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Copyright 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019 Kevin Ryde

This file is part of Math-PlanePath.

Math-PlanePath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3, or (at your option)
any later version.

Math-PlanePath 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
General Public License for more details.

You should have received a copy of the GNU General Public License along
with Math-PlanePath.  If not, see <http://www.gnu.org/licenses/>.


Version 128, August 2019
    - Base-Digits.t more careful of UV overflow
    - KochSnowflakes.t beware rounding

Version 127, June 2019
    - PlanePathTurn new turn_type "NotStraight"

Version 126, March 2018
    - new AlternateTerdragon

Version 125, December 2017
    - GosperReplicate, QuintetReplicate new numbering_type "rotate"
    - SquareReplicate new numbering_type "rotate-4","rotate-8"

Version 124, January 2017
    - new n_to_n_list()

Version 123, April 2016
    - bigfloat.t compare results with ==, needed by BigFloat 1.999720,
      as reported by Petr Pisar RT#114014
    - MultipleRings fix BigFloat output on BigRat input

Version 122, January 2016
    - tests fix sloppy condition exposed by recent Math::BigFloat

Version 121, September 2015
    - new methods xyxy_to_n_list(), xyxy_to_n_list_either(),
      turn_any_left(), turn_any_right(), turn_any_straight()

Version 120, August 2015
    - new HilbertSides
    - PlanePathTurn new turn_type "Straight"

Version 119, May 2015
    - fixes to most n_to_level()
    - Math::PlanePath::Base::Digits new round_up_pow()

Version 118, February 2015
    - new methods xyxy_to_n(), xyxy_to_n_either()
    - DekkingCurve new "arms" parameter, correction to level N range

Version 117, September 2014
    - new methods n_to_level(), level_to_n_range()
    - UlamWarburton,UlamWarburtonQuarter parameter parts=>octant,octant_up

Version 116, June 2014
    - new WythoffPreliminaryTriangle
    - new methods is_tree(), x_negative_at_n(), y_negative_at_n()

Version 115, March 2014
    - CoprimeColumns new parameter direction=down
    - MPeaks new parameter n_start
    - Math::PlanePath::Base::Generic new parameter_info_nstart0()

Version 114, February 2014
    - PlanePathDelta new delta_type=>"dRadius","dRSquared"
    - CCurve xy_to_n() by division instead of search

Version 113, December 2013
    - PythagoreanTree new tree_type="UArD", digit_order="LtoH"
    - PlanePathCoord new coordinate_type "MinAbs","MaxAbs"

Version 112, December 2013
    - PythagoreanTree new tree_type="UMT"

Version 111, November 2013
    - FactorRationals new factor_coding "odd/even","negabinary","revbinary"
    - new sumabsxy_minimum(), sumabsxy_maximum(), absdiffxy_minimum(),
      absdiffxy_maximum()

Version 110, August 2013
    - PlanePathTurn new turn_type "SLR","SRL"

Version 109, August 2013
    - TerdragonCurve correction to dx_minimum()
    - TerdragonMidpoint correction to dx_maximum()

Version 108, July 2013
    - new tree_n_to_subheight()
    - PlanePathCoord new coordinate_type "SubHeight"
    - tests skip some 64-bit perl 5.6.2 dodginess in "%" operator

Version 107, July 2013
    - PentSpiral,PentSpiralSkewed,HeptSpiralSkewed,OctagramSpiral,
      Staircase,StaircaseAlternating new parameter n_start
    - FilledRings fix parameter_info_array() missing n_start
    - StaircaseAlternating fix parameter_info_array() missing end_type

Version 106, June 2013
    - new methods tree_n_root(), tree_num_roots(), tree_root_n_list(),
      tree_depth_to_n_range(), tree_depth_to_width(), tree_num_children_list(),
      dsumxy_minimum(),dsumxy_maximum(), ddiffxy_minimum(),ddiffxy_maximum()
    - PyramidSpiral new parameter n_start
    - PlanePathCoord new coordinate_type "RootN"

Version 105, June 2013
    - PlanePathCoord new coordinate_type "NumSiblings"

Version 104, May 2013
    - new method n_to_radius()

Version 103, May 2013
    - UlamWarburton new parts=2,1
    - PythagoreanTree new coordinates="SM","SC","MC"

Version 102, April 2013
    - new sumxy_minimum(),sumxy_maximum(), diffxy_minimum(),diffxy_maximum(),
    - PlanePathDelta new delta_type=>"dSumAbs"

Version 101, April 2013
    - MultipleRings fixes for ring_shape=polygon xy_to_n(), rect_to_n_range()
    - CellularRule,CellularRule54,CellularRule57,CellularRule190
      new parameter n_start
    - DiagonalRationals new parameter direction=up

