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Binary conversion, with fixed decimal precision, of a decimal fraction
1959
Communications of the ACM
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Binary Conversion, With Fixed Decimal Precision, Of a Decimal Fraction
Donatp Taranto, International Business Machines Corp., New York, N.Y. ...
Problem
Given a decimal fraction f, find a binary approximation
f, to f, with a given decimal precision h.
1. Given O Sf < Llandh > 0. 2. Find f, such that | f — f,| Sh. ...
doi:10.1145/368370.368376
fatcat:djrw6v5kuzarnjc62h3eo7q2bi
How to print floating-point numbers accurately
1990
SIGPLAN notices
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(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .) ...
to print out with too many decimal digits. ...
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .) ...
doi:10.1145/93548.93559
fatcat:jgux6wkisrfyneshsyisls675e
How to print floating-point numbers accurately
2004
SIGPLAN notices
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(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .) ...
to print out with too many decimal digits. ...
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .) ...
doi:10.1145/989393.989431
fatcat:nigbcymncvbchcgajc3fk7qhay
How to print floating-point numbers accurately
1990
Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation - PLDI '90
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(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31][22][20] [12] .) ...
to print out with too many decimal digits. ...
(The problem of binary-to-decimal conversion is amazingly tricky, even for fixed-point fractions, let alone floatingpoint numbers [31] [22] [20] [12] .) ...
doi:10.1145/93542.93559
dblp:conf/pldi/SteeleW90
fatcat:wzdcpi2f6vhzviww4awivluvdu
EARLY ESTIMATION OF DELAY IN BINARY TO BCD CONVERTOR
2014
International Journal of Electronics and Electical Engineering
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A novel high speed architecture for fixed bit binary to BCD conversion which is better in terms of delay is presented in this paper. ...
Decimal digit multipliers are having Binary to BCD conversion as the basic building block. ...
Rational numbers whose denominator is a power of ten are decimal fractions and most them cannot be represented by binary fractions. ...
doi:10.47893/ijeee.2014.1102
fatcat:3erdghqgx5fuzcfmemyhjdycmm
Page 27 of Communications of the Association for Computing Machinery Vol. 2, Issue 7
[page]
1959
Communications of the Association for Computing Machinery
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Tg
—_
2 7 2 Qe ee
a
Binary Conversion, With Fixed Decimal Precision, Of a Decimal Fraction
Donatp Taranto, International Business Machines Corp., New York, N.Y. ...
Problem
Given a decimal fraction f, find a binary approximation
f, to f, with a given decimal precision h.
1. Given O Sf < Llandh > 0. 2. Find f, such that | f — f,| Sh. ...
Proposal for a High Precision Tensor Processing Unit
[article]
2017
arXiv
pre-print
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This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data. ...
The new generation TPU is made possible by implementing arithmetic circuits which compute using a new general purpose, fractional arithmetic based on the residue number system. ...
RNS conversion, and fractional RNS to fractional binary conversion. ...
arXiv:1706.03251v1
fatcat:2ypfksanwbfsvmsvsytxmdplba
Radix conversion in an unnormalized arithmetic system
1965
Mathematics of Computation
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The observation that the exact conversion of integers gives also a true estimate of precision (i.e., the 10-for-3 criterion is naturally achieved), suggests that binary-decimal conversion can be accomplished ...
It seems not unreasonable, however, to ask for a conversion procedure which affords the user a more precise statement of the relation between the binary form and the decimal result. ...
This stage is therefore skipped, and the integer d0 is determined from the fractional part of the initial product. Decimal-Binary Conversion. ...
doi:10.1090/s0025-5718-65-99250-1
fatcat:puc2pxy7szcbpossdhb34y7jai
Performance analysis of decimal floating-point libraries and its impact on decimal hardware and software solutions
2009
2009 IEEE International Conference on Computer Design
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A growing number of DFP solutions have emerged, and developers now have many DFP design choices including arbitrary or fixed precision, binary or decimal significand encodings, 64-bit or 128-bit DFP operands ...
DFP operation in each benchmark, and (3) highlights the tradeoffs between using 64-bit and 128-bit DFP operands for both binary and decimal significand encodings. ...
