Here's what I got so far. The code's not great, can it be improved?

Can you think of a set of inputs that will exercise it better? (Note: I haven't got around to log() scales yet.)

#! perl -slw
use strict;

sub log10{ log( $_[0] ) / log( 10 ) }

sub ticks {
    my( $start, $end, $n ) = @_;
    $n ||= 10;
    my $range = $end - $start;
    $range += $range / $n;
    my $interval = $range / $n;
    $interval  = 10**int( log10( $interval ) );
    $interval *= 10 while ( $range / $interval ) > ( $n * 2 );
    $interval /=  2 while ( $range / $interval ) < ( $n / 2 );
    $start = int( $start / $interval ) * $interval;

    my @ticks;
    while( $start < ( $end + $interval ) ) {
        push @ticks, $start;
        $start += $interval;
    }
    return @ticks;
}


for my $range (
    [0,9], [0.123,8.673], [0.022, 0.086],
    [1_123_345_456, 1_124_246_357.5], [1_123_345_456, 1_123_346_357.5]
+,
    [ 0.00011, 0.00041],
) {
    for my $n ( 0, 4, 5, 8 , 10, 15, 16, 20, 21 ) {
        my @ticks = ticks( @$range, $n );

        printf "from:%12.12g to %12.12g by:%2u -> [%2u][ %s ]\n",
            @$range, $n, scalar( @ticks ), join ' ', map{
                my $s = sprintf( "%.8g", $_ ); $s =~ s[e([+-])0*([1-9]
++)]['e' . ($1 eq '-' ? '-' : '') . $2]e;
                $s;
            } @ticks;

    }
}
[download]

Output:

