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Some folks might think: “you still use RCS”?!? And we will say, hey, at least we switched from SCCS to RCS back in … I think it was around 1994 ... at least we are keeping up! :-) :-) :-) Logs say that SCCS version 18 became RCS version 19 on 1994 March 18. RCS served us well. But now it is time to move on. And so we are switching to git. Calc releases produce a lot of file changes. In the 125 releases of calc since 1996, when I started managing calc releases, there have been 15473 file mods!
116 lines
4.0 KiB
Plaintext
116 lines
4.0 KiB
Plaintext
NAME
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digit - digit at specified position in a "decimal" representation
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SYNOPSIS
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digit(x, n [, b])
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TYPES
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x real
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n integer
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b integer >= 2, default = 10
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return integer
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DESCRIPTION
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d(x,n,b) returns the digit with index n in a standard base-b "decimal"
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representation of x, which may be described as follows:
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For an arbitrary base b >= 2, following the pattern of decimal (base 10)
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notation in elementary arithmetic, a base-b "decimal" representation of
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a positive real number may be considered to be specified by a finite or
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infinite sequence of "digits" with possibly a "decimal" point
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to indicate where the fractional part of the representation begins.
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Just as the digits for base 10 are the integers 0, 1, 2, ..., 9, the
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digits for a base-b representation are the integers d for which
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0 <= d < b. The index for a digit position is the count, positively to
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the left, of the number from the "units" position immediately to the
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left of the "decimal" point; the digit d_n at position n contributes
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additively d_n * b^n to the value of x. For example,
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; d_2 d_1 d_0 . d_-1 d_-2
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represents the number
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; d_2 * b^2 + d_1 * b + d0 + d_-1 * b^-1 + d_-2 * b^-2
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The sequence of digits has to be infinite if den(x) has a prime factor
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which is not a factor of the base b. In cases where the representation
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may terminate, the digits are considered to continue with an infinite
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string of zeros rather than the other possibility of an infinite
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sequence of (b - 1)s. Thus, for the above example, d_n = 0 for
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n = -3, -4, ... Similarly, a representation may be considered to
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continue with an infinite string of zeros on the left, so that in the
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above example d_n = 0 also for n >= 3.
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For negative x, digit(x,n,b) is given by digit(abs(x),n,b); the
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standard "decimal" representation of this x is a - sign followed by
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the representation of abs(x).
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In calc, the "real" numbers are all rational and for these the
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digits following the decimal point eventually form a recurring sequence.
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With base-b digits for x as explained above, the integer whose base-b
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representation is
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; b_n+k-1 b_n_k-2 ... b_n,
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i.e. the k digits with last digit b_n, is given by
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; digit(b^-r * x, q, b^k)
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if r and q satisfy n = q * b + r.
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EXAMPLE
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; a = 123456.789
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; for (n = 6; n >= -6; n++) print digit(a, n),; print
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0 1 2 3 4 5 6 7 8 9 0 0 0
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; for (n = 6; n >= -6; n--) print digit(a, n, 100),; print
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0 0 0 0 12 34 56 78 90 0 0 0 0
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; for (n = 6; n >= -6; n--) print digit(a, n, 256),; print
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0 0 0 0 1 226 64 201 251 231 108 139 67
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; for (n = 1; n >= -12; n++) print digit(10/7, n),; print
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; 0 1 4 2 8 5 7 1 4 2 8 5 7 1
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; print digit(10/7, -7e1000, 1e6)
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428571
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LIMITS
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The absolute value of the integral part of x is assumed to be less
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than 2^2^31, ensuring that digit(x, n, b) will be zero if n >= 2^31.
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The size of negative n is limited only by the capacity of the computer
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being used.
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LINK LIBRARY
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NUMBER * qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base)
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SEE ALSO
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bit
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## Copyright (C) 1999-2006 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 1995/10/03 10:40:01
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## File existed as early as: 1995
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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