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Floating point - Wikipedia, the free encyclopedia Floating point representation is more likely to be appropriate when proportional accuracy over a range of scales is needed. Rounding errors: unlike the fixed-point counterpart, the application of dither in a floating point environment is nearly impossible. By the nature of floating point representation, the larger a value, the less precise it is, in absolute terms. en.wikipedia.org /wiki/Floating_point   (1485 words)

Floating point unit - Wikipedia, the free encyclopedia In the the past, some systems have implemented floating point via a coprocessor rather as an integrated unit; in the microcomputer era, this was generally a single microchip, while in older systems it could be an entire circuit board or a cabinet. Typical operations are floating point arithmetic (such as addition and multiplication), but some systems may be capable of performing exponential or trigonometric calculations as well (such as square roots or cosines). A floating point unit (FPU) is a part of a computer system specially designed to carry out operations on floating point numbers. en.wikipedia.org /wiki/Floating_point_unit   (677 words)

Kids.net.au - Encyclopedia Floating point - As an example, a floating point number with four decimal digits (b=10, p=4)could be used to represent 4321 or 0.00004321, but would round 432.123 to 432.1 and 43212.3 to 43210. A floating point calculation[?] is one arithmetic calculation done with floating point numbers. The placement of the bits in the IEEE standard enables two floating point numbers to be compared bitwise (sans sign-bit) to yield a result without interpreting the actual values. www.kidsseek.com /encyclopedia-wiki/fl/Floating_Point   (970 words)

Floating Point : Java Glossary Floating point is slower still when you consider the overhead of converting between the combined int/floating point stack in the JVM and the separate stacks in the Pentium hardware. In most computers, floating point arithmetic is usually much slower than integer arithmetic, though on the Pentium it is usually faster because the integer unit was not given the same care as the floating point unit. By floating point I refer generically to the code written to use the primitives double and float and the wrapper classes Double and Float. mindprod.com /jgloss/floatingpoint.html   (1691 words)

CS267: Supplementary Notes on Floating Point This means that the floating point result fl(a op b) of the exact operation (a op b) is the nearest floating point number to (a op b), breaking ties by rounding to the floating point number whose bottom bit is zero (the "even" one). Floating point numbers are represented in the form +-significand* 2^(exponent), where the significand is a nonnegative number. More detailed material on floating point may be found in Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic. www.cs.berkeley.edu /~demmel/cs267/lecture21/lecture21.html   (4277 words)

Floating Point Operations As example, single precision floating point 10.00 (decimal) was represented as 204500000000 (octal) which yielded a sign bit of 0; a characteristic of 204 (octal); and a mantissa of 500000000 (octal). Other floating point examples: 0.00390625 (decimal) was represented by 171400000000 (octal); 44.00 (decimal) was represented by 206510000000 (octal); and -20.00 (decimal) was represented by 605500000000 (octal). Floating point hardware was standard throughout the 7090/94 family. www.frobenius.com /floating-point.htm   (410 words)

Floating Point and Integer Numbers In such cases, all numbers are converted to floating point number and the result is a floating point number. floating point numbers: these are numbers with a decimal point (which "floats" - called a floating point number) like 2.3, -14.5 (see pp. Floating point and integer numbers have different rules for thier arithmetic. www.cs.odu.edu /~wild/cs150/floatInt.htm   (332 words)

Java theory and practice: Where's your point? Floating point and decimal numbers are not nearly as well-behaved as integers, and you cannot assume that floating point calculations that "should" have integer or exact results actually do. Floating point numbers are best reserved for values such as measurements, whose values are fundamentally inexact to begin with. Because any given number can be represented in scientific notation in multiple ways, floating point numbers are normalized so that they are represented as a base 2 decimal with a 1 to the left of the decimal point, adjusting the exponent as necessary to make this requirement hold. www-128.ibm.com /developerworks/java/library/j-jtp0114   (1800 words)

Floating Point In contrast, floating point arithmetic is not exact since some number require an infinite number of digits to be represented, e.g., the mathematical constants e and π and 1/3. Java uses a subset of the IEEE 754 binary floating point standard to represent floating point numbers and define the results of arithmetic operations. Floating point has a sliding window of precision, which provides a large dynamic range and high precision. www.cs.princeton.edu /introcs/91float   (6338 words)

Fabulous Adventures In Coding : Floating Point Arithmetic, Part One We wrote a floating point extension to the BASIC on the Acorn Atom in assembly as a "class project". Floating point math does admit both +/- infinity and+/- 0, though of course +0 always equals -0. Since the whole point of denormals is to degrade into an underflow situation gracefully, it would be bad if there were such a gap. blogs.msdn.com /ericlippert/archive/2005/01/10/350108.aspx   (1069 words)

