Array.fourier() first value incorrectly calculated

[jobogono]

The first value produced from the built-in macro function Array.fourier() is always incorrect. For each example I've tried, it appears to be incorrectly scaled by 1/sqrt(2). All subsequent values appear to be correct.

I have replicated this issue on numerous data sets (i.e., it is not a result of a specific input). Array.fourier() is implemented as a discrete Hartley transform which has factors of sqrt(2) and cos(pi/4) which I think is likely related.

A simple macro example is given below with graphs showing the input and current output (incorrect) and correct dft output.

new_array = newArray(1.044,1.516,2.197,2.752,3.363,3.947,4.53,5.183,5.725,6.35,7.308,8.405,9.863,11.433,13.447,15.433,17.683,20.113,22.891,26.225,30.516,36.669,45.558,58.225,75.738,99.141,129.183,165.794,208.891,257.155,308.766,361.308,411.516,456.419,493.058,518.711,531.613,530.433,515.961,488.516,450.669,405.197,354.752,302.488,251.586,203.877,161.891,125.766,96.419,73.294,55.822,43.113,34.086,27.613,23.044,19.655,16.947,14.808,12.905,11.363,10.058,9.086,8.433,7.877,7.697,7.488,7.058,6.752,6.419,5.877,5.266,4.655);
fourier_array = Array.fourier(new_array);
Array.print(fourier_array);