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184 lines
7.0 KiB
Python
184 lines
7.0 KiB
Python
# Copyright 2019 The JAX Authors.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# https://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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from __future__ import annotations
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from collections.abc import Sequence
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from functools import partial
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import math
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import numpy as np
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from jax import lax
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from jax._src import dispatch
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from jax._src import dtypes
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from jax._src.api import jit, linear_transpose, ShapeDtypeStruct
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from jax._src.core import Primitive, is_constant_shape
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from jax._src.interpreters import ad
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from jax._src.interpreters import batching
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from jax._src.interpreters import mlir
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from jax._src.lib.mlir.dialects import hlo
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from jax._src.lib import xla_client
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__all__ = [
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"fft",
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"fft_p",
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]
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def _str_to_fft_type(s: str) -> xla_client.FftType:
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if s in ("fft", "FFT"):
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return xla_client.FftType.FFT
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elif s in ("ifft", "IFFT"):
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return xla_client.FftType.IFFT
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elif s in ("rfft", "RFFT"):
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return xla_client.FftType.RFFT
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elif s in ("irfft", "IRFFT"):
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return xla_client.FftType.IRFFT
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else:
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raise ValueError(f"Unknown FFT type '{s}'")
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@partial(jit, static_argnums=(1, 2))
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def fft(x, fft_type: xla_client.FftType | str, fft_lengths: Sequence[int]):
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if isinstance(fft_type, str):
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typ = _str_to_fft_type(fft_type)
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elif isinstance(fft_type, xla_client.FftType):
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typ = fft_type
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else:
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raise TypeError(f"Unknown FFT type value '{fft_type}'")
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if typ == xla_client.FftType.RFFT:
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if np.iscomplexobj(x):
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raise ValueError("only real valued inputs supported for rfft")
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x = lax.convert_element_type(x, dtypes.to_inexact_dtype(dtypes.dtype(x)))
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else:
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x = lax.convert_element_type(x, dtypes.to_complex_dtype(dtypes.dtype(x)))
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if len(fft_lengths) == 0:
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# XLA FFT doesn't support 0-rank.
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return x
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fft_lengths = tuple(fft_lengths)
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return fft_p.bind(x, fft_type=typ, fft_lengths=fft_lengths)
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def _fft_impl(x, fft_type, fft_lengths):
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return dispatch.apply_primitive(fft_p, x, fft_type=fft_type, fft_lengths=fft_lengths)
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_complex_dtype = lambda dtype: (np.zeros((), dtype) + np.zeros((), np.complex64)).dtype
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_real_dtype = lambda dtype: np.finfo(dtype).dtype
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def fft_abstract_eval(x, fft_type, fft_lengths):
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if len(fft_lengths) > x.ndim:
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raise ValueError(f"FFT input shape {x.shape} must have at least as many "
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f"input dimensions as fft_lengths {fft_lengths}.")
