How Can I Efficiently Convert Between Double and int64 Using SSE/AVX?

Efficient Double/int64 Conversions with SSE/AVX

While SSE2 provides instructions for converting vectors between single-precision floats and 32-bit integers, corresponding intrinsics for double-precision and 64-bit integers are missing. Even AVX does not offer these conversions.

Fallback Techniques

In the absence of dedicated instructions, there are several approaches to simulate these conversions:

• Tricks for Truncated Conversions:

  - For values in specific ranges, using a shifted add and a bitwise XOR can convert double to uint64_t or int64_t in just two instructions.
  - Reversing these steps can perform the inverse conversions.

  • Full Range Conversions:

    • Using a series of bitwise operations and shifts, it is possible to convert uint64_t or int64_t to double with 5 or 6 instructions respectively.

Implementation Details

The trick for truncated conversions relies on the fact that double-precision floating-point values in the range [2^52, 2^53) have their lowest mantissa bit aligning with the least significant bit. By adding a specific mask value and performing a bitwise operation, the integer representation can be obtained.

The full range conversions address the sign-extension issues and exploit the fact that addition in floating-point on x86 can cancel out fractional bits, enabling the accurate reconstruction of the double-precision result.

Rounding Behavior

The truncated conversion methods follow the current rounding mode, except that round towards zero may round towards negative infinity. The full range conversions ensure correct rounding for all modes.

Availability

The presented techniques provide a workaround for the lack of direct int64_t and double conversions in SSE/AVX. These methods can be particularly useful in optimizing code where these conversions are required, providing a balance between efficiency and accuracy.

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