short SinShortLP(short angle)
{
    // -32768 <= angle <= +32767 equaling -180 <= degrees < +180 or -Pi <= radians < +Pi
    // Returns -16384 <= return <= +16384 equaling -1 <= Sin(angle) <= +1
    // Non power of 2 scalings are more complex, as the multiplier has to be chosen to keep precision
    short multiplier = (short)
        (
            (angle < (short)0)
            ? (short)32767 + angle // short + short => short;  -1 <= multiplier <= +32767
            : (short)32767 - angle // short - short => short;  -1 <= multiplier <= +32767
        );
    return (short)
        (
            (
                angle * multiplier // short * short => int; -268468224 <= unscaled <= +268468224
                    + angle // added to compensate for using 32767 for multiplier
                            // int + short => int; -268435456 <= unscaled <= +268435456
                    + (int)8192  // + 8192 to round to nearest 16384; int + int => int
            )
            >> 14  // >> 14 same as divide by 16384; cast to short -16384 <= return <= +16384
        );
}

short SinShortHP(short angle)
{
    // -32768 <= angle <= +32767 equaling -180 <= degrees < +180 or -Pi <= radians < +Pi
    // Returns -16384 <= return <= +16384 equaling -1 <= Sin(angle) <= +1
    // Non power of 2 scalings are more complex, as the multiplier has to be chosen to keep precision
    short multiplier = (short)
        (
            (angle < (short)0)
            ? (short)32767 + angle // short + short => short;  -1 <= multiplier <= +32767
            : (short)32767 - angle // short - short => short;  -1 <= multiplier <= +32767
        );
    int unscaled = angle * multiplier // short * short => int; -268468224 <= unscaled <= +268468224
        + angle; // added to compensate for using 32767 for multiplier
                 // int + short => int; -268435456 <= unscaled <= +268435456
    short scaled = (short)((unscaled + (int)8192) // + 8192 to round to nearest 16384; int + int => int
        >> 14); // >> 14 is / 16384; cast to short -16384 <= scaled <= +16384
    short correction = (short)
        (
            (
                (
                    (scaled < (short)0)
                    ? -scaled * scaled // short * short => int; -268435456 <= int <= 0
                    : scaled * scaled // short * short => int; 0 <= int <= +268435456
                )
                - unscaled // int - int => int; ~-67108864 <= int <= ~+67108864; -134217728 <= int <= +134217728
                + (int)2048 // + 2048 to round to nearest 4096; int + int => int
            )
            >> 12 // >> 12 is / 4096; ~-16384 <= int <= ~+16384; -32768 <= int <= +32768
        ); // cast to short -32768 <= correctionUnscaled <= +32768
    return (short)
        (
            (
                (
                    correction * (short)29491 // short * short => int; ~-536870912 <= int <= ~+536870912
                    + (int)262144  // + 262144 to round to nearest 524288; int + int => int
                )
                >> 19 // >> 19 is / 524288;  ~-1024 <= int <= ~+1024
            )
            + scaled // int + int => int; -16384 <= return <= +16384
        ); // cast to short -16384 <= return <= +16384
}