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Arithmetic Underflow
The term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU). Arithmetic underflow can occur when the true result of a floating-point operation is smaller in magnitude (that is, closer to zero) than the smallest value representable as a normal floating-point number in the target datatype. Underflow can in part be regarded as negative overflow of the exponent of the floating-point value. For example, if the exponent part can represent values from −128 to 127, then a result with a value less than −128 may cause underflow. Underflow gap The interval between −''fminN'' and ''fminN'', where ''fminN'' is the smallest positive normal floating-point value, is called the underflow gap. This is because the size of this interval is many orders of magnitude ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Program
A computer program is a sequence or set of instructions in a programming language for a computer to Execution (computing), execute. It is one component of software, which also includes software documentation, documentation and other intangible components. A ''computer program'' in its human-readable form is called source code. Source code needs another computer program to Execution (computing), execute because computers can only execute their native machine instructions. Therefore, source code may be Translator (computing), translated to machine instructions using a compiler written for the language. (Assembly language programs are translated using an Assembler (computing), assembler.) The resulting file is called an executable. Alternatively, source code may execute within an interpreter (computing), interpreter written for the language. If the executable is requested for execution, then the operating system Loader (computing), loads it into Random-access memory, memory and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Machine Epsilon
Machine epsilon or machine precision is an upper bound on the relative approximation error due to rounding in floating point number systems. This value characterizes computer arithmetic in the field of numerical analysis, and by extension in the subject of computational science. The quantity is also called macheps and it has the symbols Greek epsilon \varepsilon. There are two prevailing definitions, denoted here as ''rounding machine epsilon'' or the ''formal definition'' and ''interval machine epsilon'' or ''mainstream definition''. In the ''mainstream definition'', machine epsilon is independent of rounding method, and is defined simply as ''the difference between 1 and the next larger floating point number''. In the ''formal definition'', machine epsilon is dependent on the type of rounding used and is also called unit roundoff, which has the symbol bold Roman u. The two terms can generally be considered to differ by simply a factor of two, with the ''formal definition'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Logarithmic Number System
A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing. Overview A number, X, is represented in an LNS by two components: the logarithm (x) of its absolute value (as a binary word usually in two's complement), and its sign bit (s): :X \rightarrow \begin x = \log_b\big, X\big, , \\ s = \begin 0\text X > 0, \\ 1\text X A VHDL library for LNS hardware generation Computer arithmetic Digital signal processing [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Integer Overflow
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the range that can be represented with a given number of digits – either higher than the maximum or lower than the minimum representable value. The most common result of an overflow is that the least significant representable digits of the result are stored; the result is said to ''wrap'' around the maximum (i.e. modulo a power of the radix, usually two in modern computers, but sometimes ten or other number). On some processors like graphics processing units (GPUs) and digital signal processors (DSPs) which support saturation arithmetic, overflowed results would be ''clamped'', i.e. set to the minimum value in the representable range if the result is below the minimum and set to the maximum value in the representable range if the result is above the maximum, rather than wrapped around. An overflow condition may give results lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Denormal Number
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest positive normal number is ''subnormal'', while ''denormal'' can also refer to numbers outside that range. Terminology In some older documents (especially standards documents such as the initial releases of IEEE 754 and the C language), "denormal" is used to refer exclusively to subnormal numbers. This usage persists in various standards documents, especially when discussing hardware that is incapable of representing any other denormalized numbers, but the discussion here uses the term "subnormal" in line with the 2008 revision of IEEE 754. In casual discussions the terms ''subnormal'' and ''denormal'' are often used interchangeably, in part because there are ''no'' denormalized IEEE binary numbers outside the subnormal range. The term "numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Trap (computing)
In digital computers, an interrupt (sometimes referred to as a trap) is a request for the processor to ''interrupt'' currently executing code (when permitted), so that the event can be processed in a timely manner. If the request is accepted, the processor will suspend its current activities, save its state, and execute a function called an ''interrupt handler'' (or an ''interrupt service routine'', ISR) to deal with the event. This interruption is often temporary, allowing the software to resume normal activities after the interrupt handler finishes, although the interrupt could instead indicate a fatal error. Interrupts are commonly used by hardware devices to indicate electronic or physical state changes that require time-sensitive attention. Interrupts are also commonly used to implement computer multitasking and system calls, especially in real-time computing. Systems that use interrupts in these ways are said to be interrupt-driven. History Hardware interrupts were ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Significand
The significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading, since the ''mantissa'' of a logarithm is always its fractional part. Although the other names mentioned are common, ''significand'' is the word used by IEEE 754, an important technical standard for floating-point arithmetic. In mathematics, the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane. Example The number 123.45 can be represented as a decimal floati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Subnormal Numbers
In computer science, subnormal numbers are the subset of denormalized numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than the smallest positive normal number is ''subnormal'', while ''denormal'' can also refer to numbers outside that range. Terminology In some older documents (especially standards documents such as the initial releases of IEEE 754 and the C language), "denormal" is used to refer exclusively to subnormal numbers. This usage persists in various standards documents, especially when discussing hardware that is incapable of representing any other denormalized numbers, but the discussion here uses the term "subnormal" in line with the 2008 revision of IEEE 754. In casual discussions the terms ''subnormal'' and ''denormal'' are often used interchangeably, in part because there are ''no'' denormalized IEEE binary numbers outside the subnormal range. The term "numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Computer Memory
Computer memory stores information, such as data and programs, for immediate use in the computer. The term ''memory'' is often synonymous with the terms ''RAM,'' ''main memory,'' or ''primary storage.'' Archaic synonyms for main memory include ''core'' (for magnetic core memory) and ''store''. Main memory operates at a high speed compared to mass storage which is slower but less expensive per bit and higher in capacity. Besides storing opened programs and data being actively processed, computer memory serves as a Page cache, mass storage cache and write buffer to improve both reading and writing performance. Operating systems borrow RAM capacity for caching so long as it is not needed by running software. If needed, contents of the computer memory can be transferred to storage; a common way of doing this is through a memory management technique called ''virtual memory''. Modern computer memory is implemented as semiconductor memory, where data is stored within memory cell (com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard #Design rationale, addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and Software portability, portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of Binary code, binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinity, infinities, and special "not a number" values (NaNs) * ''interchange formats:'' encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form * ''rounding rules:'' properties to be satisfied when rounding numbers during arithmetic and conversions * ''operations:'' arithmetic and other operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Exponent
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_.In particular, b^1=b. The exponent is usually shown as a superscript to the right of the base as or in computer code as b^n. This binary operation is often read as " to the power "; it may also be referred to as " raised to the th power", "the th power of ", or, most briefly, " to the ". The above definition of b^n immediately implies several properties, in particular the multiplication rule:There are three common notations for multiplication: x\times y is most commonly used for explicit numbers and at a very elementary level; xy is most common when variables are used; x\cdot y is used for emphasizing that one talks of multiplication or when omitting the multiplication sign would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |