Pseudo C omits carry and borrow inputs from multiword arithmetic

[plafosse]

When multiword arithmetic uses ADC/SBC, Pseudo C drops the carry or borrow computed from the low halves. The high-half result consequently ignores an essential input.

repro(1, 2, UINT64_MAX, 1) should return 4, but the displayed addition returns 3. repro_borrow(5, 2, 0, 1) should return 2, but the displayed subtraction returns 3.

Original C

#include <stdint.h>

uint64_t repro(uint64_t a, uint64_t b, uint64_t low_a, uint64_t low_b)
{
    // Add two 128-bit integers and return the high half.
    // Adding UINT64_MAX + 1 in the low half must carry into a + b.
    __uint128_t lhs = ((__uint128_t)a << 64) | low_a;
    __uint128_t rhs = ((__uint128_t)b << 64) | low_b;
    return (lhs + rhs) >> 64;
}

uint64_t repro_borrow(uint64_t a, uint64_t b, uint64_t low_a, uint64_t low_b)
{
    // Subtract two 128-bit integers and return the high half.
    // Subtracting 1 from 0 in the low half must borrow from a - b.
    __uint128_t lhs = ((__uint128_t)a << 64) | low_a;
    __uint128_t rhs = ((__uint128_t)b << 64) | low_b;
    return (lhs - rhs) >> 64;
}

Observed Pseudo C

Comments below annotate the captured output; the expressions themselves are unchanged.

uint64_t repro(uint64_t a, uint64_t b, uint64_t low_a, uint64_t low_b) __pure
{
    // BUG: the low-half addition carries 1, but that input is absent.
    return a + b;
}

uint64_t repro_borrow(uint64_t a, uint64_t b, uint64_t low_a, uint64_t low_b) __pure
{
    // BUG: the low-half subtraction borrows 1, but that input is absent.
    return a - b - 0;
}

The corresponding AArch64 code is 28 bytes across the two functions:

repro:
    cmn x2, x3        // Compute the carry from low_a + low_b.
    adc x0, x0, x1    // Include that carry in the high-half addition.
    ret
repro_borrow:
    cmp x2, x3        // Determine whether the low-half subtraction borrows.
    sub x8, x0, x1
    sbc x0, x8, xzr   // Subtract the borrow from the high-half result.
    ret

HLIL retains both inputs: return adc.q(a, b, low_a + low_b u< low_a) and return sbb.q(a - b, 0, low_a u< low_b). Those carry/borrow inputs disappear in Pseudo C.

15-carry-borrow.zip