Change align_offset to support different strides

This is necessary if we want to implement `[T]::align_to` and is more
useful in general.

This implementation effort has begun during the All Hands and represents
a month of my futile efforts to do any sort of maths. Luckily, I
found the very very nice Chris McDonald (cjm) on IRC who figured out the
core formulas for me! All the thanks for existence of this PR go to
them!

Anyway… Those formulas were mangled by yours truly into the arcane forms
you see here to squeeze out the best assembly possible on most of the
modern architectures (x86 and ARM were evaluated in practice). I mean,
just look at it: *one actual* modulo operation and everything else is
just the cheap single cycle ops! Admitedly, the naive solution might be
faster in some common scenarios, but this code absolutely butchers the
naive solution on the worst case scenario.

Alas, the result of this arcane magic also means that the code pretty
heavily relies on the preconditions holding true and breaking those
preconditions will unleash the UB-est of all UBs! So don’t.

src/libcore/intrinsics.rs

@@ -1463,15 +1463,26 @@ extern "rust-intrinsic" {
     /// source as well as std's catch implementation.
     pub fn try(f: fn(*mut u8), data: *mut u8, local_ptr: *mut u8) -> i32;
 
-    /// Computes the byte offset that needs to be applied to `ptr` in order to
-    /// make it aligned to `align`.
-    /// If it is not possible to align `ptr`, the implementation returns
+    #[cfg(stage0)]
+    /// docs my friends, its friday!
+    pub fn align_offset(ptr: *const (), align: usize) -> usize;
+
+    /// Computes the offset that needs to be applied to the pointer in order to make it aligned to
+    /// `align`.
+    ///
+    /// If it is not possible to align the pointer, the implementation returns
     /// `usize::max_value()`.
     ///
-    /// There are no guarantees whatsover that offsetting the pointer will not
-    /// overflow or go beyond the allocation that `ptr` points into.
-    /// It is up to the caller to ensure that the returned offset is correct
-    /// in all terms other than alignment.
+    /// The offset is expressed in number of `T` elements, and not bytes. The value returned can be
+    /// used with the `offset` or `offset_to` methods.
+    ///
+    /// There are no guarantees whatsover that offsetting the pointer will not overflow or go
+    /// beyond the allocation that the pointer points into. It is up to the caller to ensure that
+    /// the returned offset is correct in all terms other than alignment.
+    ///
+    /// # Unsafety
+    ///
+    /// `align` must be a power-of-two.
     ///
     /// # Examples
     ///
@@ -1485,7 +1496,7 @@ extern "rust-intrinsic" {
     /// # unsafe {
     /// let x = [5u8, 6u8, 7u8, 8u8, 9u8];
     /// let ptr = &x[n] as *const u8;
-    /// let offset = align_offset(ptr as *const (), align_of::<u16>());
+    /// let offset = align_offset(ptr, align_of::<u16>());
     /// if offset < x.len() - n - 1 {
     ///     let u16_ptr = ptr.offset(offset as isize) as *const u16;
     ///     assert_ne!(*u16_ptr, 500);
@@ -1495,7 +1506,8 @@ extern "rust-intrinsic" {
     /// }
     /// # } }
     /// ```
-    pub fn align_offset(ptr: *const (), align: usize) -> usize;
+    #[cfg(not(stage0))]
+    pub fn align_offset<T>(ptr: *const T, align: usize) -> usize;
 
     /// Emits a `!nontemporal` store according to LLVM (see their docs).
     /// Probably will never become stable.

src/libcore/ptr.rs

@@ -1433,15 +1433,22 @@ impl<T: ?Sized> *const T {
         copy_nonoverlapping(self, dest, count)
     }
 