Comparing floating point numbers Because floating point math is imperfect you may not get an answer of exactly 10,000 - you may be off by one or two in the least significant bits of your result. One is that most floating point code is designed to not produce NANs, and in fact most floating point code should treat NANs as an error by enabling floating point divide by zero and floating point illegal operation exceptions. Simple values like 0.2 cannot be precisely represented using binary floating point numbers, and the limited precision of floating point numbers means that slight changes in the order of operations can change the result. www.cygnus-software.com /papers/comparingfloats/comparingfloats.htm   (3164 words)

Floating-Point Numbers The basic idea of floating point encoding of a binary number is to normalize the number by shifting the bits either left or right until the shifted result lies between 1/2 and 1. Floating point notation is exactly analogous to ``scientific notation'' for decimal numbers, e.g. MPEG-4 audio decoder should be at least as accurate as 32-bit single-precision floating point. ccrma.stanford.edu /~jos/mdft/Floating_Point_Numbers.html   (509 words)

IEEE Standard 754 Floating-Point The range of positive floating point numbers can be split into normalized numbers (which preserve the full precision of the mantissa), and denormalized numbers (discussed later) which use only a portion of the fractions's precision. Since the sign of floating point numbers is given by a special leading bit, the range for negative numbers is given by the negation of the above values. This is an excellent article on the traps, pitfalls and solutions for comparing floating point numbers. steve.hollasch.net /cgindex/coding/ieeefloat.html   (1366 words)

PDP-10 Floating-Point In a normalized floating point number bit 9 is different from bit 0, except in a negative number bits 0 and 9 may both be one if bits 10:35 are all zero. One use of FSC is to convert an integer in AC to floating point (but FLTR, available in the KI and KL is better) To use FSC to float an integer, set E to 233 (excess 200 and shift the binary point 27 bits). A floating point zero is represented by a word with 36 bits of zero. www.inwap.com /pdp10/hbaker/pdp-10/Floating-Point.html   (978 words)

Floating Point Arithmetic In order to illustrate some of the details of floating point arithmetic, we will consider an imaginary floating point format in which the exponent is stored in 5 bits, the significand is stored in 10 bits, and 1 bit is used to store the sign of the number. Floating point arithmetic derives its name from something that happens when you use exponential notation. The step which actually performs the operation can result in another kind of error: overflows can occur in floating point arithmetic as well as in fixed, but they are detected in the exponent rather than the significand. www.rwc.uc.edu /koehler/comath/14.html   (1972 words)

Floating-point Arithmetic Precision However, the C language requires floating point values to be truncated when a conversion to an integer is involved. The -pcn option causes the compiler to change the floating point precision control when the main() function is compiled. This means that values are rounded during floating point calculations. www.nersc.gov /vendor_docs/intel/c_ug/lin1065.htm   (923 words)

Floating Point One peculiar attribute of floating point numbers is that when you stretch it to it's limit in terms of accuracy, power-of-two numbers and fractions are more accurately reproduced. But with floating point, we'd have to use at least 37 digits, which is larger than a 32bit number. In floating point, there are multiple independent sections of each number which must be compared and computed. maraist.homelinux.com:5180 /articles/floating_point.html   (1086 words)

Floating-Point Basics The floating point code does the same thing: if bit 31 is 1, the fractional part is too large to represent in our internal notation, so the code divides it by 2 and increases the exponent by 1. Multiplying two floating point values is fairly easy, although there are a couple of edge conditions that we have to be careful of. But consider the same division performed with floating point math: one divided by three is 0.333333, with however many threes are supported by the floating point package that is being used. www.petebecker.com /js200006.html   (3680 words)

Inner Float Java Applet - an Interactive Illustration of Floating Point Numbers When a floating point operation overflows to negative infinity, as when it overflows to positive infinity, all bits of precision are lost. When a floating point operation underflows to negative zero, as when it underflows to positive zero, all bits of precision are lost. Inner Float Java Applet - an Interactive Illustration of Floating Point Numbers www.artima.com /insidejvm/applets/InnerFloat.html   (484 words)

Floating point unit - Wikipedia, the free encyclopedia Floating point addition and multiplication operations are typically pipelined, but more complicated operations, like division, may not be, and some systems may even have a dedicated floating point divider circuit. Typical operations are floating point arithmetic (such as addition and multiplication), but some systems may be capable of performing exponential or trigonometric calculations as well (such as square roots or cosines). In the absence of an FPU, the CPU may use a microcode program to emulate an FPUs function using an arithmetic and logical unit (ALU), which saves the added hardware cost of an FPU but is significantly slower. en.wikipedia.org /wiki/FPU   (269 words)

