# Copyright (c) 2021, NVIDIA CORPORATION.  All rights reserved.
#
# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto.  Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
"""Fused multiply-add, with slightly faster gradients than `torch.addcmul()`."""

import torch

#----------------------------------------------------------------------------


def fma(a, b, c):    # => a * b + c
    return _FusedMultiplyAdd.apply(a, b, c)


#----------------------------------------------------------------------------


class _FusedMultiplyAdd(torch.autograd.Function):    # a * b + c
    @staticmethod
    def forward(ctx, a, b, c):    # pylint: disable=arguments-differ
        out = torch.addcmul(c, a, b)
        ctx.save_for_backward(a, b)
        ctx.c_shape = c.shape
        return out

    @staticmethod
    def backward(ctx, dout):    # pylint: disable=arguments-differ
        a, b = ctx.saved_tensors
        c_shape = ctx.c_shape
        da = None
        db = None
        dc = None

        if ctx.needs_input_grad[0]:
            da = _unbroadcast(dout * b, a.shape)

        if ctx.needs_input_grad[1]:
            db = _unbroadcast(dout * a, b.shape)

        if ctx.needs_input_grad[2]:
            dc = _unbroadcast(dout, c_shape)

        return da, db, dc


#----------------------------------------------------------------------------


def _unbroadcast(x, shape):
    extra_dims = x.ndim - len(shape)
    assert extra_dims >= 0
    dim = [
        i
        for i in range(x.ndim) if x.shape[i] > 1 and (i < extra_dims or shape[i - extra_dims] == 1)
    ]
    if len(dim):
        x = x.sum(dim=dim, keepdim=True)
    if extra_dims:
        x = x.reshape(-1, *x.shape[extra_dims + 1:])
    assert x.shape == shape
    return x


#----------------------------------------------------------------------------