AK: Implement Knuth's algorithm D for dividing UFixedBigInt's

AK/UFixedBigIntDivision.h

@@ -0,0 +1,136 @@
+/*
+ * Copyright (c) 2023, Dan Klishch <danilklishch@gmail.com>
+ *
+ * SPDX-License-Identifier: BSD-2-Clause
+ */
+
+#pragma once
+
+#include <AK/Diagnostics.h>
+#include <AK/UFixedBigInt.h>
+
+namespace AK {
+namespace Detail {
+
+template<size_t dividend_bit_size, size_t divisor_bit_size, bool restore_remainder>
+constexpr void div_mod_internal(
+    StaticStorage<false, dividend_bit_size> const& operand1,
+    StaticStorage<false, divisor_bit_size> const& operand2,
+    StaticStorage<false, dividend_bit_size>& quotient,
+    StaticStorage<false, divisor_bit_size>& remainder)
+{
+    size_t dividend_len = operand1.size(), divisor_len = operand2.size();
+    while (divisor_len > 0 && !operand2[divisor_len - 1])
+        --divisor_len;
+    while (dividend_len > 0 && !operand1[dividend_len - 1])
+        --dividend_len;
+
+    // FIXME: Should raise SIGFPE instead
+    VERIFY(divisor_len); // VERIFY(divisor != 0)
+
+    // Fast paths
+    if (divisor_len == 1 && operand2[0] == 1) { // divisor == 1
+        quotient = operand1;
+        if constexpr (restore_remainder)
+            StorageOperations::set(0, remainder);
+        return;
+    }
+
+    if (dividend_len < divisor_len) { // dividend < divisor
+        StorageOperations::set(0, quotient);
+        if constexpr (restore_remainder)
+            remainder = operand1;
+        return;
+    }
+
+    if (divisor_len == 1 && dividend_len == 1) { // NativeWord / NativeWord
+        StorageOperations::set(operand1[0] / operand2[0], quotient);
+        if constexpr (restore_remainder)
+            StorageOperations::set(operand1[0] % operand2[0], remainder);
+        return;
+    }
+
+    if (divisor_len == 1) { // BigInt by NativeWord
+        auto u = (static_cast<DoubleWord>(operand1[dividend_len - 1]) << word_size) + operand1[dividend_len - 2];
+        auto divisor = operand2[0];
+
+        auto top = u / divisor;
+        quotient[dividend_len - 1] = static_cast<NativeWord>(top >> word_size);
+        quotient[dividend_len - 2] = static_cast<NativeWord>(top);
+
+        auto carry = static_cast<NativeWord>(u % divisor);
+        for (size_t i = dividend_len - 2; i--;)
+            quotient[i] = div_mod_words(operand1[i], carry, divisor, carry);
+        for (size_t i = dividend_len; i < quotient.size(); ++i)
+            quotient[i] = 0;
+        if constexpr (restore_remainder)
+            StorageOperations::set(carry, remainder);
+        return;
+    }
+
+    // Knuth's algorithm D
+    StaticStorage<false, dividend_bit_size + word_size> dividend;
+    StorageOperations::copy(operand1, dividend);
+    auto divisor = operand2;
+
+    // D1. Normalize
+    // FIXME: Investigate GCC producing bogus -Warray-bounds when dividing u128 by u32. This code
+    //        should not be reachable at all in this case because fast paths above cover all cases
+    //        when `operand2.size() == 1`.
+    AK_IGNORE_DIAGNOSTIC("-Warray-bounds", size_t shift = count_leading_zeroes(divisor[divisor_len - 1]);)
+    StorageOperations::shift_left(dividend, shift, dividend);
+    StorageOperations::shift_left(divisor, shift, divisor);
+
+    auto divisor_approx = divisor[divisor_len - 1];
+
+    for (size_t i = dividend_len + 1; i-- > divisor_len;) {
+        // D3. Calculate qhat
+        NativeWord qhat;
+        VERIFY(dividend[i] <= divisor_approx);
+        if (dividend[i] == divisor_approx) {
+            qhat = max_word;
+        } else {
+            NativeWord rhat;
+            qhat = div_mod_words(dividend[i - 1], dividend[i], divisor_approx, rhat);
+
+            auto is_qhat_too_large = [&] {
+                return UFixedBigInt<word_size> { qhat }.wide_multiply(divisor[divisor_len - 2]) > u128 { dividend[i - 2], rhat };
+            };
+            if (is_qhat_too_large()) {
+                --qhat;
+                bool carry = false;
+                rhat = add_words(rhat, divisor_approx, carry);
+                if (!carry && is_qhat_too_large())
+                    --qhat;
+            }
+        }
+
+        // D4. Multiply & subtract
+        NativeWord mul_carry = 0;
+        bool sub_carry = false;
+        for (size_t j = 0; j < divisor_len; ++j) {
+            auto mul_result = UFixedBigInt<word_size> { qhat }.wide_multiply(divisor[j]) + mul_carry;
+            auto& output = dividend[i + j - divisor_len];
+            output = sub_words(output, mul_result.low(), sub_carry);
+            mul_carry = mul_result.high();
+        }
+        dividend[i] = sub_words(dividend[i], mul_carry, sub_carry);
+
+        if (sub_carry) {
+            // D6. Add back
+            auto dividend_part = UnsignedStorageSpan { dividend.data() + i - divisor_len, divisor_len + 1 };
+            VERIFY(StorageOperations::add<false>(dividend_part, divisor, dividend_part));
+        }
+
+        quotient[i - divisor_len] = qhat - sub_carry;
+    }
+
+    for (size_t i = dividend_len - divisor_len + 1; i < quotient.size(); ++i)
+        quotient[i] = 0;
+
+    // D8. Unnormalize
+    if constexpr (restore_remainder)
+        StorageOperations::shift_right(UnsignedStorageSpan { dividend.data(), remainder.size() }, shift, remainder);
+}
+}
+}