* E-241: fft/spec — fix amplitude normalization for non-power-of-2 records

First numerical-correctness (wrong-number, not crash) find of a correctness-audit
campaign that checked ngspice analyses against analytic and numpy oracles.
com_fft.c has two paths: FFTW3 (exact length-point transform, scale=length/2,
correct) and a Green's radix-2 FFT (no FFTW3) that zero-pads the `length` input
samples up to the next power of two N. The non-FFTW path normalized the
single-sided amplitude by the PADDED size (scale=N/2) instead of the true sample
count (length/2), so every FFT whose sample count is not a power of two reported
amplitudes too small by length/N -- up to 2x. A .tran essentially never yields
exactly 2^k points, so this bit the common case silently. The DC bin is the clean
discriminator (always exactly bin 0, no scalloping): a 2.0 V DC offset read back
as 2.0*length/N, e.g. 1.0009 for a 1025-sample record padded to 2048. spec had
the same error in its power normalization (intres = N*N instead of length*length;
the FFTW path already used length*length).

Fix: scale = length/2 and intres = length*length in the non-FFTW path, matching
FFTW. The frequency axis was already padding-aware, so only the magnitude scale
needed changing; power-of-2 records (length == N) and FFTW-linked builds are
unchanged. Validated against numpy: after the fix ngspice's fft matches
numpy.fft.rfft of the same zero-padded record (normalized by length) bin-by-bin
to ~1e-9. fft/spec amplitudes now change for non-power-of-2 records (they become
correct). Regression 199/199.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/frontend/com_fft.c

@@ -80,7 +80,14 @@ com_fft(wordlist *wl)
         M++;
     }
     fpts = N/2 + 1;
-    scale = ((double)N)/2;
+    /* E-241: normalize the amplitude by the ACTUAL sample count `length`, not the
+     * zero-padded FFT size N.  The Green's radix-2 FFT pads `length` samples up to
+     * the next power of two N; the single-sided amplitude of a bin is 2*|X|/length
+     * (independent of padding -- padding only interpolates the spectrum), so the
+     * scale must be length/2 to match the FFTW path above.  Using N/2 made every
+     * FFT whose sample count is not a power of two report amplitudes too small by
+     * length/N (up to 2x): e.g. a pure DC offset read half its value. */
+    scale = ((double)length)/2.0;
 #endif
 
     win = TMALLOC(double, length);
@@ -460,7 +467,10 @@ com_psd(wordlist *wl)
         fftFree();
 
         /* Re(x[0]), Re(x[N/2]), Re(x[1]), Im(x[1]), Re(x[2]), Im(x[2]), ... Re(x[N/2-1]), Im(x[N/2-1]). */
-        intres = (double)N * (double)N;
+        /* E-241: normalize the PSD by length^2 (the actual sample count), not the
+         * zero-padded FFT size N^2 -- matching the FFTW path above.  Using N^2 made
+         * the PSD of a non-power-of-two-length record too small by (length/N)^2. */
+        intres = (double)length * (double)length;
         fdvec[i][0].cx_real = reald[0]*reald[0]/intres;
         fdvec[i][0].cx_imag = 0;
         noipower = fdvec[i][0].cx_real;