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Computer programming condition
The term arithmetic underflow (also floating-point underflow, or just underflow) is a condition in a computer program where the result of a calculation
Arithmetic_underflow
Computer arithmetic error
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the
Integer_overflow
Computer approximation for real numbers
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a significand (a signed sequence of a fixed number of
Floating-point_arithmetic
Denormalized floating-point numbers near zero
numbers (sometimes called denormals) that fill the underflow gap around zero in floating-point arithmetic. Any non-zero number with magnitude smaller than
Subnormal_number
IEEE standard for floating-point arithmetic
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the
IEEE_754
Variant of floating-point numbers in computers
overflow or underflow conditions. In 2013, John Gustafson proposed the Unum number system, a variant of tapered floating-point arithmetic with an exact
Tapered_floating_point
N-th root of the product of n numbers
implementations, naïvely multiplying many numbers together can cause arithmetic overflow or underflow. Calculating the geometric mean using logarithms is one way
Geometric_mean
Measure of variation in statistics
become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow. The method below calculates the running sums method
Standard_deviation
Class of mathematical expression
preserves the sign of the result in case of arithmetic underflow. For example, using single-precision IEEE arithmetic, if x = − 2 − 149 {\displaystyle \textstyle
Division_by_zero
Performing the actions encoded in a computer program
errors, array subscript out of bounds errors, arithmetic underflow errors, several types of underflow and overflow errors, and many other runtime errors
Execution_(computing)
Type of arithmetic where output is limited to a fixed range of values
Saturation arithmetic is a version of arithmetic in which all operations, such as addition and multiplication, are limited to a fixed range between a
Saturation_arithmetic
Differentiating positive and negative zero
the result of certain computations, for instance as the result of arithmetic underflow on a negative number (other results may also be possible), or −1
Signed_zero
Value for unrepresentable data
the same as an arithmetic overflow (which would return an infinity or the largest finite number in magnitude) or an arithmetic underflow (which would return
NaN
errors, array subscript out of bounds errors, arithmetic underflow errors, several types of underflow and overflow errors, and many other runtime errors
Glossary_of_computer_science
Computer format for representing real numbers
or underflow may occur if |S| is very large or very small, respectively. Typical processors do not have specific support for fixed-point arithmetic. However
Fixed-point_arithmetic
Sigmoid shape special function
complementary error function (which can be used instead of erfc to avoid arithmetic underflow). Another form of erfc x for x ≥ 0 is known as Craig's formula, after
Error_function
Probabilistic classification algorithm
log-probabilities are units of information in nats. Another is that it avoids arithmetic underflow. The discussion so far has derived the independent feature model
Naive_Bayes_classifier
Hypotenuse of right triangle from its sides
lead to an inaccurate result caused by arithmetic underflow and overflow, although when overflow and underflow do not occur the output is within two ulp
Pythagorean_addition
Second edition of the IEEE 754 floating-point standard
IEEE 754r) is a revision of the IEEE 754 standard for floating-point arithmetic. It was published in August 2008 and is a significant revision to, and
IEEE_754-2008_revision
Error in numerical data
sampling, such as IQ tests, are often reported with false precision. Arithmetic underflow Limit of detection Precision bias Propagation of uncertainty Round-off
False_precision
Abstract data type
checking for underflow, and returns the item that was previously the top one: procedure pop(stk : stack): if stk.top = 0: report underflow error else:
Stack_(abstract_data_type)
Subset of x86 instruction set architecture for floating-point arithmetic
January 2017. William Kahan (8 July 1989). "How Intel 8087 stack overflow/underflow should have been handled" (PDF). Archived from the original (PDF) on 12
X87
Replacing a number with a simpler value
computations – especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms
Rounding
Formula that provides the solutions to a quadratic equation
{\displaystyle c} is represented as zero or infinite; and possible overflow or underflow when multiplying or dividing extremely large or small numbers, even in
Quadratic_formula
64-bit computer number format
synonyms. Common Lisp provides exceptions for catching floating-point underflows and overflows, and the inexact floating-point exception, as per IEEE 754
Double-precision floating-point format
Double-precision_floating-point_format
Procedural, imperative computer programming language
