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# Topic: Floating point

 Floating point - Wikipedia, the free encyclopedia For the common 32 bit "single precision" or "float" format of the IEEE standard, this constant is 127, so the exponent is said to be represented in "excess 127" format. Unlike the fixed-point counterpart, the application of dither in a floating point environment is nearly impossible. To a rough approximation, the bit representation of a floating point number is proportional to its base 2 logarithm, with an average error of about 3%. en.wikipedia.org /wiki/Floating_point   (2889 words)

 Floating Point and Integer Numbers 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. In such cases, all numbers are converted to floating point number and the result is a floating point number. www.cs.odu.edu /~wild/cs150/floatInt.htm   (332 words)

 Floating Point Types For floating point types, the error bound is specified as a relative precision by giving the required minimum number of significant decimal digits. The base decimal precision of a floating point type is the number of decimal digits of precision representable in objects of the type. The safe range of a floating point type is that part of its base range for which the accuracy corresponding to the base decimal precision is preserved by all predefined operations. www.adaic.org /standards/95lrm/html/RM-3-5-7.html   (617 words)

 Java theory and practice: Where's your point? An IEEE floating point number dedicates 1 bit to the sign of the number, 8 bits to the exponent, and 23 bits to the mantissa, or fractional part. Floating point numbers are best reserved for values such as measurements, whose values are fundamentally inexact to begin with. 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. www-106.ibm.com /developerworks/java/library/j-jtp0114   (1800 words)

 Floating Point Operations Floating point hardware was standard throughout the 7090/94 family. 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). www.frobenius.com /floating-point.htm   (410 words)

 Floating Point   (Site not responding. Last check: 2007-10-21) Java uses a subset of the IEEE 754 binary floating point standard to represent floating point numbers and define the results of arithmetic operations. 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. Although we cannot expect our floating point algorithms to correctly handle ill-conditioned problem, we can ask that they report back an error rangle associated with the solution so that at least we are alerted to potential problems. www.cs.princeton.edu /introcs/91float   (6340 words)

 Floating-Point Basics   (Site not responding. Last check: 2007-10-21) 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. Multiplying two floating point values is fairly easy, although there are a couple of edge conditions that we have to be careful of. 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. www.petebecker.com /js200006.html   (3680 words)

 CS267: Supplementary Notes on Floating Point More detailed material on floating point may be found in Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic. Floating point numbers are represented in the form +-significand * 2^(exponent), where the significand is a nonnegative number. 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). www.cs.berkeley.edu /~demmel/cs267/lecture21/lecture21.html   (4277 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. A floating point zero is represented by a word with 36 bits of 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). www.inwap.com /pdp10/hbaker/pdp-10/Floating-Point.html   (978 words)

 Inner Float Java Applet - an Interactive Illustration of Floating Point Numbers At that point, the value displayed in radix 10 is 8.3361e+06, which is the same as the radix 2 number. When a floating point operation underflows to negative zero, as when it underflows to positive zero, all bits of precision are lost. When a floating point operation overflows to negative infinity, as when it overflows to positive infinity, all bits of precision are lost. www.artima.com /insidejvm/applets/InnerFloat.html   (443 words)

 D Programming Language - Floating Point For floating point operations and expression intermediate values, a greater precision can be used than the type of the expression. Float or double types, as opposed to the extended type, should only be used for: IEEE 754 floating point arithmetic can set several flags based on what happened with a computation: [blah, blah, blah]. www.digitalmars.com /d/float.html   (493 words)

 IEEE floating-point standard - Wikipedia, the free encyclopedia The mantissa is the part at the right of the radix point, filled with 0 on the right until we get all 23 bits. The exponent is 6, but we need to convert it to binary and bias it (so the most negative exponent is 0, and all exponents are non-negative binary numbers). For Denormalised numbers the exponent is −1022 (the minimum exponent for a normalised number—it is not −1023 because normalised numbers have a leading 1 digit before the binary point and denormalised numbers do not). en.wikipedia.org /wiki/IEEE_floating-point_standard   (1480 words)

 IEEE Standard 754 Floating-Point Fixed point places a radix point somewhere in the middle of the digits, and is equivalent to using integers that represent portions of some unit. 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. steve.hollasch.net /cgindex/coding/ieeefloat.html   (1366 words)

 Floating-point Formats However, if round on load, truncate on store, is specified, then when a floating point register is loaded with a value, the less significant portion of the register which is not filled by the input value is only loaded with zeroes when the input value is zero; otherwise, it is filled with 1000...0000. Note that in the case of 32-bit floating point numbers, a temporary format of 64 bits in size is not inherently necessary; 19 bits of the exponent will not be used, but are present in the temporary format because most of them are required to represent the numeric range available in the 64-bit format. Since during an interrupt, the entire 128 bits of a floating point register are saved and restored, normally returning from an interrupt is not complicated by using guard bits with shorter formats. www.quadibloc.com /arch/ar0505.htm   (4661 words)

