Merge remote-tracking branch 'origin/master' into llvm11

The changes to install_files.h needed to put into src/libcxx.zig

1 files changed, 1786 insertions, 0 deletions

diff --git a/src/stage1/bigint.cpp b/src/stage1/bigint.cpp
new file mode 100644
index 0000000000..79a05e95a5
--- /dev/null
+++ b/src/stage1/bigint.cpp
@@ -0,0 +1,1786 @@
+/*
+ * Copyright (c) 2017 Andrew Kelley
+ *
+ * This file is part of zig, which is MIT licensed.
+ * See http://opensource.org/licenses/MIT
+ */
+
+#include "bigfloat.hpp"
+#include "bigint.hpp"
+#include "buffer.hpp"
+#include "list.hpp"
+#include "os.hpp"
+#include "softfloat.hpp"
+
+#include <limits>
+#include <algorithm>
+
+static uint64_t bigint_as_unsigned(const BigInt *bigint);
+
+static void bigint_normalize(BigInt *dest) {
+    const uint64_t *digits = bigint_ptr(dest);
+
+    size_t last_nonzero_digit = SIZE_MAX;
+    for (size_t i = 0; i < dest->digit_count; i += 1) {
+        uint64_t digit = digits[i];
+        if (digit != 0) {
+            last_nonzero_digit = i;
+        }
+    }
+    if (last_nonzero_digit == SIZE_MAX) {
+        dest->is_negative = false;
+        dest->digit_count = 0;
+    } else {
+        dest->digit_count = last_nonzero_digit + 1;
+        if (last_nonzero_digit == 0) {
+            dest->data.digit = digits[0];
+        }
+    }
+}
+
+static uint8_t digit_to_char(uint8_t digit, bool uppercase) {
+    if (digit <= 9) {
+        return digit + '0';
+    } else if (digit <= 35) {
+        return (digit - 10) + (uppercase ? 'A' : 'a');
+    } else {
+        zig_unreachable();
+    }
+}
+
+size_t bigint_bits_needed(const BigInt *op) {
+    size_t full_bits = op->digit_count * 64;
+    size_t leading_zero_count = bigint_clz(op, full_bits);
+    size_t bits_needed = full_bits - leading_zero_count;
+    return bits_needed + op->is_negative;
+}
+
+static void to_twos_complement(BigInt *dest, const BigInt *op, size_t bit_count) {
+    if (bit_count == 0 || op->digit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+    if (op->is_negative) {
+        BigInt negated = {0};
+        bigint_negate(&negated, op);
+
+        BigInt inverted = {0};
+        bigint_not(&inverted, &negated, bit_count, false);
+
+        BigInt one = {0};
+        bigint_init_unsigned(&one, 1);
+
+        bigint_add(dest, &inverted, &one);
+        return;
+    }
+
+    dest->is_negative = false;
+    const uint64_t *op_digits = bigint_ptr(op);
+    if (op->digit_count == 1) {
+        dest->data.digit = op_digits[0];
+        if (bit_count < 64) {
+            dest->data.digit &= (1ULL << bit_count) - 1;
+        }
+        dest->digit_count = 1;
+        bigint_normalize(dest);
+        return;
+    }
+    size_t digits_to_copy = bit_count / 64;
+    size_t leftover_bits = bit_count % 64;
+    dest->digit_count = digits_to_copy + ((leftover_bits == 0) ? 0 : 1);
+    if (dest->digit_count == 1 && leftover_bits == 0) {
+        dest->data.digit = op_digits[0];
+        if (dest->data.digit == 0) dest->digit_count = 0;
+        return;
+    }
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+    for (size_t i = 0; i < digits_to_copy; i += 1) {
+        uint64_t digit = (i < op->digit_count) ? op_digits[i] : 0;
+        dest->data.digits[i] = digit;
+    }
+    if (leftover_bits != 0) {
+        uint64_t digit = (digits_to_copy < op->digit_count) ? op_digits[digits_to_copy] : 0;
+        dest->data.digits[digits_to_copy] = digit & ((1ULL << leftover_bits) - 1);
+    }
+    bigint_normalize(dest);
+}
+
+static bool bit_at_index(const BigInt *bi, size_t index) {
+    size_t digit_index = index / 64;
+    if (digit_index >= bi->digit_count)
+        return false;
+    size_t digit_bit_index = index % 64;
+    const uint64_t *digits = bigint_ptr(bi);
+    uint64_t digit = digits[digit_index];
+    return ((digit >> digit_bit_index) & 0x1) == 0x1;
+}
+
+static void from_twos_complement(BigInt *dest, const BigInt *src, size_t bit_count, bool is_signed) {
+    assert(!src->is_negative);
+
+    if (bit_count == 0 || src->digit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+
+    if (is_signed && bit_at_index(src, bit_count - 1)) {
+        BigInt negative_one = {0};
+        bigint_init_signed(&negative_one, -1);
+
+        BigInt minus_one = {0};
+        bigint_add(&minus_one, src, &negative_one);
+
+        BigInt inverted = {0};
+        bigint_not(&inverted, &minus_one, bit_count, false);
+
+        bigint_negate(dest, &inverted);
+        return;
+
+    }
+
+    bigint_init_bigint(dest, src);
+}
+
+void bigint_init_unsigned(BigInt *dest, uint64_t x) {
+    if (x == 0) {
+        dest->digit_count = 0;
+        dest->is_negative = false;
+        return;
+    }
+    dest->digit_count = 1;
+    dest->data.digit = x;
+    dest->is_negative = false;
+}
+
+void bigint_init_signed(BigInt *dest, int64_t x) {
+    if (x >= 0) {
+        return bigint_init_unsigned(dest, x);
+    }
+    dest->is_negative = true;
+    dest->digit_count = 1;
+    dest->data.digit = ((uint64_t)(-(x + 1))) + 1;
+}
+
+void bigint_init_data(BigInt *dest, const uint64_t *digits, size_t digit_count, bool is_negative) {
+    if (digit_count == 0) {
+        return bigint_init_unsigned(dest, 0);
+    } else if (digit_count == 1) {
+        dest->digit_count = 1;
+        dest->data.digit = digits[0];
+        dest->is_negative = is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+
+    dest->digit_count = digit_count;
+    dest->is_negative = is_negative;
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(digit_count);
+    memcpy(dest->data.digits, digits, sizeof(uint64_t) * digit_count);
+
+    bigint_normalize(dest);
+}
+
+void bigint_init_bigint(BigInt *dest, const BigInt *src) {
+    if (src->digit_count == 0) {
+        return bigint_init_unsigned(dest, 0);
+    } else if (src->digit_count == 1) {
+        dest->digit_count = 1;
+        dest->data.digit = src->data.digit;
+        dest->is_negative = src->is_negative;
+        return;
+    }
+    dest->is_negative = src->is_negative;
+    dest->digit_count = src->digit_count;
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+    memcpy(dest->data.digits, src->data.digits, sizeof(uint64_t) * dest->digit_count);
+}
+
+void bigint_deinit(BigInt *bi) {
+    if (bi->digit_count > 1)
+        heap::c_allocator.deallocate(bi->data.digits, bi->digit_count);
+}
+
+void bigint_init_bigfloat(BigInt *dest, const BigFloat *op) {
+    float128_t zero;
+    ui32_to_f128M(0, &zero);
+
+    dest->is_negative = f128M_lt(&op->value, &zero);
+    float128_t abs_val;
+    if (dest->is_negative) {
+        f128M_sub(&zero, &op->value, &abs_val);
+    } else {
+        memcpy(&abs_val, &op->value, sizeof(float128_t));
+    }
+
+    float128_t max_u64;
+    ui64_to_f128M(UINT64_MAX, &max_u64);
+    if (f128M_le(&abs_val, &max_u64)) {
+        dest->digit_count = 1;
+        dest->data.digit = f128M_to_ui64(&op->value, softfloat_round_minMag, false);
+        bigint_normalize(dest);
+        return;
+    }
+
+    float128_t amt;
+    f128M_div(&abs_val, &max_u64, &amt);
+    float128_t remainder;
+    f128M_rem(&abs_val, &max_u64, &remainder);
+
+    dest->digit_count = 2;