-    /// Computes the byte offset that needs to be applied in order to
-    /// make the pointer aligned to `align`.
+    /// Computes the offset that needs to be applied to the pointer in order to make it aligned to
+    /// `align`.
+    ///
     /// If it is not possible to align the pointer, the implementation returns
     /// `usize::max_value()`.
     ///
-    /// There are no guarantees whatsover that offsetting the pointer will not
-    /// overflow or go beyond the allocation that the pointer points into.
-    /// It is up to the caller to ensure that the returned offset is correct
-    /// in all terms other than alignment.
+    /// The offset is expressed in number of `T` elements, and not bytes. The value returned can be
+    /// used with the `offset` or `offset_to` methods.
+    ///
+    /// There are no guarantees whatsover that offsetting the pointer will not overflow or go
+    /// beyond the allocation that the pointer points into. It is up to the caller to ensure that
+    /// the returned offset is correct in all terms other than alignment.
+    ///
+    /// # Panics
+    ///
+    /// The function panics if `align` is not a power-of-two.
     ///
     /// # Examples
     ///
@@ -1465,13 +1472,30 @@ impl<T: ?Sized> *const T {
     /// # } }
     /// ```
     #[unstable(feature = "align_offset", issue = "44488")]
-    pub fn align_offset(self, align: usize) -> usize {
+    #[cfg(not(stage0))]
+    pub fn align_offset(self, align: usize) -> usize where T: Sized {
+        if !align.is_power_of_two() {
+            panic!("align_offset: align is not a power-of-two");
+        }
         unsafe {
-            intrinsics::align_offset(self as *const _, align)
+            intrinsics::align_offset(self, align)
+        }
+    }
+
+    /// definitely docs.
+    #[unstable(feature = "align_offset", issue = "44488")]
+    #[cfg(stage0)]
+    pub fn align_offset(self, align: usize) -> usize where T: Sized {
+        if !align.is_power_of_two() {
+            panic!("align_offset: align is not a power-of-two");
+        }
+        unsafe {
+            intrinsics::align_offset(self as *const (), align)
         }
     }
 }
 
+
 #[lang = "mut_ptr"]
 impl<T: ?Sized> *mut T {
     /// Returns `true` if the pointer is null.
@@ -1804,44 +1828,6 @@ impl<T: ?Sized> *mut T {
         (self as *const T).wrapping_offset_from(origin)
     }
 
-    /// Computes the byte offset that needs to be applied in order to
-    /// make the pointer aligned to `align`.
-    /// If it is not possible to align the pointer, the implementation returns
-    /// `usize::max_value()`.
-    ///
-    /// There are no guarantees whatsover that offsetting the pointer will not
-    /// overflow or go beyond the allocation that the pointer points into.
-    /// It is up to the caller to ensure that the returned offset is correct
-    /// in all terms other than alignment.
-    ///
-    /// # Examples
-    ///
-    /// Accessing adjacent `u8` as `u16`
-    ///
-    /// ```
-    /// # #![feature(align_offset)]
-    /// # fn foo(n: usize) {
-    /// # use std::mem::align_of;
-    /// # unsafe {
-    /// let x = [5u8, 6u8, 7u8, 8u8, 9u8];
-    /// let ptr = &x[n] as *const u8;
-    /// let offset = ptr.align_offset(align_of::<u16>());
-    /// if offset < x.len() - n - 1 {
-    ///     let u16_ptr = ptr.offset(offset as isize) as *const u16;
-    ///     assert_ne!(*u16_ptr, 500);
-    /// } else {
-    ///     // while the pointer can be aligned via `offset`, it would point
-    ///     // outside the allocation
-    /// }
-    /// # } }
-    /// ```
-    #[unstable(feature = "align_offset", issue = "44488")]
-    pub fn align_offset(self, align: usize) -> usize {
-        unsafe {
-            intrinsics::align_offset(self as *const _, align)
-        }
-    }
-
     /// Calculates the offset from a pointer (convenience for `.offset(count as isize)`).
     ///
     /// `count` is in units of T; e.g. a `count` of 3 represents a pointer
@@ -2511,8 +2497,189 @@ impl<T: ?Sized> *mut T {
     {
         swap(self, with)
     }
+
+    /// Computes the offset that needs to be applied to the pointer in order to make it aligned to
+    /// `align`.
+    ///
+    /// If it is not possible to align the pointer, the implementation returns
+    /// `usize::max_value()`.
+    ///
+    /// The offset is expressed in number of `T` elements, and not bytes. The value returned can be
+    /// used with the `offset` or `offset_to` methods.
+    ///
+    /// There are no guarantees whatsover that offsetting the pointer will not overflow or go
+    /// beyond the allocation that the pointer points into. It is up to the caller to ensure that
+    /// the returned offset is correct in all terms other than alignment.
+    ///
+    /// # Panics
+    ///
+    /// The function panics if `align` is not a power-of-two.
+    ///
+    /// # Examples
+    ///
+    /// Accessing adjacent `u8` as `u16`
+    ///
+    /// ```
+    /// # #![feature(align_offset)]
+    /// # fn foo(n: usize) {
+    /// # use std::mem::align_of;
+    /// # unsafe {
+    /// let x = [5u8, 6u8, 7u8, 8u8, 9u8];
+    /// let ptr = &x[n] as *const u8;
+    /// let offset = ptr.align_offset(align_of::<u16>());
+    /// if offset < x.len() - n - 1 {
+    ///     let u16_ptr = ptr.offset(offset as isize) as *const u16;
+    ///     assert_ne!(*u16_ptr, 500);
+    /// } else {
+    ///     // while the pointer can be aligned via `offset`, it would point
+    ///     // outside the allocation
+    /// }
+    /// # } }
+    /// ```
+    #[unstable(feature = "align_offset", issue = "44488")]
+    #[cfg(not(stage0))]
+    pub fn align_offset(self, align: usize) -> usize where T: Sized {
+        if !align.is_power_of_two() {
+            panic!("align_offset: align is not a power-of-two");
+        }
+        unsafe {
+            intrinsics::align_offset(self, align)
+        }
+    }
+
+    /// definitely docs.
+    #[unstable(feature = "align_offset", issue = "44488")]
+    #[cfg(stage0)]
+    pub fn align_offset(self, align: usize) -> usize where T: Sized {
+        if !align.is_power_of_two() {
+            panic!("align_offset: align is not a power-of-two");
+        }
+        unsafe {
+            intrinsics::align_offset(self as *const (), align)
+        }
+    }
 }
 
