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| Summary / Description | Knuth's famous series includes a chapter on multiprecision arithmetic including the use of base 10**n big digits |
| Type of Prior Art | Print Publication |
| Publication Title * | The Art of Computer Programming, Volume 2, Seminumerical Algorithms |
| Author | Donald E. Knuth |
| ISBN | 0-201-03822-6 |
| Page Range | 250-309 |
| Medium | Book excerpt |
| Publication Date * | July 1, 1980 |
| URL | http://www-cs-faculty.stanford.... |
| Notes | This has to be one of the most famous texts in computing, how can the applicant not have heard of it? I've cited the 2nd edition; the 1st edition was from 1968. Everything in this application is completely obvious to anyone who has studied section 4.3. |
Excerpt [page 309] E. Multiple-precision conversion. "suppose that 10**n is the highest power of 10 less than the word size"[page 250] ... 100 decimal digits, but we will consider it to be a 10-place number to the base 10**10 [page 251] "by adjusting the word size, if necessary" [page 263] The use of 10**n as an assumed radix when multiplying large numbers ... was discussed by D. N. Lehmer and J. P. Ballantyne, American Mathematical Monthly 30 (1923) 67-69. |
A method of converting a number to a binary representation, the method comprising the step of:
converting a predetermined size segment of a number to a binary representation, the predetermined size segment based on a processor word size.
| Relevance | Knuth specifically mentions the use of base 10**n and specifically mentions adjusting the radix ("segment" size) to fit the computer |
The method of claim 1, wherein the predetermined size segment is one or more digits and the number of digits equal to the maximum number of digits storable in one word of the processor word size wherein each digit is able to be all of the range of number system numbers.
| Relevance | When the quantity "b" in chapter 4.3 is a power of 10, this is the representation used in that chapter. Knuth's imaginary machine MIX, in which these algorithms are presented, is treated as a decimal machine but usually implemented on a binary one, so it's _precisely_ this representation. |
The method of claim 1, further comprising the step of:
setting the segment size to the number of digits of the largest number having a given number of digits, if the largest number having a given number of digits is greater than a largest storable number in the processor word size.
| Relevance | Knuth basically explains when you can do this (when you have a double precision multiply) and when you can't; he also explains the relevance of 2s complement on page 261. |
The method of claim 1, wherein the number in binary form is larger than a single processor word.
| Relevance | That's what section 4.3 is all about. |
A method of converting a number represented in binary form and comprised of more than one segment to a decimal representation, the method comprising the steps of:
combining a first decimal segment resulting from converting a segment of the more than one binary segments to decimal form with a second decimal segment resulting from converting another segment of the more than one binary segment to decimal form, wherein the segment size is determined based on processor word size.
| Relevance | The idea of using single-big-digit conversions is arguably mentioned on page 309. That's certainly where the DEC-10 Prolog library file LONG.PL got the idea. |
A method of converting a number having one or more digits to a binary representation, comprising the steps of:
determining a maximum number of digits storable in one word of a processor having a predetermined word size; and
converting the determined maximum storable number of digits of the number to a binary representation in a first word.
| Relevance | See claim 7. |
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