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+    dest->data.digits[0] = f128M_to_ui64(&remainder, softfloat_round_minMag, false);
+    dest->data.digits[1] = f128M_to_ui64(&amt, softfloat_round_minMag, false);
+    bigint_normalize(dest);
+}
+
+bool bigint_fits_in_bits(const BigInt *bn, size_t bit_count, bool is_signed) {
+    assert(bn->digit_count != 1 || bn->data.digit != 0);
+    if (bit_count == 0) {
+        return bigint_cmp_zero(bn) == CmpEQ;
+    }
+    if (bn->digit_count == 0) {
+        return true;
+    }
+
+    if (!is_signed) {
+        if(bn->is_negative) return false;
+        size_t full_bits = bn->digit_count * 64;
+        size_t leading_zero_count = bigint_clz(bn, full_bits);
+        return bit_count >= full_bits - leading_zero_count;
+    }
+
+    BigInt one = {0};
+    bigint_init_unsigned(&one, 1);
+
+    BigInt shl_amt = {0};
+    bigint_init_unsigned(&shl_amt, bit_count - 1);
+
+    BigInt max_value_plus_one = {0};
+    bigint_shl(&max_value_plus_one, &one, &shl_amt);
+
+    BigInt max_value = {0};
+    bigint_sub(&max_value, &max_value_plus_one, &one);
+
+    BigInt min_value = {0};
+    bigint_negate(&min_value, &max_value_plus_one);
+
+    Cmp min_cmp = bigint_cmp(bn, &min_value);
+    Cmp max_cmp = bigint_cmp(bn, &max_value);
+
+    return (min_cmp == CmpGT || min_cmp == CmpEQ) && (max_cmp == CmpLT || max_cmp == CmpEQ);
+}
+
+void bigint_write_twos_complement(const BigInt *big_int, uint8_t *buf, size_t bit_count, bool is_big_endian) {
+    if (bit_count == 0)
+        return;
+
+    BigInt twos_comp = {0};
+    to_twos_complement(&twos_comp, big_int, bit_count);
+
+    const uint64_t *twos_comp_digits = bigint_ptr(&twos_comp);
+
+    size_t bits_in_last_digit = bit_count % 64;
+    if (bits_in_last_digit == 0) bits_in_last_digit = 64;
+    size_t bytes_in_last_digit = (bits_in_last_digit + 7) / 8;
+    size_t unwritten_byte_count = 8 - bytes_in_last_digit;
+
+    if (is_big_endian) {
+        size_t last_digit_index = (bit_count - 1) / 64;
+        size_t digit_index = last_digit_index;
+        size_t buf_index = 0;
+        for (;;) {
+            uint64_t x = (digit_index < twos_comp.digit_count) ? twos_comp_digits[digit_index] : 0;
+
+            for (size_t byte_index = 7;;) {
+                uint8_t byte = x & 0xff;
+                if (digit_index == last_digit_index) {
+                    buf[buf_index + byte_index - unwritten_byte_count] = byte;
+                    if (byte_index == unwritten_byte_count) break;
+                } else {
+                    buf[buf_index + byte_index] = byte;
+                }
+
+                if (byte_index == 0) break;
+                byte_index -= 1;
+                x >>= 8;
+            }
+
+            if (digit_index == 0) break;
+            digit_index -= 1;
+            if (digit_index == last_digit_index) {
+                buf_index += bytes_in_last_digit;
+            } else {
+                buf_index += 8;
+            }
+        }
+    } else {
+        size_t digit_count = (bit_count + 63) / 64;
+        size_t buf_index = 0;
+        for (size_t digit_index = 0; digit_index < digit_count; digit_index += 1) {
+            uint64_t x = (digit_index < twos_comp.digit_count) ? twos_comp_digits[digit_index] : 0;
+
+            for (size_t byte_index = 0;
+                byte_index < 8 && (digit_index + 1 < digit_count || byte_index < bytes_in_last_digit);
+                byte_index += 1)
+            {
+                uint8_t byte = x & 0xff;
+                buf[buf_index] = byte;
+                buf_index += 1;
+                x >>= 8;
+            }
+        }
+    }
+}
+
+
+void bigint_read_twos_complement(BigInt *dest, const uint8_t *buf, size_t bit_count, bool is_big_endian,
+        bool is_signed)
+{
+    if (bit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+
+    dest->digit_count = (bit_count + 63) / 64;
+    uint64_t *digits;
+    if (dest->digit_count == 1) {
+        digits = &dest->data.digit;
+    } else {
+        digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+        dest->data.digits = digits;
+    }
+
+    size_t bits_in_last_digit = bit_count % 64;
+    if (bits_in_last_digit == 0) {
+        bits_in_last_digit = 64;
+    }
+    size_t bytes_in_last_digit = (bits_in_last_digit + 7) / 8;
+    size_t unread_byte_count = 8 - bytes_in_last_digit;
+
+    if (is_big_endian) {
+        size_t buf_index = 0;
+        uint64_t digit = 0;
+        for (size_t byte_index = unread_byte_count; byte_index < 8; byte_index += 1) {
+            uint8_t byte = buf[buf_index];
+            buf_index += 1;
+            digit <<= 8;
+            digit |= byte;
+        }
+        digits[dest->digit_count - 1] = digit;
+        for (size_t digit_index = 1; digit_index < dest->digit_count; digit_index += 1) {
+            digit = 0;
+            for (size_t byte_index = 0; byte_index < 8; byte_index += 1) {
+                uint8_t byte = buf[buf_index];
+                buf_index += 1;
+                digit <<= 8;
+                digit |= byte;
+            }
+            digits[dest->digit_count - 1 - digit_index] = digit;
+        }
+    } else {
+        size_t buf_index = 0;
+        for (size_t digit_index = 0; digit_index < dest->digit_count; digit_index += 1) {
+            uint64_t digit = 0;
+            size_t end_byte_index = (digit_index == dest->digit_count - 1) ? bytes_in_last_digit : 8;
+            for (size_t byte_index = 0; byte_index < end_byte_index; byte_index += 1) {
+                uint64_t byte = buf[buf_index];
+                buf_index += 1;
+
+                digit |= byte << (8 * byte_index);
+            }
+            digits[digit_index] = digit;
+        }
+    }
+
+    if (is_signed) {
+        bigint_normalize(dest);
+        BigInt tmp = {0};
+        bigint_init_bigint(&tmp, dest);
+        from_twos_complement(dest, &tmp, bit_count, true);
+    } else {
+        dest->is_negative = false;
+        bigint_normalize(dest);
+    }
+}
+
+#if defined(_MSC_VER)
+static bool add_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+   *result = op1 + op2;
+   return *result < op1 || *result < op2;
+}
+
+static bool sub_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+   *result = op1 - op2;
+   return *result > op1;
+}
+
+bool mul_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+    *result = op1 * op2;
+
+    if (op1 == 0 || op2 == 0)
+        return false;
+
+    if (op1 > UINT64_MAX / op2)
+        return true;
+
+    if (op2 > UINT64_MAX / op1)
+        return true;
+
+    return false;
+}
+#else
+static bool add_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+    return __builtin_uaddll_overflow((unsigned long long)op1, (unsigned long long)op2,
+            (unsigned long long *)result);
+}
+
+static bool sub_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+    return __builtin_usubll_overflow((unsigned long long)op1, (unsigned long long)op2,
+            (unsigned long long *)result);
+}
+
+bool mul_u64_overflow(uint64_t op1, uint64_t op2, uint64_t *result) {
+    return __builtin_umulll_overflow((unsigned long long)op1, (unsigned long long)op2,
+            (unsigned long long *)result);
+}
+#endif
+
+void bigint_add(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->digit_count == 0) {
