Why Does My Multi-Precision Floating-Point (mpfl) Addition Fail to Propagate Carry Bits Correctly?

Carry Propagation Issue in mpfl Addition

Your mpfl addition function encounters an issue with propagating the carry value correctly, resulting in an incorrect sum. Specifically, after adding two 32-bit values, if the result exceeds the range of a single 32-bit value, the carry bit is not propagated properly, leading to an incorrect sum.

Architectural Approach

To resolve this issue, it's beneficial to consider an ALU (Arithmetic Logic Unit) architecture similar to those used in hardware implementations. By modeling your code after the operation of an ALU, you can simplify and improve the accuracy of your calculations.

Correcting the Code

The following code provides a revised version of your addition function that addresses the carry propagation issue:

mpfl operator+(const mpfl &lhs, const mpfl &rhs)
{
    unsigned long i;
    mpfl ret(0);
    mpfl trhs(rhs);

    ALU32 alu;

    for (i = lhs.nbytes; i >= 0; i--)
    {
        alu.adc(ret.data[i].data,
                lhs.data[i].data,
                trhs.data[i].data);
        if (i < lhs.nbytes)
        {
            if (ret.data[i].data == 255 && ret.data[i + 1].carry == 1)
                increment(&trhs, i + 1);
        }
    }
    return ret;
}

Key Modifications

• Using an ALU: The ALU32 class implements an ALU architecture, allowing you to perform arithmetic operations in a manner similar to a real-world ALU.
• Carry Preservation: The adc() function is used to perform the addition with carry, ensuring that the carry bit is propagated correctly.
• Overflow Handling: The increment() function ensures that if the sum of two 8-bit values exceeds 255, the carry bit is propagated to the next digit.

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