Release calc version 2.11.2t1

help/digit

@@ -1,93 +1,38 @@
 NAME
-    digit - digit at specified position in a "decimal" representation
+    digit - digit at specified position in a decimal representation
 
 SYNOPSIS
-    digit(x, n [, b])
+    digit(x, y)
 
 TYPES
     x		real
-    n		integer
-    b		integer >= 2, default = 10
+    y		integer
 
     return	integer
 
 DESCRIPTION
+    By extending the digits on the left, and if necessary, the digits
+    on the right, by infinite strings of zeros, abs(x) may be considered
+    to have the decimal representation:
 
-    d(x,n,b) returns the digit with index n in a standard base-b "decimal"
-    representation of x, which may be described as follows:
-   
-    For an arbitrary base b >= 2, following the pattern of decimal (base 10)
-    notation in elementary arithmetic, a base-b "decimal" representation of
-    a positive real number may be considered to be specified by a finite or
-    infinite sequence of "digits" with possibly a "decimal" point
-    to indicate where the fractional part of the representation begins.
-    Just as the digits for base 10 are the integers 0, 1, 2, ..., 9, the
-    digits for a base-b representation are the integers d for which
-    0 <= d < b.   The index for a digit position is the count, positively to
-    the left, of the number from the "units" position immediately to the
-    left of the "decimal" point; the digit  d_n  at position n contributes
-    additively  d_n * b^n  to the value of x.  For example,
-
-		d_2 d_1 d_0 . d_-1 d_-2
-
-    represents the number
-	
-		d_2 * b^2 + d_1 * b + d0 + d_-1 * b^-1 + d_-2 * b^-2
-
-    The sequence of digits has to be infinite if den(x) has a prime factor
-    which is not a factor of the base b.  In cases where the representation
-    may terminate, the digits are considered to continue with an infinite
-    string of zeros rather than the other possibility of an infinite
-    sequence of (b - 1)s.  Thus, for the above example, d_n = 0 for 
-    n = -3, -4, ...  Similarly, a representation may be considered to
-    continue with an infinite string of zeros on the left, so that in the
-    above example d_n = 0 also for n >= 3.
-    
-    For negative x, digit(x,n,b) is given by digit(abs(x),n,b); the
-    standard "decimal" representation of this x is a - sign followed by
-    the representation of abs(x).
-
-    In calc, the "real" numbers are all rational and for these the
-    digits following the decimal point eventually form a recurring sequence.
-
-    With base-b digits for x as explained above, the integer whose base-b
-    representation is
-
-		b_n+k-1 b_n_k-2 ... b_n,
-
-    i.e. the k digits with last digit b_n, is given by
-
-		digit(b^-r * x, q, b^k)
-
-    if r and q satisfy  n = q * b + r.
+		... d_2 d_1 d_0.d_-1 d_-2 ...
 
+    digit(x,y) then returns the digit d_y.
 
 EXAMPLE
-	> a = 123456.789
-	> for (n = 6; n >= -6; n++) print digit(a, n),; print
-	0 1 2 3 4 5 6 7 8 9 0 0 0
+    > x = 12.34
+    > print digit(x,2), digit(x,1), digit(x,0), digit(x,-1), digit(x,-2)
+    0 1 2 3 4
 
-	> for (n = 6; n >= -6; n--) print digit(a, n, 100),; print
-	0 0 0 0 12 34 56 78 90 0 0 0 0
-
-	> for (n = 6; n >= -6; n--) print digit(a, n, 256),; print
-	0 0 0 0 1 226 64 201 251 231 108 139 67 
-
-  	> for (n = 1; n >= -12; n++) print digit(10/7, n),; print
-    	> 0 1 4 2 8 5 7 1 4 2 8 5 7 1
-
-	> print digit(10/7, -7e1000, 1e6)
-	428571
+    > x = 10/7
+    > print digit(x,1), digit(x,0), digit(x,-1), digit(x,-2), digit(x,-3)
+    0 1 4 2 8
 
 LIMITS
-
-    The absolute value of the integral part of x is assumed to be less
-    than 2^2^31, ensuring that digit(x, n, b) will be zero if n >= 2^31.
-    The size of negative n is limited only by the capacity of the computer
-    being used.
+    If x is not an integer, y > -2^31
 
 LINK LIBRARY
-    NUMBER * qdigit(NUMBER *q, ZVALUE dpos, ZVALUE base)
+    long qdigit(NUMBER *x, long y)
 
 SEE ALSO
     bit
@@ -108,8 +53,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 ##
-## @(#) $Revision: 29.3 $
-## @(#) $Id: digit,v 29.3 2000/12/14 10:32:24 chongo Exp $
+## @(#) $Revision: 29.2 $
+## @(#) $Id: digit,v 29.2 2000/06/07 14:02:33 chongo Exp $
 ## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/digit,v $
 ##
 ## Under source code control:	1995/10/03 10:40:01