+        return bigint_init_bigint(dest, op2);
+    }
+    if (op2->digit_count == 0) {
+        return bigint_init_bigint(dest, op1);
+    }
+    if (op1->is_negative == op2->is_negative) {
+        dest->is_negative = op1->is_negative;
+
+        const uint64_t *op1_digits = bigint_ptr(op1);
+        const uint64_t *op2_digits = bigint_ptr(op2);
+        bool overflow = add_u64_overflow(op1_digits[0], op2_digits[0], &dest->data.digit);
+        if (overflow == 0 && op1->digit_count == 1 && op2->digit_count == 1) {
+            dest->digit_count = 1;
+            bigint_normalize(dest);
+            return;
+        }
+        size_t i = 1;
+        uint64_t first_digit = dest->data.digit;
+        dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(max(op1->digit_count, op2->digit_count) + 1);
+        dest->data.digits[0] = first_digit;
+
+        for (;;) {
+            bool found_digit = false;
+            uint64_t x = overflow;
+            overflow = 0;
+
+            if (i < op1->digit_count) {
+                found_digit = true;
+                uint64_t digit = op1_digits[i];
+                overflow += add_u64_overflow(x, digit, &x);
+            }
+
+            if (i < op2->digit_count) {
+                found_digit = true;
+                uint64_t digit = op2_digits[i];
+                overflow += add_u64_overflow(x, digit, &x);
+            }
+
+            dest->data.digits[i] = x;
+            i += 1;
+
+            if (!found_digit) {
+                dest->digit_count = i;
+                bigint_normalize(dest);
+                return;
+            }
+        }
+    }
+    const BigInt *op_pos;
+    const BigInt *op_neg;
+    if (op1->is_negative) {
+        op_neg = op1;
+        op_pos = op2;
+    } else {
+        op_pos = op1;
+        op_neg = op2;
+    }
+
+    BigInt op_neg_abs = {0};
+    bigint_negate(&op_neg_abs, op_neg);
+    const BigInt *bigger_op;
+    const BigInt *smaller_op;
+    switch (bigint_cmp(op_pos, &op_neg_abs)) {
+        case CmpEQ:
+            bigint_init_unsigned(dest, 0);
+            return;
+        case CmpLT:
+            bigger_op = &op_neg_abs;
+            smaller_op = op_pos;
+            dest->is_negative = true;
+            break;
+        case CmpGT:
+            bigger_op = op_pos;
+            smaller_op = &op_neg_abs;
+            dest->is_negative = false;
+            break;
+    }
+    const uint64_t *bigger_op_digits = bigint_ptr(bigger_op);
+    const uint64_t *smaller_op_digits = bigint_ptr(smaller_op);
+    uint64_t overflow = sub_u64_overflow(bigger_op_digits[0], smaller_op_digits[0], &dest->data.digit);
+    if (overflow == 0 && bigger_op->digit_count == 1 && smaller_op->digit_count == 1) {
+        dest->digit_count = 1;
+        bigint_normalize(dest);
+        return;
+    }
+    uint64_t first_digit = dest->data.digit;
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(bigger_op->digit_count);
+    dest->data.digits[0] = first_digit;
+    size_t i = 1;
+
+    for (;;) {
+        bool found_digit = false;
+        uint64_t x = bigger_op_digits[i];
+        uint64_t prev_overflow = overflow;
+        overflow = 0;
+
+        if (i < smaller_op->digit_count) {
+            found_digit = true;
+            uint64_t digit = smaller_op_digits[i];
+            overflow += sub_u64_overflow(x, digit, &x);
+        }
+        if (sub_u64_overflow(x, prev_overflow, &x)) {
+            found_digit = true;
+            overflow += 1;
+        }
+        dest->data.digits[i] = x;
+        i += 1;
+
+        if (!found_digit || i >= bigger_op->digit_count)
+            break;
+    }
+    assert(overflow == 0);
+    dest->digit_count = i;
+    bigint_normalize(dest);
+}
+
+void bigint_add_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed) {
+    BigInt unwrapped = {0};
+    bigint_add(&unwrapped, op1, op2);
+    bigint_truncate(dest, &unwrapped, bit_count, is_signed);
+}
+
+void bigint_sub(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    BigInt op2_negated = {0};
+    bigint_negate(&op2_negated, op2);
+    return bigint_add(dest, op1, &op2_negated);
+}
+
+void bigint_sub_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed) {
+    BigInt op2_negated = {0};
+    bigint_negate(&op2_negated, op2);
+    return bigint_add_wrap(dest, op1, &op2_negated, bit_count, is_signed);
+}
+
+static void mul_overflow(uint64_t op1, uint64_t op2, uint64_t *lo, uint64_t *hi) {
+    uint64_t u1 = (op1 & 0xffffffff);
+    uint64_t v1 = (op2 & 0xffffffff);
+    uint64_t t = (u1 * v1);
+    uint64_t w3 = (t & 0xffffffff);
+    uint64_t k = (t >> 32);
+
+    op1 >>= 32;
+    t = (op1 * v1) + k;
+    k = (t & 0xffffffff);
+    uint64_t w1 = (t >> 32);
+
+    op2 >>= 32;
+    t = (u1 * op2) + k;
+    k = (t >> 32);
+
+    *hi = (op1 * op2) + w1 + k;
+    *lo = (t << 32) + w3;
+}
+
+static void mul_scalar(BigInt *dest, const BigInt *op, uint64_t scalar) {
+    bigint_init_unsigned(dest, 0);
+
+    BigInt bi_64;
+    bigint_init_unsigned(&bi_64, 64);
+
+    const uint64_t *op_digits = bigint_ptr(op);
+    size_t i = op->digit_count - 1;
+
+    for (;;) {
+        BigInt shifted;
+        bigint_shl(&shifted, dest, &bi_64);
+
+        uint64_t result_scalar;
+        uint64_t carry_scalar;
+        mul_overflow(scalar, op_digits[i], &result_scalar, &carry_scalar);
+
+        BigInt result;
+        bigint_init_unsigned(&result, result_scalar);
+
+        BigInt carry;
+        bigint_init_unsigned(&carry, carry_scalar);
+
+        BigInt carry_shifted;
+        bigint_shl(&carry_shifted, &carry, &bi_64);
+
+        BigInt tmp;
+        bigint_add(&tmp, &shifted, &carry_shifted);
+
+        bigint_add(dest, &tmp, &result);
+
+        if (i == 0) {
+            break;
+        }
+        i -= 1;
+    }
+}
+
+void bigint_mul(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->digit_count == 0 || op2->digit_count == 0) {
+        return bigint_init_unsigned(dest, 0);
+    }
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    const uint64_t *op2_digits = bigint_ptr(op2);
+
+    uint64_t carry;
+    mul_overflow(op1_digits[0], op2_digits[0], &dest->data.digit, &carry);
+    if (carry == 0 && op1->digit_count == 1 && op2->digit_count == 1) {
+        dest->is_negative = (op1->is_negative != op2->is_negative);
+        dest->digit_count = 1;
+        bigint_normalize(dest);
+        return;
+    }
+
+    bigint_init_unsigned(dest, 0);
+
+    BigInt bi_64;
+    bigint_init_unsigned(&bi_64, 64);
+
+    size_t i = op2->digit_count - 1;
+    for (;;) {
+        BigInt shifted;
+        bigint_shl(&shifted, dest, &bi_64);
+
+        BigInt scalar_result;
+        mul_scalar(&scalar_result, op1, op2_digits[i]);
+
+        bigint_add(dest, &scalar_result, &shifted);
+
+        if (i == 0) {
+            break;
+        }
+        i -= 1;
+    }
+
+    dest->is_negative = (op1->is_negative != op2->is_negative);
+    bigint_normalize(dest);
+}
+
+void bigint_mul_wrap(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed) {
+    BigInt unwrapped = {0};
+    bigint_mul(&unwrapped, op1, op2);
+    bigint_truncate(dest, &unwrapped, bit_count, is_signed);
+}
+
+enum ZeroBehavior {
+  /// \brief The returned value is undefined.