+/// Align pointer `p`.
+///
+/// Calculate offset (in terms of elements of `stride` stride) that has to be applied
+/// to pointer `p` so that pointer `p` would get aligned to `a`.
+///
+/// This is an implementation of the `align_offset` intrinsic for the case where `stride > 1`.
+///
+/// Note: This implementation has been carefully tailored to not panic. It is UB for this to panic.
+/// The only real change that can be made here is change of `INV_TABLE_MOD_16` and associated
+/// constants.
+///
+/// If we ever decide to make it possible to call the intrinsic with `a` that is not a
+/// power-of-two, it will probably be more prudent to just change to a naive implementation rather
+/// than trying to adapt this to accomodate that change.
+///
+/// Any questions go to @nagisa.
+#[lang="align_offset"]
+#[cfg(not(stage0))]
+unsafe fn align_offset(p: *const (), a: usize, stride: usize) -> usize {
+    /// Calculate multiplicative modular inverse of `x` modulo `m`.
+    ///
+    /// This implementation is tailored for align_offset and has following preconditions:
+    ///
+    /// * `m` is a power-of-two;
+    /// * `x < m`; (if `x ≥ m`, pass in `x % m` instead)
+    ///
+    /// Implementation of this function shall not panic. Ever.
+    fn mod_inv(x: usize, m: usize) -> usize {
+        /// Multiplicative modular inverse table modulo 2⁴ = 16.
+        ///
+        /// Note, that this table does not contain values where inverse does not exist (i.e. for
+        /// `0⁻¹ mod 16`, `2⁻¹ mod 16`, etc.)
+        static INV_TABLE_MOD_16: [usize; 8] = [1, 11, 13, 7, 9, 3, 5, 15];
+        /// Modulo for which the `INV_TABLE_MOD_16` is intended.
+        const INV_TABLE_MOD: usize = 16;
+        /// INV_TABLE_MOD²
+        const INV_TABLE_MOD_SQUARED: usize = INV_TABLE_MOD * INV_TABLE_MOD;
+
+        let table_inverse = INV_TABLE_MOD_16[(x & (INV_TABLE_MOD - 1)) >> 1];
+        if m <= INV_TABLE_MOD {
+            return table_inverse & (m - 1);
+        } else {
+            // We iterate "up" using the following formula:
+            //
+            // $$ xy ≡ 1 (mod 2ⁿ) → xy (2 - xy) ≡ 1 (mod 2²ⁿ) $$
+            //
+            // until 2²ⁿ ≥ m. Then we can reduce to our desired `m` by taking the result `mod m`.
+            let mut inverse = table_inverse;
+            let mut going_mod = INV_TABLE_MOD_SQUARED;
+            loop {
+                // y = y * (2 - xy) mod n
+                //
+                // Note, that we use wrapping operations here intentionally – the original formula
+                // uses e.g. subtraction `mod n`. It is entirely fine to do them `mod
+                // usize::max_value()` instead, because we take the result `mod n` at the end
+                // anyway.
+                inverse = inverse.wrapping_mul(
+                    2usize.wrapping_sub(x.wrapping_mul(inverse))
+                ) & (going_mod - 1);
+                if going_mod > m {
+                    return inverse & (m - 1);
+                }
+                going_mod = going_mod.wrapping_mul(going_mod);
+            }
+        }
+    }
+
+    let a_minus_one = a.wrapping_sub(1);
+    let pmoda = p as usize & a_minus_one;
+    let smoda = stride & a_minus_one;
+    // a is power-of-two so cannot be 0. stride = 0 is handled by the intrinsic.
+    let gcdpow = intrinsics::cttz_nonzero(stride).min(intrinsics::cttz_nonzero(a));
+    let gcd = 1usize << gcdpow;
+
+    if pmoda == 0 {
+        // Already aligned. Yay!
+        return 0;
+    }
+
+    if gcd == 1 {
+        // This branch solves for the variable $o$ in following linear congruence equation:
+        //
+        // ⎰ p + o ≡ 0 (mod a)   # $p + o$ must be aligned to specified alignment $a$
+        // ⎱     o ≡ 0 (mod s)   # offset $o$ must be a multiple of stride $s$
+        //
+        // where
+        //
+        // * a, s are co-prime
+        //
+        // This gives us the formula below:
+        //
+        // o = (a - (p mod a)) * (s⁻¹ mod a) * s
+        //
+        // The first term is “the relative alignment of p to a”, the second term is “how does
+        // incrementing p by one s change the relative alignment of p”, the third term is
+        // translating change in units of s to a byte count.
+        //
+        // Furthermore, the result produced by this solution is not “minimal”, so it is necessary
+        // to take the result $o mod lcm(s, a)$. Since $s$ and $a$ are co-prime (i.e. $gcd(s, a) =
+        // 1$) and $lcm(s, a) = s * a / gcd(s, a)$, we can replace $lcm(s, a)$ with just a $s * a$.
+        //
+        // (Author note: we decided later on to express the offset in "elements" rather than bytes,
+        // which drops the multiplication by `s` on both sides of the modulo.)
+        return intrinsics::unchecked_rem(a.wrapping_sub(pmoda).wrapping_mul(mod_inv(smoda, a)), a);
+    }
+
+    if p as usize & (gcd - 1) == 0 {
+        // This can be aligned, but `a` and `stride` are not co-prime, so a somewhat adapted
+        // formula is used.
+        let j = a.wrapping_sub(pmoda) >> gcdpow;
+        let k = smoda >> gcdpow;
+        return intrinsics::unchecked_rem(j.wrapping_mul(mod_inv(k, a)), a >> gcdpow);
+    }
+
+    // Cannot be aligned at all.
+    return usize::max_value();
+}
+
+
+
 // Equality for pointers
 #[stable(feature = "rust1", since = "1.0.0")]
 impl<T: ?Sized> PartialEq for *const T {

