Hi all !
Eugene mentions a circular dependency between Floor and Residue in his
paper. I didn't understand what would stop the recursion, so I tried it
out, and indeed, I got stack error. Didn't he test his theories? Have I
misunderstood something? Do I have a bug somewhere?
See below.
Cheers,
Erling Hellenäs
fr=: 3 : 0
:
if. ( x = 0 ) +. ( >.s ) = <. s =. y % x + x = 0
do. y * x = 0
else. y - x * <. s
end.
)
9!:19 [ 5.68434e_14
9!:18''
5.68434e_14
2 fr 5
1
a=: _5 + i. 11
b=: |. a
a
_5 _4 _3 _2 _1 0 1 2 3 4 5
b
5 4 3 2 1 0 _1 _2 _3 _4 _5
*./(0<:(a fr b)%a) *. ((a fr b)%a)<1
1
m=: a
z=: b
*./z=(m*<.z%m)+m fr z
1
(14^2) fr 5729082486784839
0
196 fr 5729082486784839
0
9!:19 [ 0
9!:18''
0
(14^2) fr 5729082486784839
147
196 fr 5729082486784839
147
ff=: 3 : 0
NB. y - 1 fr y
y - 1 | y
)
fc=: 3 : 0
NB. - ff - y
- ff - y
)
fr=: 3 : 0
:
if. ( x = 0 ) +. ( fc s ) = ff s =. y % x + x = 0
do. y * x = 0
else. y - x * ff s
end.
)
9!:19 [ 5.68434e_14
9!:18''
5.68434e_14
2 fr 5
1
ff 1.5
1
fc 1.5
2
a=: _5 + i. 11
b=: |. a
a
_5 _4 _3 _2 _1 0 1 2 3 4 5
b
5 4 3 2 1 0 _1 _2 _3 _4 _5
*./(0<:(a fr b)%a) *. ((a fr b)%a)<1
1
m=: a
z=: b
*./z=(m*<.z%m)+m fr z
1
(14^2) fr 5729082486784839
0
196 fr 5729082486784839
0
9!:19 [ 0
9!:18''
0
(14^2) fr 5729082486784839
147
196 fr 5729082486784839
147
ff=: 3 : 0
y - 1 fr y
NB. y - 1 | y
)
fc=: 3 : 0
- ff - y
NB.- ff - y
)
9!:19 [ 5.68434e_14
9!:18''
5.68434e_14
2 fr 5
|stack error: fc
| (x=0)+.( fc s)=ff s=.y%x+x=0
Den 2017-09-14 kl. 11:29, skrev Erling Hellenäs:
Hi all !
I programmed Eugenes proposal, and indeed, it gives the same result
for the actual problem that our Residue does.
There are some other differences.
Check me, there might well be some bug somewhere.
fr=: 3 : 0
:
if. ( x = 0 ) +. ( >.s ) = <. s =. y % x + x = 0
do. y * x = 0
else. y - x * <. s
end.
)
9!:19 [ 5.68434e_14
9!:18''
5.68434e_14
2 fr 5
1
a=: _5 + i. 11
b=: |. a
a
_5 _4 _3 _2 _1 0 1 2 3 4 5
b
5 4 3 2 1 0 _1 _2 _3 _4 _5
*./(0<:(a fr b)%a) *. ((a fr b)%a)<1
1
m=: a
z=:b
*./z=(m*<.z%m)+m fr z
1
(14^2) fr 5729082486784839
0
196 fr 5729082486784839
0
9!:19 [ 0
9!:18''
0
(14^2) fr 5729082486784839
147
196 fr 5729082486784839
147
Cheers,
Erling Hellenäs
Den 2017-09-13 kl. 22:53, skrev Jimmy Gauvin:
Fuzzy Residue by Eugene McDonnell is an enlightening source of
information
on residue even though it pertains to APL running on IBM hardware:
http://www.jsoftware.com/papers/eem/residue1.htm
Section 2 is about the relation between floor and residue
Two other articles, Comparison Tolerance by Robert Bernecky and APL
Comparison Tolerance by R.H. Lathwell, are both available under this
link:
http://www.jsoftware.com/papers/satn23.htm
On Wed, Sep 13, 2017 at 3:48 PM, Erling Hellenäs
<[email protected]>
wrote:
I looked briefly in those references. I don't see any statements
about the
use of comparison tolerance in Residue. /Erling
On 2017-09-13 18:30, Raul Miller wrote:
Tolerance is an ugly thing, I guess.
http://code.jsoftware.com/wiki/Essays/Tolerant_Comparison
Thanks,
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