Version 100, March 2013
    - new absdx_minimum(),absdx_maximum(), absdy_minimum(),absdy_maximum(),
      dir_minimum_dxdy(),dir_maximum_dxdy()
    - AztecDiamondRings new parameter n_start
    - TriangleSpiralSkewed new parameter skew=right,up,down
    - WythoffArray new parameters x_start,y_start
    - PlanePathDelta new delta_type=>"dAbsDiff"

Version 99, February 2013
    - oops, correction to IntXY on negatives

Version 98, February 2013
    - CoprimeColumns,DiagonalRationals,DivisibleColumns new n_start parameter
    - PlanePathCoord new coordinate_type "IntXY"

Version 97, January 2013
    - new tree_num_children_minimum(), tree_num_children_maximum()

Version 96, January 2013
    - AnvilSpiral,HexSpiral,HexSpiralSkewed new n_start, which was in
      parameter_info but did nothing
    - FilledRings new n_start parameter

Version 95, December 2012
    - new tree_any_leaf()
    - PythagoreanTree new coordinates="AC" and "BC"

Version 94, December 2012
    - new rsquared_minimum(), rsquared_maximum()
    - PlanePathCoord new coordinate_type "IsLeaf","IsNonLeaf"
    - ImaginaryHalf new option "digit_order"
    - Math::PlanePath::Base::Generic new parameter_info_nstart1()

Version 93, November 2012
    - new xy_is_visited()
    - PlanePathCoord new coordinate_type "Min","Max","BitAnd","BitOr","BitXor"

Version 92, October 2012
    - new x_minimum(),x_maximum(), y_minimum(),y_maximum(),
      dx_minimum(),dx_maximum(), dy_minimum(),dy_maximum()

Version 91, October 2012
    - new tree_depth_to_n(), tree_depth_to_n_end()
    - RationalsTree new tree_type "HCS"
    - UlamWarburton,UlamWarburtonQuarter new "n_start" parameter
    - PlanePathN new line_type=>"Depth_start","Depth_end"
    - Math::PlanePath::Base::Digits new bit_split_lowtohigh()

Version 90, October 2012
    - new CfracDigits, ChanTree
    - tree_n_num_children() return undef when no such N
    - Diagonals new x_start,y_start parameters
    - PlanePathCoord new coordinate_type "GCD"

Version 89, September 2012
    - RationalsTree new tree_type=L

Version 88, September 2012
    - new DekkingCurve, DekkingCentres
    - new tree_n_to_depth()
    - PlanePathCoord new coordinate_type "Depth"
    - DiamondSpiral new "n_start" parameter

Version 87, August 2012
    - new tree_n_num_children()
    - PlanePathCoord new coordinate_type "NumChildren"
    - SierpinskiArrowhead,SierpinskiArrowheadCentres new parameter
      align=right,left,diagonal
    - Rows,Columns new "n_start" parameter
    - KnightSpiral,PentSpiral,SierpinskiCurve fixes for n_to_xy() on
      some fractional N

Version 86, August 2012
    - Diagonals,DiagonalsOctant,DiagonalsAlternating,PyramidRows,PyramidSides,
      Corner new "n_start" parameter

Version 85, August 2012
    - SquareSpiral new "n_start" parameter
    - PlanePathDelta new delta_type=>"AbsdX","AbsdY"

Version 84, August 2012
    - PyramidRows new "align" parameter

Version 83, July 2012
    - new n_to_dxdy()
    - SierpinskiTriangle new parameter align=right,left,diagonal
    - SierpinskiTriangle,TriangleSpiral,TriangleSpiralSkewed,Hypot new
      "n_start" parameter
    - PlanePathDelta new delta_type=>"dDiffYX"
    - PlanePathN new line_type=>"Diagonal_NW","Diagonal_SW","Diagonal_SE"
    - Math::PlanePath::Base::Digits new digit_join_lowtohigh()
    - new Math::PlanePath::Base::Generic round_nearest()

Version 82, July 2012
    - new tree_n_children(), tree_n_parent()
    - PlanePathDelta new delta_type=>"dDiffXY"
    - ImaginaryBase,ImaginaryHalf rect_to_n_range() exact
    - new Math::PlanePath::Base::Digits round_down_pow(),
      digit_split_lowtohigh(), parameter_info_array(), parameter_info_radix2()

Version 81, July 2012
    - TriangularHypot new points=hex,hex_rotated,hex_centred