For example, the binary floating-point (BFP) single-precision number closest to the decimal fraction 0.1 is actually equal to 0.100000001490116119384765625. ...
doi:10.1109/iccd.2009.5413114
dblp:conf/iccd/AndersonTWCS09
fatcat:oth2e7dhvzfa5lfymot7zyivpy
Functions to Support Input and Output of Intervals
[article]
2007
arXiv
pre-print
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Equally essential for interval methods is directed rounding for conversion between the external decimal and internal binary numerals. This is not provided by the standard I/O libraries. ...
Although it may be possible to adapt these algorithms for use in decimal interval I/O, we argue that outward rounding in radix conversion is computationally a simpler problem than guaranteeing identity ...
Acknowledgements This research was supported by the University of Victoria and by the Natural Science and Engineering Research Council of Canada. ...
arXiv:cs/0703003v1
fatcat:cvoicxehxzb2rp5man5xixarve
A new math library
2009
International Journal of Quantum Chemistry
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many digits: more than 11 500 decimal digits for binary-to-decimal conversion of 128-bit format, J base-conversion problem not properly solved until 1990s J few (if any) languages guarantee accurate base ...
J for a fixed number of exponent digits, larger bases provide a wider exponent range, and reduce incidence of rounding J for a fixed storage size, granularity (the spacing between successive representable ...
Beebe (University of Utah) MAA/BYU: A new math library
/ 25
/ 25 ...
doi:10.1002/qua.22266
fatcat:l6cujysyvncwtkl7iw4kezalzm
The Programming Algorithm Based on Embedded System for the Output Conversion of the Humidity & Temperature Sensor SHTxx
2012
Advanced Engineering Forum
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The polynomials are precise equivalent to the conversion formulas provided by the manufacturers, but contain only Binary fixed-point integer, fractional part, and 2N. ...
In order to avoid the digital humidity & temperature sensor SHTxx's output values conversion consume many quantity of storage location, and spend more operation time, a group new type of conversion polynomials ...
integer and binary fractional part, so the item can be calculated with fixed-point addition and subtraction, the conversion error of fractional part relative to the quondam formula (1) is only 1.5‰. ...
doi:10.4028/www.scientific.net/aef.6-7.294
fatcat:tsnoulm7vre67msd3vpl6w2czu
Page 318 of Mathematics of Computation Vol. 3, Issue 24
[page]
1948
Mathematics of Computation
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The conversion to binary should be no more difficult than the conversion to decimal. For control purposes it may be required to convert the output of the computer back into continuous form. ...
Many machines are provided with equipment for operating at two different precisions—a low precision which is usually standard, and a high precision, double the low one, which is the less frequently employed ...
On Basic Financial Decimal Operations on Binary Machines
2012
IEEE transactions on computers
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In addition, we describe methods for correctly performing basic decimal operations, such as addition, subtraction, multiplication, and division, on binary machines, which are not conformant with IEEE 754 ...
In this paper, we show that if binary arithmetic is used to emulate decimal operations, then arbitrary error sequences can be generated by carefully chosen sequences of transactions which can lead to monotonically ...
The ideas can be analogously extended for 34 digits of precision, but will come with a conversion overhead. ...
doi:10.1109/tc.2012.89
fatcat:ekhuprxg5vaunbzvlg6kdvqday
A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format
2007
Computer Arithmetic
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New algorithms and properties are presented in this paper which are used in a software implementation of the IEEE 754R decimal floatingpoint arithmetic, with emphasis on using binary operations efficiently ...
This is intended mainly to provide a robust, reliable framework for financial applications that are often subject to legal requirements concerning rounding and precision of the results, because the binary ...
Conversion from Double Precision to 64-bit Decimal The double precision argument encodes the value a = (−1) sa · 2 ea · m a = (−1) sa · 2 k · C a , with C a an integer in the range [0, 2 53 ) and k an ...
doi:10.1109/arith.2007.7
dblp:conf/arith/CorneaAHTST07
fatcat:6q6vu5f5bvdanpg7inwchogle4
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