# Go deh!

Mainly Tech projects on Python and Electronic Design Automation.

## Thursday, November 29, 2012

### Some identities for Python int.to_bytes and int.from_bytes

I read the documentation for int.to_bytes and int.from_bytes and thought that what was missing was a description of what they did in terms of other Python code, rather like what is done for several of the generators in the docs for the itertools module; (I was completing this RC task at the time).

I came up with the following code snippet that I would have found helpful and that I hope helps you.

```>>> n = 2491969579123783355964723219455906992268673266682165637887
>>> length = 25
>>> n2bytesbig    = n.to_bytes(length, 'big')
>>> n2byteslittle = n.to_bytes(length, 'little')
>>> assert n2bytesbig    == bytes( (n >> i*8) & 0xff for i in reversed(range(length)))
>>> assert n2byteslittle == bytes( (n >> i*8) & 0xff for i in range(length))
>>> assert n == sum( n2bytesbig[::-1][i] << i*8 for i in range(length) )
>>> assert n == sum( n2byteslittle[i]    << i*8 for i in range(length) )
>>> assert n == int.from_bytes(n2bytesbig,    byteorder='big')
>>> assert n == int.from_bytes(n2byteslittle, byteorder='little')
>>>```

## Friday, November 23, 2012

### Topswop and a convoluted multiple assignments warning

I was messing around with John Conways Topswop problem:

Given a starting permutation of 1..n items, consider the leftmost value and call it L:

• If L is not 1 then reverse the leftmost L values in the sequence.
• Repeat, counting the number of reversions required until L becomes 1
Repeat the process for all permutations of 1..n items and report the maximum number of reversions required amongst all the permutations.

I initially came up with this doodle:

```>>> def f1(p):
i = 0
while p != 1:
i += 1
print(i,p)
p[:p] = p[:p][::-1]
return i

>>> f1([4,2,1,5,3])
1 [4, 2, 1, 5, 3]
2 [5, 1, 2, 4, 3]
3 [3, 4, 2, 1, 5]
4 [2, 4, 3, 1, 5]
5 [4, 2, 3, 1, 5]
5
>>> def f1(p):
i = 0
while p != 1:
i += 1
#print(i,p)
p[:p] = p[:p][::-1]
return i

>>> f1([4,2,1,5,3])
5
>>> from itertools import permutations
>>> def fannkuch(n):
return max(f1(list(p)) for p in permutations(range(1, n+1)))

>>> for n in range(1, 11): print(n,fannkuch(n))

1 0
2 1
3 2
4 4
5 7
6 10
7 16
8 22
9 30
10 38
>>>```

### Range

Python usually uses ranges 0..n-1 so I made that modification:

```>>> def f1(p):
i = 0
while p:
i += 1
p[:p + 1] = p[:p + 1][::-1]
return i

>>> def fannkuch(n):
return max(f1(list(p)) for p in permutations(range(n)))
```

### Speed

I had to wait for fannkuch(10) so decided to do some quick optimization and created name p0 to mop up some array lookups:

```>>> def f1(p):
i, p0 = 0, p
while p0:
i  += 1
p0 += 1
p[:p0] = p[:p0][::-1]
p0  = p
return i
```

## Those assignments

It was at this stage that I thought "Ooh, I haven't used that new assignment in Python 3 where you can use *name on the left hand side of an assignment", plus, I could add it in to an already complex assignment  just for the hell of it.

I am creating p, so I should be able to assign p to p0 and discard p[1:] for the purposes of the assignment into *_. I tried:

```>>> def f1(p):
i, p0 = 0, p
while p0:
i  += 1
p0 += 1
p0, *_ = p[:p0] = p[:p0][::-1]
return i

>>> for n in range(1, 11): print(n,fannkuch(n))

1 0
2 1
3 2
Traceback (most recent call last):
File "", line 1, in
for n in range(1, 11): print(n,fannkuch(n))
File "", line 2, in fannkuch
return max(f1(list(p)) for p in permutations(range(n)))
File "", line 2, in
return max(f1(list(p)) for p in permutations(range(n)))
File "", line 6, in f1
p0, *_ = p[:p0] = p[:p0][::-1]
KeyboardInterrupt
>>>```

I had to interrupt it as it failed to return. Something was wrong!

I thought it might be the order of assignment and tried:

```>>> def f1(p):
i, p0 = 0, p
while p0:
i  += 1
p0 += 1
p[:p0] = p0, *_ = p[:p0][::-1]
return i

>>> for n in range(1, 11): print(n,fannkuch(n))

1 0
2 1
3 2
4 4
5 7
6 10
7 16
8 22
9 30
10 38
>>>```

Yay Success!!

