Decent sqrt() - makes sqrt(-1+0i) == i

[p6rt]

Migrated from rt.perl.org#127126 (status was 'resolved')

Searchable as RT127126$

[p6rt]

From dankogai@gmail.com

Oops, the previous message does not contain the patch so I am submitting again. Use the patch below or just pull rakudo/rakudo#667 .

====

I am glad perl6 supports complex numbers natively. What I am not glad is that its definition of i does not agree with mathematics​:

% perl6

sqrt(-1+0i)
6.12323399573677e-17+1i

Though (-1+0i)**0.5 != 1i for most other platforms, they still get sqrt(-1+0i) right​:

% python

  Python 2.7.10 (default, Oct 23 2015, 18​:05​:06)
  [GCC 4.2.1 Compatible Apple LLVM 7.0.0 (clang-700.0.59.5)] on darwin
  Type "help", "copyright", "credits" or "license" for more information.

from cmath import *
sqrt(-1+0j)
  1j
(-1+0j)**0.5
  (6.123233995736766e-17+1j)
^D

% irb

  irb(main)​:001​:0> require 'cmath'
  => true
  irb(main)​:002​:0> CMath.sqrt(-1)
  => (0+1.0i)
  irb(main)​:003​:0> ^D

% perl -MMath​::Complex -dE 1

  Loading DB routines from perl5db.pl version 1.49
  Editor support available.

  Enter h or 'h h' for help, or 'man perldebug' for more help.

  main​::(-e​:1)​: 1
  DB<1> p sqrt(-1+0*i)
  i
  DB<2> p (-1+0*i)**0.5
  6.12323399573677e-17+i

So here is the patch that defines sqrt in sqrt.

Dan the Complex Perl6 Newbie

---

src/core/Complex.pm | 6 ++++--
1 file changed, 4 insertions(+), 2 deletions(-)

Inline Patch

diff --git a/src/core/Complex.pm b/src/core/Complex.pm
index 8314025..74b1d5b 100644
--- a/src/core/Complex.pm
+++ b/src/core/Complex.pm
@@ -80,8 +80,10 @@ my class Complex is Cool does Numeric {
     }
 
     method sqrt(Complex:D:) {
-        my Num ($mag, $angle) = self.polar;
-        $mag.sqrt.unpolar($angle/2);
+        my Num $abs = self.abs;
+        my Num $re = (($abs + self.re)/2).sqrt;
+        my Num $im = (($abs - self.re)/2).sqrt;
+        Complex.new($re, self.im < 0 ?? -$im !! $im);
     }
 
     multi method exp(Complex:D:) {
-- 
2.5.4 (Apple Git-61)

[p6rt]

From @lizmat

On 02 Jan 2016, at 20​:54, Dan Kogai (via RT) <perl6-bugs-followup@​perl.org> wrote​:

# New Ticket Created by Dan Kogai
# Please include the string​: [perl #​127126]
# in the subject line of all future correspondence about this issue.
# <URL​: https://rt-archive.perl.org/perl6/Ticket/Display.html?id=127126 >

Oops, the previous message does not contain the patch so I am submitting again. Use the patch below or just pull rakudo/rakudo#667 .

====

I am glad perl6 supports complex numbers natively. What I am not glad is that its definition of i does not agree with mathematics​:

% perl6

sqrt(-1+0i)
6.12323399573677e-17+1i

Though (-1+0i)**0.5 != 1i for most other platforms, they still get sqrt(-1+0i) right​:

% python

Python 2.7.10 (default, Oct 23 2015, 18​:05​:06)
[GCC 4.2.1 Compatible Apple LLVM 7.0.0 (clang-700.0.59.5)] on darwin
Type "help", "copyright", "credits" or "license" for more information.

from cmath import *
sqrt(-1+0j)
1j
(-1+0j)**0.5
(6.123233995736766e-17+1j)
^D

% irb

irb(main)​:001​:0> require 'cmath'
=> true
irb(main)​:002​:0> CMath.sqrt(-1)
=> (0+1.0i)
irb(main)​:003​:0> ^D

% perl -MMath​::Complex -dE 1

Loading DB routines from perl5db.pl version 1.49
Editor support available.

