The FAU Adder

When computing with unsigned integers

The FAU adder is an adder that speed up the computation of the sum by splitting the carry chain. In order to keep the error small, some bits of the least-significant part are used in a carry prediction unit.

See the uses cases and [Echavarria2016] for details.

Header aaarith/integer/integer_approx_operations.hpp

template<size_t width, size_t lsp_width, size_t shared_bits = 0>
uinteger<width + 1> aarith::FAUadder(const uinteger<width> &a, const uinteger<width> &b)
template<size_t width, size_t lsp_width, size_t shared_bits = 0>
uinteger<width + 1> aarith::FAUsubtractor(const uinteger<width> &a, const uinteger<width> &b)

When computing with floating_points

The FAU adder can also be used when computing with floating_point numbers. Here, the FAU adder ist used to approximately compute the mantissa.

Header aaarith/float/float_approx_operations.hpp

template<size_t E, size_t M, size_t LSP, size_t SHARED>
auto aarith::FAU_add(const floating_point<E, M> lhs, const floating_point<E, M> rhs) -> floating_point<E, M>

Addition of two floating_points using the FAU adder: lhs+rhs.

Parameters

  • lhs – The first number that is to be summed up

  • rhs – The second number that is to be summed up

  • bits – The number of most-significant bits that are calculated of the mantissa addition

Template Parameters

  • E – Width of exponent

  • M – Width of mantissa including the leading 1

Returns

The sum

template<size_t E, size_t M, size_t LSP, size_t SHARED>
auto aarith::FAU_sub(const floating_point<E, M> lhs, const floating_point<E, M> rhs) -> floating_point<E, M>

Subtraction with floating_points using the FAU adder: lhs-rhs.

Parameters

  • lhs – The minuend

  • rhs – The subtrahend

  • bits – The number of most-significant bits that are calculated of the mantissa subtraction

Template Parameters

  • E – Width of exponent

  • M – Width of mantissa including the leading 1

Returns

The difference lhs-rhs