But I did this so you don't have to :-)

It is a few optimizations too far, and, when you look in the docs they state:

"
WARNING: Although the definition of assignment implies that overlaps between the left-hand side and the right-hand side are ‘safe’ (for example a, b= b, a swaps two variables), overlaps within the collection of assigned-to variables are not safe! For instance, the following program prints [0, 2]:
```x = [0, 1]
i = 0
i, x[i] = 1, 2
print(x)
```
"

## Wednesday, November 21, 2012

### RGB spectrum. 3D to 2D with smooth transition?

I was messing about with HTML red, green, blue triplets of 0..255 values each that are used for specifying HTML colours (with a u as I am English). I decided that I wanted to be able to take a spread of rgb values and arrange them in a spectrum.

Easily said, but hard to do. I went down a blind alley of converting to Hue, Saturation, Luminance; but could do nothing with that. I decided to ignore our eyes different sensitivities and any difference in 'purity' of pure red/green/blue from monitors and decided to try and work out mathematically how to create such a spectra.

The values for the three colours are independently variable over their ranges and so I got to thinking of the available colours as a colour cube. Think of a a 3D graph with three perpendicular axes red, green and blue. You can do the physics trick of taking your hand; stick the thumb straight up, the finger directly below the thumb straight out in front and the second finger below the thumb at right angles to them both pointing towards your body. There you have it! three perpendicular axes for red, green and blue, with the origin being towards your palm.

The available colours fill the cube of integers (0, 0, 0) up to (255, 255, 255). I want to create a linear 'spectrum'.

If you consider the three points R, G, B, = (255, 0, 0), (0, 255, 0), (0, 0, 255) respectively,  they are the points of maximum r,g,b intensity, unsullied by other colours. If you cut the cube to expose the plane linking those three points then I would ideally like a spectra that  traversed R->G->B (->R); but what about the off-plane colour triplets?

If given a list of colour triplets to sort into a spectrum I decided to
1. Find out which of the three cardinal points/primary colours R, G, or B each triplet was closest-to.
2. Sort all the triplets on their closeness to a primary.
3. Extract three lists of the triplets for each primary colour in such a way that they would be sorted with the primaries near the centre of their list; and those with more of the next primary to the 'right' and to the previous primary to the 'left'.
For example the Red list would have reddy-greens to the right and reddy-blues to the left; the green list would have greeny-reds to the left and greeny-blues to the right; similarly the blue list would have bluey-greens to the left and bluey-reds to the right.
4. Join the three lists in the R, G,B order - assuming that B wraps-round to R to form the spectrum.

