Abstract:
Methods and systems for verifying a hardware design for an integrated circuit that implements a function that is polynomial in an input variable x over a set of values of x. The method includes formally verifying that a first instantiation of the hardware design implements a function that is polynomial of degree k in x by formally verifying that for all x in the set of values of x the first instantiation of the hardware design has a constant kth difference; and verifying that a second instantiation of the hardware design generates an expected output in response to each of at least k different values of x in the set of values of x.
Abstract:
A binary logic circuit for determining the ratio x/d where x is a variable integer input, the binary logic circuit comprising: a logarithmic tree of modulo units each configured to calculate x[a:b]mod d for respective block positions a and b in x where b>a with the numbering of block positions increasing from the most significant bit of x up to the least significant bit of x, the modulo units being arranged such that a subset of M−1 modulo units of the logarithmic tree provide x[0:m]mod d for all m∈{1, M}, and, on the basis that any given modulo unit introduces a delay of 1: all of the modulo units are arranged in the logarithmic tree within a delay envelope of ┌log 2M┐; and more than M−2u of the subset of modulo units are arranged at the maximal delay of ┌log 2M┐, where 2u is the power of 2 immediately smaller than M.
Abstract:
A hardware design for a component that evaluates a main algebraic expression comprising at least two variables is verified, the main algebraic expression being representable as a lossless combination of a plurality of sub-algebraic expressions, and one or more of the at least two variables can be constrained to cause an instantiation of the hardware design to evaluate each of the sub-algebraic expressions. An instantiation of the hardware design is verified as correctly evaluating each of the plurality of sub-algebraic expressions, and the instantiation of the hardware design is formally evaluated as correctly evaluating one or more combinations of sub-algebraic expressions, wherein the one or more combinations comprises a combination that is equivalent to the main algebraic expression.
Abstract:
A hardware design for a main data transformation component is verified. The main data transformation component is representable as a hierarchical set of data transformation components which includes (i) a plurality of leaf data transformation components which do not have children, and (ii) one or more parent data transformation components which each comprise one or more child data transformation components. For each of the plurality of leaf data transformation components, it is verified that an instantiation of the hardware design for the leaf data transformation component generates an expected output transaction in response to each of a plurality of test input transactions. For each of the one or more parent data transformation components, it is formally verified, using a formal verification tool, that an instantiation of an abstracted hardware design for the parent data transformation component generates an expected output transaction in response to each of a plurality of test input transactions. The abstracted hardware design for the parent data transformation component represents each of the one or more child data transformation components of the parent data transformation component with a corresponding abstracted component that for a specific input transaction to the child data transformation component is configured to produce a specific output transaction with a causal deterministic relationship to the specific input transaction.
Abstract:
Methods and systems for verifying that logic for implementing a pipelined process in hardware correctly moves data through the pipelined process. The method includes: (a) monitoring data input to the pipelined process to determine when watched data has been input to the pipelined process; (b) in response to determining the watched data has been input to the pipelined process counting a number of progressing clock cycles for the watched data; and (c) evaluating an assertion written in an assertion based language, the assertion establishing that when the watched data is output from the pipelined process the counted number of progressing clock cycles for the watched data should be equal to one of one or more predetermined values.
Abstract:
A method of exhaustively verifying a property of a hardware design to implement a floating point power function. The method includes, formally verifying that the hardware design is recurrent over sets of β input exponents, wherein β is an integer that is a multiple of the reciprocal of the exponent of the power function; and for each recurrent input range of the hardware design, exhaustively simulating the hardware design over a simulation range to verify the property is true over the simulation range, wherein the simulation range comprises only β input exponents.
Abstract:
Methods and systems for verifying, via formal verification, a hardware design for a data transformation pipeline comprising one or more data transformation elements that perform a data transformation on one or more inputs, wherein the formal verification is performed under conditions that simplify the data transformations calculations that the formal verification tool has to perform. In one embodiment the hardware design for the data transformation pipeline is verified by formally verifying that the output of an instantiation of the hardware design produces the same output as an instantiation of a hardware design for another data transformation pipeline for a predetermined set of transactions under a constraint that substantially equivalent data transformation elements between the data transformation pipelines produce the same output(s) in response to the same input(s).
Abstract:
A method of exhaustively verifying a property of a hardware design to implement a floating point power function. The method includes, formally verifying that the hardware design is recurrent over sets of β input exponents, wherein β is an integer that is a multiple of the reciprocal of the exponent of the power function; and for each recurrent input range of the hardware design, exhaustively simulating the hardware design over a simulation range to verify the property is true over the simulation range, wherein the simulation range comprises only β input exponents.
Abstract:
Methods and systems for verifying that logic for implementing a pipelined process in hardware correctly moves data through the pipelined process. The method includes: (a) monitoring data input to the pipelined process to determine when watched data has been input to the pipelined process; (b) in response to determining the watched data has been input to the pipelined process counting a number of progressing clock cycles for the watched data; and (c) evaluating an assertion written in an assertion based language, the assertion establishing that when the watched data is output from the pipelined process the counted number of progressing clock cycles for the watched data should be equal to one of one or more predetermined values.
Abstract:
Methods and systems of verifying a hardware design for a sorter are disclosed. The methods include generating a modified version of the hardware design of the sorter accepting extended inputs and performing formal verification comprising: implementing a constraint that the least significant bits of each input in a set of extended inputs represent a unique value; and formally verifying aspects of the modified version of the hardware design of the sorter for the set of extended inputs.