C:\test>calcTicks.pl
from:           0 to            9 by: 0 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:           0 to            9 by: 4 -> [ 3][ 0 5 10 ]
from:           0 to            9 by: 5 -> [ 5][ 0 2.5 5 7.5 10 ]
from:           0 to            9 by: 8 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:           0 to            9 by:10 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:           0 to            9 by:15 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:           0 to            9 by:16 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:           0 to            9 by:20 -> [19][ 0 0.5 1 1.5 2 2.5 3 3
+.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 ]
from:           0 to            9 by:21 -> [19][ 0 0.5 1 1.5 2 2.5 3 3
+.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 ]
from:       0.123 to        8.673 by: 0 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:       0.123 to        8.673 by: 4 -> [ 3][ 0 5 10 ]
from:       0.123 to        8.673 by: 5 -> [ 5][ 0 2.5 5 7.5 10 ]
from:       0.123 to        8.673 by: 8 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:       0.123 to        8.673 by:10 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:       0.123 to        8.673 by:15 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:       0.123 to        8.673 by:16 -> [10][ 0 1 2 3 4 5 6 7 8 9 ]
from:       0.123 to        8.673 by:20 -> [19][ 0 0.5 1 1.5 2 2.5 3 3
+.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 ]
from:       0.123 to        8.673 by:21 -> [19][ 0 0.5 1 1.5 2 2.5 3 3
+.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 ]
from:       0.022 to        0.086 by: 0 -> [ 8][ 0.02 0.03 0.04 0.05 0
+.06 0.07 0.08 0.09 ]
from:       0.022 to        0.086 by: 4 -> [ 5][ 0 0.025 0.05 0.075 0.
+1 ]
from:       0.022 to        0.086 by: 5 -> [ 5][ 0 0.025 0.05 0.075 0.
+1 ]
from:       0.022 to        0.086 by: 8 -> [ 8][ 0.02 0.03 0.04 0.05 0
+.06 0.07 0.08 0.09 ]
from:       0.022 to        0.086 by:10 -> [ 8][ 0.02 0.03 0.04 0.05 0
+.06 0.07 0.08 0.09 ]
from:       0.022 to        0.086 by:15 -> [15][ 0.02 0.025 0.03 0.035
+ 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 ]
from:       0.022 to        0.086 by:16 -> [15][ 0.02 0.025 0.03 0.035
+ 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 ]
from:       0.022 to        0.086 by:20 -> [15][ 0.02 0.025 0.03 0.035
+ 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 ]
from:       0.022 to        0.086 by:21 -> [15][ 0.02 0.025 0.03 0.035
+ 0.04 0.045 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 ]
from:  1123345456 to 1124246357.5 by: 0 -> [11][ 1.1233e9 1.1234e9 1.1
+235e9 1.1236e9 1.1237e9 1.1238e9 1.1239e9 1.124e9 1.1241e9 1.1242e9 1
+.1243e9 ]
from:  1123345456 to 1124246357.5 by: 4 -> [ 4][ 1.123e9 1.1235e9 1.12
+4e9 1.1245e9 ]
from:  1123345456 to 1124246357.5 by: 5 -> [ 5][ 1.12325e9 1.1235e9 1.
+12375e9 1.124e9 1.12425e9 ]
from:  1123345456 to 1124246357.5 by: 8 -> [11][ 1.1233e9 1.1234e9 1.1
+235e9 1.1236e9 1.1237e9 1.1238e9 1.1239e9 1.124e9 1.1241e9 1.1242e9 1
+.1243e9 ]
from:  1123345456 to 1124246357.5 by:10 -> [11][ 1.1233e9 1.1234e9 1.1
+235e9 1.1236e9 1.1237e9 1.1238e9 1.1239e9 1.124e9 1.1241e9 1.1242e9 1
+.1243e9 ]
from:  1123345456 to 1124246357.5 by:15 -> [11][ 1.1233e9 1.1234e9 1.1
+235e9 1.1236e9 1.1237e9 1.1238e9 1.1239e9 1.124e9 1.1241e9 1.1242e9 1
+.1243e9 ]
from:  1123345456 to 1124246357.5 by:16 -> [11][ 1.1233e9 1.1234e9 1.1
