Efficient extended-precision processing

A system comprising:

• a memory;
• and
• one or more processors coupled to the memory, and configured to:
• divide each of the first series of numbers into a first value, comprising the N most significant bits of the number, where N is an integer greater than two, and a second value, comprising a plurality of less significant bits of the number, to form a first set of values, comprising the first values across the first series of numbers, and a second set of values, comprising the second values across the first series of numbers and divides each of the second series of numbers into a first value, comprising the N most significant bits of the number, and a second value, comprising a plurality of less significant bits of the number, to form a third set of values, comprising the first values across the second series of numbers, and a fourth set of values, comprising the second values across the second series of numbers;
• compute a first dot product of the first set of values and the fourth set of values to provide a first partial sum;
• compute a second dot product of the first set of values and the third set of values to provide a second partial sum;
• compute a third dot product of the second set of values and the third set of values to provide a third partial sum;
• and
• sum the first partial sum, the second partial sum, and the third partial sum to provide a result for the dot product between the first series of numbers and the second series of numbers.

A non-transitory computer readable medium storing machine readable instructions, that when executed by a processor, cause one or more processors to:

• divide each of a first series of numbers into a first value, comprising the N most significant bits of the number, where N is an integer greater than two that is determined according to a native resolution of the processor, and a second value, comprising a plurality of less significant bits of the number, to form a first set of values, comprising the first values across the first series of numbers, and a second set of values, comprising the second values across the first series of numbers;
• divide each of a second series of numbers into a third value, comprising the N most significant bits of the number, and a fourth value, comprising a plurality of less significant bits of the number, to form a third set of values, comprising the third values across the second series of numbers, and a fourth set of values, comprising the fourth values across the second series of numbers;
• compute a dot product of the first set of values and the fourth set of values to provide a first partial sum;
• compute a dot product of the first set of values and the third set of values to provide a second partial sum;
• compute a dot product of the second set of values and the third set of values to provide a third partial sum;
• and
• sum the first partial sum, the second partial sum, and the third partial sum to provide a result for the dot product between the first series of numbers and the second series of numbers.