Abstract: An application processor includes a security processor. An operating method of the security processor includes generating a recoder input including a digit-unit multiplier and a reference bit. At least one random bits having a random value are generated. When the recoder input has a predetermined pattern, the recoder input is converted into a first recoding value or a second recoding value according to a random bit corresponding to the recoder input to generate a recoding result.

Abstract: A method to produce a final product from a multiplicand and a multiplier is provided. The method is executed by a parallel decimal multiplication hardware architecture, which includes a 3× generator, at least one additional generator, a multiplier recoder, a partial product tree, and a decimal adder. The 3× generator, the at least one additional generator, and the multiplier recoder generate decimal partial products from the multiplicand and the multiplier. The partial product tree executes a reduction of the decimal partial products to produce two corresponding partial product accumulations. The decimal adder adds the two corresponding partial product accumulations of the decimal partial products to produce the final product.

Abstract: Embodiments of a processor are disclosed for performing arithmetic operations on a machine independent number format. The processor may include a floating point unit, and a number unit. The number format may include a sign/exponent block, a length block, and multiple mantissa digits. The number unit may be configured to perform an operation on two operands by converting the digit format of each mantissa digit of each operand, to perform the operation using the converted mantissa digits, and then to convert each mantissa digit of the result of the operation back into the original digit format.

Abstract: A method to produce a final product from a multiplicand and a multiplier is provided. The method is executed by a parallel decimal multiplication hardware architecture, which includes a 3× generator, at least one additional generator, a multiplier recoder, a partial product tree, and a decimal adder. The 3× generator, the at least one additional generator, and the multiplier recoder generate decimal partial products from the multiplicand and the multiplier. The partial product tree executes a reduction of the decimal partial products to produce two corresponding partial product accumulations. The decimal adder adds the two corresponding partial product accumulations of the decimal partial products to produce the final product.

Abstract: Examples of the present disclosure provide apparatuses and methods for performing signed division operations. An apparatus can include a first group of memory cells coupled to a first access line and a number of sense lines. The apparatus can include a second group of memory cells coupled to a second access line and the number of sense lines. The apparatus can include a controller configured to cause sensing circuitry to divide a signed dividend element stored in the first group of memory cells by a signed divisor element stored in the second group of memory cells by performing a number of operations. At least one of the number of operations can be performed without transferring data via an input/output (I/O) line.

Abstract: Examples of the present disclosure provide apparatuses and methods for performing variable bit-length division operations in a memory. An example method comprises performing a variable length division operation on a first vector comprising variable length elements representing a number of dividends and stored in a group of memory cells coupled to a first access line and a number of sense lines of a memory array and a second vector comprising variable length elements representing a number of divisors stored in a group of memory cells coupled to a second access line and the number of sense lines of the memory array. The method can include dividing the first vector by the second vector by performing a number of operations. The method can include performing at least one of the number of operations without transferring data via an input/output (I/O) line.

Abstract: A combined binary/decimal fixed-point multiplier that uses BCD-4221 recoding for the decimal digits. This allows the use of binary carry-save hardware to perform decimal addition with a small correction. The described designs provide an improved reduction tree organization to reduce the area and delay of the multiplier and improved reduction tree components that leverage the redundant decimal encodings to help reduce delay. A split reduction tree architecture is also introduced that reduces the delay of the binary product with only a small increase in total area. Area and delay estimates are presented that show that the proposed designs have significant area improvements over separate binary and decimal multipliers while still maintaining similar latencies for both decimal and binary operations.

Abstract: A decimal floating point (DFP) unit is used to execute fixed point instructions. Two or more operands are accepted, wherein each operand is in a packed binary coded decimal (BCD) format. Any invalid BCD formats are detected by checking the operands for any invalid BCD codes. It is determined if an exception flag exists and, if so, outputting the flag; it is determined if a condition code exists and, if so, outputting the code. An operation is performed on the two or more operands to generate a result; wherein the operation takes place directly on BCD data, thus using the DFP unit to perform a BCD operation; appending a result sign to the result of the operation; and providing the result of the operation and the appended result sign as a result output in a packed BCD format.

Abstract: Several implementations and a design structure for decimal multiplication that uses a BCD 4221 encoding scheme, separate accumulation of partial products, accumulation of the partial products into a final product and conversion from and to a BCD 8421 coding scheme.

Abstract: A decimal multiplication mechanism for fixed and floating point computation in a computer having a coefficient mechanism without resulting leading zero detection (LZD) and process which assumes that the final product will be M+N digits in length and performs all calculations based on this assumption. Least significant digits that would be truncated are no longer stored, but retained as sticky information which is used to finalize the result product. Once the computation of the product is complete, a final check based on the examination of key bits observed during partial product accumulation is used to determine if the final product is truly M+N digits in length, or M+N?1 digits. If the latter is true, then corrective final product shifting is employed to obtain the proper result. This eliminates the need for dedicated leading zero detection hardware used to determine the number of significant digits in the final product.

Abstract: The digital propagate, digit generate, sum+0, and sum+1 terms used in typical carry-propagate adders are generated directly off the multiplicand. During the direct generation, the logic takes into account that each digit will be tripled and if each digit's next less significant digit is greater than 4. Using this technique, the generation of the multiplicand is significantly faster and uses less circuitry.

Abstract: Several implementations and a design structure for decimal multiplication that uses a BCD 4221 encoding scheme, separate accumulation of partial products, accumulation of the partial products into a final product and conversion from and to a BCD 8421 coding scheme.

Abstract: A combined binary/decimal fixed-point multiplier that uses BCD-4221 recoding for the decimal digits. This allows the use of binary carry-save hardware to perform decimal addition with a small correction. The described designs provide an improved reduction tree organization to reduce the area and delay of the multiplier and improved reduction tree components that leverage the redundant decimal encodings to help reduce delay. A split reduction tree architecture is also introduced that reduces the delay of the binary product with only a small increase in total area. Area and delay estimates are presented that show that the proposed designs have significant area improvements over separate binary and decimal multipliers while still maintaining similar latencies for both decimal and binary operations.

Abstract: Systems and methods configured for recoding an odd integer and elliptic curve point multiplication are disclosed, having general utility and also specific application to elliptic curve point multiplication and cryptosystems. In one implementation, the recoding is performed by converting an odd integer k into a binary representation. The binary representation could be, for example, coefficients for powers of two representing the odd integer. The binary representation is then configured as comb bit-columns, wherein every bit-column is a signed odd integer. Another implementation applies this recoding method and discloses a variation of comb methods that computes elliptic curve point multiplication more efficiently and with less saved points than known comb methods. The disclosed point multiplication methods are then modified to be Simple Power Analysis (SPA)-resistant.

Abstract: A circuit and methodology for higher radix multiplication with improved partial product generation. The invention relates to the design of a high precision multiplier for an arithmetic unit of a digital processor.