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| | 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. |
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http://en.wikipedia.org/wiki/FPU
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| | Floating Point Unit |
| | DownGradePrecision Code by Kevin Rhoads to allow precision to be deliberately thrown away in an IEEE floating point compliant computing environment in order to more closely model computations in less precise floating point systems. | | | Floating Point Computer Services Focused technology company working for small businesses. | | | Assembly Language Floating Point Simple input and output in assembly language for floating point and integer double word sized values. |
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http://www.serebella.com/encyclopedia/article-Floating_Point_Unit.html
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| | Art of Assembly: Chapter Fourteen |
| | When Intel planned to introduce a floating point coprocessor for their new 8086 microprocessor, they were smart enough to realize that the electrical engineers and solid-state physicists who design chips were, perhaps, not the best people to do the necessary numerical analysis to pick the best possible binary representation for a floating point format. | | | However, on processors eariler than the 80486 (or on the 80486sx), the floating point processor is an optional device; it this device is not present you must simulate it in software. | | | However, if you compute a value which is the result of a sequence of floating point operations, the error can accumulate and greatly affect the computation itself. |
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http://webster.cs.ucr.edu/AoA/DOS/ch14/CH14-1.html
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| | Floating point - Wikipedia, the free encyclopedia |
| | In computers, floating-point numbers are sized by the number of bits used to store them. | | | Rounding errors: unlike the fixed-point counterpart, the application of dither in a floating point environment is nearly impossible. | | | Floating point representation is more likely to be appropriate when proportional accuracy over a range of scales is needed. |
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http://en.wikipedia.org/wiki/Floating_point
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| | Central processing unit - Encyclopedia.WorldSearch |
| | The central processing unit (CPU) is the part of a computer that interprets and carries out the instructions contained in the software. | | | Manufacturers of desktop computers often erroneously describe the entire personal computer (the system unit or sometimes white box, including the computer case and the computer hardware it contains) as the CPU. | | | Rather, the CPU, as a functional unit, consists of that part of the computer which actually executes the instructions (add, subtract, shift, fetch, etc.). |
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http://encyclopedia.worldsearch.com/central_processing_unit.htm
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| | Embedded Pentium® Processor Family Technical Information Center - Floating-Point Unit |
| | A pointer to the FPU data register that is currently at the top of the FPU register stack is contained in bits 11 through 13 of the FPU status word. | | | The first Intel Math Coprocessors (the Intel 8087, Intel 287, and Intel 387) were companion processors to the Intel 8086/8088, Intel 286, and Intel386 processors, respectively, and were designed to improve and extend the numeric processing capability of the Intel Architecture. | | | The FPU can operate on and/or return any of these values, depending on the type of computation being performed. |
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http://www.engr.udayton.edu/faculty/jloomis/ece314/notes/fpu/fpu.html
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| | Floating Point Encoding |
| | Specifically, for example, the value 0 is represented by a floating point encoding with all 0's in both the exponent and mantissa fields. | | | The main point here is that a "normalized" base 2 floating point value will always have a single 1 to the left of the decimal point. | | | For example, "dollar values" may often be stored as fixed point values with 2 digits to the right of the decimal point; in fact, the value is stored as an integer number of cents and only divided by 100 for output display. |
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http://blackboard.algonquincollege.com/coursemat/dat2343/lectures.f03/10-Floating-Point.htm
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| | The S/390 G5 floating-point unit |
| | Since the FXU and FPU cannot execute in parallel, the FXU is used for the starting of floating-point instructions to access data from the register files and align storage data for the FPU. | | | The key feature of the G5 FPU is its ability to implement both the hexadecimal and binary floating-point formats on one FPU. | | | Both the execution unit (E-unit) and the instruction unit (I-unit) are duplicated on chip and execute on the same instruction stream, and the results are compared by the recovery unit and L1 cache unit. |
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http://www.research.ibm.com/journal/rd/435/schwarz.html
