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Topic: Single Precision

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Ross Perot

	lapack/single
		gams d4b1 file sspgv.f sspgv.f plus dependencies prec single for Computes all eigenvalues and eigenvectors of a generalized, symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage.
		gams d4b1 file sspgvd.f sspgvd.f plus dependencies prec single for Computes all eigenvalues and eigenvectors of a generalized, symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage.
		gams d4a1 file sspgvx.f sspgvx.f plus dependencies prec single for Computes selected eigenvalues, and optionally, eigenvectors of, a generalized symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage.
	www.netlib.org /lapack/single (4427 words)

	Single Precision (Site not responding. Last check: 2007-10-11)
		A single precision number consists of the following.
		Therefore, the string 0 0000 1110 1010 0000 0000 0000 0000 000, as a single precision number, represents a positive number (0 as leading bit), with exponent 0000 1110 - 0111 111 = - 0111 0001, and significand 1.1010 0000 0000 0000 0000 000.
		Please verify that the smallest single precision positive number is
	www.math.buffalo.edu /~pitman/courses/mth437/na/node10.html (126 words)

	Less is More: Exploiting Single Precision Math in HPC
		And while that's true, the difference in performance between single precision and double precision is a tempting target for people who want to squeeze more computational power out of their hardware.
		The overall approach of the ICL team was to use single precision math whenever possible, especially for the most compute-intensive parts of the software, and then fall back to double precision only when necessary.
		In this case, the optimized single precision version would have to be distinguished from the existing benchmark that has been used to measure supercomputer performance for the past 13 years.
	www.hpcwire.com /hpc/692906.html (978 words)

	Single precision - Wikipedia, the free encyclopedia
		In computing, single precision is a computer numbering format that occupies one storage location in computer memory at a given
		A single-precision number, sometimes simply a single, may be defined to be an integer, fixed point, or floating point.
		Single precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 4 bytes.
	en.wikipedia.org /wiki/Single_precision (265 words)

	Document Title
		The increase in precision from one to the next is better than it appears: 32-bit floats only give you 24 bits of mantissa, while 64-bit ones give you 53 bits.
		Single precision will at least double the speed of divides and sqrts.
		I use a C++ class that sets the precision while it's in scope and then drops back to the previous rounding and precision mode as it goes out -- very convenient, so you don't forget to reset the precision, and you can handle error cases properly.
	www.stereopsis.com /FPU.html (1443 words)

	The IEEE standard for floating point arithmetic (Site not responding. Last check: 2007-10-11)
		This standard specifies how single precision (32 bit) and double precision (64 bit) floating point numbers are to be represented, as well as how arithmetic should be carried out on them.
		The IEEE single precision floating point standard representation requires a 32 bit word, which may be represented as numbered from 0 to 31, left to right.
		The IEEE double precision floating point standard representation requires a 64 bit word, which may be represented as numbered from 0 to 63, left to right.
	www.psc.edu /general/software/packages/ieee/ieee.html (496 words)

	The MathWorks - MATLAB Digest - July 2004 - Integer and Single-Precision Math in MATLAB 7
		In order to precisely match the overflow and rounding effects that occur in the integer or fixed-point arithmetic of any C compiler or embedded processor, you can use the Fixed-Point Toolbox.
		By using singles to represent data instead of converting to doubles, you can process single-precision data sets twice the size that could be processed in earlier MATLAB versions.
		We can see that some of the variables are of type single and that the variable A (the single-precision version of Ad) takes half the number of bytes of memory to store because singles require only 4 bytes (32 bits), whereas doubles require 8 bytes (64 bits).
	www.mathworks.com /company/newsletters/digest/july04/intmath.html (1475 words)

	IEEE Standard 754 Floating-Point
		For double precision, the exponent field is 11 bits, and has a bias of 1023.
		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.
		Underflow is a less serious problem because is just denotes a loss of precision, which is guaranteed to be closely approximated by zero.
	steve.hollasch.net /cgindex/coding/ieeefloat.html (1366 words)

	single precision on Sparcs (Site not responding. Last check: 2007-10-11)
		Perhaps this is because without this assumption, you will be doing 2 4-byte loads for each double, so it doubles the total number of loads (and stores), and slows you down for that reason.
		There is nothing in the UltraSparc specifications that I know of that suggest that a single floating point load is slower than a double floating point load.
		The only thing I can think of is that for single, with the same degree of unrolling, you might be increasing your chances of direct-mapped conflicts in the top-level cache: still that would not seem to be able to account for so large a difference.
	www.netlib.org /atlas/atlas-comm/msg00310.html (431 words)

