Abstract: An integrated circuit may be provided with a modular multiplication circuit. The modular multiplication circuit may include an input multiplier for computing the product of two input signals, truncated multipliers for computing another product based on a modulus value and the product, a subtraction circuit for computing a difference between the two products. An error correction circuit may use the difference to look up an estimated quotient value and to subtract out an integer multiple of the modulus value from the difference in a single step, wherein the integer multiple is equal to the estimated quotient value. A final adjustment stage may be used to remove any remaining residual estimation error.

Abstract: An integrated circuit with a large multiplier is provided. The multiplier may be configured to receive large input operands with thousands of bits. The multiplier may be implemented using a multiplier decomposition scheme that is recursively flattened into multiple decomposition levels to expose a tree of adders. The adders may be collapsed into a merged pipelined structure, where partial sums are forwarded from one level to the next while bypassing intervening prefix networks. The final correct sum is not calculated until later. In accordance with the decomposition technique, the partial sums are successively halved, which allows the prefix networks to be smaller from one level to the next. This allows all sums to be calculated at approximately the same pipeline depth, which significantly reduces latency with no or limited pipeline balancing.

Abstract: An integrated circuit may include a floating-point adder. The adder may be implemented using a dual-path adder architecture having a near path and a far path. The near path may include a leading zero anticipator (LZA), a comparison circuit for comparing an exponent value to an LZA count, and associated circuitry for handling subnormal numbers. The far path may include a subtraction circuit for computing the difference between a received exponent value and a minimum exponent value, at least two shifters for shifting far greater and far lesser mantissa values in parallel, and associated circuitry for handling subnormal numbers. The adder may be dynamically configured to support a first mode that processes FP16 at inputs and outputs, a second mode that processes modified FP16? inputs, and a third mode that processes FP16? at inputs and outputs.

Abstract: The present disclosure relates generally to techniques for enhancing recurrent neural networks (RNNs) implemented on an integrated circuit. In particular, approximations of activation functions used in an RNN, such as sigmoid and hyperbolic tangent, may be implemented in an integrated circuit, which may result in increased efficiencies, reduced latency, increased accuracy, and reduced resource consumption involved with implementing machine learning.

Abstract: Integrated circuits with digital signal processing (DSP) blocks are provided. A DSP block may include one or more large multiplier circuits. A large multiplier circuit (e.g., an 18×18 or 18×19 multiplier circuit) may be used to support two or more smaller multiplication operations sharing one or two sets of multiplier operands, a complex multiplication, and a sum of two multiplications. If the multiplier products overflow and interfere with one another, correction operations can be performed. Partial products from two or more larger multiplier circuits can be used to combine decomposed partial products. A large multiplier circuit can also be used to support two floating-point mantissa multipliers.

Abstract: Adder trees may be constructed for efficient packing of arithmetic operators into an integrated circuit. The operands of the trees may be truncated to pack an integer number of nodes per logic array block. As a result, arithmetic operations may pack more efficiently onto the integrated circuit while providing increased precision and performance.

Abstract: The present embodiments relate to integrated circuits with circuitry that implements floating-point trigonometric functions. The circuitry may include an approximation circuit that generates an approximation of the output of the trigonometric functions, a storage circuit that stores predetermined output values of the trigonometric functions, and a selector circuit that selects between different possible output values based on a control signal from a control circuit. In some embodiments, the circuitry may include a mapping circuit and a restoration circuit. The mapping circuit may map an input value from an original quadrant of the trigonometric circle to a predetermined input interval, and the restoration circuit may map the output value selected by the selection circuit back to the original quadrant of the trigonometric circle. If desired, the circuitry may be implemented in specialized processing blocks.

Abstract: An integrated circuit may include normalization circuitry that can be used when converting a fixed-point number to a floating-point number. The normalization circuitry may include at least a floating-point generation circuit that receives the fixed-point number and that creates a corresponding floating-point number. The normalization circuitry may then leverage an embedded digital signal processing (DSP) block on the integrated circuit to perform an arithmetic operation by removing the leading one from the created floating-point number. The resulting number may have a fractional component and an exponent value, which can then be used to derive the final normalized value.