ON-unit and return to the point of interrupt (e.g., the STRINGRANGE, UNDERFLOW, CONVERSION, OVERFLOW, AREA, and FILE conditions) and resume normal execution
PL/I
Algorithm to compute rounding error
in IEEE 754, and provided the sum does not overflow and, if it underflows, underflows gradually, it can be proven that s + t = a + b {\displaystyle s+t=a+b}
2Sum
Exact floating-point subtraction theorem
In floating-point arithmetic, the Sterbenz lemma or Sterbenz's lemma is a theorem giving conditions under which floating-point differences are computed
Sterbenz_lemma
First edition of the IEEE 754 floating-point standard
leading binary digit is a 1. To reduce the loss of precision when an underflow occurs, IEEE 754 includes the ability to represent fractions smaller than
IEEE_754-1985
Smooth approximation to the maximum function
purpose of using log-domain computations is to increase accuracy and avoid underflow and overflow problems when very small or very large numbers are represented
LogSumExp
System of digitally encoding numbers
digit may be used to indicate special numeric values, such as infinity, underflow/overflow, and error (a blinking display). Signed decimal values may be
Binary-coded_decimal
with the new floating-point facilities Bit 22 is renamed as HFP exponent underflow in ESA/390 Bit 23 is renamed as HFP significance in ESA/390 The data returned
IBM Enterprise Systems Architecture
IBM_Enterprise_Systems_Architecture
Open-source CPU instruction set architecture
exceptions on arithmetic errors, including overflow, underflow, subnormal, and divide by zero. Instead, both integer and floating-point arithmetic produce reasonable
RISC-V
operate at the same average data rate to prevent eventual FIFO overflow or underflow. Some older FIFOs have no clock at all. These are less common and not
FIFO_(electronic)
Algorithm to calculate the day of the week
Zeller's congruence is a modular arithmetic algorithm devised by Christian Zeller in the 19th century for calculating the day of the week for a given date
Zeller's_congruence
Floating-point number formats
the base format. In contrast to extended precision, arbitrary-precision arithmetic refers to implementations of much larger numeric types (with a storage
Extended_precision
Decimal representation of real numbers in computing
Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal
Decimal_floating_point
Inherent flaw in computer instructions
precision due to rounding, numerically unstable algorithms, arithmetic overflow and underflow, or from lack of awareness of how calculations are handled
Software_bug
Topics referred to by the same term
the act of a counter restarting its count sequence upon overflow or underflow Rollover (key), the ability of a computer keyboard to handle several simultaneous
Rollover
Type of linear congruential generator with no additive constant
is d, the sum is at least d, and subtracting the offset never causes underflow. (For the case of a Lehmer generator specifically, a zero state or its
Lehmer random number generator
Lehmer_random_number_generator
Algorithm in modular arithmetic
1/n} , which can cause underflows. Thus m = ⌊ 2 k / n ⌋ {\displaystyle m=\lfloor {2^{k}}/{n}\rfloor } is used for unsigned arithmetic. Thus we can approximate
Barrett_reduction
Floating-point number format by Microsoft
mitigate problems caused by underflow; and a better balanced exponent bias, which could help avoid overflow and underflow when taking the reciprocal of
Microsoft_Binary_Format
Interval of binary floating-point numbers with a common sign and exponent
06953. doi:10.1002/cpe.7856. ISSN 1532-0626. Coonen, Jerome T. (1981). "Underflow and the Denormalized Numbers". Computer. 14 (3). IEEE: 75–87. doi:10.1109/C-M
Binade
Internal representation of numeric values in a digital computer
numbers can be represented with a given number of bits. Arithmetic operations can overflow or underflow, producing a value too large or too small to be represented
Computer_number_format
Early scientific pocket calculator
display indicated an error, such as a calculation error or an overflow or underflow condition. Like most scientific calculators, the SR-50 mostly used ordinary
TI_SR-50
Model independent architecture for the S/360 line of mainframe computers
characteristic in a floating-point arithmetic operation exceeds 127 and the fraction is not zero. An exponent underflow exception is recognized when the
IBM_System/360_architecture
Minicomputer product line
subroutines, simplified to omit issues such as testing for stack overflow and underflow: *100 /make routines accessible for next example PUSH, 0 DCA DATA CLA
PDP-8
String searching algorithm
modulo, or remainder after integer division, operator. (-ve avoider) = "underflow avoider". Necessary if using unsigned integers for calculations. Because
Rabin–Karp_algorithm
Floating-point microprocessor
microprocessors. The purpose of the chip was to speed up floating-point arithmetic operations, such as addition, subtraction, multiplication, division, and
Intel_8087
Form of inter-process communication in computer systems
