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Binary conversion, with fixed decimal precision, of a decimal fraction

1959
*
Communications of the ACM
*

Tg
—_
2 7 2 Qe ee

doi:10.1145/368370.368376
fatcat:djrw6v5kuzarnjc62h3eo7q2bi
*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. ...##
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How to print floating-point numbers accurately

1990
*
SIGPLAN notices
*

(The problem

doi:10.1145/93548.93559
fatcat:jgux6wkisrfyneshsyisls675e
*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] .) ...##
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How to print floating-point numbers accurately

2004
*
SIGPLAN notices
*

(The problem

doi:10.1145/989393.989431
fatcat:nigbcymncvbchcgajc3fk7qhay
*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] .) ...##
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How to print floating-point numbers accurately

1990
*
Proceedings of the ACM SIGPLAN 1990 conference on Programming language design and implementation - PLDI '90
*

(The problem

doi:10.1145/93542.93559
dblp:conf/pldi/SteeleW90
fatcat:wzdcpi2f6vhzviww4awivluvdu
*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] .) ...##
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EARLY ESTIMATION OF DELAY IN BINARY TO BCD CONVERTOR

2014
*
International Journal of Electronics and Electical Engineering
*

*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*. ...

##
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Page 27 of Communications of the Association for Computing Machinery Vol. 2, Issue 7
[page]

1959
*
Communications of the Association for Computing Machinery
*

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. ...##
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Proposal for a High Precision Tensor Processing Unit
[article]

2017
*
arXiv
*
pre-print

This whitepaper proposes the design and adoption

arXiv:1706.03251v1
fatcat:2ypfksanwbfsvmsvsytxmdplba
*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*. ...##
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Radix conversion in an unnormalized arithmetic system

1965
*
Mathematics of Computation
*

The observation that the exact

doi:10.1090/s0025-5718-65-99250-1
fatcat:puc2pxy7szcbpossdhb34y7jai
*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*. ...##
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Performance analysis of decimal floating-point libraries and its impact on decimal hardware and software solutions

2009
*
2009 IEEE International Conference on Computer Design
*

*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. ...

##
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Functions to Support Input and Output of Intervals
[article]

2007
*
arXiv
*
pre-print

Equally essential for interval methods is directed rounding for

arXiv:cs/0703003v1
fatcat:cvoicxehxzb2rp5man5xixarve
*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. ...##
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A new math library

2009
*
International Journal of Quantum Chemistry
*

many digits: more than 11 500

doi:10.1002/qua.22266
fatcat:l6cujysyvncwtkl7iw4kezalzm
*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 ...##
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The Programming Algorithm Based on Embedded System for the Output Conversion of the Humidity & Temperature Sensor SHTxx

2012
*
Advanced Engineering Forum
*

The polynomials are

doi:10.4028/www.scientific.net/aef.6-7.294
fatcat:tsnoulm7vre67msd3vpl6w2czu
*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‰. ...##
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Page 318 of Mathematics of Computation Vol. 3, Issue 24
[page]

1948
*
Mathematics of Computation
*

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 ...##
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On Basic Financial Decimal Operations on Binary Machines

2012
*
IEEE transactions on computers
*

In addition, we describe methods for correctly performing basic

doi:10.1109/tc.2012.89
fatcat:ekhuprxg5vaunbzvlg6kdvqday
*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. ...##
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A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format

2007
*
Computer Arithmetic
*

New algorithms and properties are presented in this paper which are used in

doi:10.1109/arith.2007.7
dblp:conf/arith/CorneaAHTST07
fatcat:6q6vu5f5bvdanpg7inwchogle4
*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 ...
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