian_digits: &mut Vec<u16>, multiplicand: u16) {
-        ///     let mut carry = 0;
-        ///     for d in little_endian_digits.iter_mut() {
-        ///         (*d, carry) = d.carrying_mul(multiplicand, carry);
-        ///     }
-        ///     if carry != 0 {
-        ///         little_endian_digits.push(carry);
-        ///     }
-        /// }
-        ///
-        /// let mut v = vec![10, 20];
-        /// scalar_mul_eq(&mut v, 3);
-        /// assert_eq!(v, [30, 60]);
-        ///
-        /// assert_eq!(0x87654321_u64 * 0xFEED, 0x86D3D159E38D);
-        /// let mut v = vec![0x4321, 0x8765];
-        /// scalar_mul_eq(&mut v, 0xFEED);
-        /// assert_eq!(v, [0xE38D, 0xD159, 0x86D3]);
-        /// ```
-        ///
-        /// If `carry` is zero, this is similar to [`overflowing_mul`](Self::overflowing_mul),
-        /// except that it gives the value of the overflow instead of just whether one happened:
-        ///
-        /// ```
-        /// #![feature(bigint_helper_methods)]
-        /// let r = u8::carrying_mul(7, 13, 0);
-        /// assert_eq!((r.0, r.1 != 0), u8::overflowing_mul(7, 13));
-        /// let r = u8::carrying_mul(13, 42, 0);
-        /// assert_eq!((r.0, r.1 != 0), u8::overflowing_mul(13, 42));
-        /// ```
-        ///
-        /// The value of the first field in the returned tuple matches what you'd get
-        /// by combining the [`wrapping_mul`](Self::wrapping_mul) and
-        /// [`wrapping_add`](Self::wrapping_add) methods:
-        ///
-        /// ```
-        /// #![feature(bigint_helper_methods)]
-        /// assert_eq!(
-        ///     789_u16.carrying_mul(456, 123).0,
-        ///     789_u16.wrapping_mul(456).wrapping_add(123),
-        /// );
-        /// ```
-        #[unstable(feature = "bigint_helper_methods", issue = "85532")]
-        #[must_use = "this returns the result of the operation, \
-                      without modifying the original"]
-        #[inline]
-        pub const fn carrying_mul(self, rhs: Self, carry: Self) -> (Self, Self) {
-            // note: longer-term this should be done via an intrinsic,
-            //   but for now we can deal without an impl for u128/i128
-            // SAFETY: overflow will be contained within the wider types
-            let wide = unsafe {
-                (self as $WideT).unchecked_mul(rhs as $WideT).unchecked_add(carry as $WideT)
-            };
-            (wide as $SelfT, (wide >> $BITS) as $SelfT)
-        }
-    };
-}
-
 impl i8 {
     int_impl! {
         Self = i8,
@@ -576,7 +448,6 @@ impl u8 {
         from_xe_bytes_doc = u8_xe_bytes_doc!(),
         bound_condition = "",
     }
-    widening_impl! { u8, u16, 8, unsigned }
     midpoint_impl! { u8, u16, unsigned }
 
     /// Checks if the value is within the ASCII range.
@@ -1192,7 +1063,6 @@ impl u16 {
         from_xe_bytes_doc = "",
         bound_condition = "",
     }
-    widening_impl! { u16, u32, 16, unsigned }
     midpoint_impl! { u16, u32, unsigned }
 
     /// Checks if the value is a Unicode surrogate code point, which are disallowed values for [`char`].
@@ -1240,7 +1110,6 @@ impl u32 {
         from_xe_bytes_doc = "",
         bound_condition = "",
     }
-    widening_impl! { u32, u64, 32, unsigned }
     midpoint_impl! { u32, u64, unsigned }
 }
 
@@ -1264,7 +1133,6 @@ impl u64 {
         from_xe_bytes_doc = "",
         bound_condition = "",
     }
-    widening_impl! { u64, u128, 64, unsigned }
     midpoint_impl! { u64, u128, unsigned }
 }
 
@@ -1314,7 +1182,6 @@ impl usize {
         from_xe_bytes_doc = usize_isize_from_xe_bytes_doc!(),
         bound_condition = " on 16-bit targets",
     }
-    widening_impl! { usize, u32, 16, unsigned }
     midpoint_impl! { usize, u32, unsigned }
 }
 
@@ -1339,7 +1206,6 @@ impl usize {
         from_xe_bytes_doc = usize_isize_from_xe_bytes_doc!(),
         bound_condition = " on 32-bit targets",
     }
-    widening_impl! { usize, u64, 32, unsigned }
     midpoint_impl! { usize, u64, unsigned }
 }
 
@@ -1364,7 +1230,6 @@ impl usize {
         from_xe_bytes_doc = usize_isize_from_xe_bytes_doc!(),
         bound_condition = " on 64-bit targets",
     }
-    widening_impl! { usize, u128, 64, unsigned }
     midpoint_impl! { usize, u128, unsigned }
 }