tools/factory/specs/audio_mel_spectrogram_fused.py

"""Spec for `audio-mel-spectrogram-fused` — Whisper's log-mel front end from the complex STFT."""
import pathlib
import sys

sys.path.insert(0, str(pathlib.Path(__file__).resolve().parents[1]))
from spec import TaskSpec

SPEC = TaskSpec(
    name="audio-mel-spectrogram-fused",
    title="Write a fast fused log-mel spectrogram kernel",
    blurb=("Between the FFT and the encoder, every ASR request runs the same chain: power spectrum, mel "
           "filterbank projection, log10, and a per-clip dynamic-range clamp that depends on the maximum of "
           "the whole clip. The complex STFT of a batch of 30-second clips is well over a gigabyte, the "
           "filterbank collapses it 1.6x, and the clamp forces a second pass — so the naive version writes "
           "and re-reads four full-size temporaries for what should be one streaming kernel with a "
           "reduction in the middle."),
    keywords=["mle", "kernel-generation", "audio", "whisper", "asr", "mel-spectrogram", "reduction",
              "memory-bound"],
    module="log_mel.py",
    func="log_mel_spectrogram",
    signature="log_mel_spectrogram(stft, mel_filters)",
    returns_doc="""Whisper's log-mel spectrogram from a complex STFT.

Args:
    stft:        (B, F, NF) complex64 — STFT, F frames of NF frequency bins per clip.
    mel_filters: (NM, NF)   float32   — mel filterbank, NM mel bands.

Returns:
    out: (B, F, NM) float32 — the normalised log-mel spectrogram.""",

    reference_imports="import torch",
    reference_src='''
def log_mel_spectrogram(stft, mel_filters):
    """Power -> mel -> log10 -> per-clip clamp -> rescale, in fp32.

    Correct and simple — it is the numerical SPECIFICATION, not a performance target.
    """
    mag = stft.real.float() ** 2 + stft.imag.float() ** 2          # power spectrum (B, F, NF)
    mel = mag @ mel_filters.float().t()                            # (B, F, NM)
    log_spec = torch.log10(mel.clamp(min=1e-10))
    hi = log_spec.amax(dim=(1, 2), keepdim=True)                   # per-clip maximum
    log_spec = torch.maximum(log_spec, hi - 8.0)                   # 80 dB dynamic range
    return (log_spec + 4.0) / 4.0
''',
    make_inputs_src='''
def _mk(B, F_, NF, NM, seed):
    gen = torch.Generator(device="cuda").manual_seed(seed)
    # STFT of speech: strong low-frequency content, ~60 dB of dynamic range across frames
    tilt = torch.exp(-torch.arange(NF, device="cuda", dtype=torch.float32) / (NF / 3.0)).view(1, 1, NF)
    env = (0.05 + torch.rand(B, F_, 1, device="cuda", generator=gen) ** 2)
    re = torch.randn(B, F_, NF, device="cuda", generator=gen) * tilt * env
    im = torch.randn(B, F_, NF, device="cuda", generator=gen) * tilt * env
    stft = torch.complex(re, im)
    # triangular mel filterbank: NM overlapping triangles spread over the NF bins
    centres = torch.linspace(0, NF - 1, NM + 2, device="cuda")
    bins = torch.arange(NF, device="cuda", dtype=torch.float32).view(1, NF)
    lo, mid, hi = centres[:-2].view(NM, 1), centres[1:-1].view(NM, 1), centres[2:].view(NM, 1)
    left = (bins - lo) / (mid - lo).clamp(min=1e-6)
    right = (hi - bins) / (hi - mid).clamp(min=1e-6)
    mel_filters = torch.minimum(left, right).clamp(min=0.0).contiguous()
    return stft, mel_filters
''',
    flops_src='''
def canonical_work(B, F_, NF, NM):
    """BYTES moved, from the SHAPE ALONE.

    The complex64 STFT is read once (8 bytes per bin) and the fp32 log-mel written once (4 bytes per band).
    The per-clip maximum forces a second pass over SOMETHING, but the cheapest thing to revisit is the mel
    output, which is already counted -- so the unavoidable HBM traffic is one read of the source and one
    write of the result. The (NM, NF) filterbank is at most 400 KB and stays resident.
    """
    return B * F_ * NF * 8 + B * F_ * NM * 4
''',
    flops_formula="B * F * NF * 8   +   B * F * NM * 4",

    metric="GB/s",
    compare="tensor",
    tol=1e-4,
    shape_names=("B", "F", "NF", "NM"),
    grader_shapes=[(256, 3000, 201, 128), (224, 3000, 201, 128), (512, 1500, 201, 128),
                   (128, 3000, 401, 80), (256, 3000, 201, 80)],
    measure_shapes=[(208, 3000, 201, 128), (176, 3000, 201, 128), (416, 1500, 201, 128),
                    (104, 3000, 401, 80), (208, 3000, 201, 80)],
    measure_quick_shapes=[(16, 3000, 201, 128), (32, 1500, 201, 80), (8, 3000, 401, 128)],
    correct_shapes=[(3, 301, 201, 128), (5, 128, 65, 40), (2, 3000, 201, 128), (7, 97, 129, 80)],

    spec_md="""Per clip `b`:

```
mag[b, f, k]      = real(stft[b, f, k])^2 + imag(stft[b, f, k])^2          # power, not magnitude
mel[b, f, n]      = sum over k of  mag[b, f, k] * mel_filters[n, k]
log_spec[b, f, n] = log10( max(mel[b, f, n], 1e-10) )
hi[b]             = max over (f, n) of log_spec[b, f, n]                   # the WHOLE clip
out[b, f, n]      = (max(log_spec[b, f, n], hi[b] - 8.0) + 4.0) / 4.0
```

