Methods apparatus and computer program products for accumulating logarithmic values

A method for summing on a computer having memory and a processing means a plurality of quantities, each of which is quantitized to one of a discrete number of values on a non-linear, monotonic scale, the method comprising the steps of:

• initializing a plurality of single bit memory elements, each of which correspond to one of the discrete number of values, to zero;
• obtaining one of the plurality of quantities;
• incrementing a first one of the single bit memory elements corresponding to the quantitized value of the obtained one of the plurality of quantities using modulo-2 arithmetic;
• and
• incrementing a second one of the single bit memory elements corresponding to twice the quantitized value of the first one of the single bit memory elements using modulo-2 arithmetic if a carry is generated by said step of incrementing a first one of the single bit memory elements.

A method for combining a first number and a second number, said first and second number each having a sign and logmagnitude, the method comprising the following steps performed on a data processing apparatus having a memory:

• comparing the sign of the first number to the sign of the second number to determine if an add or subtract operation is required to combine the first number and the second number;
• determining a difference between the logmagnitude of the second number and the logmagnitude of the first number;
• identifying a larger magnitude one of the first number or the second number as an output value;
• determining if a desired precision threshold has been reached;
• identifying a most significant portion and a least significant portion of the determined difference;
• obtaining a first value associated with the most significant portion from a first table;
• accumulating the obtained first value with the output value;
• accumulating the obtained first value with the determined difference to provide a new determined difference;
• and
• repeating said determining, identifying a most significant portion, obtaining a first value, accumulating the obtained first value with the output value and accumulating the obtained first value with the determined difference steps until the desired precision threshold is reached.

An apparatus for summing a plurality of logarithmic numbers, comprising:

• means for converting each of the plurality of logarithmic numbers to one of a predetermined number of values;
• means for accumulating a number of occurrences of each of the plurality of logarithmic numbers in a plurality of counters, each one of said plurality of counters being associated with one of the predetermined number of values;
• and
• means for reducing a value count of a first one of the plurality of counters having a value count greater than one by decreasing the value count of a first one of the plurality of counters and incrementing a second one of the plurality of counters, wherein the second one of the plurality of counters has an associated one of the predetermined number of values corresponding to a multiple of the associated one of the predetermined number of values of the first one of the plurality of counters.

An apparatus for providing a summation of a plurality of quantities, each of which is quantitized to one of a discrete number of values on a non-linear, monotonic scale, comprising:

• a processor;
• a plurality of single bit memory elements, each of which correspond to one of the discrete number of values, operatively associated with the processor;
• means operatively associated with the plurality of single bit memory elements for initializing the plurality of single bit memory to zero;
• means electrically connected to the processor for inputting one of the plurality of quantities;
• the processor including:
• means for incrementing a first one of the plurality of single bit memory elements corresponding to a quantitized value of an input one of the plurality of quantities using modulo-2 arithmetic;
• and
• means for incrementing a second one of the plurality of single bit memory elements corresponding to twice the quantitized value of the input one of the plurality of quantities using modulo-2 arithmetic if a carry is generated by said means for incrementing a first one of the plurality of single bit memory elements.

An apparatus for combining a first number and a second number, comprising:

• an input bus for inputting a logmagnitude and a sign of the first number and a logmagnitude and a sign of the second number;
• an input accumulator operatively associated with the input bus;
• first storage means operatively associated with the input accumulator for storing a first set of values;
• second storage means operatively associated with the input accumulator for storing a second set of values;
• an output register operatively associated with the first storage means;
• and
• a processor, operatively associated with the input accumulator, the processor comprising:
• means for comparing the sign of the first number to the sign of the second number to determine if an add or subtract operation is required to combine the first number and the second number;
• means for determining a difference between the logmagnitude of the first number and the logmagnitude of the second number and for storing the larger logmagnitude in the output register as an output value;
• means for determining if a desired precision threshold has been reached;
• means for obtaining a first value associated with a most significant portion of the difference between the logmagnitude of the first number and the logmagnitude of the second number;
• means for initiating accumulating the obtained first value with the output value;
• and
• means for initiating accumulating the obtained first value with the difference between the logmagnitude of the first number and the logmagnitude of the second number to provide a new determined difference.

A computer program product for summing a plurality of logarithmic numbers, the computer program product comprising:

• a computer-readable storage medium having computer-readable program code means embodied in said medium, said computer-readable program code means comprising:
• computer-readable program means for converting each of the plurality of logarithmic numbers to one of a predetermined number of values;
• computer-readable program code means for accumulating a number of occurrences of each of the plurality of logarithmic numbers in a plurality of counters, each one of said plurality of counters being associated with one of the predetermined number of values;
• and
• computer-readable program code means for reducing a value count of a first one of the plurality of counters having a value count greater than one by decreasing the value count of a first one of the plurality of counters and incrementing a second one of the plurality of counters, wherein the second one of the plurality of counters has an associated one of the predetermined number of values corresponding to a multiple of the associated one of the predetermined number of values of the first one of the plurality of counters.

A computer program product for combining a first number and a second number, said first and second number each having a sign and logmagnitude, the computer program product comprising:

• a computer-readable storage medium having computer-readable program code means embodied in said medium, said computer-readable program code means comprising:
• computer-readable program means for comparing the sign of the first number to the sign of the second number to determine if an add or subtract operation is required to combine the first number and the second number;
• computer-readable program means for determining a difference between the logmagnitude of the second number and the logmagnitude of the first number;
• computer-readable program means for identifying a larger magnitude one of the first number or the second number as an output value;
• computer-readable program means for determining if a desired precision threshold has been reached;
• computer-readable program means for identifying a most significant portion and a least significant portion of the determined difference;
• computer-readable program means for obtaining a first value associated with the most significant portion from a first table;
• computer-readable program means for accumulating the obtained first value with the output value;
• computer-readable program means for accumulating the obtained first value with the determined difference to provide a new determined difference;
• and
• computer-readable program means for determining if a desired precision threshold has been reached.