Enhancement-241 fixed an amplitude normalization that divided by the ZERO-PADDED
transform size instead of the number of input samples -- in the `fft` COMMAND
(frontend/com_fft.c). The identical mistake survived in maths/cmaths/cmath4.c, the
vector-expression function reached by `let F = fft(v)`: a separate implementation of
the same computation.
Found by continuing the oracle campaign that produced E-241, and located with E-241's
own discriminator, the DC bin. One signal, 4001 samples padded to 4096, DC offset 2.0:
fft s ; the COMMAND -> mag(s)[0] = 2.000000 correct
let F = fft(s) ; the FUNCTION -> mag(F)[0] = 1.953613 = 2.0 * 4001/4096
X[0] is the sum of the samples, D*length for a DC offset D, so dividing by the padded N
reads back D*length/N. As E-241 put it: a DC value cannot depend on how many samples
were taken.
This is a contradiction, not a matter of convention. cx_fft holds TWO complete
implementations -- one for complex input, one for real -- and each has an FFTW branch
and a Green's radix-2 branch. In BOTH, the FFTW branch already used the input length
while Green's used the padded size:
real branch FFTW: scale = ((double)length)/2.0 Green: ((double)N)/2 <- wrong
complex branch FFTW: scale = (double) fpts Green: (double) N <- wrong
the correct version sitting a few lines from the wrong one inside the same function --
the same shape as `avg` disagreeing with `integ` in E-302. HAVE_LIBFFTW3 is undefined in
this build, so Green's is the live path and the defect was reachable.
oracle before after closed form
real-input, DC bin 1.953613 2.000000 2.0
real-input, ifft(fft(x)) 2.3e-02 1.1e-16 0
complex-input, bin 0 0.9766780 0.9998683 0.9998683
The round trip is an INDEPENDENT confirmation: nothing here touches ifft, so its going
from 2.3% error to machine precision is evidence from a direction the fix did not aim
at -- the pair only inverts when the forward normalization is right. cx_ifft was
audited and deliberately left alone for that reason.
Every caller of the Green's radix-2 kernel was audited, not only the one that failed:
com_fft.c's fft (x2) and spec/PSD (x2) are correct from E-241; cx_ifft is correct;
trannoise/1-f-code.c cannot pad at all, since n_pts is grown to 2^n_exp by construction;
and fft/ifft are the only transform functions in the expression table, so there is no
spec twin to miss.
Verification: examples/fftexpr_examples/verify_fftexpr.py -- 6 checks under both
solvers, all against closed form (DC bin on both paths, round trip padded and unpadded,
complex-input bin 0 against the analytic mean of an RC response). It scores 3/6 on the
pre-fix binary, so it is a real regression guard. E-241's own suite (fftnorm_examples)
and ifftreal_examples pass unchanged. Full sweep 241/241 OK.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
For each type of device, a *convTest function determines if the
current through that device is converged within tolerance,
and sets CKTnoncon if the current is not yet converged.
ASCRconvTest() erroneously subtracted old current from old,
rather than old from new, when evaluating convergence.
Also, since at least 3f5, the calling function NIconvTest assumed
that the worker functions indicated non-convergence through their
return value, so was ignoring the reports of current nonconvergence.
Window of fixed time width given by 'set mtimeavgwindow=400u'
Length and scale of newvec resembles the original vetor vec.
Large vec and large mtimeavgwindow take their time.
OpenMP is used if available.
node history, interpolation may produce an infinite value at digital edges.
Remove vertical edges when interpolating and make some other improvements:
do not calculate a polynomial approximation for unused frames;
center the target x-value in the frame; and do not propogate a reduction
in degree to later frames.
does not have any means to further analyze or repair the issue:
Warning: KLU ReFactor failed. Factoring again...
Warning (ReFactor Complex): KLU Matrix is SINGULAR
Numerical Rank: %d\n
Singular Node: %d\n
So print these messages only in debug mode.
Meisam Bahadori
Brian Taylor
Holger Vogt
Keith OHara
geraldfournier
dwarning
dwarning
dwarning
Giles Atkinson
Francesco Lannutti
Francesco Lannutti