+  ZB_Undefined,
+  /// \brief The returned value is numeric_limits<T>::max()
+  ZB_Max,
+  /// \brief The returned value is numeric_limits<T>::digits
+  ZB_Width
+};
+
+template <typename T, std::size_t SizeOfT> struct LeadingZerosCounter {
+  static std::size_t count(T Val, ZeroBehavior) {
+    if (!Val)
+      return std::numeric_limits<T>::digits;
+
+    // Bisection method.
+    std::size_t ZeroBits = 0;
+    for (T Shift = std::numeric_limits<T>::digits >> 1; Shift; Shift >>= 1) {
+      T Tmp = Val >> Shift;
+      if (Tmp)
+        Val = Tmp;
+      else
+        ZeroBits |= Shift;
+    }
+    return ZeroBits;
+  }
+};
+
+#if __GNUC__ >= 4 || defined(_MSC_VER)
+template <typename T> struct LeadingZerosCounter<T, 4> {
+  static std::size_t count(T Val, ZeroBehavior ZB) {
+    if (ZB != ZB_Undefined && Val == 0)
+      return 32;
+
+#if defined(_MSC_VER)
+    unsigned long Index;
+    _BitScanReverse(&Index, Val);
+    return Index ^ 31;
+#else
+    return __builtin_clz(Val);
+#endif
+  }
+};
+
+#if !defined(_MSC_VER) || defined(_M_X64)
+template <typename T> struct LeadingZerosCounter<T, 8> {
+  static std::size_t count(T Val, ZeroBehavior ZB) {
+    if (ZB != ZB_Undefined && Val == 0)
+      return 64;
+
+#if defined(_MSC_VER)
+    unsigned long Index;
+    _BitScanReverse64(&Index, Val);
+    return Index ^ 63;
+#else
+    return __builtin_clzll(Val);
+#endif
+  }
+};
+#endif
+#endif
+
+/// \brief Count number of 0's from the most significant bit to the least
+///   stopping at the first 1.
+///
+/// Only unsigned integral types are allowed.
+///
+/// \param ZB the behavior on an input of 0. Only ZB_Width and ZB_Undefined are
+///   valid arguments.
+template <typename T>
+std::size_t countLeadingZeros(T Val, ZeroBehavior ZB = ZB_Width) {
+  static_assert(std::numeric_limits<T>::is_integer &&
+                    !std::numeric_limits<T>::is_signed,
+                "Only unsigned integral types are allowed.");
+  return LeadingZerosCounter<T, sizeof(T)>::count(Val, ZB);
+}
+
+/// Make a 64-bit integer from a high / low pair of 32-bit integers.
+constexpr inline uint64_t Make_64(uint32_t High, uint32_t Low) {
+  return ((uint64_t)High << 32) | (uint64_t)Low;
+}
+
+/// Return the high 32 bits of a 64 bit value.
+constexpr inline uint32_t Hi_32(uint64_t Value) {
+  return static_cast<uint32_t>(Value >> 32);
+}
+
+/// Return the low 32 bits of a 64 bit value.
+constexpr inline uint32_t Lo_32(uint64_t Value) {
+  return static_cast<uint32_t>(Value);
+}
+
+/// Implementation of Knuth's Algorithm D (Division of nonnegative integers)
+/// from "Art of Computer Programming, Volume 2", section 4.3.1, p. 272. The
+/// variables here have the same names as in the algorithm. Comments explain
+/// the algorithm and any deviation from it.
+static void KnuthDiv(uint32_t *u, uint32_t *v, uint32_t *q, uint32_t* r,
+                     unsigned m, unsigned n)
+{
+    assert(u && "Must provide dividend");
+    assert(v && "Must provide divisor");
+    assert(q && "Must provide quotient");
+    assert(u != v && u != q && v != q && "Must use different memory");
+    assert(n>1 && "n must be > 1");
+
+    // b denotes the base of the number system. In our case b is 2^32.
+    const uint64_t b = uint64_t(1) << 32;
+
+    // D1. [Normalize.] Set d = b / (v[n-1] + 1) and multiply all the digits of
+    // u and v by d. Note that we have taken Knuth's advice here to use a power
+    // of 2 value for d such that d * v[n-1] >= b/2 (b is the base). A power of
+    // 2 allows us to shift instead of multiply and it is easy to determine the
+    // shift amount from the leading zeros.  We are basically normalizing the u
+    // and v so that its high bits are shifted to the top of v's range without
+    // overflow. Note that this can require an extra word in u so that u must
+    // be of length m+n+1.
+    unsigned shift = countLeadingZeros(v[n-1]);
+    uint32_t v_carry = 0;
+    uint32_t u_carry = 0;
+    if (shift) {
+        for (unsigned i = 0; i < m+n; ++i) {
+            uint32_t u_tmp = u[i] >> (32 - shift);
+            u[i] = (u[i] << shift) | u_carry;
+            u_carry = u_tmp;
+        }
+        for (unsigned i = 0; i < n; ++i) {
+            uint32_t v_tmp = v[i] >> (32 - shift);
+            v[i] = (v[i] << shift) | v_carry;
+            v_carry = v_tmp;
+        }
+    }
+    u[m+n] = u_carry;
+
+    // D2. [Initialize j.]  Set j to m. This is the loop counter over the places.
+    int j = m;
+    do {
+        // D3. [Calculate q'.].
+        //     Set qp = (u[j+n]*b + u[j+n-1]) / v[n-1]. (qp=qprime=q')
+        //     Set rp = (u[j+n]*b + u[j+n-1]) % v[n-1]. (rp=rprime=r')
+        // Now test if qp == b or qp*v[n-2] > b*rp + u[j+n-2]; if so, decrease
+        // qp by 1, increase rp by v[n-1], and repeat this test if rp < b. The test
+        // on v[n-2] determines at high speed most of the cases in which the trial
+        // value qp is one too large, and it eliminates all cases where qp is two
+        // too large.
+        uint64_t dividend = Make_64(u[j+n], u[j+n-1]);
+        uint64_t qp = dividend / v[n-1];
+        uint64_t rp = dividend % v[n-1];
+        if (qp == b || qp*v[n-2] > b*rp + u[j+n-2]) {
+            qp--;
+            rp += v[n-1];
+            if (rp < b && (qp == b || qp*v[n-2] > b*rp + u[j+n-2]))
+                qp--;
+        }
+
+        // D4. [Multiply and subtract.] Replace (u[j+n]u[j+n-1]...u[j]) with
+        // (u[j+n]u[j+n-1]..u[j]) - qp * (v[n-1]...v[1]v[0]). This computation
+        // consists of a simple multiplication by a one-place number, combined with
+        // a subtraction.
+        // The digits (u[j+n]...u[j]) should be kept positive; if the result of
+        // this step is actually negative, (u[j+n]...u[j]) should be left as the
+        // true value plus b**(n+1), namely as the b's complement of
+        // the true value, and a "borrow" to the left should be remembered.
+        int64_t borrow = 0;
+        for (unsigned i = 0; i < n; ++i) {
+            uint64_t p = uint64_t(qp) * uint64_t(v[i]);
+            int64_t subres = int64_t(u[j+i]) - borrow - Lo_32(p);
+            u[j+i] = Lo_32(subres);
+            borrow = Hi_32(p) - Hi_32(subres);
+        }
+        bool isNeg = u[j+n] < borrow;
+        u[j+n] -= Lo_32(borrow);
+
+        // D5. [Test remainder.] Set q[j] = qp. If the result of step D4 was
+        // negative, go to step D6; otherwise go on to step D7.
+        q[j] = Lo_32(qp);
+        if (isNeg) {
+            // D6. [Add back]. The probability that this step is necessary is very
+            // small, on the order of only 2/b. Make sure that test data accounts for
+            // this possibility. Decrease q[j] by 1
+            q[j]--;
+            // and add (0v[n-1]...v[1]v[0]) to (u[j+n]u[j+n-1]...u[j+1]u[j]).
+            // A carry will occur to the left of u[j+n], and it should be ignored
+            // since it cancels with the borrow that occurred in D4.