Version 80, July 2012
    - new AlternatePaperMidpoint
    - AlternatePaper new "arms"
    - GreekKeySpiral new "turns"
    - ComplexPlus, Flowsnake, FlowsnakeCentres, TerdragonMidpoint,
      TerdragonRounded, R5DragonMidpoint fix for arms>1 fractional N

Version 79, June 2012
    - TriangularHypot new option points=odd,even

Version 78, June 2012
    - new WythoffArray, PowerArray
    - GcdRationals new option pairs_order
    - Hypot,HypotOctant new option points=odd,even
    - Diagonals new options direction=up,down

Version 77, June 2012
    - new DiagonalsOctant

Version 76, May 2012
    - tests allow for as_float() only in recent Math::BigRat

Version 75, May 2012
    - new CubicBase, CCurve, R5DragonCurve, R5DragonMidpoint, TerdragonRounded
    - MultipleRings new ring_shape=>"polygon"
    - PlanePathDelta new delta_type=>"dSum"
    - fix TheodorusSpiral n_to_rsquared() on fractional N

Version 74, May 2012
    - new ImaginaryBase
    - new method n_to_rsquared()
    - PlanePathN new line_type X_neg,Y_neg
    - fix ImaginaryBase xy_to_n() possible infloop on floating point rounding
    - fix TerdragonMidpoint xy_to_n() undef on points outside requested arms

Version 73, April 2012
    - new GrayCode, SierpinskiCurveStair, WunderlichSerpentine
    - fix GcdRationals xy_to_n() on BigInt
    - PlanePathCoord new coordinate_type "SumAbs","TRadius","TRSquared"

Version 72, March 2012
    - PlanePathTurn new turn_type "Right"

Version 71, February 2012
    - new FilledRings
    - misc fixes for Math::NumSeq::PlanePathCoord etc values_min etc

Version 70, February 2012
    - TheodorusSpiral fix n_to_xy() position saving
    - StaircaseAlternating new end_type=>"square"

Version 69, February 2012
    - new Math::NumSeq::PlanePathTurn
    - Math::NumSeq::PlanePathN new pred()

Version 68, February 2012
    - new xy_to_n_list()
    - new CretanLabyrinth

Version 67, February 2012
    - oops, DragonMidpoint,DragonRounded xy_to_n() exclude points on the
      arm one past what was requested
    - new CellularRule57

Version 66, February 2012
    - new TerdragonMidpoint
    - DragonCurve,DragonMidpoint,DragonRounded,TerdragonCurve faster xy_to_n()

Version 65, January 2012
    - new parameter_info_hash(), n_frac_discontinuity()

Version 64, January 2012
    - new AnvilSpiral, AlternatePaper, ComplexPlus, TerdragonCurve

Version 63, January 2012
    - new class_x_negative() and class_y_negative() methods
    - new CellularRule, ComplexRevolving, Math::NumSeq::PlanePathN
    - Math::NumSeq::PlanePathCoord etc new planepath_object option

Version 62, December 2011
    - new FractionsTree

Version 61, December 2011
    - new FactorRationals

Version 60, December 2011
    - new GcdRationals

Version 59, December 2011
    - new AR2W2Curve

Version 58, December 2011
    - new DiagonalRationals, StaircaseAlternating,
      Math::NumSeq::PlanePathDelta

Version 57, December 2011
    - new HilbertSpiral
    - LTiling new L_fill "left" and "upper"

Version 56, December 2011
    - new CincoCurve, DiagonalsAlternating, LTiling

Version 55, November 2011
    - new KochelCurve, MPeaks
    - Flowsnake,QuintetCurve faster xy_to_n()

Version 54, November 2011
    - new WunderlichMeander
    - PlanePathCoord new coordinate_type "Product","DiffXY","DiffYX","AbsDiff"
    - BetaOmega,CellularRule190 exact rect_to_n_range()

Version 53, November 2011
    - new FibonacciWordFractal, Math::NumSeq::PlanePathCoord

Version 52, November 2011
    - new BetaOmega, CornerReplicate, DigitGroups, HIndexing

Version 51, October 2011
    - new CellularRule190

Version 50, October 2011
    - DragonRounded fix xy_to_n() with arms=2,3,4 on innermost XY=0,1
    - SierpinskiCurve fixes for rect_to_n_range()

Version 49, October 2011
    - new AztecDiamondRings, DivisibleColumns, SierpinskiCurve,
      UlamWarburtonQuarter
    - SierpinskiArrowheadCentres fix for n_to_xy() on fractional $n

Version 48, October 2011
    - new UlamWarburton

Version 47, October 2011
    - new SquareReplicate

Version 46, September 2011
    - new GosperReplicate

Version 45, September 2011
    - new QuintetCurve, QuintetCentres, QuintetReplicate

