Floating point in the context of Z3 (computer)

In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers. It is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs).

The inputs to an ALU are the data to be operated on, called operands, and a code indicating the operation to be performed (opcode); the ALU's output is the result of the performed operation. In many designs, the ALU also has status inputs or outputs, or both, which convey information about a previous operation or the current operation, respectively, between the ALU and external status registers.

A programming language consists of a system of allowed sequences of symbols (constructs) together with rules that define how each construct is interpreted. For example, a language might allow expressions representing various types of data, expressions that provide structuring rules for data, expressions representing various operations on data, and constructs that provide sequencing rules for the order in which to perform operations.

A simple type system for a programming language is a set of rules that associates a data type (for example, integer, floating point, string) with each term (data-valued expression) in a computer program. In more ambitious type systems, a variety of constructs, such as variables, expressions, functions, and modules, may be assigned types.

In computer science and computer programming, a data type (or simply type) is a collection or grouping of data values, usually specified by a set of possible values, a set of allowed operations on these values, and/or a representation of these values as machine types. A data type specification in a program constrains the possible values that an expression, such as a variable or a function call, might take. On literal data, it tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers (which approximate real numbers), characters and Booleans.

In computing, a fatal exception error or fatal error is an error that causes a program to abort (ABEND) and may therefore return the user to the operating system. When this happens, data that the program was processing may be lost. A fatal error is usually distinguished from a fatal system error (colloquially referred to in the MS Windows operating systems by the error message it produces as a "blue screen of death"). A fatal error occurs typically in any of the following cases:

• An illegal instruction has been attempted
• Invalid data or code has been accessed
• An operation is not allowed in the current ring or CPU mode
• A program attempts to divide by zero (only for integers; with the IEEE floating point standard, this creates an infinity instead).

In some systems, such as macOS and Microsoft Windows, a fatal error causes the operating system to create a log entry or to save an image (core dump) of the process.