detected in the floating-point or integer arithmetic hardware. This may include division by zero, floating-point underflow or overflow, integer overflow, an invalid
Signal_(IPC)
8-bit microprocessor
P/V flag (since adding or subtracting zero never causes an overflow or underflow) instead of assigning P to correctly indicate the parity of the byte—as
Zilog_Z80
Algorithm that estimates unknowns from a series of measurements over time
easily be computed as a simple recursive update; however, to avoid numeric underflow, in a practical implementation it is usually desirable to compute the
Kalman_filter
a slope function to go to a minimum. If the slope is very small, then underflow errors can cause the algorithm to wander, seemingly aimlessly; this is
Guess_value
Concept in numerical linear algebra
a/r\\s&{}\leftarrow -b/r.\end{aligned}}} However, the computation for r may overflow or underflow. An alternative formulation avoiding this problem (Golub & Van Loan 1996
Givens_rotation
8-bit microprocessor
loop. Likewise the XCD instruction will skip if BL, after decrementing, underflows to 15 (decimal). The following assembler source code is for three subroutines
American_Microsystems_S2000
Method of numerical integration
large steps. This likely also applies to the tolerance/interval width underflows in the simplistic case. G.F. Kuncir (1962), "Algorithm 103: Simpson's
Adaptive_Simpson's_method
sequence of unfused multiplications and additions - rounding and overflow/underflow checking are performed for each multiplication and addition step separately
List_of_x86_SIMD_instructions
8-bit microcontroller
program status word contains carry and half-carry flags for multi-byte arithmetic. Rather, there are a number of compare-and-skip instructions. For example
COP8
List of x86 microprocessor instructions
80387. For FSCALE, rounding is only applied in the case of overflow, underflow or subnormal result. The x87 transcendental instructions do not obey PC
List_of_x86_instructions
Instruction for x86 microprocessors
INTEL-SA-00598, 4 Aug 2022. Archived on 11 Feb 2024. Intel, Return Stack Buffer Underflow / CVE-2022-29901, CVE-2022-28693 / INTEL-SA-00702, 12 Jul 2022. Archived
CPUID
Single-chip 16-bit microprocessor
in a priority fashion. IE1 is set only in the case of a stack overflow/underflow. The other four can be used to disable individual interrupt lines, or
National_Semiconductor_PACE
Comparison of two programming languages
use checked and unchecked contexts for fine-grained control of overflow/underflow checking Iterative for-loops can contain multiple conditionals, such as
Comparison of C Sharp and Visual Basic .NET
Comparison_of_C_Sharp_and_Visual_Basic_.NET
Flow measurements in open channels using structures – Use of vertical underflow gates and radial gates ISO 13559:2002 Butter, fermented milks and fresh
List of ISO standards 12000–13999
List_of_ISO_standards_12000–13999
4-bit microcontroller family
loop. Likewise the XDS instruction will skip if Bd, after decrementing, underflows to 15 (decimal). Types supported: Type 1 is very low-end such as COP410
COP400
8-bit microcontroller product lines from STMicroelectronics
processors use the "carry" convention, which clears the bit if the subtract underflows, while the ST62 and ST63 processors use the "borrow" convention, which
ST6_and_ST7
ARITHMETIC UNDERFLOW
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Devoted to God.
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The Woman
Girl/Female
Hindu, Indian, Sanskrit, Traditional
A Form of Durga; Wind of Vindhyas
Girl/Female
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Hindu, Indian
Always Ready
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warrior.
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Capacity
ARITHMETIC UNDERFLOW
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ARITHMETIC UNDERFLOW
n.
Arithmetic.
v. t.
To subtract by arithmetical operation; to deduct.
adv.
The arithmetical character 0; a cipher. See Cipher.
a.
Having equal differences; as, the terms of arithmetical progression are equidifferent.
a.
Having an assignable arithmetical or numerical value or meaning; not imaginary.
n.
One skilled in arithmetic.
v. i.
To perform the arithmetical operation of addition; as, he adds rapidly.
n.
Arithmetical subtraction.
n.
The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional.
n.
The four "liberal arts," arithmetic, music, geometry, and astronomy; -- so called by the schoolmen. See Trivium.
a.
Of or pertaining to arithmetic; according to the rules or method of arithmetic.
v. i.
To use figures in a mathematical process; to do sums in arithmetic.
a.
Of or pertaining to a unit or units; relating to unity; as, the unitary method in arithmetic.
n.
That part of arithmetic which treats of adding numbers.
a.
Sexagesimal, or made on the scale of 60; as, logistic, or sexagesimal, arithmetic.
n.
The science of numbers; the art of computation by figures.
n.
A book containing the principles of this science.
v. t.
To subject to arithmetical division.
n.
A system of arithmetic, in which numbers are expressed in a scale of 60; logistic arithmetic.
adv.
Conformably to the principles or methods of arithmetic.