Version 44, September 2011
    - new ComplexMinus
    - RationalsTree new tree_type=Drib
    - Corner new wider parameter

Version 43, September 2011
    - new KochSquareflakes, RationalsTree
    - new parameter_info_array(), parameter_info_list()

Version 42, September 2011
    - new SierpinskiArrowheadCentres, SierpinskiTriangle

Version 41, August 2011
    - new QuadricCurve, QuadricIslands, ImaginaryBase

Version 40, August 2011
    - new DragonRounded, CellularRule54
    - new arms_count() method
    - Flowsnake, FlowsnakeCentres new "arms" parameter

Version 39, August 2011
    - new DragonCurve, DragonMidpoint

Version 38, August 2011
    - new Flowsnake, FlowsnakeCentres

Version 37, July 2011
    - new SquareArms, DiamondArms, File

Version 36, July 2011
    - new HexArms
    - PeanoCurve new radix parameter

Version 35, July 2011
    - new GosperSide
    - fixes for experimental BigFloat support

Version 34, July 2011
    - ZOrderCurve new radix parameter

Version 33, July 2011
    - new GosperIslands

Version 32, June 2011
    - new SierpinskiArrowhead, CoprimeColumns

Version 31, June 2011
    - KochCurve fix for fractional N

Version 31, June 2011
    - PythagoreanTree avoid dubious hypot() on darwin 8.11.0

Version 30, May 2011
    - new TriangularHypot, KochCurve, KochPeaks, KochSnowflakes

Version 29, May 2011
    - GreekKeySpiral rect_to_n_range() tighter $n_lo
    - tests more diagnostics on PythagoreanTree

Version 28, May 2011
    - PixelRings xy_to_n() fix some X==Y points should be undef

Version 27, May 2011
    - new GreekKeySpiral

Version 26, May 2011
    - new PythagoreanTree
    - Rows,Columns more care against width<=0 or height<=0

Version 25, May 2011
    - tests fix neg zero for long double NV

Version 24, May 2011
    - tests fix OEIS file comparisons
    - MultipleRings xy_to_n() fix for x=-0,y=0

Version 23, April 2011
    - new ArchimedeanChords
    - TheodorusSpiral rect_to_n_range() tighter $n_lo

Version 22, March 2011
    - new n_start() method
    - SacksSpiral rect_to_n_range() include N=0

Version 21, February 2011
    - new Hypot, HypotOctant, OctagramSpiral
    - TheodorusSpiral, VogelFloret allow for xy_to_n() result bigger than IV
      (though that big is probably extremely slow)

Version 20, February 2011
    - fix Makefile.PL for perl 5.6.0
    - tests avoid stringized "-0" from perl 5.6.x

Version 19, January 2011
    - new PixelRings

Version 18, January 2011
    - avoid some 5.12 warnings on infs

Version 17, January 2011
    - avoid some inf loops and div by zeros for n=infinity or x,y=infinity
      (handling of infinity is unspecified, but at least don't hang)
    - PyramidRows, PyramidSides exact rect_to_n_range()

Version 16, January 2011
    - new PeanoCurve, Staircase

Version 15, January 2011
    - MultipleRings fix xy_to_n() and rect_to_n_range() at 0,0
    - Corners,Diagonals,MultipleRings tighter rect_to_n_range()

Version 14, December 2010
    - HilbertCurve exact rect_to_n_range()

Version 13, December 2010
    - new HilbertCurve, ZOrderCurve

Version 12, October 2010
    - oops, VogelFloret botched rect_to_n_range()

Version 11, October 2010
    - VogelFloret new rotation and radius parameters
    - SacksSpiral,VogelFloret tighter rect_to_n_range() when away from origin

Version 10, October 2010
    - fix MultipleRings xy_to_n()

Version 9, September 2010
    - HexSpiral and HexSpiralSkewed new "wider" parameter

Version 8, September 2010
    - tests fix stray 5.010 should be just 5.004

Version 7, August 2010
    - new MultipleRings
    - VogelFloret xy_to_n() fix for positions away from exact N
    - Rows, Columns rect_to_n_range() tighter

Version 6, August 2010
    - new TheodorusSpiral

Version 5, July 2010
    - SquareSpiral new "wider" parameter

Version 4, July 2010
    - new PentSpiral, HeptSpiralSkewed
    - PyramidRows "step" parameter

Version 3, July 2010
    - new PyramidSpiral, TriangleSpiral, TriangleSpiralSkewed, PentSpiralSkewed

Version 2, July 2010
    - in Diagonals don't negative sqrt() if n=0

Version 1, July 2010
    - the first version
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