WO2002052401A3 - Method of obtaining correctly rounded results in ieee double precision format of transcendental functions - Google Patents

Method of obtaining correctly rounded results in ieee double precision format of transcendental functions Download PDF

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Publication number
WO2002052401A3
WO2002052401A3 PCT/US2001/049052 US0149052W WO02052401A3 WO 2002052401 A3 WO2002052401 A3 WO 2002052401A3 US 0149052 W US0149052 W US 0149052W WO 02052401 A3 WO02052401 A3 WO 02052401A3
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WO
WIPO (PCT)
Prior art keywords
precision
double precision
pair
arithmetic
result
Prior art date
Application number
PCT/US2001/049052
Other languages
French (fr)
Other versions
WO2002052401A2 (en
Inventor
Kwok Choi
Original Assignee
Sun Microsystems Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Sun Microsystems Inc filed Critical Sun Microsystems Inc
Priority to AU2002227437A priority Critical patent/AU2002227437A1/en
Publication of WO2002052401A2 publication Critical patent/WO2002052401A2/en
Publication of WO2002052401A3 publication Critical patent/WO2002052401A3/en

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Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/544—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices for evaluating functions by calculation

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computational Mathematics (AREA)
  • Computing Systems (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Complex Calculations (AREA)

Abstract

A method for correctly rounding a result of transcendental function such as sine, cosine, tangent, arc tangent, exponent, logarithm, or power in double precision arithmetic is disclosed. All arguments of the functions that are undefined, overflow or underflow are fist purged off. Then the given argument is reduced within a primary range to compute the function as a pair of double precision numbers. Multi-precision arithmetic with a specified word length is used if the sum of the pair of double precision number is close to the boundary case. The multi-precision arithmetic is repeated with greater precision each time until the result of the multi-precision arithmetic is not close to the boundary case. The result of the multi-precision arithmetic or the sum of said pair of double precision numbers is finally rounded according to the given rounding mode.
PCT/US2001/049052 2000-12-27 2001-12-17 Method of obtaining correctly rounded results in ieee double precision format of transcendental functions WO2002052401A2 (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
AU2002227437A AU2002227437A1 (en) 2000-12-27 2001-12-17 Method of obtaining correctly rounded results in ieee double precision format of transcendental functions

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US75262800A 2000-12-27 2000-12-27
US09/752,628 2000-12-27

Publications (2)

Publication Number Publication Date
WO2002052401A2 WO2002052401A2 (en) 2002-07-04
WO2002052401A3 true WO2002052401A3 (en) 2003-01-23

Family

ID=25027107

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US2001/049052 WO2002052401A2 (en) 2000-12-27 2001-12-17 Method of obtaining correctly rounded results in ieee double precision format of transcendental functions

Country Status (2)

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AU (1) AU2002227437A1 (en)
WO (1) WO2002052401A2 (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109271134B (en) * 2018-12-13 2020-08-25 上海燧原科技有限公司 Transcendental function operation method and device, storage medium and electronic equipment

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
"CORRECTLY ROUNDED ELEMENTARY FUNCTIONS", IBM TECHNICAL DISCLOSURE BULLETIN, IBM CORP. NEW YORK, US, vol. 33, no. 1A, 1 June 1990 (1990-06-01), pages 353 - 355, XP000117760, ISSN: 0018-8689 *
LEFEVRE V ET AL: "Towards correctly rounded transcendentals", PROCEEDINGS 13TH IEEE SYMPOSIUM ON COMPUTER ARITHMETIC. ASILOMAR, CA, JULY 6 - 9, 1997, IEEE SYMPOSIUM ON COMPUTER ARITHMETIC, LOS ALAMITOS, CA: IEEE COMP. SOC. PRESS, US, 6 July 1997 (1997-07-06), pages 132 - 137, XP010241202, ISBN: 0-8186-7846-1 *
LYNCH T ET AL: "The K5 transcendental functions", COMPUTER ARITHMETIC, 1995., PROCEEDINGS OF THE 12TH SYMPOSIUM ON BATH, UK 19-21 JULY 1995, LOS ALAMITOS, CA, USA,IEEE COMPUT. SOC, US, 19 July 1995 (1995-07-19), pages 163 - 170, XP010146644, ISBN: 0-8186-7089-4 *
SCHULTE M ET AL: "Exact rounding of certain elementary functions", COMPUTER ARITHMETIC, 1993. PROCEEDINGS., 11TH SYMPOSIUM ON WINDSOR, ONT., CANADA 29 JUNE-2 JULY 1993, LOS ALAMITOS, CA, USA,IEEE COMPUT. SOC, 29 June 1993 (1993-06-29), pages 138 - 145, XP010128520, ISBN: 0-8186-3862-1 *
ZIV A: "FAST EVALUATION OF ELEMENTARY MATHEMATICAL FUNCTIONS WITH CORRECTLY ROUNDED LAST BIT", ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, ASSOCIATION FOR COMPUTING MACHINERY, NEW YORK, US, vol. 17, no. 3, 1 September 1991 (1991-09-01), pages 410 - 423, XP000446457, ISSN: 0098-3500 *

Also Published As

Publication number Publication date
WO2002052401A2 (en) 2002-07-04
AU2002227437A1 (en) 2002-07-08

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