+            bool carry = false;
+            for (unsigned i = 0; i < n; i++) {
+                uint32_t limit = std::min(u[j+i],v[i]);
+                u[j+i] += v[i] + carry;
+                carry = u[j+i] < limit || (carry && u[j+i] == limit);
+            }
+            u[j+n] += carry;
+        }
+
+        // D7. [Loop on j.]  Decrease j by one. Now if j >= 0, go back to D3.
+    } while (--j >= 0);
+
+    // D8. [Unnormalize]. Now q[...] is the desired quotient, and the desired
+    // remainder may be obtained by dividing u[...] by d. If r is non-null we
+    // compute the remainder (urem uses this).
+    if (r) {
+        // The value d is expressed by the "shift" value above since we avoided
+        // multiplication by d by using a shift left. So, all we have to do is
+        // shift right here.
+        if (shift) {
+            uint32_t carry = 0;
+            for (int i = n-1; i >= 0; i--) {
+                r[i] = (u[i] >> shift) | carry;
+                carry = u[i] << (32 - shift);
+            }
+        } else {
+            for (int i = n-1; i >= 0; i--) {
+                r[i] = u[i];
+            }
+        }
+    }
+}
+
+// Implementation ported from LLVM/lib/Support/APInt.cpp
+static void bigint_unsigned_division(const BigInt *op1, const BigInt *op2, BigInt *Quotient, BigInt *Remainder) {
+    Cmp cmp = bigint_cmp(op1, op2);
+    if (cmp == CmpLT) {
+        if (Quotient != nullptr) {
+            bigint_init_unsigned(Quotient, 0);
+        }
+        if (Remainder != nullptr) {
+            bigint_init_bigint(Remainder, op1);
+        }
+        return;
+    }
+    if (cmp == CmpEQ) {
+        if (Quotient != nullptr) {
+            bigint_init_unsigned(Quotient, 1);
+        }
+        if (Remainder != nullptr) {
+            bigint_init_unsigned(Remainder, 0);
+        }
+        return;
+    }
+
+    const uint64_t *LHS = bigint_ptr(op1);
+    const uint64_t *RHS = bigint_ptr(op2);
+    unsigned lhsWords = op1->digit_count;
+    unsigned rhsWords = op2->digit_count;
+
+    // First, compose the values into an array of 32-bit words instead of
+    // 64-bit words. This is a necessity of both the "short division" algorithm
+    // and the Knuth "classical algorithm" which requires there to be native
+    // operations for +, -, and * on an m bit value with an m*2 bit result. We
+    // can't use 64-bit operands here because we don't have native results of
+    // 128-bits. Furthermore, casting the 64-bit values to 32-bit values won't
+    // work on large-endian machines.
+    unsigned n = rhsWords * 2;
+    unsigned m = (lhsWords * 2) - n;
+
+    // Allocate space for the temporary values we need either on the stack, if
+    // it will fit, or on the heap if it won't.
+    uint32_t SPACE[128];
+    uint32_t *U = nullptr;
+    uint32_t *V = nullptr;
+    uint32_t *Q = nullptr;
+    uint32_t *R = nullptr;
+    if ((Remainder?4:3)*n+2*m+1 <= 128) {
+        U = &SPACE[0];
+        V = &SPACE[m+n+1];
+        Q = &SPACE[(m+n+1) + n];
+        if (Remainder)
+            R = &SPACE[(m+n+1) + n + (m+n)];
+    } else {
+        U = new uint32_t[m + n + 1];
+        V = new uint32_t[n];
+        Q = new uint32_t[m+n];
+        if (Remainder)
+            R = new uint32_t[n];
+    }
+
+    // Initialize the dividend
+    memset(U, 0, (m+n+1)*sizeof(uint32_t));
+    for (unsigned i = 0; i < lhsWords; ++i) {
+        uint64_t tmp = LHS[i];
+        U[i * 2] = Lo_32(tmp);
+        U[i * 2 + 1] = Hi_32(tmp);
+    }
+    U[m+n] = 0; // this extra word is for "spill" in the Knuth algorithm.
+
+    // Initialize the divisor
+    memset(V, 0, (n)*sizeof(uint32_t));
+    for (unsigned i = 0; i < rhsWords; ++i) {
+        uint64_t tmp = RHS[i];
+        V[i * 2] = Lo_32(tmp);
+        V[i * 2 + 1] = Hi_32(tmp);
+    }
+
+    // initialize the quotient and remainder
+    memset(Q, 0, (m+n) * sizeof(uint32_t));
+    if (Remainder)
+        memset(R, 0, n * sizeof(uint32_t));
+
+    // Now, adjust m and n for the Knuth division. n is the number of words in
+    // the divisor. m is the number of words by which the dividend exceeds the
+    // divisor (i.e. m+n is the length of the dividend). These sizes must not
+    // contain any zero words or the Knuth algorithm fails.
+    for (unsigned i = n; i > 0 && V[i-1] == 0; i--) {
+        n--;
+        m++;
+    }
+    for (unsigned i = m+n; i > 0 && U[i-1] == 0; i--)
+        m--;
+
+    // If we're left with only a single word for the divisor, Knuth doesn't work
+    // so we implement the short division algorithm here. This is much simpler
+    // and faster because we are certain that we can divide a 64-bit quantity
+    // by a 32-bit quantity at hardware speed and short division is simply a
+    // series of such operations. This is just like doing short division but we
+    // are using base 2^32 instead of base 10.
+    assert(n != 0 && "Divide by zero?");
+    if (n == 1) {
+        uint32_t divisor = V[0];
+        uint32_t remainder = 0;
+        for (int i = m; i >= 0; i--) {
+            uint64_t partial_dividend = Make_64(remainder, U[i]);
+            if (partial_dividend == 0) {
+                Q[i] = 0;
+                remainder = 0;
+            } else if (partial_dividend < divisor) {
+                Q[i] = 0;
+                remainder = Lo_32(partial_dividend);
+            } else if (partial_dividend == divisor) {
+                Q[i] = 1;
+                remainder = 0;
+            } else {
+                Q[i] = Lo_32(partial_dividend / divisor);
+                remainder = Lo_32(partial_dividend - (Q[i] * divisor));
+            }
+        }
+        if (R)
+            R[0] = remainder;
+    } else {
+        // Now we're ready to invoke the Knuth classical divide algorithm. In this
+        // case n > 1.
