DOI: 10.1145/980175.980177. A comparison of methods for accurate summation

A comparison of methods for accurate summation

10.1145/980175.980177

Crossref journal-article

Association for Computing Machinery (ACM)

ACM SIGSAM Bulletin (320)

Abstract

The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of "Cascading Accumulators" is the fastest of several methods. The Double Compensation method (in both single and double precision versions) is also perfectly accurate in all the tests performed. Although slower than the Cascade method, it is recommended when double precision accuracy is required. C programs that implement both these methods are available in the BULLETIN online repository.

Authors 1

John Michael McNamee (first)

References 11 Referenced 18

10.1145/355769.355776
10.1137/0914050
{'key': 'e_1_2_1_3_1', 'first-page': '96', 'article-title': 'Accuracy and Stablility of Numerical Algorithms', 'author': 'HIGHAM', 'year': '1996', 'journal-title': 'Soc. Ind. Appl. Math.'} / Soc. Ind. Appl. Math. / Accuracy and Stablility of Numerical Algorithms by HIGHAM (1996)
10.1145/363707.363723
10.1145/362384.362498
10.1145/362854.362889
10.1016/0304-3975(95)00253-7
10.1007/BF01404922
{'key': 'e_1_2_1_9_1', 'volume-title': 'Ph. D. Thesis, Mathematics Dept.', 'author': 'PRIEST', 'year': '1992'} / Ph. D. Thesis, Mathematics Dept. by PRIEST (1992)
10.1145/42288.42343
{'key': 'e_1_2_1_11_1', 'volume-title': 'Rounding Errors in Algebraic Processes', 'author': 'WILKINSON', 'year': '1963'} / Rounding Errors in Algebraic Processes by WILKINSON (1963)

Dates

Type	When
Created	18 years, 7 months ago (Jan. 17, 2007, 1:32 p.m.)
Deposited	2 years, 7 months ago (Jan. 3, 2023, 5:27 a.m.)
Indexed	1 year, 11 months ago (Sept. 29, 2023, 1:06 a.m.)
Issued	21 years, 6 months ago (March 1, 2004)
Published	21 years, 6 months ago (March 1, 2004)
Published Online	21 years, 6 months ago (March 1, 2004)
Published Print	21 years, 6 months ago (March 1, 2004)

Funders 0

None

BibTeX

@article{McNamee_2004, title={A comparison of methods for accurate summation}, volume={38}, ISSN={0163-5824}, url={http://dx.doi.org/10.1145/980175.980177}, DOI={10.1145/980175.980177}, number={1}, journal={ACM SIGSAM Bulletin}, publisher={Association for Computing Machinery (ACM)}, author={McNamee, John Michael}, year={2004}, month=mar, pages={1–7} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2023,
        9,
        29
      ]
    ],
    "date-time": "2023-09-29T05:06:00Z",
    "timestamp": 1695963960214
  },
  "reference-count": 11,
  "publisher": "Association for Computing Machinery (ACM)",
  "issue": "1",
  "content-domain": {
    "domain": [
      "dl.acm.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2004,
        3
      ]
    ]
  },
  "abstract": "<jats:p>The summation of large sets of numbers is prone to serious rounding errors. Several methods of controlling these errors are compared, with respect to both speed and accuracy. It is found that the method of \"Cascading Accumulators\" is the fastest of several methods. The Double Compensation method (in both single and double precision versions) is also perfectly accurate in all the tests performed. Although slower than the Cascade method, it is recommended when double precision accuracy is required. C programs that implement both these methods are available in the BULLETIN online repository.</jats:p>",
  "DOI": "10.1145/980175.980177",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2007,
        1,
        17
      ]
    ],
    "date-time": "2007-01-17T18:32:02Z",
    "timestamp": 1169058722000
  },
  "page": "1-7",
  "update-policy": "http://dx.doi.org/10.1145/crossmark-policy",
  "source": "Crossref",
  "is-referenced-by-count": 18,
  "title": "A comparison of methods for accurate summation",
  "prefix": "10.1145",
  "volume": "38",
  "author": [
    {
      "given": "John Michael",
      "family": "McNamee",
      "sequence": "first",
      "affiliation": [
        {
          "name": "York University, Toronto, Ontario, Canada"
        }
      ]
    }
  ],
  "member": "320",
  "published-online": {
    "date-parts": [
      [
        2004,
        3
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_2_1_1_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1145/355769.355776"
    },
    {
      "key": "e_1_2_1_2_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1137/0914050"
    },
    {
      "key": "e_1_2_1_3_1",
      "first-page": "96",
      "article-title": "Accuracy and Stablility of Numerical Algorithms",
      "author": "HIGHAM",
      "year": "1996",
      "journal-title": "Soc. Ind. Appl. Math."
    },
    {
      "key": "e_1_2_1_4_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1145/363707.363723"
    },
    {
      "key": "e_1_2_1_5_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1145/362384.362498"
    },
    {
      "key": "e_1_2_1_6_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1145/362854.362889"
    },
    {
      "key": "e_1_2_1_7_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1016/0304-3975(95)00253-7"
    },
    {
      "key": "e_1_2_1_8_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1007/BF01404922"
    },
    {
      "key": "e_1_2_1_9_1",
      "volume-title": "Ph. D. Thesis, Mathematics Dept.",
      "author": "PRIEST",
      "year": "1992"
    },
    {
      "key": "e_1_2_1_10_1",
      "doi-asserted-by": "publisher",
      "DOI": "10.1145/42288.42343"
    },
    {
      "key": "e_1_2_1_11_1",
      "volume-title": "Rounding Errors in Algebraic Processes",
      "author": "WILKINSON",
      "year": "1963"
    }
  ],
  "container-title": "ACM SIGSAM Bulletin",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://dl.acm.org/doi/pdf/10.1145/980175.980177",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        1,
        3
      ]
    ],
    "date-time": "2023-01-03T10:27:04Z",
    "timestamp": 1672741624000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://dl.acm.org/doi/10.1145/980175.980177"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2004,
        3
      ]
    ]
  },
  "references-count": 11,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          2004,
          3
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1145/980175.980177"
  ],
  "URL": "http://dx.doi.org/10.1145/980175.980177",
  "relation": {},
  "ISSN": [
    "0163-5824"
  ],
  "subject": [],
  "container-title-short": "SIGSAM Bull.",
  "published": {
    "date-parts": [
      [
        2004,
        3
      ]
    ]
  },
  "assertion": [
    {
      "value": "2004-03-01",
      "order": 2,
      "name": "published",
      "label": "Published",
      "group": {
        "name": "publication_history",
        "label": "Publication History"
      }
    }
  ]
}