	Garbage Assigning VAL or Single Precision to Double Precision (Site not responding. Last check: 2007-10-11)
		In binary math, to force constants that have a decimal point and seven or fewer digits to higher precision, you must append a number sign (#) character to the constant.
		Then, assigning that constant to a double-precision variable will convert with double precision (up to 15 significant digits).
		To avoid accumulation of nonsignificant digits when converting a single-precision constant to double precision, you should type-cast the constant with # or add trailing zeros to make it longer than seven digits.
	support.microsoft.com /kb/45421 (374 words)

	Eric Fleegal's WebLog : Single Vs. Double ... (Site not responding. Last check: 2007-10-11)
		· singles are half the size of doubles, reducing memory and bandwidth requirements.
		If double-precision is the native precision, the extra cost of narrowing results to single-precision MAY be quite high… much higher, in fact, than the cost associated with the memory overhead of doubles (cache misses etc).
		For many applications, it’s preferable to store input and final results in single precision, but to perform all the intermediate computations in the highest precision that is practical on the target architecture.
	blogs.msdn.com /ericflee/archive/2004/12/21/329228.aspx (300 words)

	Become.com - Shop results for blanco precision super single
		Blanco 513-686 Precision 10 Super Single Bowl Undermount Stainless Steel...
		The Blanco Precision 513686 is part of Blanco's Precision Series of stainless kitchen sinks.
		The Blanco Precision 513692 is part of Blanco's Precision Series of stainless kitchen sinks.
	www.become.com /shop?q=blanco+precision+super+single (218 words)

	Floating-Point FFT Processor (IEEE 754 Single Precision) Cores (Site not responding. Last check: 2007-10-11)
		IEEE 754 single precision data and twiddle ROMs and RAMs
		The floating-point fast Fourier transform (FFT) processor calculates FFTs with IEEE 754 single precision (1 sign bit, 8 exponent bits, and 23 mantissa bits) accuracy.
		The processor uses extended precision arithmetic (1 sign bit, 8 exponent bits, and 32 mantissa bits) internally for higher accuracy.
	www.altera.com /products/ip/dsp/transforms/m-ham-fft-float.html (396 words)

	Single Precision
		One way that we find that we can reduce the size of a database is by changing the precision of fields from double to single.
		In some cases changing all the double precision number fields in a table from double to single real can trim the space used by about 40%.
		Basically if the number is going to have over 6 significant figures in it, then think very carefully about this change as those precise number will get trimmed.
	www.vb123.com /toolshed/99/singleprecision.htm (357 words)

	Floating-Point Formats (Site not responding. Last check: 2007-10-11)
		The IEEE standard does not require an implementation to support single-extended precision and double-extended precision in order to be standard-conforming.
		Also, all numbers representable as some number over a power of 2, such as 0.1875 (3/16) or 27.375 (219/8), can be represented exactly if they have no more decimal digits than the chosen precision can faithfully represent.
		Values that are represented by a sign bit, a fraction, and an exponent whose bits are not all zeros and not all ones are called
	docs.hp.com /en/B3906-90006/ch02s02.html (2166 words)

	IEEE floating-point standard - Wikipedia, the free encyclopedia
		IEEE 754 specifies four formats for representing floating-point values: single-precision (32-bit), double-precision (64-bit), single-extended precision (≥ 43-bit, not commonly used) and double-extended precision (≥ 79-bit, usually implemented with 80 bits).
		Double precision is essentially the same except that the fields are wider:
		This is because precision is more valued than range, according to the creators of the standard.
	en.wikipedia.org /wiki/IEEE_floating-point_standard (1648 words)

	Precision Pneumatics - Single Action Slide - Main Features
		Precision Pneumatics - Single Action Slide - Main Features
		Multiple Precision Mounting Surfaces with Tooling Holes for Grippers and Tooling.
		Precision Pneumatics, L.L.C. 2071 Ninth Avenue, Ronkonkoma, NY 11779
	www.precision-pneumatics.com /single_action_slides/main_features.html (67 words)

	LMC6081 - Precision CMOS Single Operational Amplifier
		The LMC6081 is a precision low offset voltage operational amplifier, capable of single supply operation.
		Performance characteristics include ultra low input bias current, high voltage gain, rail-to-rail output swing, and an input common mode voltage range that includes ground.
		Other applications using the LMC6081 include precision full-wave rectifiers, integrators, references, and sample-and-hold circuits.
	www.national.com /pf/LM/LMC6081.html (254 words)

	Precision Single Plunger Limit Switch
		home >> Limit Switches >> Precision Single Plunger Switch
		EUCHNER Precision Single Plunger Limit Switches are used in Mechanical and Plant Engineering for control and positioning tasks.
		Their robust housings are made of a die cast anodized alloy, offering high performance and corrosion resistance.
	www.euchner-usa.com /LimitNB.asp (102 words)

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