The Java Community Process(SM) Program - JSRs: Java Specification Requests - detail JSR# 84 Floating point operations may be reordered, assuming floating-point arithmetic to be associative. As a result, in some cases, the rules also significantly impaired floating point performance by effectively prohibiting certain code generation optimizations and the use of certain native operations on some processors. The FP-strict and the default floating point mode are each a valid implementation of the FP-fast mode; thus, any Java virtual machine implementation can trivially provide support for FP-fast methods. www.jcp.org /en/jsr/detail?id=84   (1652 words)

Define floating point unit - a Whatis.com definition - see also: FPU, math coprocessor, floating-point unit, numeric coprocessor A floating point number is a binary number carried out to a specific number of digits, and containing a radix (or decimal) point somewhere in the digit sequence. A floating point unit (FPU), also known as a math coprocessor or numeric coprocessor, is a specialized coprocessor that manipulates numbers more quickly than the basic microprocessor circuitry. Such numbers are stored in three parts: the sign (either plus or minus), the mantissa (sequence of meaningful digits), and the exponent (power or order of magnititude), which determines the position in the mantissa where the radix point is placed. searchwinit.techtarget.com /sDefinition/0,,sid1_gci213965,00.html   (345 words)

Introduction to Floating point calculations and IEEE 754 standard Representation As in all floating point representations, the IEEE representation divides the number of bits into three groups, the exponent and the fractional part. Floating Point is a representation of real (fractional) numbers. Which means if k is the value of the exponent bits, then the exponent of the floating point number is k www.geocities.com /SiliconValley/Pines/6639/docs/fp_summary.html   (1258 words)

Floating point follies The reason for all this is that floating point numbers (as defined by the IEEE) support a number of special values that aren't usually surfaced to VB programmers. As a result, VB.NET floating point operations are much "closer to the metal," which is either a good thing or a bad thing depending on your perspective. A related issue is that most processors' FPU registers can handle floating point numbers with a higher precision than can be stored in the standard.NET Double datatype. www.panopticoncentral.net /archive/2003/08/13/177.aspx   (702 words)

ASPN : Python Cookbook : Floating Point Simulator Since the underlying representation is regular floating point, the demonstration only works up to the 15 digits (the typical limit for double precision floating point). This is reasonable since real floating point systems have to start with representable constants; however, if the original representation error needs to be tracked, enter the number twice in the constructor: F(2.7181, 2.7181). This is helpful because it isolates accumulated floating point operation errors from the artifacts of the orignal data entry. aspn.activestate.com /ASPN/Cookbook/Python/Recipe/265894   (344 words)

Floating Point A floating point number system uses 16-bit numbers. Bits to the left of this point would be the integer part and bits to the right of it would be the fraction part. The binary point is fixed as being after the 4th bit. www.thevickerage.worldonline.co.uk /theteacher/newalevel/index4_2_4.htm   (337 words)

Floating Point Make sure that everything is consistently compiled for hardware floating point, especially if you've assembled your toolkit yourself, or are using an 8xx toolkit to compile for the 8260. In general, you're better off choosing one or the other, and choosing hardware floating point with kernel instruction emulation is much easier to get working correctly. Programs compiled for hardware floating point can still run on a CPU without an FPU, provided the kernel is built with the floating point instruction emulator. www.penguinppc.org /embedded/howto/floating.html   (337 words)

Floating-point arithmetic A normalized radix 10 floating-point number has its decimal point just to the left of the first non-zero digit in the mantissa. A normalized mantissa has its binary point (the base-two equivalent of a decimal point) just to the left of the most significant non-zero digit. For example, an exponent field in a float of 00000001 yields a power of two by subtracting the bias (126) from the exponent field interpreted as a positive integer (1). www.javaworld.com /javaworld/jw-10-1996/jw-10-hood.html   (1583 words)

Ken Henderson's WebLog : Floating point fun Languages that don't correct for floating point rounding errors are susceptible to returning different results for the same numeric computation stated in different ways -- heresy in the world of mathematics. One of those is when performing certain types of floating point calculations. IOW, the best solution of all may be to avoid doing floating point computations of any complexity in Transact-SQL in the first place. blogs.msdn.com /khen1234/archive/2005/05/13/417153.aspx   (849 words)

Adding Floating Point Numbers We'll do addition using the one byte floating point representation discussed in the other class notes. Shift the radix point of the mantissa (signficand) Y left by x - y to compensate for the change in exponent. www.cs.umd.edu /class/spring2003/cmsc311/Notes/BinMath/addFloat.html   (901 words)

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