+        KnuthDiv(U, V, Q, R, m, n);
+    }
+
+    // If the caller wants the quotient
+    if (Quotient) {
+        Quotient->is_negative = false;
+        Quotient->digit_count = lhsWords;
+        if (lhsWords == 1) {
+            Quotient->data.digit = Make_64(Q[1], Q[0]);
+        } else {
+            Quotient->data.digits = heap::c_allocator.allocate<uint64_t>(lhsWords);
+            for (size_t i = 0; i < lhsWords; i += 1) {
+                Quotient->data.digits[i] = Make_64(Q[i*2+1], Q[i*2]);
+            }
+        }
+    }
+
+    // If the caller wants the remainder
+    if (Remainder) {
+        Remainder->is_negative = false;
+        Remainder->digit_count = rhsWords;
+        if (rhsWords == 1) {
+            Remainder->data.digit = Make_64(R[1], R[0]);
+        } else {
+            Remainder->data.digits = heap::c_allocator.allocate<uint64_t>(rhsWords);
+            for (size_t i = 0; i < rhsWords; i += 1) {
+                Remainder->data.digits[i] = Make_64(R[i*2+1], R[i*2]);
+            }
+        }
+    }
+}
+
+void bigint_div_trunc(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    assert(op2->digit_count != 0); // division by zero
+    if (op1->digit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    const uint64_t *op2_digits = bigint_ptr(op2);
+    if (op1->digit_count == 1 && op2->digit_count == 1) {
+        dest->data.digit = op1_digits[0] / op2_digits[0];
+        dest->digit_count = 1;
+        dest->is_negative = op1->is_negative != op2->is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+    if (op2->digit_count == 1 && op2_digits[0] == 1) {
+        // X / 1 == X
+        bigint_init_bigint(dest, op1);
+        dest->is_negative = op1->is_negative != op2->is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+
+    const BigInt *op1_positive;
+    BigInt op1_positive_data;
+    if (op1->is_negative) {
+        bigint_negate(&op1_positive_data, op1);
+        op1_positive = &op1_positive_data;
+    } else {
+        op1_positive = op1;
+    }
+
+    const BigInt *op2_positive;
+    BigInt op2_positive_data;
+    if (op2->is_negative) {
+        bigint_negate(&op2_positive_data, op2);
+        op2_positive = &op2_positive_data;
+    } else {
+        op2_positive = op2;
+    }
+
+    bigint_unsigned_division(op1_positive, op2_positive, dest, nullptr);
+    dest->is_negative = op1->is_negative != op2->is_negative;
+    bigint_normalize(dest);
+}
+
+void bigint_div_floor(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->is_negative != op2->is_negative) {
+        bigint_div_trunc(dest, op1, op2);
+        BigInt mult_again = {0};
+        bigint_mul(&mult_again, dest, op2);
+        mult_again.is_negative = op1->is_negative;
+        if (bigint_cmp(&mult_again, op1) != CmpEQ) {
+            BigInt tmp = {0};
+            bigint_init_bigint(&tmp, dest);
+            BigInt neg_one = {0};
+            bigint_init_signed(&neg_one, -1);
+            bigint_add(dest, &tmp, &neg_one);
+        }
+        bigint_normalize(dest);
+    } else {
+        bigint_div_trunc(dest, op1, op2);
+    }
+}
+
+void bigint_rem(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    assert(op2->digit_count != 0); // division by zero
+    if (op1->digit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    const uint64_t *op2_digits = bigint_ptr(op2);
+
+    if (op1->digit_count == 1 && op2->digit_count == 1) {
+        dest->data.digit = op1_digits[0] % op2_digits[0];
+        dest->digit_count = 1;
+        dest->is_negative = op1->is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+    if (op2->digit_count == 2 && op2_digits[0] == 0 && op2_digits[1] == 1) {
+        // special case this divisor
+        bigint_init_unsigned(dest, op1_digits[0]);
+        dest->is_negative = op1->is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+
+    if (op2->digit_count == 1 && op2_digits[0] == 1) {
+        // X % 1 == 0
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+
+    const BigInt *op1_positive;
+    BigInt op1_positive_data;
+    if (op1->is_negative) {
+        bigint_negate(&op1_positive_data, op1);
+        op1_positive = &op1_positive_data;
+    } else {
+        op1_positive = op1;
+    }
+
+    const BigInt *op2_positive;
+    BigInt op2_positive_data;
+    if (op2->is_negative) {
+        bigint_negate(&op2_positive_data, op2);
+        op2_positive = &op2_positive_data;
+    } else {
+        op2_positive = op2;
+    }
+
+    bigint_unsigned_division(op1_positive, op2_positive, nullptr, dest);
+    dest->is_negative = op1->is_negative;
+    bigint_normalize(dest);
+}
+
+void bigint_mod(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->is_negative) {
+        BigInt first_rem;
+        bigint_rem(&first_rem, op1, op2);
+        first_rem.is_negative = !op2->is_negative;
+        BigInt op2_minus_rem;
+        bigint_add(&op2_minus_rem, op2, &first_rem);
+        bigint_rem(dest, &op2_minus_rem, op2);
+        dest->is_negative = false;
+    } else {
+        bigint_rem(dest, op1, op2);
+        dest->is_negative = false;
+    }
+}
+
+void bigint_or(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->digit_count == 0) {
+        return bigint_init_bigint(dest, op2);
+    }
+    if (op2->digit_count == 0) {
+        return bigint_init_bigint(dest, op1);
+    }
+    if (op1->is_negative || op2->is_negative) {
+        size_t big_bit_count = max(bigint_bits_needed(op1), bigint_bits_needed(op2));
+
+        BigInt twos_comp_op1 = {0};
+        to_twos_complement(&twos_comp_op1, op1, big_bit_count);
+
+        BigInt twos_comp_op2 = {0};
+        to_twos_complement(&twos_comp_op2, op2, big_bit_count);
+
+        BigInt twos_comp_dest = {0};
+        bigint_or(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
+
+        from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
+    } else {
+        dest->is_negative = false;
+        const uint64_t *op1_digits = bigint_ptr(op1);
+        const uint64_t *op2_digits = bigint_ptr(op2);
+        if (op1->digit_count == 1 && op2->digit_count == 1) {
+            dest->digit_count = 1;
+            dest->data.digit = op1_digits[0] | op2_digits[0];
+            bigint_normalize(dest);
+            return;
+        }
+        dest->digit_count = max(op1->digit_count, op2->digit_count);
+        dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+        for (size_t i = 0; i < dest->digit_count; i += 1) {
+            uint64_t digit = 0;
+            if (i < op1->digit_count) {
+                digit |= op1_digits[i];
+            }
+            if (i < op2->digit_count) {
+                digit |= op2_digits[i];
+            }
+            dest->data.digits[i] = digit;
+        }
+        bigint_normalize(dest);
+    }
+}
+
+void bigint_and(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->digit_count == 0 || op2->digit_count == 0) {
+        return bigint_init_unsigned(dest, 0);
+    }
+    if (op1->is_negative || op2->is_negative) {
+        size_t big_bit_count = max(bigint_bits_needed(op1), bigint_bits_needed(op2));
+
+        BigInt twos_comp_op1 = {0};
+        to_twos_complement(&twos_comp_op1, op1, big_bit_count);
+
+        BigInt twos_comp_op2 = {0};
+        to_twos_complement(&twos_comp_op2, op2, big_bit_count);
+
+        BigInt twos_comp_dest = {0};
+        bigint_and(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
+
+        from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
+    } else {
+        dest->is_negative = false;
+        const uint64_t *op1_digits = bigint_ptr(op1);
+        const uint64_t *op2_digits = bigint_ptr(op2);
+        if (op1->digit_count == 1 && op2->digit_count == 1) {
+            dest->digit_count = 1;
+            dest->data.digit = op1_digits[0] & op2_digits[0];