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| | FPU - a Whatis.com definition - see also: floating point unit, floating-point unit |
| | An floating point unit (FPU), also known as a numeric coprocessor, is a microprocessor or special circuitry in a more general microprocessor that manipulates numbers more quickly than the basic microprocessor your computer uses. | | | Personal computers that don't have floating point units can sometimes handle software that requires them by installing a floating point emulator. | | | Some software you might download from the World Wide Web, such as Macromedia's Shockwave, may require that your computer have a floating point unit. |
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http://whatis.techtarget.com/definition/0,289893,sid9_gci213965,00.html
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| | Floating Point : Java Glossary |
| | By floating point I refer generically to the code written to use the primitives double and float and the wrapper classes Double and Float. | | | The computer floating point unit works internally in base 2, binary. | | | 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. |
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http://mindprod.com/jgloss/floatingpoint.html
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| | The IBM eServer z990 floating-point unit - Author Bios |
| | Schwarz provides support to IBM floating-point unit teams and is on the program committee of the IEEE Symposium on Computer Arithmetic. | | | In particular, he was involved in the design of the floating-point unit of the z990 microprocessor. | | | His recent contributions are the design of the integer and floating-point execution units of the z990 processor. |
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http://www.research.ibm.com/journal/rd/483/gerwiaut.html
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| | Decimal Arithmetic Bibliography - Alphabetic |
| | The input problem considered by this paper is the inverse of an output problem considered by Steele and White: Given a binary floating point number, print a correctly rounded decimal representation of it using the smallest number of digits that will allow the number to be read without loss of accuracy. | | | Floating point implementations and a theorem that characterizes their truncations are presented. | | | This inexpensive system can be as fast as fixed-point arithmetic on integers, is faster than normalized arithmetic in floating point, gets answers identical to those of normalized arithmetic, and automatically satisfies the Algol-60 mixed-mode rules. |
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http://www2.hursley.ibm.com/decimal/decbibalpha.html
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| | IEEE 754 Floating-Point Division Unit |
| | With the preceding IEEE 754 specifications in mind the divider unit was designed using verilog, found in appendix A. The unit has three basic components to handle each of the three fields of the floating point data. | | | The interface of the floating point unit to the socks environment via the AMBA bus was also tested. | | | Several tests were performed with the floating point divide unit. |
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http://www.iit.edu/~robewil1
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| | Floating |
| | This work proposes a floating-point to fixed-point conversion (FFC) methodology for digital VLSI signal processing systems, based on a statistical approach and global optimization which allows a high degree of automation. | | | System designers concoct a design in SIMULINK using large word-lengths, and our design flow will perform the subsequent steps to resolve connectivity, perform grouping, estimate hardware, run simulations, do optimization and output fixed-point system. | | | The fixed-point system becomes the input of BEE/SSHAFT design flow. |
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http://bwrc.eecs.berkeley.edu/Research/MCMA/FFC/ffc.htm
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| | Spacecraft onboard computers from the Rapid-I and -II programs, applicability of FlightLinux |
| | It is superscalar, incorporating dual integer units and an IEEE 754 floating- point unit. | | | Floating- point operations support single- and double- precision format; they, and include the four basic math operations, rounding, conversion, and compare. | | | The NSSC-1 is a fixed point, 18-bit machine constructed with discrete logic components, and using core or plated wire memory. |
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http://flightlinux.gsfc.nasa.gov/docs/Target_Arch_Report.html
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| | Fractal eXtreme: x86 and Infinity |
| | Their non-standard format causes difficulty for many floating point units, and was the cause of much wrangling when IEEE 754 was being worked on. | | | Maybe the stack based architecture of the original floating point unit made further optimizations too difficult, or maybe Intel decided to devote their transistors to SSE2 instead, but for whatever reason, if you want reliably fast math on the Pentium 4, you need to think about SSE2. | | | A number that is a denormal in double precision' is no longer a denormal once it's loaded into the 80-bit registers of an Intel compatible floating point unit (because the exponent range is increased), so denormals add just fine in many tests, but there is a substantial penalty for loading and saving them. |
