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convert ASCII TABs to ASCII SPACEs

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Converted all ASCII tabs to ASCII spaces using a 8 character
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Landon Curt Noll
2024-07-11 22:03:52 -07:00
parent fe9cefe6ef
commit db77e29a23
631 changed files with 90607 additions and 90600 deletions
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44
help/cfsim
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@@ -5,10 +5,10 @@ SYNOPSIS
cfsim(x [,rnd])
TYPES
x real
rnd integer, defaults to config("cfsim")
x real
rnd integer, defaults to config("cfsim")
return real
return real
DESCRIPTION
If x is not an integer, cfsim(x, rnd) returns either the nearest
@@ -20,23 +20,23 @@ DESCRIPTION
For 0 <= rnd < 4, the sign of the remainder x - cfsim(x, rnd) is
as follows:
rnd sign of x - cfsim(x, rnd)
rnd sign of x - cfsim(x, rnd)
0 +, as if rounding down
1 -. as if rounding up
2 sgn(x), as if rounding to zero
3 -sgn(x), as if rounding from zero
0 +, as if rounding down
1 -. as if rounding up
2 sgn(x), as if rounding to zero
3 -sgn(x), as if rounding from zero
This corresponds to the use of rnd for functions like round(x, n, rnd).
If bit 3 or 4 of rnd is set, the lower order bits are ignored; bit 3
is ignored if bit 4 is set. Thus, for rnd > 3, it sufficient to
is ignored if bit 4 is set. Thus, for rnd > 3, it sufficient to
consider the two cases rnd = 8 and rnd = 16.
If den(x) > 2, cfsim(x, 8) returns the value of the penultimate simple
continued-fraction approximate to x, i.e. if:
x = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/a_n) ...)),
x = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/a_n) ...)),
where a_0 is an integer, a_1, ..., a_n are positive integers,
and a_n >= 2, the value returned is that of the continued fraction
@@ -53,10 +53,10 @@ DESCRIPTION
In summary, for cfsim(x, rnd) when rnd = 8 or 16, the results are:
rnd integer x half-integer x den(x) > 2
rnd integer x half-integer x den(x) > 2
8 0 x - sgn(x)/2 approximate
16 x - sgn(x) x + sgn(x)/2 nearest
8 0 x - sgn(x)/2 approximate
16 x - sgn(x) x + sgn(x)/2 nearest
From either cfsim(x, 0) and cfsim(x, 1), the other is easily
determined: if one of them has value w, the other has value
@@ -72,7 +72,7 @@ DESCRIPTION
Iteration of cfsim(x,8) until an integer is obtained gives a sequence of
"good" approximations to x with decreasing denominators and
correspondingly decreasing accuracy; each denominator is less than half
the preceding denominator. (Unlike the "forward" sequence of
the preceding denominator. (Unlike the "forward" sequence of
continued-fraction approximates these are not necessarily alternately
greater than and less than x.)
@@ -80,19 +80,19 @@ DESCRIPTION
For rnd = 0 or 1 and any x, or rnd = 8 or 16 and x with den(x) > 2:
cfsim(n + x, rnd) = n + cfsim(x, rnd).
cfsim(n + x, rnd) = n + cfsim(x, rnd).
This equation also holds for the other values of rnd if n + x and x
have the same sign.
For rnd = 2, 3, 8 or 16, and any x:
cfsim(-x, rnd) = -cfsim(x, rnd).
cfsim(-x, rnd) = -cfsim(x, rnd).
If rnd = 8 or 16, except for integer x or 1/x for rnd = 8, and
zero x for rnd = 16:
cfsim(1/x, rnd) = 1/cfsim(x, rnd).
cfsim(1/x, rnd) = 1/cfsim(x, rnd).
EXAMPLE
; c = config("mode", "frac");
@@ -121,7 +121,7 @@ SEE ALSO
##
## Calc is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -129,8 +129,8 @@ SEE ALSO
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## Under source code control: 1994/09/30 01:29:45
## File existed as early as: 1994
## Under source code control: 1994/09/30 01:29:45
## File existed as early as: 1994
##
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/