+            bigint_normalize(dest);
+            return;
+        }
+
+        dest->digit_count = max(op1->digit_count, op2->digit_count);
+        dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+
+        size_t i = 0;
+        for (; i < op1->digit_count && i < op2->digit_count; i += 1) {
+            dest->data.digits[i] = op1_digits[i] & op2_digits[i];
+        }
+        for (; i < dest->digit_count; i += 1) {
+            dest->data.digits[i] = 0;
+        }
+        bigint_normalize(dest);
+    }
+}
+
+void bigint_xor(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    if (op1->digit_count == 0) {
+        return bigint_init_bigint(dest, op2);
+    }
+    if (op2->digit_count == 0) {
+        return bigint_init_bigint(dest, op1);
+    }
+    if (op1->is_negative || op2->is_negative) {
+        size_t big_bit_count = max(bigint_bits_needed(op1), bigint_bits_needed(op2));
+
+        BigInt twos_comp_op1 = {0};
+        to_twos_complement(&twos_comp_op1, op1, big_bit_count);
+
+        BigInt twos_comp_op2 = {0};
+        to_twos_complement(&twos_comp_op2, op2, big_bit_count);
+
+        BigInt twos_comp_dest = {0};
+        bigint_xor(&twos_comp_dest, &twos_comp_op1, &twos_comp_op2);
+
+        from_twos_complement(dest, &twos_comp_dest, big_bit_count, true);
+    } else {
+        dest->is_negative = false;
+        const uint64_t *op1_digits = bigint_ptr(op1);
+        const uint64_t *op2_digits = bigint_ptr(op2);
+
+        assert(op1->digit_count > 0 && op2->digit_count > 0);
+        if (op1->digit_count == 1 && op2->digit_count == 1) {
+            dest->digit_count = 1;
+            dest->data.digit = op1_digits[0] ^ op2_digits[0];
+            bigint_normalize(dest);
+            return;
+        }
+        dest->digit_count = max(op1->digit_count, op2->digit_count);
+        dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+        size_t i = 0;
+        for (; i < op1->digit_count && i < op2->digit_count; i += 1) {
+            dest->data.digits[i] = op1_digits[i] ^ op2_digits[i];
+        }
+        for (; i < dest->digit_count; i += 1) {
+            if (i < op1->digit_count) {
+                dest->data.digits[i] = op1_digits[i];
+            } else if (i < op2->digit_count) {
+                dest->data.digits[i] = op2_digits[i];
+            } else {
+                zig_unreachable();
+            }
+        }
+        bigint_normalize(dest);
+    }
+}
+
+void bigint_shl(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    assert(!op2->is_negative);
+
+    if (op2->digit_count == 0) {
+        bigint_init_bigint(dest, op1);
+        return;
+    }
+
+    if (op1->digit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+
+    if (op2->digit_count != 1) {
+        zig_panic("TODO shift left by amount greater than 64 bit integer");
+    }
+
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    uint64_t shift_amt = bigint_as_unsigned(op2);
+
+    if (op1->digit_count == 1 && shift_amt < 64) {
+        dest->data.digit = op1_digits[0] << shift_amt;
+        if (dest->data.digit > op1_digits[0]) {
+            dest->digit_count = 1;
+            dest->is_negative = op1->is_negative;
+            return;
+        }
+    }
+
+    uint64_t digit_shift_count = shift_amt / 64;
+    uint64_t leftover_shift_count = shift_amt % 64;
+
+    dest->data.digits = heap::c_allocator.allocate<uint64_t>(op1->digit_count + digit_shift_count + 1);
+    dest->digit_count = digit_shift_count;
+    uint64_t carry = 0;
+    for (size_t i = 0; i < op1->digit_count; i += 1) {
+        uint64_t digit = op1_digits[i];
+        dest->data.digits[dest->digit_count] = carry | (digit << leftover_shift_count);
+        dest->digit_count += 1;
+        if (leftover_shift_count > 0) {
+            carry = digit >> (64 - leftover_shift_count);
+        } else {
+            carry = 0;
+        }
+    }
+    dest->data.digits[dest->digit_count] = carry;
+    dest->digit_count += 1;
+    dest->is_negative = op1->is_negative;
+    bigint_normalize(dest);
+}
+
+void bigint_shl_trunc(BigInt *dest, const BigInt *op1, const BigInt *op2, size_t bit_count, bool is_signed) {
+    BigInt unwrapped = {0};
+    bigint_shl(&unwrapped, op1, op2);
+    bigint_truncate(dest, &unwrapped, bit_count, is_signed);
+}
+
+void bigint_shr(BigInt *dest, const BigInt *op1, const BigInt *op2) {
+    assert(!op2->is_negative);
+
+    if (op1->digit_count == 0) {
+        return bigint_init_unsigned(dest, 0);
+    }
+
+    if (op2->digit_count == 0) {
+        return bigint_init_bigint(dest, op1);
+    }
+
+    if (op2->digit_count != 1) {
+        zig_panic("TODO shift right by amount greater than 64 bit integer");
+    }
+
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    uint64_t shift_amt = bigint_as_unsigned(op2);
+
+    if (op1->digit_count == 1) {
+        dest->data.digit = (shift_amt < 64) ? op1_digits[0] >> shift_amt : 0;
+        dest->digit_count = 1;
+        dest->is_negative = op1->is_negative;
+        bigint_normalize(dest);
+        return;
+    }
+
+    size_t digit_shift_count = shift_amt / 64;
+    size_t leftover_shift_count = shift_amt % 64;
+
+    if (digit_shift_count >= op1->digit_count) {
+        return bigint_init_unsigned(dest, 0);
+    }
+
+    dest->digit_count = op1->digit_count - digit_shift_count;
+    uint64_t *digits;
+    if (dest->digit_count == 1) {
+        digits = &dest->data.digit;
+    } else {
+        digits = heap::c_allocator.allocate<uint64_t>(dest->digit_count);
+        dest->data.digits = digits;
+    }
+
+    uint64_t carry = 0;
+    for (size_t op_digit_index = op1->digit_count - 1;;) {
+        uint64_t digit = op1_digits[op_digit_index];
+        size_t dest_digit_index = op_digit_index - digit_shift_count;
+        digits[dest_digit_index] = carry | (digit >> leftover_shift_count);
+        carry = (leftover_shift_count != 0) ? (digit << (64 - leftover_shift_count)) : 0;
+
+        if (dest_digit_index == 0) { break; }
+        op_digit_index -= 1;
+    }
+    dest->is_negative = op1->is_negative;
+    bigint_normalize(dest);
+}
+
+void bigint_negate(BigInt *dest, const BigInt *op) {
+    bigint_init_bigint(dest, op);
+    dest->is_negative = !dest->is_negative;
+    bigint_normalize(dest);
+}
+
+void bigint_negate_wrap(BigInt *dest, const BigInt *op, size_t bit_count) {
+    BigInt zero;
+    bigint_init_unsigned(&zero, 0);
+    bigint_sub_wrap(dest, &zero, op, bit_count, true);
+}
+
+void bigint_not(BigInt *dest, const BigInt *op, size_t bit_count, bool is_signed) {
+    if (bit_count == 0) {
+        bigint_init_unsigned(dest, 0);
+        return;
+    }
+
+    if (is_signed) {
+        BigInt twos_comp = {0};
+        to_twos_complement(&twos_comp, op, bit_count);
+
+        BigInt inverted = {0};
+        bigint_not(&inverted, &twos_comp, bit_count, false);
+
+        from_twos_complement(dest, &inverted, bit_count, true);
+        return;
+    }
+
+    assert(!op->is_negative);
+
+    dest->is_negative = false;
+    const uint64_t *op_digits = bigint_ptr(op);
+    if (bit_count <= 64) {
+        dest->digit_count = 1;
+        if (op->digit_count == 0) {
+            if (bit_count == 64) {
+                dest->data.digit = UINT64_MAX;
+            } else {
+                dest->data.digit = (1ULL << bit_count) - 1;
+            }
+        } else if (op->digit_count == 1) {
+            dest->data.digit = ~op_digits[0];
+            if (bit_count != 64) {
+                uint64_t mask = (1ULL << bit_count) - 1;
+                dest->data.digit &= mask;
+            }
+        }
+        bigint_normalize(dest);
+        return;
+    }
+    dest->digit_count = (bit_count + 63) / 64;
+    assert(dest->digit_count >= op->digit_count);
