Some Toom-Cook Methods For Even Long Integers

نویسنده

  • Alberto Zanoni
چکیده

We present a new approach to evaluation and interpolation phases of some (balanced and unbalanced) Toom-Cook multiplication methods for long integers when at least one factor is even. Some other optimization are also indicated. AMS Subject Classification: 11A05, 11A25, 11K65, 11Y70

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ACTA UNIVERSITATIS APULENSIS Special Issue KARATSUBA AND TOOM-COOK METHODS FOR MULTIVARIATE POLYNOMIALS

Karatsuba and Toom-Cook are well-known methods used to efficiently multiply univariate polynomials and long integers. For multivariate polynomials, asymptotically good approaches like Kronecker’s trick combined with FFT become truly effective only when the degree is above some threshold. In this paper we analyze Karatsuba and some of Toom-Cook methods for multivariate polynomials, considering d...

متن کامل

What About Toom-Cook Matrices Optimality ?

Karatsuba and Toom-Cook are well-known methods used to multiply efficiently two long integers. There have been different proposal about the interpolating values used to determine the matrix to be inverted and the sequence of operations to invert it. A definitive word about which is the optimal matrix (values) and the (number of) basic operations to invert it seems still not to have been said. I...

متن کامل

Toom-Cook Multiplication: Some Theoretical and Practical Aspects

Toom-Cook multiprecision multiplication is a well-known multiprecision multiplication method, which can make use of multiprocessor systems. In this paper the Toom-Cook complexity is derived, some explicit proofs of the Toom-Cook interpolation method are given, the even-odd method for interpolation is explained, and certain aspects of a 32-bit C++ and assembler implementation, which is in develo...

متن کامل

Another Sugar Cube , Please ! or Sweetening Third Power computation

A new approach to the computation of long integers cube third power computation based on a splitting in two divide et impera approach and on a modified Toom-Cook unbalanced method is presented. A detailed description of its practical implementation by using the GMP library and performance comparison are also described. AMS Subject Classification: 11A05, 11A25, 11K65, 11Y70

متن کامل

Multiplication by an Integer Constant

We present and compare various algorithms, including a new one, allowing to perform multiplications by integer constants using elementary operations. Such algorithms are useful, as they occur in several problems, such as the Toom-Cook-like algorithms to multiply large multiple-precision integers, the approximate computation of consecutive values of a polynomial, and the generation of integer mu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009