Systems and methods for design parameter selection

A method for determining statistics information concerning a noise of a system, comprising:

• for a model representing a behavior of the system, wherein the model has an input and an output and includes an operation representable by a matrix, obtaining a size of the matrix, an overflow probability for the operation, and a numerical input range and a numerical output range of the model;
• determining a singular value bound for the matrix based on the size, numerical input range, and numerical output range;
• determining, using the singular value bound and the overflow probability, statistics information concerning a noise of the system;
• and
• providing an indication of the minimum noise value.

A method for determining, for a model representing a behavior of a device, the model having an input and an output and including a matrix representing characteristics or operations of the device, dimensions of the matrix, comprising:

• obtaining an input range, output range, noise value for a noise in the device, and overflow probability for the device;
• determining, using the input range and the output range, a scaled singular value bound for the matrix;
• determining, using the scaled singular value bound, the overflow probability, and the noise value
• a size of the matrix, the size specifying a number of observations and a number of values for each observation;
• and
• providing an indication of the determined size of the matrix.

A system for selecting a datatype for use by software running on a device, comprising:

• at least one processor;
• and
• at least one non-transitory computer-readable medium containing instructions, that when executed by the at least one processor, cause the system to perform operations comprising:
• for a model representing a behavior of the device, wherein the model has an input and an output and includes an operation representable by a matrix,
• obtaining a size of the matrix, an overflow probability for the operation, and
• statistics information concerning a noise of the device;
• determining a singular value bound for the matrix based on the size, the overflow probability, and the statistics information;
• determining one or more of:
• a numerical range for the output based on information about the input and the singular value bound, or
• a numerical range for the input based on information about the output and the singular value bound;
• selecting the datatype for the input or the output, based at least in part on:
• the determined numerical range of the output, or
• the determined numerical range of the input;
• and
• providing an indication of the selected datatype.

A non-transitory computer-readable medium containing instructions, that when executed by at least one processor, cause a system to perform operations comprising:

• for a model representing a behavior of a device, wherein the model has an input and an output and includes an operation representable by a matrix,
• obtaining a size of the matrix, an overflow probability for the operation, and statistics information concerning a noise of the device;
• determining a singular value bound for the matrix based on the size, the overflow probability, and the statistics information;
• determining one or more of:
• a numerical range for the output based on information about the input and the singular value bound, or
• a numerical range for the input based on information about the output and the singular value bound;
• selecting the datatype for the input or the output, based at least in part on:
• the determined numerical range of the output, or
• the determined numerical range of the input;
• and
• providing an indication of the selected datatype.