+235e9 1.1236e9 1.1237e9 1.1238e9 1.1239e9 1.124e9 1.1241e9 1.1242e9 1
+.1243e9 ]
from:  1123345456 to 1124246357.5 by:20 -> [20][ 1.1233e9 1.12335e9 1.
+1234e9 1.12345e9 1.1235e9 1.12355e9 1.1236e9 1.12365e9 1.1237e9 1.123
+75e9 1.1238e9 1.12385e9 1.1239e9 1.12395e9 1.124e9 1.12405e9 1.1241e9
+ 1.12415e9 1.1242e9 1.12425e9 ]
from:  1123345456 to 1124246357.5 by:21 -> [20][ 1.1233e9 1.12335e9 1.
+1234e9 1.12345e9 1.1235e9 1.12355e9 1.1236e9 1.12365e9 1.1237e9 1.123
+75e9 1.1238e9 1.12385e9 1.1239e9 1.12395e9 1.124e9 1.12405e9 1.1241e9
+ 1.12415e9 1.1242e9 1.12425e9 ]
from:  1123345456 to 1123346357.5 by: 0 -> [11][ 1.1233454e9 1.1233455
+e9 1.1233456e9 1.1233457e9 1.1233458e9 1.1233459e9 1.123346e9 1.12334
+61e9 1.1233462e9 1.1233463e9 1.1233464e9 ]
from:  1123345456 to 1123346357.5 by: 4 -> [ 4][ 1.123345e9 1.1233455e
+9 1.123346e9 1.1233465e9 ]
from:  1123345456 to 1123346357.5 by: 5 -> [ 6][ 1.1233453e9 1.1233455
+e9 1.1233458e9 1.123346e9 1.1233463e9 1.1233465e9 ]
from:  1123345456 to 1123346357.5 by: 8 -> [11][ 1.1233454e9 1.1233455
+e9 1.1233456e9 1.1233457e9 1.1233458e9 1.1233459e9 1.123346e9 1.12334
+61e9 1.1233462e9 1.1233463e9 1.1233464e9 ]
from:  1123345456 to 1123346357.5 by:10 -> [11][ 1.1233454e9 1.1233455
+e9 1.1233456e9 1.1233457e9 1.1233458e9 1.1233459e9 1.123346e9 1.12334
+61e9 1.1233462e9 1.1233463e9 1.1233464e9 ]
from:  1123345456 to 1123346357.5 by:15 -> [11][ 1.1233454e9 1.1233455
+e9 1.1233456e9 1.1233457e9 1.1233458e9 1.1233459e9 1.123346e9 1.12334
+61e9 1.1233462e9 1.1233463e9 1.1233464e9 ]
from:  1123345456 to 1123346357.5 by:16 -> [11][ 1.1233454e9 1.1233455
+e9 1.1233456e9 1.1233457e9 1.1233458e9 1.1233459e9 1.123346e9 1.12334
+61e9 1.1233462e9 1.1233463e9 1.1233464e9 ]
from:  1123345456 to 1123346357.5 by:20 -> [20][ 1.1233455e9 1.1233455
+e9 1.1233456e9 1.1233456e9 1.1233457e9 1.1233457e9 1.1233458e9 1.1233
+458e9 1.1233459e9 1.1233459e9 1.123346e9 1.123346e9 1.1233461e9 1.123
+3461e9 1.1233462e9 1.1233462e9 1.1233463e9 1.1233463e9 1.1233464e9 1.
+1233464e9 ]
from:  1123345456 to 1123346357.5 by:21 -> [20][ 1.1233455e9 1.1233455
+e9 1.1233456e9 1.1233456e9 1.1233457e9 1.1233457e9 1.1233458e9 1.1233
+458e9 1.1233459e9 1.1233459e9 1.123346e9 1.123346e9 1.1233461e9 1.123
+3461e9 1.1233462e9 1.1233462e9 1.1233463e9 1.1233463e9 1.1233464e9 1.
+1233464e9 ]
from:     0.00011 to      0.00041 by: 0 -> [ 8][ 0.0001 0.00015 0.0002
+ 0.00025 0.0003 0.00035 0.0004 0.00045 ]
from:     0.00011 to      0.00041 by: 4 -> [ 5][ 0.0001 0.0002 0.0003 
+0.0004 0.0005 ]
from:     0.00011 to      0.00041 by: 5 -> [ 5][ 0.0001 0.0002 0.0003 
+0.0004 0.0005 ]
from:     0.00011 to      0.00041 by: 8 -> [ 8][ 0.0001 0.00015 0.0002
+ 0.00025 0.0003 0.00035 0.0004 0.00045 ]
from:     0.00011 to      0.00041 by:10 -> [ 8][ 0.0001 0.00015 0.0002
+ 0.00025 0.0003 0.00035 0.0004 0.00045 ]
from:     0.00011 to      0.00041 by:15 -> [14][ 0.0001 0.000125 0.000
+15 0.000175 0.0002 0.000225 0.00025 0.000275 0.0003 0.000325 0.00035 
+0.000375 0.0004 0.000425 ]
from:     0.00011 to      0.00041 by:16 -> [14][ 0.0001 0.000125 0.000
+15 0.000175 0.0002 0.000225 0.00025 0.000275 0.0003 0.000325 0.00035 
+0.000375 0.0004 0.000425 ]
from:     0.00011 to      0.00041 by:20 -> [14][ 0.0001 0.000125 0.000
+15 0.000175 0.0002 0.000225 0.00025 0.000275 0.0003 0.000325 0.00035 
+0.000375 0.0004 0.000425 ]
from:     0.00011 to      0.00041 by:21 -> [14][ 0.0001 0.000125 0.000
+15 0.000175 0.0002 0.000225 0.00025 0.000275 0.0003 0.000325 0.00035 
+0.000375 0.0004 0.000425 ]
[download]

