# tff.aggregators.secure_quantized_sum

Quantizes and sums values securely.

Provided `client_value` can be either a Tensor or a nested structure of Tensors. If it is a nested structure, `lower_bound` and `upper_bound` must be either both scalars, or both have the same structure as `client_value`, with each element being a scalar, representing the bounds to be used for each corresponding Tensor in `client_value`.

This method converts each Tensor in provided `client_value` to appropriate format and uses the `tff.federated_secure_sum` operator to realize the sum.

The dtype of Tensors in provided `client_value` can be one of ```[tf.int32, tf.int64, tf.float32, tf.float64]```.

If the dtype of `client_value` is `tf.int32` or `tf.int64`, the summation is possibly exact, depending on `lower_bound` and `upper_bound`: In the case that `upper_bound - lower_bound < 2**32`, the summation will be exact. If it is not, `client_value` will be quantized to precision of 32 bits, so the worst case error introduced for the value of each client will be approximately `(upper_bound - lower_bound) / 2**32`. Deterministic rounding to nearest value is used in such cases.

If the dtype of `client_value` is `tf.float32` or `tf.float64`, the summation is generally not accurate up to full floating point precision. Instead, the values are first clipped to the `[lower_bound, upper_bound]` range. These values are then uniformly quantized to 32 bit resolution, using deterministic rounding to round the values to the quantization points. Rounding happens roughly as follows (implementation is a bit more complex to mitigate numerical stability issues):

``````values = tf.round(
(client_value - lower_bound) * ((2**32 - 1) / (upper_bound - lower_bound))
``````

After summation, the inverse operation if performed, so the return value is of the same dtype as the input `client_value`.

In terms of accuracy, it is safe to assume accuracy within 7-8 significant digits for `tf.float32` inputs, and 8-9 significant digits for `tf.float64` inputs, where the significant digits refer to precision relative to the range of the provided bounds. Thus, these bounds should not be set extremely wide. Accuracy losses arise due to (1) quantization within the given clipping range, (2) float precision of final outputs (e.g. `tf.float32` has 23 bits in its mantissa), and (3) precision losses that arise in doing math on `tf.float32` and `tf.float64` inputs.

As a concrete example, if the range is `+/- 1000`, errors up to `1e-4` per element should be expected for `tf.float32` and up to `1e-5` for `tf.float64`.

`client_value` A `tff.Value` placed at `tff.CLIENTS`.
`lower_bound` The smallest possible value for `client_value` (inclusive). Values smaller than this bound will be clipped. Must be either a scalar or a nested structure of scalars, matching the structure of `client_value`. Must be either a Python constant or a `tff.Value` placed at `tff.SERVER`, with dtype matching that of `client_value`.
`upper_bound` The largest possible value for `client_value` (inclusive). Values greater than this bound will be clipped. Must be either a scalar or a nested structure of scalars, matching the structure of `client_value`. Must be either a Python constant or a `tff.Value` placed at `tff.SERVER`, with dtype matching that of `client_value`.

Summed `client_value` placed at `tff.SERVER`, of the same dtype as `client_value`.

TypeError (or its subclasses): If input arguments do not satisfy the type constraints specified above.

[]
[]