Matsushita Electric Industrial Co., Ltd.

Semiconductor Technology Academic Research Center

Naofumi Takagi

Tamotsu Nishiyama

Takashi Taniguchi

Shigeo Kuninobu

Tsuguyasu Hatsuda

Toru Kakiage

A reciprocal square root for a radix ofis calculated when S[j] represents the partial result obtained afteriterations of calculation, W[j], a residual, and P[j], the product of an operand X and the S[j]. Firstly, appropriate values are set to the initial values S[0], W[0], and P[0]. Secondly,iterations of calculations from j=0 to n&#x2212;1 are performed. One calculation includes selecting a reciprocal square root digit qfrom the digit set {&#x2212;a, . . . , &#x2212;1, 0, 1, . . . , a}, and calculating a recurrence equation of the S[j], i.e., S[j+1]:=S[j]+qr, a recurrence equation of the W[j], i.e., W[j+1]:=rW[j]&#x2212;(2P[j]+Xqr)q, and a recurrence equation of the P[j], i.e., P[j+1]:=P[j]+Xqr.

Method and hardware for computing reciprocal square root and program for the same

This an arithmetic processor which represents internal arithmetic operands as signed-digit numbers, each digit of which may have either positive, zero, or negative values and which executes addition of a plurality of numbers each of whose most significant digit is offset with respect to the other numbers. The arithmetic processor includes an adder tree which is so constituted that a pair of said plurality of numbers are added to obtain a partial sum and further pairs of partial sums are successively added to obtain a final sum of all numbers. The arithmetic processor further comprises first means for adding a portion of the two numbers where both digits are present, second means for causing a lower order portion where only one of the numbers has a digit present to directly become part of the sum, third means for retaining or outputting a carry created by the first means, and fourth means for adding the carry created in each add stage of the adder tree to the later add stages of the adder tree to obtain the sum.

Arithmetic processor using signed-digit representation of external

This invention discloses an arithmetic processor which represents internal arithmetic operands as signed-digit numbers, each digit of which may have either positive, zero, or negative values and which executes addition of a plurality of numbers each of whose most significant digit is offset with respect to the other numbers. The arithmetic processor includes an adder tree which is so constituted that a pair of said plurality of numbers are added to obtain a partial sum and further pairs of partial sums are successively added to obtain a final sum of all numbers. The arithmetic processor further comprises first means for adding a portion of the two numbers where both digits are present, second means for causing a lower order portion where only one of the numbers has a digit present to directly become part of the sum, third means for retaining or outputting a carry created by the first means, and fourth means for adding the carry created in each add stage of the adder tree to the later add stages of the adder tree to obtain the sum.

Arithmetic processor using signed digit representation of internal

An arithmetic processor cable of performing successive multiplication operations at high speeds is described in which the resultant product, internally represented as a carry-save or signed-digit expression, may be directly input in that form as the multiplier for the next successive multiplication operation. Additionally, a multiplier recoder circuit is provided which recodes the binary multiplier, in the form of a carry-save or signed-digit expression into a radix 4 signed-digit number, in order to further increase the operating speed.

High speed multiplier utilizing signed-digit and carry-save operands

A high speed arithmetic processor and adder circuitry thereof are disclosed in which carry (borrow) propagation is never more than one digit. Addition (or subtraction) are performed by: (a) determining an intermediate carry (or borrow) at the i-th order position and an intermediate sum (or difference) at the i-th order position from the addend (or subtrahend) and the augend (or minuend) and (b) determining the sum (or difference) of the intermediate sum (or difference) at the i-th order position and the intermediate carry (or borrow) at the (i-1)-th or next-lower-order position. Logic equations, truth tables and circuitry are disclosed for implementing several embodiments of the invention.

Adder circuitry utilizing redundant signed digit operands

An arithmetic processor is disclosed for performing arithmetic operations utilizing an arithmetic operand represented by a signed digit expression having a plurality of digits which may have a positive, zero or negative value. The processor comprises: first circuitry coupled to receive a signal related to the most significant digit of a signed digit expression number Y having nonnegative (or nonpositive) digits other than the most significant digit, and for providing in response to a control signal, a signal representing the logical negation or inversion of the sign of the most significant digit; second circuitry coupled to receive at least one signal related to digits other than the most significant digit of the number Y, and for providing in response to a control signal, at least one signal representing the logical negation or inversion of those digits; and third circuitry coupled to receive a signal related to the least significant digit of the number Y, and for providing in response to a control signal, a signal representing the least significant digit plus 1 (or minus 1). The first and second circuitry invert the signs of the digits of the number Y, and the third circuitry adds (or subtracts) 1 from the least significant digit. The processor also includes circuitry coupled to receive the signals provided by the first, second and third circuitry and a signal representing a number X, and providing a signal representing the sum or difference of the numbers X and Y depending on the control signal.

Arithmetic processor and divider using redundant signed digit

A high speed processor including a multiplier is disclosed. The multiplier includes a multiplier recorder circuit which may record multipliers in groups of digits, and intermediate partial product generators which generate partial products from the recorded digits and a multiplicand. Addition/subtraction is then carried out on the intermediate partial products generated by the partial product generators. The processor may operate using signed digit expressions.

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Kyoto, Japan

Naofumi Takagi