+    dest->data.digits = heap::c_allocator.allocate_nonzero<uint64_t>(dest->digit_count);
+    size_t i = 0;
+    for (; i < op->digit_count; i += 1) {
+        dest->data.digits[i] = ~op_digits[i];
+    }
+    for (; i < dest->digit_count; i += 1) {
+        dest->data.digits[i] = 0xffffffffffffffffULL;
+    }
+    size_t digit_index = dest->digit_count - 1;
+    size_t digit_bit_index = bit_count % 64;
+    if (digit_bit_index != 0) {
+        uint64_t mask = (1ULL << digit_bit_index) - 1;
+        dest->data.digits[digit_index] &= mask;
+    }
+    bigint_normalize(dest);
+}
+
+void bigint_truncate(BigInt *dest, const BigInt *op, size_t bit_count, bool is_signed) {
+    BigInt twos_comp;
+    to_twos_complement(&twos_comp, op, bit_count);
+    from_twos_complement(dest, &twos_comp, bit_count, is_signed);
+}
+
+Cmp bigint_cmp(const BigInt *op1, const BigInt *op2) {
+    if (op1->is_negative && !op2->is_negative) {
+        return CmpLT;
+    } else if (!op1->is_negative && op2->is_negative) {
+        return CmpGT;
+    } else if (op1->digit_count > op2->digit_count) {
+        return op1->is_negative ? CmpLT : CmpGT;
+    } else if (op2->digit_count > op1->digit_count) {
+        return op1->is_negative ? CmpGT : CmpLT;
+    } else if (op1->digit_count == 0) {
+        return CmpEQ;
+    }
+    const uint64_t *op1_digits = bigint_ptr(op1);
+    const uint64_t *op2_digits = bigint_ptr(op2);
+    for (size_t i = op1->digit_count - 1; ;) {
+        uint64_t op1_digit = op1_digits[i];
+        uint64_t op2_digit = op2_digits[i];
+
+        if (op1_digit > op2_digit) {
+            return op1->is_negative ? CmpLT : CmpGT;
+        }
+        if (op1_digit < op2_digit) {
+            return op1->is_negative ? CmpGT : CmpLT;
+        }
+
+        if (i == 0) {
+            return CmpEQ;
+        }
+        i -= 1;
+    }
+}
+
+void bigint_append_buf(Buf *buf, const BigInt *op, uint64_t base) {
+    if (op->digit_count == 0) {
+        buf_append_char(buf, '0');
+        return;
+    }
+    if (op->is_negative) {
+        buf_append_char(buf, '-');
+    }
+    if (op->digit_count == 1 && base == 10) {
+        buf_appendf(buf, "%" ZIG_PRI_u64, op->data.digit);
+        return;
+    }
+    if (op->digit_count == 1 && base == 16) {
+        buf_appendf(buf, "%" ZIG_PRI_x64, op->data.digit);
+        return;
+    }
+    size_t first_digit_index = buf_len(buf);
+
+    BigInt digit_bi = {0};
+    BigInt a1 = {0};
+    BigInt a2 = {0};
+
+    BigInt *a = &a1;
+    BigInt *other_a = &a2;
+    bigint_init_bigint(a, op);
+
+    BigInt base_bi = {0};
+    bigint_init_unsigned(&base_bi, base);
+
+    for (;;) {
+        bigint_rem(&digit_bi, a, &base_bi);
+        uint8_t digit = bigint_as_unsigned(&digit_bi);
+        buf_append_char(buf, digit_to_char(digit, false));
+        bigint_div_trunc(other_a, a, &base_bi);
+        {
+            BigInt *tmp = a;
+            a = other_a;
+            other_a = tmp;
+        }
+        if (bigint_cmp_zero(a) == CmpEQ) {
+            break;
+        }
+    }
+
+    // reverse
+    for (size_t i = first_digit_index; i < buf_len(buf) / 2; i += 1) {
+        size_t other_i = buf_len(buf) + first_digit_index - i - 1;
+        uint8_t tmp = buf_ptr(buf)[i];
+        buf_ptr(buf)[i] = buf_ptr(buf)[other_i];
+        buf_ptr(buf)[other_i] = tmp;
+    }
+}
+
+size_t bigint_popcount_unsigned(const BigInt *bi) {
+    assert(!bi->is_negative);
+    if (bi->digit_count == 0)
+        return 0;
+
+    size_t count = 0;
+    size_t bit_count = bi->digit_count * 64;
+    for (size_t i = 0; i < bit_count; i += 1) {
+        if (bit_at_index(bi, i))
+            count += 1;
+    }
+    return count;
+}
+
+size_t bigint_popcount_signed(const BigInt *bi, size_t bit_count) {
+    if (bit_count == 0)
+        return 0;
+    if (bi->digit_count == 0)
+        return 0;
+
+    BigInt twos_comp = {0};
+    to_twos_complement(&twos_comp, bi, bit_count);
+
+    size_t count = 0;
+    for (size_t i = 0; i < bit_count; i += 1) {
+        if (bit_at_index(&twos_comp, i))
+            count += 1;
+    }
+    return count;
+}
+
+size_t bigint_ctz(const BigInt *bi, size_t bit_count) {
+    if (bit_count == 0)
+        return 0;
+    if (bi->digit_count == 0)
+        return bit_count;
+
+    BigInt twos_comp = {0};
+    to_twos_complement(&twos_comp, bi, bit_count);
+
+    size_t count = 0;
+    for (size_t i = 0; i < bit_count; i += 1) {
+        if (bit_at_index(&twos_comp, i))
+            return count;
+        count += 1;
+    }
+    return count;
+}
+
+size_t bigint_clz(const BigInt *bi, size_t bit_count) {
+    if (bi->is_negative || bit_count == 0)
+        return 0;
+    if (bi->digit_count == 0)
+        return bit_count;
+
+    size_t count = 0;
+    for (size_t i = bit_count - 1;;) {
+        if (bit_at_index(bi, i))
+            return count;
+        count += 1;
+
+        if (i == 0) break;
+        i -= 1;
+    }
+    return count;
+}
+
+static uint64_t bigint_as_unsigned(const BigInt *bigint) {
+    assert(!bigint->is_negative);
+    if (bigint->digit_count == 0) {
+        return 0;
+    } else if (bigint->digit_count == 1) {
+        return bigint->data.digit;
+    } else {
+        zig_unreachable();
+    }
+}
+
+uint64_t bigint_as_u64(const BigInt *bigint)
+{
+    return bigint_as_unsigned(bigint);
+}
+
+uint32_t bigint_as_u32(const BigInt *bigint) {
+    uint64_t value64 = bigint_as_unsigned(bigint);
+    uint32_t value32 = (uint32_t)value64;
+    assert (value64 == value32);
+    return value32;
+}
+
+size_t bigint_as_usize(const BigInt *bigint) {
+    uint64_t value64 = bigint_as_unsigned(bigint);
+    size_t valueUsize = (size_t)value64;
+    assert (value64 == valueUsize);
+    return valueUsize;
+}
+
+int64_t bigint_as_signed(const BigInt *bigint) {
+    if (bigint->digit_count == 0) {
+        return 0;
+    } else if (bigint->digit_count == 1) {
+        if (bigint->is_negative) {
+            if (bigint->data.digit <= 9223372036854775808ULL) {
+                return (-((int64_t)(bigint->data.digit - 1))) - 1;
+            } else {
+                zig_unreachable();
+            }
+        } else {
+            return bigint->data.digit;
+        }
+    } else {
+        zig_unreachable();
+    }
+}
+
+Cmp bigint_cmp_zero(const BigInt *op) {
+    if (op->digit_count == 0) {
+        return CmpEQ;
+    }
+    return op->is_negative ? CmpLT : CmpGT;
+}
+
+uint32_t bigint_hash(BigInt x) {
+    if (x.digit_count == 0) {
+        return 0;
+    } else {
+        return bigint_ptr(&x)[0];
+    }
+}
+
+bool bigint_eql(BigInt a, BigInt b) {
+    return bigint_cmp(&a, &b) == CmpEQ;
+}
+
+void bigint_incr(BigInt *x) {
+    if (x->digit_count == 0) {
+        bigint_init_unsigned(x, 1);
+        return;
+    }
+
+    if (x->digit_count == 1) {
+        if (x->is_negative && x->data.digit != 0) {
+            x->data.digit -= 1;
+            return;
+        } else if (!x->is_negative && x->data.digit != UINT64_MAX) {
+            x->data.digit += 1;
+            return;
+        }
+    }
+
+    BigInt copy;
+    bigint_init_bigint(&copy, x);
+
+    BigInt one;
+    bigint_init_unsigned(&one, 1);
+
+    bigint_add(x, &copy, &one);
+}
+
+void bigint_decr(BigInt *x) {
+    if (x->digit_count == 0) {
+        bigint_init_signed(x, -1);
+        return;
+    }
+
+    if (x->digit_count == 1) {
+        if (x->is_negative && x->data.digit != UINT64_MAX) {
+            x->data.digit += 1;
+            return;
+        } else if (!x->is_negative && x->data.digit != 0) {
+            x->data.digit -= 1;
+            return;
+        }
+    }
+
+    BigInt copy;
+    bigint_init_bigint(&copy, x);
+
+    BigInt neg_one;
+    bigint_init_signed(&neg_one, -1);
+
+    bigint_add(x, &copy, &neg_one);
+}