handle multi-word division edge case

Signed-off-by: Andrew Whitehead <cywolf@gmail.com>

Author: andrewwhitehead

src/uint/div_limb.rs

@@ -151,11 +151,12 @@ pub(crate) const fn div3by2(
     v: Word,
 ) -> (Word, WideWord) {
     let d = word::join(d0, d1);
+    let u_hi = word::join(u1, u2);
 
     debug_assert!(d >= (1 << (WideWord::BITS - 1)), "divisor top bit unset");
-    debug_assert!(word::join(u1, u2) < d, "dividend >= divisor");
+    debug_assert!(u_hi <= d, "dividend > divisor");
 
-    let q = (v as WideWord * u2 as WideWord) + word::join(u1, u2);
+    let q = (v as WideWord * u2 as WideWord) + u_hi;
     let q1w = q >> Word::BITS;
     let r1 = u1.wrapping_sub((q1w as Word).wrapping_mul(d1));
     let t = d0 as WideWord * q1w;
@@ -170,6 +171,13 @@ pub(crate) const fn div3by2(
     let q1 = word::select(q1, q1.wrapping_add(1), r_ge_d);
     let r = word::select_wide(r, r.wrapping_sub(d), r_ge_d);
 
+    // When the leading dividend word equals the leading divisor word, cap the quotient
+    // at WideWord::MAX and update the remainder. This differs from the original algorithm
+    // but is required for multi-word division.
+    let maxed = word::choice_from_wide_eq(u_hi, d);
+    let q1 = word::select(q1, Word::MAX, maxed);
+    let r = word::select_wide(r, d.saturating_add(u0 as WideWord), maxed);
+
     (q1, r)
 }
 

src/word.rs

@@ -64,6 +64,12 @@ pub(crate) const fn choice_from_eq(x: Word, y: Word) -> Choice {
     choice_from_nz(x ^ y).not()
 }
 
+/// Returns the truthy value if `x == y`, and the falsy value otherwise.
+#[inline]
+pub(crate) const fn choice_from_wide_eq(x: WideWord, y: WideWord) -> Choice {
+    choice_from_wide_nz(x ^ y).not()
+}
+
 /// Returns the truthy value if `x > y`, and the falsy value otherwise.
 #[inline]
 pub(crate) const fn choice_from_gt(x: Word, y: Word) -> Choice {
@@ -95,6 +101,12 @@ pub(crate) const fn choice_from_nz(value: Word) -> Choice {
     choice_from_lsb((value | value.wrapping_neg()) >> (Word::BITS - 1))
 }
 
+/// Returns the truthy value if `value != 0`, and the falsy value otherwise.
+#[inline]
+pub(crate) const fn choice_from_wide_nz(value: WideWord) -> Choice {
+    choice_from_lsb(((value | value.wrapping_neg()) >> (WideWord::BITS - 1)) as Word)
+}
+
 /// Return `b` if `self` is truthy, otherwise return `a`.
 #[inline]
 pub(crate) const fn select(a: Word, b: Word, choice: Choice) -> Word {