src/libcore/slice/mod.rs

@@ -1696,6 +1696,28 @@ impl<T> [T] {
                 self.as_mut_ptr(), other.as_mut_ptr(), self.len());
         }
     }
+
+    // #[unstable(feature = "slice_align_to", issue = "44488")]
+    // pub fn align_to<U>(&self) -> (&[T], &[U], &[T]) {
+    //     // First, find at what point do we split between the first and 2nd slice.
+    //     let x = self.as_ptr();
+    //     let offset = x.align_offset(::mem::align_of::<U>());
+    //     if offset > x * ::mem::size_of::<T>() {
+    //         return (self, [], []);
+    //     }
+
+    // }
+
+    // #[unstable(feature = "slice_align_to", issue = "44488")]
+    // pub fn align_to_mut<U>(&mut self) -> (&mut [T], &mut [U], &mut [T]) {
+    // }
+}}
+
+#[lang = "slice"]
+#[cfg(not(test))]
+#[cfg(not(stage0))]
+impl<T> [T] {
+    slice_core_methods!();
 }
 
 #[lang = "slice_u8"]

src/librustc/middle/lang_items.rs

@@ -348,6 +348,9 @@ language_item_table! {
     I128ShroFnLangItem,              "i128_shro",               i128_shro_fn;
     U128ShroFnLangItem,              "u128_shro",               u128_shro_fn;
 
+    // Align offset for stride != 1, must not panic.
+    AlignOffsetLangItem,             "align_offset",            align_offset_fn;
+
     TerminationTraitLangItem,        "termination",             termination;
 }