q15mulr_sat_s: Wasm SIMD arithmetic instruction

Try it

(module
  (import "console" "log" (func $log (param i32)))
  (func $main
    v128.const i16x8 16384 32767 8192 -32768 16384 16384 0 -16384
    v128.const i16x8 16384 16384 16384  32767 -16384 16384 99  16384

    i16x8.q15mulr_sat_s
    i16x8.extract_lane_s 7
    call $log
  )
  (start $main)
)

WebAssembly.instantiateStreaming(fetch("{%wasm-url%}"), { console });

The q15mulr_sat_s instruction performs a fixed-point multiplication on 8 pairs of Q15-encoded 16-bit signed integers, simultaneously, with rounding and saturation. Such operations are common in audio processing and machine learning, for example FIR/IIR audio filters and neural network inference.

Q15 is a fixed-point number format where a signed 16-bit integer represents a real number in the range −1.0 to 1.0. The value 32767 (0x7FFF) is equivalent to 1.0, and −32768 (0x8000) is equivalent to −1.0. Multiplying two Q15 numbers produces a Q30 result stored as a 32-bit integer. To get back to Q15 (16-bit), you shift right by 15.

Specifically, for each of the corresponding lanes of the two 16x8 input values, the q15mulr_sat_s instruction:

Multiplies the two values together.
Rounds the product by adding 0x4000 (2¹⁴, or 16384) to it, which rounds to the nearest integer rather than truncating.
Shifts the result right by 15, converting Q30 back to Q15.
If needed, saturates the result to clamp it to the range −32768 to 32767 and avoid wrapping. This keeps the result inside the allowable range for the Q15 format.

let's look at how we arrive at the result of our example -8192, which is the value stored in lane 7 of the output value.