Function pow2

libs/JSystem/JAudio/System/JASCalc.cpp:312–357

Thanks Lazy Pony on decomp.me for documenting this! * Calculate 2^x as a float */

     * Calculate 2^x as a float
     */
    f32 pow2(f32 x)
    {
        s32 frac_index = 0;
        union {
            s32 l;
            f32 f;
        } exponent;
        exponent.l = (x >= 0.0f ? (s32)(x - 0.5f) : (s32)(x + 0.5f)); // Shift towards 0 and round
        f32 pannedval = x - exponent.l; // strictly between 1.5 and -1.5

        // 2^x will not fit in an IEEE-754 float
        if(exponent.l > 128) {
            return INFINITY;
        }

        // convert to exponent of IEEE-754 float
        exponent.l += 127;
        exponent.l <<= 23;

        // Calculate the mantissa

        static const f32 scale_frac[] = { 0.0f, 0.5f };
        // { 1 , 1/sqrt2 }
        static const f32 two_to_frac[] = {1.0f, 0.70710677f};
        // coefficients of Taylor polynomial of 2^x - 1 at 0:
        // 2^x - 1 = (log2) * x + (log2)^2 / 2! * x^2 + ...
        static const f32 __two_to_x[] = {
            0.6931472f, 0.24022661,
            0.055502914f, 0.009625022f,
            0.0013131053f, 1.8300806E-4f        
        };

        if (pannedval < 0.0f) {
            frac_index += 1;
        }
        
        f32 ret = pannedval + scale_frac[frac_index];

        // Evaluate Taylor polynomial using Horner's method
        ret = ret * (ret * (ret * (ret * (ret * (ret * __two_to_x[5] + __two_to_x[4]) +
            __two_to_x[3]) + __two_to_x[2]) + __two_to_x[1]) + __two_to_x[0]);
        // 2^n * (corrected mantissa)
        ret = exponent.f * (0.75f * two_to_frac[frac_index] + ((0.25f + ret) * two_to_frac[frac_index]));

        return ret;
    }
}