/usr/share/calc/help/bround is in apcalc-common 2.12.4.4-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 | NAME
bround - round numbers to a specified number of binary digits
SYNOPSIS
bround(x [,plcs [, rnd]])
TYPES
If x is a matrix or a list, bround(x[[i]], ...) is to return
a value for each element x[[i]] of x; the value returned will be
a matrix or list with the same structure as x.
Otherwise, if x is an object of type tt, or if x is not an object or
number but y is an object of type tt, and the function tt_bround has
to be defined; the types for x, plcs, rnd, and the returned value,
if any, are as required for specified in tt_bround. For the object
case, plcs and rnd default to the null value.
For other cases:
x number (real or complex)
plcs integer, defaults to zero
rnd integer, defaults to config("round")
return number
DESCRIPTION
For real x, bround(x, plcs, rnd) returns x rounded to either
plcs significant binary digits (if rnd & 32 is nonzero) or to plcs
binary places (if rnd & 32 is zero). In the significant-figure
case the rounding is to plcs - ilog10(x) - 1 binary places.
If the number of binary places is n and eps = 10^-n, the
result is the same as for appr(x, eps, rnd). This will be
exactly x if x is a multiple of eps; otherwise rounding occurs
to one of the nearest multiples of eps on either side of x. Which
of these multiples is returned is determined by z = rnd & 31, i.e.
the five low order bits of rnd, as follows:
z = 0 or 4: round down, i.e. towards minus infinity
z = 1 or 5: round up, i.e. towards plus infinity
z = 2 or 6: round towards zero
z = 3 or 7: round away from zero
z = 8 or 12: round to the nearest even multiple of eps
z = 9 or 13: round to the nearest odd multiple of eps
z = 10 or 14: round to nearest even or odd multiple of eps
according as x > or < 0
z = 11 or 15: round to nearest odd or even multiple of eps
according as x > or < 0
z = 16 to 31: round to the nearest multiple of eps when
this is uniquely determined. Otherwise
rounding is as if z is replaced by z - 16
For complex x:
The real and imaginary parts are rounded as for real x; if the
imaginary part rounds to zero, the result is real.
For matrix or list x:
The returned values has element bround(x[[i]], plcs, rnd) in
the same position as x[[i]] in x.
For object x or plcs:
When bround(x, plcs, rnd) is called, x is passed by address so may be
changed by assignments; plcs and rnd are copied to temporary
variables, so their values are not changed by the call.
EXAMPLES
; a = 7/32, b = -7/32
; print a, b
.21875 -.21875
; print round(a,3,0), round(a,3,1), round(a,3,2), print round(a,3,3)
.218, .219, .218, .219
; print round(b,3,0), round(b,3,1), round(b,3,2), print round(b,3,3)
-.219, -.218, -.218, -.219
; print round(a,3,16), round(a,3,17), round(a,3,18), print round(a,3,19)
.2188 .2188 .2188 .2188
; print round(a,4,16), round(a,4,17), round(a,4,18), print round(a,4,19)
.2187 .2188 .2187 .2188
; print round(a,2,8), round(a,3,8), round(a,4,8), round(a,5,8)
.22 .218 .2188 .21875
; print round(a,2,24), round(a,3,24), round(a,4,24), round(a,5,24)
.22 .219 .2188 .21875
; c = 21875
; print round(c,-2,0), round(c,-2,1), round(c,-3,0), round(c,-3,16)
21800 21900 21000 22000
; print round(c,2,32), round(c,2,33), round(c,2,56), round(c,4,56)
21000 22000 22000 21880
; A = list(1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8)
; print round(A,2,24)
list(7 elements, 7 nonzero):
[[0]] = .12
[[1]] = .25
[[3]] = .38
[[4]] = .5
[[5]] = .62
[[6]] = .75
[[7]] = .88
LIMITS
For non-object case:
0 <= abs(plcs) < 2^31
0 <= abs(rnd) < 2^31
LINK LIBRARY
void broundvalue(VALUE *x, VALUE *plcs, VALUE *rnd, VALUE *result)
MATRIX *matbround(MATRIX *m, VALUE *plcs, VALUE *rnd);
LIST *listbround(LIST *m, VALUE *plcs, VALUE *rnd);
NUMBER *qbround(NUMBER *m, long plcs, long rnd);
SEE ALSO
round, trunc, btrunc, int, appr
## Copyright (C) 1999 Landon Curt Noll
##
## Calc is open software; you can redistribute it and/or modify it under
## the terms of the version 2.1 of the GNU Lesser General Public License
## as published by the Free Software Foundation.
##
## 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
## Public License for more details.
##
## A copy of version 2.1 of the GNU Lesser General Public License is
## distributed with calc under the filename COPYING-LGPL. You should have
## received a copy with calc; if not, write to Free Software Foundation, Inc.
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
##
## @(#) $Revision: 30.1 $
## @(#) $Id: bround,v 30.1 2007/03/16 11:10:42 chongo Exp $
## @(#) $Source: /usr/local/src/cmd/calc/help/RCS/bround,v $
##
## Under source code control: 1994/09/30 00:22:35
## 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/
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