Enter h or 'h h' for help, or 'man perldebug' for more help.

main​::(-e​:1)​: 1
DB<1> p sqrt(-1+0*i)
i
DB<2> p (-1+0*i)**0.5
6.12323399573677e-17+i

So here is the patch that defines sqrt in sqrt.

Dan the Complex Perl6 Newbie

---
src/core/Complex.pm | 6 ++++--
1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/core/Complex.pm b/src/core/Complex.pm
index 8314025..74b1d5b 100644
--- a/src/core/Complex.pm
+++ b/src/core/Complex.pm
@​@​ -80,8 +80,10 @​@​ my class Complex is Cool does Numeric {
}

method sqrt\(Complex​:D​:\) \{

- my Num ($mag, $angle) = self.polar;
- $mag.sqrt.unpolar($angle/2);
+ my Num $abs = self.abs;
+ my Num $re = (($abs + self.re)/2).sqrt;
+ my Num $im = (($abs - self.re)/2).sqrt;
+ Complex.new($re, self.im < 0 ?? -$im !! $im);
}

multi method exp\(Complex​:D​:\) \{

--
2.5.4 (Apple Git-61)

Pull request 667 has been merged, this ticket can be closed.

Liz

[p6rt]

The RT System itself - Status changed from 'new' to 'open'

[p6rt]

From @usev6

On Sat Jan 02 15​:19​:11 2016, elizabeth wrote​:

On 02 Jan 2016, at 20​:54, Dan Kogai (via RT) <perl6-bugs-
followup@​perl.org> wrote​:

# New Ticket Created by Dan Kogai
# Please include the string​: [perl #​127126]
# in the subject line of all future correspondence about this issue.
# <URL​: https://rt-archive.perl.org/perl6/Ticket/Display.html?id=127126 >

Oops, the previous message does not contain the patch so I am
submitting again. Use the patch below or just pull
rakudo/rakudo#667 .

====

I am glad perl6 supports complex numbers natively. What I am not glad
is that its definition of i does not agree with mathematics​:

% perl6

sqrt(-1+0i)
6.12323399573677e-17+1i

Though (-1+0i)**0.5 != 1i for most other platforms, they still get
sqrt(-1+0i) right​:

% python

Python 2.7.10 (default, Oct 23 2015, 18​:05​:06)
[GCC 4.2.1 Compatible Apple LLVM 7.0.0 (clang-700.0.59.5)] on darwin
Type "help", "copyright", "credits" or "license" for more
information.

from cmath import *
sqrt(-1+0j)
1j
(-1+0j)**0.5
(6.123233995736766e-17+1j)
^D

% irb

irb(main)​:001​:0> require 'cmath'
=> true
irb(main)​:002​:0> CMath.sqrt(-1)
=> (0+1.0i)
irb(main)​:003​:0> ^D

% perl -MMath​::Complex -dE 1

Loading DB routines from perl5db.pl version 1.49
Editor support available.

Enter h or 'h h' for help, or 'man perldebug' for more help.

main​::(-e​:1)​: 1
DB<1> p sqrt(-1+0*i)
i
DB<2> p (-1+0*i)**0.5
6.12323399573677e-17+i

So here is the patch that defines sqrt in sqrt.

Dan the Complex Perl6 Newbie

---
src/core/Complex.pm | 6 ++++--
1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/src/core/Complex.pm b/src/core/Complex.pm
index 8314025..74b1d5b 100644
--- a/src/core/Complex.pm
+++ b/src/core/Complex.pm
@​@​ -80,8 +80,10 @​@​ my class Complex is Cool does Numeric {
}

method sqrt(Complex​:D​:) {
- my Num ($mag, $angle) = self.polar;
- $mag.sqrt.unpolar($angle/2);
+ my Num $abs = self.abs;
+ my Num $re = (($abs + self.re)/2).sqrt;
+ my Num $im = (($abs - self.re)/2).sqrt;
+ Complex.new($re, self.im < 0 ?? -$im !! $im);
}

multi method exp(Complex​:D​:) {
--
2.5.4 (Apple Git-61)

Pull request 667 has been merged, this ticket can be closed.

Liz

Thanks! I'm closing this ticket as 'resolved'.

[p6rt]

@usev6 - Status changed from 'open' to 'resolved'