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if fft_type == xla_client.FftType.RFFT:
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if x.dtype not in (np.float32, np.float64):
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raise ValueError(f"RFFT input must be float32 or float64, got {x.dtype}")
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if x.shape[-len(fft_lengths):] != fft_lengths:
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raise ValueError(f"RFFT input shape {x.shape} minor dimensions must "
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f"be equal to fft_lengths {fft_lengths}")
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shape = (x.shape[:-len(fft_lengths)] + fft_lengths[:-1]
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+ (fft_lengths[-1] // 2 + 1,))
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dtype = _complex_dtype(x.dtype)
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elif fft_type == xla_client.FftType.IRFFT:
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if not np.issubdtype(x.dtype, np.complexfloating):
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raise ValueError("IRFFT input must be complex64 or complex128, got "
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f"{x.dtype}")
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if x.shape[-len(fft_lengths):-1] != fft_lengths[:-1]:
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raise ValueError(f"IRFFT input shape {x.shape} minor dimensions must "
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"be equal to all except the last fft_length, got "
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f"{fft_lengths=}")
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shape = x.shape[:-len(fft_lengths)] + fft_lengths
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dtype = _real_dtype(x.dtype)
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else:
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if not np.issubdtype(x.dtype, np.complexfloating):
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raise ValueError("FFT input must be complex64 or complex128, got "
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f"{x.dtype}")
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if x.shape[-len(fft_lengths):] != fft_lengths:
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raise ValueError(f"FFT input shape {x.shape} minor dimensions must "
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f"be equal to fft_lengths {fft_lengths}")
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shape = x.shape
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dtype = x.dtype
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return x.update(shape=shape, dtype=dtype)
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def _fft_lowering(ctx, x, *, fft_type, fft_lengths):
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if not is_constant_shape(fft_lengths):
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# TODO: https://github.com/openxla/stablehlo/issues/1366
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raise NotImplementedError("Shape polymorphism for FFT with non-constant fft_length is not implemented for TPU and GPU")
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return [
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hlo.FftOp(x, hlo.FftTypeAttr.get(fft_type.name),
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mlir.dense_int_array(fft_lengths)).result
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]
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def _naive_rfft(x, fft_lengths):
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y = fft(x, xla_client.FftType.FFT, fft_lengths)
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n = fft_lengths[-1]
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return y[..., : n//2 + 1]
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@partial(jit, static_argnums=1)
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def _rfft_transpose(t, fft_lengths):
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# The transpose of RFFT can't be expressed only in terms of irfft. Instead of
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# manually building up larger twiddle matrices (which would increase the
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# asymptotic complexity and is also rather complicated), we rely JAX to
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# transpose a naive RFFT implementation.
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dummy_shape = t.shape[:-len(fft_lengths)] + fft_lengths
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dummy_primal = ShapeDtypeStruct(dummy_shape, _real_dtype(t.dtype))
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transpose = linear_transpose(
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partial(_naive_rfft, fft_lengths=fft_lengths), dummy_primal)
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result, = transpose(t)
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assert result.dtype == _real_dtype(t.dtype), (result.dtype, t.dtype)
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return result
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def _irfft_transpose(t, fft_lengths):
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# The transpose of IRFFT is the RFFT of the cotangent times a scaling
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# factor and a mask. The mask scales the cotangent for the Hermitian
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# symmetric components of the RFFT by a factor of two, since these components
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# are de-duplicated in the RFFT.
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x = fft(t, xla_client.FftType.RFFT, fft_lengths)
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n = x.shape[-1]
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is_odd = fft_lengths[-1] % 2
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full = partial(lax.full_like, t, dtype=x.dtype)
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mask = lax.concatenate(
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[full(1.0, shape=(1,)),
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full(2.0, shape=(n - 2 + is_odd,)),
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full(1.0, shape=(1 - is_odd,))],
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dimension=0)
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scale = 1 / math.prod(fft_lengths)
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out = scale * lax.expand_dims(mask, range(x.ndim - 1)) * x
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assert out.dtype == _complex_dtype(t.dtype), (out.dtype, t.dtype)
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# Use JAX's convention for complex gradients
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# https://github.com/jax-ml/jax/issues/6223#issuecomment-807740707
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return lax.conj(out)
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def _fft_transpose_rule(t, operand, fft_type, fft_lengths):
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if fft_type == xla_client.FftType.RFFT:
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result = _rfft_transpose(t, fft_lengths)
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elif fft_type == xla_client.FftType.IRFFT:
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result = _irfft_transpose(t, fft_lengths)
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else:
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result = fft(t, fft_type, fft_lengths)
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return result,
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def _fft_batching_rule(batched_args, batch_dims, fft_type, fft_lengths):
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x, = batched_args
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bd, = batch_dims
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x = batching.moveaxis(x, bd, 0)
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return fft(x, fft_type, fft_lengths), 0
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fft_p = Primitive('fft')
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fft_p.def_impl(_fft_impl)
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fft_p.def_abstract_eval(fft_abstract_eval)
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mlir.register_lowering(fft_p, _fft_lowering)
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ad.deflinear2(fft_p, _fft_transpose_rule)
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batching.primitive_batchers[fft_p] = _fft_batching_rule
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