### The Code

``` 1
2 '''
3 Generate rgb colours in order
4 '''
5
6 from pprint import pprint as pp
7 from collections import namedtuple
8 from itertools import product, groupby
9
10
11 Rgb = namedtuple('Rgb', 'r g b')
12 # red, green, blue, dark, light. 'cardinal' points
13 RGBDL = ( Rgb(255, 0, 0), Rgb(0, 255, 0), Rgb(0, 0, 255), Rgb(0, 0, 0), Rgb(255, 255, 255) )
14 RGB   = ( Rgb(255, 0, 0), Rgb(0, 255, 0), Rgb(0, 0, 255) )
15
16 def dist(p, q):
17     'dist squared between two points'
18     return sum((pp - qq)**2 for pp,qq in zip(p,q))
19
20 def cmp(x,y):
21     return 1 if x>y else (0 if x==y else -1)
22
23 def rgbsort2(rgblist):
24     'reddest to greenest to bluest (... to redest, circularly)'
25     # , ,
26     # cindex = 0 for red; 1 for green; 2 for blue.
27     Closest = namedtuple('Closest', 'distance, cindex, col')
28     # find Closest info for all colours
29     colourdistances = []
30     for col in rgblist:
31         # distance to each cardinal colour in turn
32         rgbdistances = tuple(dist(col, cardinal) for cardinal in RGB)
33         distance = min(rgbdistances)        # closest
34         cindex = rgbdistances.index(distance)
35         colourdistances.append(Closest(distance, cindex, col))
36     # Sort closest to a cardinal point first
37     colourdistances.sort()
38
39     # clist accumulates redder, greener, bluer colours separately.
40     # Most intense colour towards the middle of each sublist.
41     clist = [list() for i in range(3)]
42
43     # Accumulate the sub-spectra for each cardinal colour
44     for _, cindex, col in colourdistances:
45         # add right if closest to next colour cardinal point
46         addright = col[(cindex + 1) % 3] > col[(cindex + 2) % 3]
48             clist[cindex].append(col)
49         else:
50             clist[cindex].insert(0, col)
51     # Final spectrum
52     return clist + clist + clist```
```53
54 def rgb2HTML(colours):
55     f, ht = 4, 50
```
`...`

```67     return txt
68
69
70 if __name__ == '__main__':
71     if 1:
72         # See http://www.lynda.com/resources/webpalette.aspx# for info on
73         # HTML colours without dithering on Windows & Mac.
74         nondithers = (0xFF, 0xCC, 0x99, 0x66, 0x33, 0x00)
75     else:
76         nondithers = tuple(range(0,256,32))
77     rgblist = [Rgb(*rgb) for rgb in product(*(nondithers,)*3)]
78     spectra2 = rgbsort2(rgblist)
79     #assert spectra == spectra2
80     with open('rgbgen.htm', 'w') as f:
81         f.write(rgb2HTML(spectra2))
82
83
```

`I have had to miss-out the guts of the rgb2HTML function as Blogger has problems with rendering the HTML tags `

### The result

`I get some sort of progression, but could do better:`

