/**
 * @license
 * Copyright 2018 Google Inc. All Rights Reserved.
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 * =============================================================================
 */

import {ENGINE} from '../engine';
import {Tensor} from '../tensor';
import {convertToTensor} from '../tensor_util_env';
import {TensorLike} from '../types';
import * as util from '../util';
import {op} from './operation';
import {scalar, zerosLike} from './tensor_ops';

/**
 * Computes `-1 * x` element-wise.
 *
 * ```js
 * const x = tf.tensor2d([1, 2, -2, 0], [2, 2]);
 *
 * x.neg().print();  // or tf.neg(x)
 * ```
 *
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function neg_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'neg');

  const grad = (dy: T) => {
    return {$x: () => dy.neg()};
  };
  return ENGINE.runKernel(backend => backend.neg($x), {$x}, grad);
}

/**
 * Computes ceiling of input `tf.Tensor` element-wise: `ceil(x)`
 *
 * ```js
 * const x = tf.tensor1d([.6, 1.1, -3.3]);
 *
 * x.ceil().print();  // or tf.ceil(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function ceil_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'ceil');

  // TODO(manrajgrover): Return null for gradients when backprop supports it.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.ceil($x), {$x}, grad);
}

/**
 * Computes floor of input `tf.Tensor` element-wise: `floor(x)`.
 *
 * ```js
 * const x = tf.tensor1d([.6, 1.1, -3.3]);
 *
 * x.floor().print();  // or tf.floor(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function floor_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'floor');

  // TODO(nsthorat): Let gradients be null for cases where we want to stop
  // backpropgation.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.floor($x), {$x}, grad);
}

/**
 * Returns an element-wise indication of the sign of a number.
 *
 * ```js
 * const x = tf.tensor1d([.6, 1.1, -3.3, NaN, 0]);
 *
 * x.sign().print();  // or tf.sign(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function sign_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'sign');

  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.sign($x), {$x}, grad);
}

/**
 * RReturns which elements of x are NaN.
 *
 * ```js
 * const x = tf.tensor1d([NaN, Infinity, -Infinity, 0, 1]);
 *
 * x.isNaN().print();  // or tf.isNaN(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function isNaN_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'isNaN');

  // TODO(nsthorat): Let gradients be null for cases where we want to stop
  // backpropgation.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.isNaN($x), {$x}, grad);
}

/**
 * Returns which elements of x are Infinity or -Infinity.
 *
 * ```js
 * const x = tf.tensor1d([NaN, Infinity, -Infinity, 0, 1]);
 *
 * x.isInf().print();  // or tf.isNaN(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function isInf_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'isInf');

  // TODO(nsthorat): Let gradients be null for cases where we want to stop
  // backpropgation.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.isInf($x), {$x}, grad);
}

/**
 * Returns which elements of x are finite.
 *
 * ```js
 * const x = tf.tensor1d([NaN, Infinity, -Infinity, 0, 1]);
 *
 * x.isFinite().print();  // or tf.isNaN(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function isFinite_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'isFinite');

  // TODO(nsthorat): Let gradients be null for cases where we want to stop
  // backpropgation.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.isFinite($x), {$x}, grad);
}