Abstract: A floating-point arithmetic block for performing arithmetic operations on floating-point numbers on an integrated circuit includes a unit to handle exceptions, a unit to handle the exponent, a unit for normalization and rounding, and a core having a multiplier, a subtractor, storage circuitry to store multiple initial mantissa values, and configurable interconnect circuitry. The configurable interconnect circuitry may be configured to route signals throughout the floating-point arithmetic block. The configuration may be performed by a finite state machine that controls the configurable interconnect depending on the selected floating-point arithmetic operation. The floating-point arithmetic block may be configured to implement a variety of floating-point arithmetic operations including the inverse square root operation, the square root operation, the inverse operation, the division, the multiplication, the addition, and the subtraction.

Abstract: Methods for implementing fixed-point functions with user-defined input/output ranges and formats on a programmable integrated circuit are provided. A particular function may include one or more input intrusion intervals where generic fixed-point approximation methods are not sufficiently precise. Output values for these intrusion intervals may be pre-computed during function generation time using a mathematical library running on a computer-aided design tool and stored in a lookup table. During normal operation of the integrated circuit, a multiplexing network may be used to select among values generated by generic approximation methods and values obtained from one or more lookup tables depending on the current input to the function.

Abstract: Circuitry that performs floating-point operations on an integrated circuit is provided. The circuitry may execute a floating-point operation by decomposing the floating-point operation into multiple steps and decomposing the floating-point number on which to perform the floating-point operation into multiple portions. The circuitry may include storage circuits that store at least some results of the multiple steps, and memory access operations may be performed using some portions of the floating-point number. The circuitry may use arithmetic floating-point and arithmetic fixed-point circuits to implement Taylor series expansion circuits that may perform a subset of the multiple steps, thereby reducing the complexity of the subset of these steps.

Abstract: In accordance with some embodiments, a floating point number datapath circuitry, e.g., within an integrated circuit programmable logic device is provided. The datapath circuitry may be used for computing a rounded absolute value of a mantissa of a floating point number. The floating point datapath circuitry may have only a single adder stage for computing a rounded absolute value of a mantissa of the floating point number based on one or more bits of an unrounded mantissa of the floating point number. The unrounded and rounded mantissas may include a sign bit, a sticky bit, a round bit, and/or a least significant bit, and/or other bits. The unrounded mantissa may be in a format that includes negative numbers (e.g., 2's complement) and the rounded mantissa may be in a format that may include a portion of the floating point number represented as a positive number, (e.g., signed magnitude).

Abstract: In accordance with some embodiments, a floating point number datapath circuitry, e.g., within an integrated circuit programmable logic device is provided. The datapath circuitry may be used for computing a rounded absolute value of a mantissa of a floating point number. The floating point datapath circuitry may have only a single adder stage for computing a rounded absolute value of a mantissa of the floating point number based on one or more bits of an unrounded mantissa of the floating point number. The unrounded and rounded mantissas may include a sign bit, a sticky bit, a round bit, and/or a least significant bit, and/or other bits. The unrounded mantissa may be in a format that includes negative numbers (e.g., 2's complement) and the rounded mantissa may be in a format that may include a portion of the floating point number represented as a positive number, (e.g., signed magnitude).

Abstract: Polynomial circuitry for calculating a polynomial having terms including powers of an input variable, where the input variable is represented by a mantissa and an exponent, includes at least one respective coefficient table for each respective term, each respective coefficient table being loaded with a plurality of respective instances of a coefficient for said respective term, each respective instance being shifted by a different number of bits. The circuitry also includes decoder circuitry for selecting one of the respective instances of the coefficient for each respective term based on the exponent and on a range, from among a plurality of ranges, of values into which that input variable falls.