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http://www.cygnus-software.com/papers/x86andinfinity.html
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| | Citations: A proposed radix- and word-lengthindependent standard for floating-point arithmetic - Cody, Coonen, Gay, Hanson (ResearchIndex) |
| | The IEEE 754 standard is for binary floating point numbers and specifies bit level layout while IEEE 854 covers both binary and decimal floating point numbers but does not specify encodings for.... | | | implemented also in the INMOS transputers Floating Point Unit (FPU) compare also [16] Thus, computed irregular values do not raise exceptions, but are propagated to the subsequent or higher level blocks, which must be able to handle them. | | | It is not the purpose of this paper to ar gue that the IEEE standard is the best possible floating point standard but rather to accept the standar d as given and pr ovide an introduction to its use. |
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http://citeseer.ist.psu.edu/context/226152/0
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| | Floating Point Unit Design |
| | All floating point instructions are some combination of FP add and FP multiply, often using the fmadd instruction. | | | The floating point unit consists of a four stage pipelimne with a one entry instruction queue. | | | Since the logic of the various pipeline stages was not discussed in great detail in any of the references used in coding the FPU, the FPU may need to be modified to reflect a greater knowledge and accuracy in the future. |
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http://www.cs.utexas.edu/users/chris/ppc/fpu_design.html
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| | Floating-Point Fallacies |
| | How the relations work on a given floating-point system often depends on whether a relation is considered an arithmetic operation or not. | | | Even in a floating-point system where the relations cannot be determined with complete certainty, the relations are usually reflexive. | | | The sample floating-point system we will use is a base-10 system with five mantissa digits and two exponent digits but the examples will have analogs in any floating-point system. |
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http://www.zuras.net/FPFallacies.html
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| | WinNT 3.5 Software Update for the Pentium Floating Point Error |
| | The floating point software emulation's libraries are used on systems with 486SX or 386 processors. | | | This parameter is useful for testing software emulators and for working around floating point hardware defects known to the operating system. | | | The user of such applications will be able to choose between the higher speed of hardware floating point, or slower floating point software emulation libraries, which will not encounter the Pentium floating point division error. |
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http://support.microsoft.com/kb/122323/EN-US
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| | Floating Point |
| | Floating point can be performed either by instruction emulation in the kernel, or by compiling | | | Some of the embedded PowerPC processors do not have a floating point unit(FPU), and so must perform all floating point operations in software. | | | 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. |
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http://penguinppc.org/embedded/howto/floating.html
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| | Floating Point |
| | The method is to first convert it to binary scientific notation, and then use what we know about the representation of floating point numbers to show the 32 bits that will represent it. | | | The single precision floating point unit is a packet of 32 bits, divided into three sections one bit, eight bits, and twenty-three bits, in that order. | | | It explains the binary representation of these numbers, how to convert to decimal from floating point, how to convert from floating point to decimal, discusses special cases in floating point, and finally ends with some C code to further one's understanding of floating point. |
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http://www.duke.edu/~twf/cps104/floating.html
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| | What Every Computer Scientist Should Know About Floating-Point Arithmetic |
| | The section Guard Digits pointed out that computing the exact difference or sum of two floating-point numbers can be very expensive when their exponents are substantially different. | | | This is rather surprising because floating-point is ubiquitous in computer systems. | | | It was already pointed out in Floating-point Formats that this requires a special convention for 0. |
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http://soren.org/linux/lisp/ncg_goldberg.html
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| | Architecture and software support in IBM S/390 Parallel Enterprise Servers for IEEE Floating-Point arithmetic |