/**
 * Computes round of input `tf.Tensor` element-wise: `round(x)`.
 * It implements banker's rounding.
 *
 * ```js
 * const x = tf.tensor1d([.6, 1.1, -3.3]);
 *
 * x.round().print();  // or tf.round(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function round_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'round');

  // TODO(nsthorat): Let gradients be null for cases where we want to stop
  // backpropgation.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.round($x), {$x}, grad);
}

/**
 * Computes exponential of the input `tf.Tensor` element-wise. `e ^ x`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, -3]);
 *
 * x.exp().print();  // or tf.exp(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function exp_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'exp');

  const bck = (dy: T, saved: Tensor[]) => {
    return {$x: () => dy.mulStrict(saved[0] as T)};
  };
  return ENGINE.runKernel((backend, save) => {
    const y = backend.exp($x);
    save([y]);
    return y;
  }, {$x}, bck);
}

/**
 * Computes exponential of the input `tf.Tensor` minus one element-wise.
 * `e ^ x - 1`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, -3]);
 *
 * x.expm1().print();  // or tf.expm1(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function expm1_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'expm1');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.mul($x.exp()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.expm1($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes natural logarithm of the input `tf.Tensor` element-wise: `ln(x)`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, Math.E]);
 *
 * x.log().print();  // or tf.log(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function log_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'log');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.toFloat()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.log($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes natural logarithm of the input `tf.Tensor` plus one
 * element-wise: `ln(1 + x)`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, Math.E - 1]);
 *
 * x.log1p().print();  // or tf.log1p(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function log1p_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'log1p');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.add(1)) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.log1p($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes square root of the input `tf.Tensor` element-wise: `y = sqrt(x)`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, 4, -1]);
 *
 * x.sqrt().print();  // or tf.sqrt(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function sqrt_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'sqrt');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.toFloat().sqrt().mul(2)) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.sqrt($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes reciprocal of square root of the input `tf.Tensor` element-wise:
 * `y = 1 / sqrt(x)`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, 4, -1]);
 *
 * x.rsqrt().print();  // or tf.rsqrt(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function rsqrt_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'rsqrt');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.pow(1.5).mul(2)).neg() as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.rsqrt($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes square of `x` element-wise: `x ^ 2`
 *
 * ```js
 * const x = tf.tensor1d([1, 2, Math.sqrt(2), -1]);
 *
 * x.square().print();  // or tf.square(x)
 * ```
 * @param x The input Tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function square_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'square');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.mul($x.toFloat().mul(2)) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    save([$x]);
    return backend.square($x);
  }, {$x}, grad);
}

/**
 * Computes reciprocal of x element-wise: `1 / x`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, 2]);
 *
 * x.reciprocal().print();  // or tf.reciprocal(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function reciprocal_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'reciprocal');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.square().neg()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.reciprocal($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes absolute value element-wise: `abs(x)`
 *
 * ```js
 * const x = tf.tensor1d([-1, 2, -3, 4]);
 *
 * x.abs().print();  // or tf.abs(x)
 * ```
 * @param x The input `tf.Tensor`.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function abs_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'abs');

  if ($x.dtype === 'complex64') {
    return ENGINE.runKernel(backend => backend.complexAbs($x), {$x});
  }

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.mul($x.toFloat().step(-1)) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.abs($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Clips values element-wise. `max(min(x, clipValueMax), clipValueMin)`
 *
 * ```js
 * const x = tf.tensor1d([-1, 2, -3, 4]);
 *
 * x.clipByValue(-2, 3).print();  // or tf.clipByValue(x, -2, 3)
 * ```
 * @param x The input tensor.
 * @param clipValueMin Lower-bound of range to be clipped to.
 * @param clipValueMax Upper-bound of range to be clipped to.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function clipByValue_<T extends Tensor>(
    x: T|TensorLike, clipValueMin: number, clipValueMax: number): T {
  const $x = convertToTensor(x, 'x', 'clipByValue');
  util.assert(
      (clipValueMin <= clipValueMax),
      () => `Error in clip: min (${clipValueMin}) must be ` +
          `less than or equal to max (${clipValueMax}).`);

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {
      $x: () => dy.where(
                    $x.greaterEqual(clipValueMin)
                        .logicalAnd($x.lessEqual(clipValueMax)),
                    zerosLike(dy)) as T,
    };
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.clip($x, clipValueMin, clipValueMax);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes sigmoid element-wise, `1 / (1 + exp(-x))`
 *
 * ```js
 * const x = tf.tensor1d([0, -1, 2, -3]);
 *
 * x.sigmoid().print();  // or tf.sigmoid(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function sigmoid_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'sigmoid');

  const grad = (dy: T, saved: Tensor[]) => {
    const [y] = saved;
    return {$x: () => dy.mul(y.mul(scalar(1).sub(y))) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const y = backend.sigmoid($x);
    save([y]);
    return y;
  }, {$x}, grad);
}

/**
 * Computes log sigmoid of the input `tf.Tensor` element-wise:
 * `logSigmoid(x)`. For numerical stability, we use `-tf.softplus(-x)`.
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.logSigmoid().print();  // or tf.logSigmoid(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function logSigmoid_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'logSigmoid');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.mul($x.neg().sigmoid()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.softplus($x.neg()).neg();
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes softplus of the input `tf.Tensor` element-wise: `log(exp(x) + 1)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.softplus().print();  // or tf.softplus(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function softplus_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'softplus');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.mul($x.sigmoid()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.softplus($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes sin of the input Tensor element-wise: `sin(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, Math.PI / 2, Math.PI * 3 / 4]);
 *
 * x.sin().print();  // or tf.sin(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function sin_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'sin');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => $x.toFloat().cos().mul(dy) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.sin($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes cos of the input `tf.Tensor` element-wise: `cos(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, Math.PI / 2, Math.PI * 3 / 4]);
 *
 * x.cos().print();  // or tf.cos(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function cos_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'cos');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => $x.toFloat().sin().neg().mul(dy) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.cos($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes tan of the input `tf.Tensor` element-wise, `tan(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, Math.PI / 2, Math.PI * 3 / 4]);
 *
 * x.tan().print();  // or tf.tan(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function tan_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'tan');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.cos().square()) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.tan($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes asin of the input `tf.Tensor` element-wise: `asin(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.asin().print();  // or tf.asin(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function asin_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'asin');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {
      $x: () => dy.divStrict(scalar(1).sub($x.toFloat().square()).sqrt() as T)
    };
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.asin($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes acos of the input `tf.Tensor` element-wise: `acos(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.acos().print();  // or tf.acos(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function acos_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'acos');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {
      $x: () =>
          dy.divStrict(scalar(1).sub($x.toFloat().square()).sqrt() as T).neg()
    };
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.acos($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes atan of the input `tf.Tensor` element-wise: `atan(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.atan().print();  // or tf.atan(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function atan_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'atan');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div($x.toFloat().square().add(1)) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.atan($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes hyperbolic sin of the input `tf.Tensor` element-wise: `sinh(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.sinh().print();  // or tf.sinh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function sinh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'sinh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => $x.toFloat().cosh().mulStrict(dy) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.sinh($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes hyperbolic cos of the input `tf.Tensor` element-wise: `cosh(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.cosh().print();  // or tf.cosh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function cosh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'cosh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => $x.toFloat().sinh().mulStrict(dy) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.cosh($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes hyperbolic tangent of the input `tf.Tensor` element-wise: `tanh(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, 70]);
 *
 * x.tanh().print();  // or tf.tanh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function tanh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'tanh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [y] = saved;
    return {$x: () => scalar(1).sub(y.square()).mulStrict(dy) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const y = backend.tanh($x);
    save([y]);
    return y;
  }, {$x}, grad);
}

