#!/usr/bin/env python
### graph_iterate_log1.py -- Limit original points to pi i +/- ~100
# Steve Witham ess doubleyou at tiac remove-this dot net.
# http://www.tiac.net/~sw

from reportlab.pdfgen import canvas
from reportlab.lib.pagesizes import letter, A4 
from reportlab.lib.units import inch
from arrowline import arrowLine

from math import sqrt, pow, pi, e
from cmath import log, exp, sinh, asinh

from os import system


# From iterate_log.py:

e0 = ( 0.31813150520476413 + 1.3372357014306895j )
BIGGEST = pow(2.0,1023) * (2.0-pow(2.0,-52))
SMALLEST = pow(2,-1074)

def graph_iterate_log(c): 
    # choose some colors 
    c.setStrokeColorRGB(0,0,0)
    c.setFillColorRGB(0,0,0)

    c.setFont("Helvetica", 14 ) 
    c.drawString( 1 * inch, 10 * inch, "Iterated Complex Natural Log" )


    # initial set of points:
    nPoints = 33
    # points = [ 0j + (i+.5)/nPoints for i in range( nPoints ) ]
    original_points = [ (pi * 1j) + sinh( i/3.0 ) for i in 
               range( -(nPoints-1)/2, nPoints-(nPoints-1)/2 ) ]
    pmin, pmax  =  original_points[0].real, original_points[-1].real
    c.setFont("Helvetica", 11 ) 
    c.drawString( 1 * inch, 9.5 * inch, 
        "Original points at y = pi range from x = %f to %+f ." % 
                  ( pmin, pmax ) )
    c.drawString( 1 * inch, 9.25 * inch, 
        "(Only those from about -5 to +5 are visible.)" )


    # Set the origin in the middle of the page:
    c.translate( 8.5 * inch / 2, 11 * inch / 2 )

    # Scale so that range of the graph is about +/- 5:
    # NOTE: THIS MEANS LINE WIDTHS AND FONTS AREN'T IN POINTS ANY MORE.
    c.scale( .7*inch, .7*inch )
    point = 1/( .7*inch )

    # Draw the axes:
    c.setLineWidth( .25 * point )
    # c.line( -4,0, 4,0 ) # No x axis, it obscures the little arrows.
    c.line( 0,-4, 0,4 )

    points = original_points
    for i in range(4):
        points = [ expsafe(z) for z in points ]
        c.setStrokeColorRGB( 1, 0, 0 )
        for j in range( len(points) - 1 ):
            if   j == len(points) / 2: c.setStrokeColorRGB( 0, 0, 0 )
            if points[j] == None  or  points[ j+1 ] == None:
                continue

            size = abs( points[j] - points[j+1] )
            if size < 10:
                c.setLineWidth( size / 10 )
                arrowLine( c, points[j].real, points[j].imag,
                           points[j+1].real, points[j+1].imag )

    points = original_points
    for i in range(24):
        c.setStrokeColorRGB( 1, 0, 0 )
        for j in range( len(points) - 1 ):
            if j == len(points) / 2: c.setStrokeColorRGB( 0, 0, 0 )
            size = abs( points[j] - points[j+1] )
            if size < 10  and  ( abs(points[j])<10 or abs(points[j+1])<10 ):
                c.setLineWidth( size / 10 )
                arrowLine( c, points[j].real, points[j].imag,
                           points[j+1].real, points[j+1].imag )
        
        points = [ log(z) for z in points ]

    ticks = [ -1, e**-1, 1, e**(e**-1), e, e**(e**(e**-1)) ]
    names = [ "-1", "e^-1", "1", "e^e^-1", "e", "e^e^e^-1" ]

    c.setFont("Helvetica", 10 * point )
    c.setLineWidth( .25 * point )
    for i in range( len( ticks ) ):
        x, name  =  ticks[i], names[i]
        c.line( x, -.3,  x, -.1 )
        printexp( c, x, -.55, name, "Helvetica", 10 * point )


def expsafe( z ):
    if z != None  and  abs(z) < 706:  return exp(z)
    else: return None


def printexp( c, x, y, name, fontname, fontsize ):
    width = c.stringWidth( name.replace('^',''), fontname, fontsize )
    pieces = name.split( '^' )
    jump = fontsize * .5
    y -= ( len(pieces) - 1 ) * jump * .5
    x -= width / 2
    for piece in pieces:
        c.drawString( x, y, piece )
        x += c.stringWidth( piece, fontname, fontsize )
        y += jump

    

    

output_file = "graph_iterate_log1.pdf"

# pageCompression = 0 if I can look at the text in the output.
# set to 1 in rl_config.py.
c = canvas.Canvas( output_file, pagesize=letter )
width, height = letter  #keep for later 

graph_iterate_log(c)
c.showPage() 
c.save()
system( "open " + output_file )