use strict;
use warnings;

use feature 'say';

display_parts( 0, 9, 10 );
display_parts( 0.022, 0.086, 10 );
display_parts( 0.123, 8.672, 10 );
display_parts( 1_123_345_456, 1_124_246_357.5, 11 );

sub display_parts {
    my $result = get_ticks(@_);

    printf "start: %s, end: %s, parts: %s\n",
        map pretty($_), @_;

    for ( 0 .. $#$result ) {
        printf "  %2d => %s\n", $_, pretty( $result->[$_] );
    }

    print "\n";
}

sub get_ticks {
    my ( $start, $end, $parts ) = @_;

    my $tick = ( $end - $start ) / ( $parts - 1 );

    my @result;
    push @result, $start;
    push @result, $result[-1] + $tick for 1 .. ($parts - 1);

    return \@result;
}

sub pretty {
    return shift =~ s/\d \K (?= (?: \d{3} )+ \b )/_/xgr;
}
[download]

start: 0, end: 9, parts: 10
   0 => 0
   1 => 1
   2 => 2
   3 => 3
   4 => 4
   5 => 5
   6 => 6
   7 => 7
   8 => 8
   9 => 9

start: 0.022, end: 0.086, parts: 10
   0 => 0.022
   1 => 0.0_291_111_111_111_111
   2 => 0.0_362_222_222_222_222
   3 => 0.0_433_333_333_333_333
   4 => 0.0_504_444_444_444_444
   5 => 0.0_575_555_555_555_555
   6 => 0.0_646_666_666_666_667
   7 => 0.0_717_777_777_777_778
   8 => 0.0_788_888_888_888_889
   9 => 0.086

start: 0.123, end: 8.672, parts: 10
   0 => 0.123
   1 => 1.07_288_888_888_889
   2 => 2.02_277_777_777_778
   3 => 2.97_266_666_666_667
   4 => 3.92_255_555_555_556
   5 => 4.87_244_444_444_445
   6 => 5.82_233_333_333_333
   7 => 6.77_222_222_222_222
   8 => 7.72_211_111_111_111
   9 => 8.672

start: 1_123_345_456, end: 1_124_246_357.5, parts: 11
   0 => 1_123_345_456
   1 => 1_123_435_546.15
   2 => 1_123_525_636.3
   3 => 1_123_615_726.45
   4 => 1_123_705_816.6
   5 => 1_123_795_906.75
   6 => 1_123_885_996.9
   7 => 1_123_976_087.05
   8 => 1_124_066_177.2
   9 => 1_124_156_267.35
  10 => 1_124_246_357.5
[download]

Hint: Retaining .05 precision in tick marks distributed over a range of 900+ doesn't make much sense.

The kind of output I'm looking for for that example is:

1,123,345,400 1,123,346,500 1,123,345,600 1,123,345,600 1,123,345,700 
+1,123,345,800 1,123,345,900 1,123,346,000 1,123,346,100 1,123,346,200
+ 1,123,346,300 1,123,346,400
[download]

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I'm with torvalds on this

In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked

Hint: Retaining .05 precision in tick marks distributed over a range of 900+ doesn't make much sense.

Makes perfect sense to me. I just thought that getting 8.721 as max is strange when the real max is 8.672. I actually thought your 'not so nice!' refers to that. I don't know how to produce "aethetically pleasing" numbers, sorry.

Eg. rounding to the nearest integer works above, but how about if the inputs are: 0.022 .. 0.086 by 10?

Kinda like dollars/cents, multiply by 1000 (or 10**$precision) ?

!google calculate the best Interval between tick marks -> http://stackoverflow.com/questions/14923812/displaying-axis-from-min-to-max-value-calculating-scale-and-labels

-> http://stackoverflow.com/questions/361681/algorithm-for-nice-grid-line-intervals-on-a-graph -> http://search.cpan.org/dist/Chart-Math-Axis/lib/Chart/Math/Axis.pm

http://stackoverflow.com/questions/14923812/displaying-axis-from-min-to-max-value-calculating-scale-and-labels

Dog! I hate that site: So many jumped up little hitlers and so much dross.

1. Eg. "(EDIT -- I've found an implementation of Scale1() that I did in Perl)" Liar. The code he posted contains (amongst others):
   • use strict;
   • @vInt = {1, 2, 5, 10};
   • if ($xMaxp < $xMax) $xMaxp = $xMax;
   • $par = (-3.1, 11.1, 5, 5.2, 10.1, 5, -12000, -100, 9);
2. Another "perl" answer contains (amongst others):    $label_arr[] = array('label' => $label, 'x_pos' => $width_between * $i);.

Not sure what's worse. Trying to decode Javascript kiddy "perl"; or the COBOLFortran?! they were trying to transcribe :)

Damn! I'd forgotten just how horrible '70s languages were.

---

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority". I'm with torvalds on this

In the absence of evidence, opinion is indistinguishable from prejudice. Agile (and TDD) debunked