 5.6 decimal -- Decimal floating point arithmetic Unlike hardware based binary floating point, the decimal module has a user settable precision (defaulting to 28 places) which can be as large as needed for a given problem: Both binary and decimal floating point are implemented in terms of published standards. While the built-in float type exposes only a modest portion of its capabilities, the decimal module exposes all required parts of the standard. docs.python.org /lib/module-decimal.html   (337 words)

 Floating Point Arithmetic Floating point arithmetic derives its name from something that happens when you use exponential notation. 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. 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)

 IEEE Floating Point Data For regular IEEE 32-bit floating point numbers, the sign is contained in bit 1, the exponent in bits 2-9, and the fraction in bits 10-32. For regular IEEE 64-bit floating point numbers, the sign is contained in bit 1, the exponent in bits 2-12, and the fraction in bits 13-64. This convention allows IEEE floating point to represent numbers that are smaller than those represented by the regularly defined values, although the number of significant digits decreases for smaller values. archive.stsci.edu /fits/users_guide/node27.html   (516 words)

 IEEE Float The IEEE floating point standard is a floating point arithmetic system adopted by the Institute for Electrical and Electronics Engineer in the early 1980s. Note that only the fraction from the normalized mantissa is stored and so there is a hidden bit and the mantissa is actually represented by 53 binary digits. Basically, given a real number x, its correctly rounded value is the floating point number fl(x) that is closest to x. www.math.byu.edu /~schow/work/IEEEFloatingPoint.htm   (495 words)

 NetWinder Floating Point Notes ARM manufactures a coprocessor floating point unit; the FPA11, however it is only available on the ARM 7500FE and it is not compatible with the Intel StrongARM chips. Russell King distributes a port of the Acorn floating point emulator that is compatible with ARM Linux kernels. If the opcode is not a floating point opcode, control is returned to the kernel and the invalid instruction trap handler is executed, resulting in the process dumping core. netwinder.osuosl.org /users/s/scottb/public_html/notes/FP-Notes-all.html   (1658 words)

 Lecture notes - Chapter 7 - Floating Point Arithmetic about FLOATING POINT ARITHMETIC ------------------------------- arithmetic operations on floating point numbers consist of addition, subtraction, multiplication and division the operations are done with algorithms similar to those used on sign magnitude integers (because of the similarity of representation) -- example, only add numbers of the same sign. 1 01000001 10.00110000 normalize the result: (moving the radix point one place to the left increases the exponent by 1.) 1 01000001 10.00110000 becomes 1 01000010 1.000110000 this is the value stored (not the hidden bit!): 1 01000010 000110000 DIVISION similar to multiplication. ISSUES in floating point note: this discussion only touches the surface of some issues that people deal with. www.cs.wisc.edu /~smoler/x86text/lect.notes/arith.flpt.html   (868 words)

 Floating-point arithmetic For each bytecode that performs arithmetic on floats, there is a corresponding bytecode that performs the same operation on doubles. The mantissa occupies the 23 least significant bits of a float and the 52 least significant bits of a double. 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)

 Fixed-Point vs. Floating-Point DSP for Superior Audio   (Site not responding. Last check: 2007-10-21) What they fail to point out is the "rest of the story," which is that the 24-bit fixed-point DSP box can operate in "double-precision" mode, making it a 48-bit box. Another possibility is if the floating point DSPs evolve to offer significantly more processing power for the same price (enough to overcome the low-frequency, high-Q issues in firmware) and offer a compatible peripheral chip set, then this could tip the scales even if they still offer only a 32-bit fixed numerical format. Often the result of this multiply-and-add is the starting point for the next calculation, so it forms a running total, or an accumulation, of all the results over time. www.rane.com /note153.html   (2993 words)

 RPL Floating Point Library This gives the designer full control over where and when to normalize floating point calculations, and results in savings of area in their hardware implementation. The currently implemented arithmetic operators are floating point add/sub and floating point multiply. Floating Point Divide, Square Root, and Multiply Accumulate (MAC) are planned in the near future. www.ece.neu.edu /groups/rpl/projects/floatingpoint   (567 words)

 IEEE Floating Point Standard   (Site not responding. Last check: 2007-10-21) The IEEE FPS is the most widely accepted standard representation for floating point numbers. The maximum value of E = 255 is reserved to indicate overflow values (usually the result of floating point arithmetic) with exponents that are too large or too small to be represented. Floating point division by zero produces a number with E=255 and nonzero M called NaN (Not a Number). www.cs.uaf.edu /~cs301/notes/Chapter4/node13.html   (303 words)

 Floating Point 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. The mantissa would be a fixed point fraction and the exponent would be an integer. www.thevickerage.worldonline.co.uk /theteacher/newalevel/index4_2_4.htm   (337 words)

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