/**
 * Computes inverse hyperbolic sin of the input `tf.Tensor` element-wise:
 * `asinh(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, 1, -1, .7]);
 *
 * x.asinh().print();  // or tf.asinh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function asinh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'asinh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {
      $x: () => dy.divStrict(scalar(1).add($x.toFloat().square()).sqrt() as T)
    };
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.asinh($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes the inverse hyperbolic cos of the input `tf.Tensor` element-wise:
 * `acosh(x)`
 *
 * ```js
 * const x = tf.tensor1d([10, 1, 3, 5.7]);
 *
 * x.acosh().print();  // or tf.acosh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function acosh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'acosh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.divStrict($x.toFloat().square().sub(1).sqrt() as T)};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.acosh($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes inverse hyperbolic tan of the input `tf.Tensor` element-wise:
 * `atanh(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, .1, -.1, .7]);
 *
 * x.atanh().print();  // or tf.atanh(x)
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function atanh_<T extends Tensor>(x: T|TensorLike): T {
  const $x = convertToTensor(x, 'x', 'atanh');

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {$x: () => dy.div(scalar(1).sub($x.toFloat().square())) as T};
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.atanh($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes gause error function of the input `tf.Tensor` element-wise:
 * `erf(x)`
 *
 * ```js
 * const x = tf.tensor1d([0, .1, -.1, .7]);
 *
 * x.erf().print(); // or tf.erf(x);
 * ```
 * @param x The input tensor.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function erf_<T extends Tensor>(x: T|TensorLike): T {
  let $x = convertToTensor(x, 'x', 'erf');
  util.assert(
      $x.dtype === 'int32' || $x.dtype === 'float32',
      () => 'Input dtype must be `int32` or `float32`.');

  if ($x.dtype === 'int32') {
    $x = $x.toFloat();
  }

  const grad = (dy: T, saved: Tensor[]) => {
    const [$x] = saved;
    return {
      $x: () => dy.mul($x.square().neg().exp().mul(2 / Math.sqrt(Math.PI))) as T
    };
  };
  return ENGINE.runKernel((backend, save) => {
    const res = backend.erf($x);
    save([$x]);
    return res;
  }, {$x}, grad);
}

/**
 * Computes step of the input `tf.Tensor` element-wise: `x > 0 ? 1 : alpha * x`
 *
 * ```js
 * const x = tf.tensor1d([0, 2, -1, -3]);
 *
 * x.step(.5).print();  // or tf.step(x, .5)
 * ```
 * @param x The input tensor.
 * @param alpha The gradient when input is negative.
 */
/** @doc {heading: 'Operations', subheading: 'Basic math'} */
function step_<T extends Tensor>(x: T|TensorLike, alpha = 0.0): T {
  const $x = convertToTensor(x, 'x', 'step');

  // TODO(manrajgrover): Return null for gradients when backprop supports
  // it.
  const grad = (dy: T) => {
    return {$x: () => zerosLike(dy)};
  };
  return ENGINE.runKernel(backend => backend.step($x, alpha), {$x}, grad);
}

export const abs = op({abs_});
export const acos = op({acos_});
export const acosh = op({acosh_});
export const asin = op({asin_});
export const asinh = op({asinh_});
export const atan = op({atan_});
export const atanh = op({atanh_});
export const ceil = op({ceil_});
export const clipByValue = op({clipByValue_});
export const cos = op({cos_});
export const cosh = op({cosh_});
export const erf = op({erf_});
export const exp = op({exp_});
export const expm1 = op({expm1_});
export const floor = op({floor_});
export const log = op({log_});
export const log1p = op({log1p_});
export const logSigmoid = op({logSigmoid_});
export const neg = op({neg_});
export const reciprocal = op({reciprocal_});
export const round = op({round_});
export const rsqrt = op({rsqrt_});
export const sigmoid = op({sigmoid_});
export const sign = op({sign_});
export const isNaN = op({isNaN_});
export const isInf = op({isInf_});
export const isFinite = op({isFinite_});
export const sin = op({sin_});
export const sinh = op({sinh_});
export const softplus = op({softplus_});
export const sqrt = op({sqrt_});
export const square = op({square_});
export const step = op({step_});
export const tan = op({tan_});
export const tanh = op({tanh_});