This is exactly `whisper.audio.log_mel_spectrogram`. The two subtleties are both in the last two lines: the
floor is **per clip**, not per frame and not per batch — it implements an 80 dB dynamic-range window relative
to that clip's loudest mel bin — and the `1e-10` clamp comes *before* the log, so silent bins do not produce
`-inf`.

The mel projection is a small dense matmul: `NF` (129–401) bins in, `NM` (40–128) bands out, applied at every
frame. The filterbank is triangular and therefore sparse-ish, but it is given to you as a dense matrix and the
counted work does not depend on how you exploit that.

`/app/reference.py` materialises `mag`, `mel` and two more full-size fp32 tensors before returning. That is
the numerical specification, not a performance target.""",

    contract_md="""| arg | shape | dtype | meaning |
|-----|-------|-------|---------|
| `stft` | `(B, F, NF)` | `complex64` | STFT, contiguous; real and imaginary interleaved |
| `mel_filters` | `(NM, NF)` | `float32` | mel filterbank, contiguous, row-major over bands |

**Return** a single tensor `out` of shape `(B, F, NM)` and dtype **float32** (fp32 is required — this feeds
the encoder's first convolution and the contract fixes it).

Both inputs are **read-only**. `F` is ragged (`97`, `301` in the correctness shapes), `NF` is 65–401 and `NM`
is 40–128; none is a multiple of a convenient tile size, and `NF` is always odd (it is `n_fft/2 + 1`).""",

    regime_md="""**Shape regime you are graded in** (the exact grader sizes are *not* disclosed): `F` in
{1500, 3000} frames (3000 = 30 s at a 10 ms hop), `NF` in {201, 401} bins, `NM` in {80, 128} mel bands, and
`B` — clips in the batch — from 128 to 512. Every graded shape moves **1.3–1.6 GiB**, dominated by the
complex64 source. Batches this size are what an offline transcription queue looks like.""",

    correctness_md="""`out` must match the reference within **relative Frobenius error `1e-4`** at every
graded shape, including the timed ones. This gate is tight because the whole pipeline is fp32 — there is no
low-precision storage to hide behind, and an independent fp32 implementation agrees to ~2e-8. It is tight
enough to catch a per-frame or per-batch clamp instead of the specified per-clip one.""",

    perf_md="""The counted traffic is one read of the complex64 STFT and one write of the fp32 result — about
1.5 GiB per graded shape. The mel projection is only ~40 GFLOP, an order of magnitude short of being the
bottleneck, so this is a bandwidth kernel with a matmul in it, not the other way round.

The reference costs about 4x the roofline: `mag` is a full-size fp32 temporary (as big as the source), `mel`
another, `log10` another, and the `amax` and `maximum` each make their own pass.

The dependency to design around is the per-clip maximum: nothing can be written in final form until the whole
clip has been reduced. Two workable shapes, and it is worth measuring both. (1) Compute `mel` and its
per-clip max in one pass, store `mel` (or `log_spec`), then a second cheap pass applies the floor and the
rescale — the second pass touches only the small output, which `canonical_work` already counts once, so the
extra traffic is the output size, not the source size. (2) Keep a clip's frames resident across a persistent
block and never write the intermediate at all — possible when `F * NM` is small enough, and a clear win when
it is.

Inside the main pass, the mel projection is `NF -> NM` per frame with the filterbank (at most 400 KB) fully
resident in shared memory or L2. Loading the complex64 source as `float2` gives 8-byte vector loads; the
power spectrum is then two FMAs per bin, and the reduction over `NF` is short enough that a warp per frame,
or a tile of frames per block, both work.""",

    precision_md="""Everything here is **float32**: the power spectrum, the filterbank projection, the
logarithm, the reduction and the output. The complex input is complex64 (two fp32 values).

Do **not** be tempted to run the mel projection through bf16 tensor cores. The power spectrum spans ~10
orders of magnitude within a clip (that is exactly why the pipeline takes a logarithm), and bf16 has three
decimal digits: the small mel bands, which are the ones the dynamic-range floor is about to act on, would be
destroyed. The `1e-4` gate is set to catch this — a bf16 projection lands around 5e-3.

fp32 accumulation over `NF` (up to 401) terms is exact enough that reduction order is irrelevant; an
independent implementation that reduces in a different order agrees to ~2e-8.

The `1e-10` clamp before the log and the `hi - 8.0` floor after it are part of the specification, in that
order.

**fp8 and bf16 are not acceptable** anywhere on this data path.""",
).validate()