| | The only point worth mentioning is that an indefinite number of digits is accepted, but if more digits are given than are necessary to represent the longest exact decimal representation, the extra digits are only checked to see whether they are all zero; in effect, they are coalesced into a single “sticky” digit. | | | A fixed-point bignum consists of an array of 32-bit words in storage; the position of the radix point is implicit (i.e., the software knows where it is), and is chosen to reflect the desired output precision. | | | The point is that the given numerator and denominator may be very large, whereas the partial convergents start out as very simple fractions (the crudest being 1/1 when the rational number is between 1/2 and 2), and require progressively more digits as the approximations converge to the true value. |
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http://www.research.ibm.com/journal/rd/435/abbott.html
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| | SH Options - Using the GNU Compiler Collection (GCC) |
| | This has a very high latency, but needs only a few instructions, so it might be a good choice if your code has enough easily exploitable ILP to allow the compiler to schedule the floating point instructions together with other instructions. | | | Generate code for the SH4 assuming the floating-point unit is in single-precision mode by default. | | | Generate code for the SH4a, in such a way that no double-precision floating point operations are used. |
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http://gcc.gnu.org/onlinedocs/gcc/SH-Options.html
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| | Computer History Museum - Timeline |
| | What set the 486 apart was its optimized instruction set, with an on-chip unified instruction and data cache and an optional on-chip floating-point unit. | | | The RISC microprocessor had a 32-bit integer arithmetic and logic unit (the part of the CPU that performs operations such as addition and subtraction), a 64-bit floating-point unit, and a clock rate of 33 MHz. | | | A step up from the 68020, it built on a 32-bit enhanced microprocessor with a central processing unit core, a data cache, an instruction cache, an enhanced bus controller, and a memory management unit in a single VLSI device — all operating at speeds of at least 20 MHz. |
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http://www.computerhistory.org/timeline/timeline.php?timeline_category=cmpnt
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| | README.NONSTOP-FP |
| | However, in 1998, IBM added the G5 processor boards on System/390 (Z series) with full IEEE 754 support (including 128-bit quadruple precision in hardware), and GNU/Linux on that system uses only IEEE 754 arithmetic (even though the S/360 arithmetic is available, the GNU/Linux compilers and library don't support it). | | | The first implementation was the Intel 8087 on which the original IBM PC was based in 1981. | | | The two OSF/1 builds do not create shared-object libraries, so the dynamic module feature of zsh needed to get the elementary-function library loaded is not available. |
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http://www.math.utah.edu/pub/zsh/README.NONSTOP-FP
(1997 words)
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| | Compaq Fortran |
| | On OpenVMS Alpha systems, you specify the floating-point format in memory with the /FLOAT qualifier. | | | This format is found on Compaq Tru64 UNIX® (formerly DIGITAL UNIX) systems, Compaq OpenVMS Alpha systems, and Microsoft® Windows® operating systems (for IBM-compatible PC systems). | | | On porting Compaq Tru64 UNIX Fortran data files to a OpenVMS system for use by Compaq Fortran, see the Compaq Fortran user manual for Tru64 UNIX (formerly DIGITAL UNIX) systems. |
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http://h18000.www1.hp.com/fortran/docs/vms-um/dfumconv.htm
(1997 words)
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| | IEEE 754 floating-point test software |
| | Mike Cowlishaw and his group at IBM Hursley Laboratory in the UK have developed an implementation of IEEE 754/854 decimal arithmetic that is being used as a testbed for both the revision of the IEEE 754 standard, as well as for possible future decimal floating-point arithmetic hardware. | | | Computer systems are now so ubiquitous that most users assume that computers are reliable (at least, once their desktop system has been rebooted for the seventh time today). | | | There have also been cases where lower-cost entry-level computer systems used more software components in the arithmetic implementation than in higher-cost advanced systems, so even within an architecture family, there can be differences in behavior of the same program from the same executable file. |
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http://www.math.utah.edu/~beebe/software/ieee
(1997 words)
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| | EETimes.com - Floating point unit added to Coldfire with enhanced core |
| | "The availability of a floating point unit means that, as processors move above a certain performance point, suddenly design engineers can change how they view existing problems. | | | The FPU is a 64-bit double-precision implementation of the MC68060 floating point instruction set, and is IEEE-754 standard compliant with a software assist. | | | With many embedded applications dealing with streaming multimedia data forms, floating point and an enhanced MAC unit were clear options. |
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http://www.eetimes.com/story/OEG20001017S0041
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