```
#FFFFFF
(255,255,255)#FFCCFF
(255,204,255)#FF99FF
(255,153,255)#CCCCCC
(204,204,204)
#FFCCCC
(255,204,204)#FF66FF
(255,102,255)#FF33FF
(255,51,255)#CC99CC
(204,153,204)
#FF99CC
(255,153,204)#FF00FF
(255,0,255)#000000
(0,0,0)#999999
(153,153,153)
#CC66CC
(204,102,204)#FF66CC
(255,102,204)#CC9999
(204,153,153)#FF9999
(255,153,153)
#CC33CC
(204,51,204)#333333
(51,51,51)#FF33CC
(255,51,204)#CC00CC
(204,0,204)
#996699
(153,102,153)#666666
(102,102,102)#330033
(51,0,51)#FF00CC
(255,0,204)
#330000
(51,0,0)#CC6699
(204,102,153)#993399
(153,51,153)#663366
(102,51,102)
#FF6699
(255,102,153)#990099
(153,0,153)#660066
(102,0,102)#996666
(153,102,102)
#CC3399
(204,51,153)#663333
(102,51,51)#FF3399
(255,51,153)#CC0099
(204,0,153)
#660033
(102,0,51)#FF0099
(255,0,153)#CC6666
(204,102,102)#993366
(153,51,102)
#660000
(102,0,0)#FF6666
(255,102,102)#990066
(153,0,102)#CC3366
(204,51,102)
#993333
(153,51,51)#FF3366
(255,51,102)#CC0066
(204,0,102)#990033
(153,0,51)
#FF0066
(255,0,102)#990000
(153,0,0)#CC3333
(204,51,51)#FF3333
(255,51,51)
#CC0033
(204,0,51)#FF0033
(255,0,51)#CC0000
(204,0,0)#FF0000
(255,0,0)
#FF3300
(255,51,0)#CC3300
(204,51,0)#FF6600
(255,102,0)#993300
(153,51,0)
#CC6600
(204,102,0)#FF6633
(255,102,51)#CC6633
(204,102,51)#996600
(153,102,0)
#996633
(153,102,51)#FF9900
(255,153,0)#663300
(102,51,0)#CC9900
(204,153,0)
#FF9933
(255,153,51)#CC9933
(204,153,51)#666600
(102,102,0)#999900
(153,153,0)
#FF9966
(255,153,102)#666633
(102,102,51)#999933
(153,153,51)#CC9966
(204,153,102)
#FFCC00
(255,204,0)#333300
(51,51,0)#999966
(153,153,102)#CCCC00
(204,204,0)
#FFCC33
(255,204,51)#CCCC33
(204,204,51)#FFCC66
(255,204,102)#CCCC66
(204,204,102)
#FFCC99
(255,204,153)#FFFF00
(255,255,0)#CCCC99
(204,204,153)#FFFF33
(255,255,51)
#FFFF66
(255,255,102)#FFFF99
(255,255,153)#FFFFCC
(255,255,204)#CCFFCC
(204,255,204)
#CCFF99
(204,255,153)#CCFF66
(204,255,102)#99CC99
(153,204,153)#99FF99
(153,255,153)
#CCFF33
(204,255,51)#CCFF00
(204,255,0)#003300
(0,51,0)#99CC66
(153,204,102)
#99FF66
(153,255,102)#669966
(102,153,102)#99CC33
(153,204,51)#336633
(51,102,51)
#99FF33
(153,255,51)#99CC00
(153,204,0)#336600
(51,102,0)#99FF00
(153,255,0)
#66CC66
(102,204,102)#669933
(102,153,51)#006600
(0,102,0)#66FF66
(102,255,102)
#669900
(102,153,0)#66CC33
(102,204,51)#339933
(51,153,51)#66FF33
(102,255,51)
#66CC00
(102,204,0)#339900
(51,153,0)#66FF00
(102,255,0)#009900
(0,153,0)
#33CC33
(51,204,51)#33FF33
(51,255,51)#33CC00
(51,204,0)#33FF00
(51,255,0)
#00CC00
(0,204,0)#00FF00
(0,255,0)#00FF33
(0,255,51)#00CC33
(0,204,51)
#00FF66
(0,255,102)#009933
(0,153,51)#00CC66
(0,204,102)#33FF66
(51,255,102)
#33CC66
(51,204,102)#009966
(0,153,102)#00FF99
(0,255,153)#339966
(51,153,102)
#006633
(0,102,51)#00CC99
(0,204,153)#33FF99
(51,255,153)#33CC99
(51,204,153)
#006666
(0,102,102)#009999
(0,153,153)#66FF99
(102,255,153)#336666
(51,102,102)
#339999
(51,153,153)#66CC99
(102,204,153)#00FFCC
(0,255,204)#003333
(0,51,51)
#00CCCC
(0,204,204)#33FFCC
(51,255,204)#669999
(102,153,153)#33CCCC
(51,204,204)
#66FFCC
(102,255,204)#66CCCC
(102,204,204)#00FFFF
(0,255,255)#99FFCC
(153,255,204)
#33FFFF
(51,255,255)#99CCCC
(153,204,204)#66FFFF
(102,255,255)#99FFFF
(153,255,255)
#CCFFFF
(204,255,255)#CCCCFF
(204,204,255)#99CCFF
(153,204,255)#66CCFF
(102,204,255)
#9999CC
(153,153,204)#9999FF
(153,153,255)#33CCFF
(51,204,255)#00CCFF
(0,204,255)
#000033
(0,0,51)#6699CC
(102,153,204)#6699FF
(102,153,255)#666699
(102,102,153)
#3399CC
(51,153,204)#333366
(51,51,102)#3399FF
(51,153,255)#0099CC
(0,153,204)
#003366
(0,51,102)#6666CC
(102,102,204)#336699
(51,102,153)#0099FF
(0,153,255)
#000066
(0,0,102)#6666FF
(102,102,255)#006699
(0,102,153)#3366CC
(51,102,204)
#333399
(51,51,153)#3366FF
(51,102,255)#0066CC
(0,102,204)#003399
(0,51,153)
#0066FF
(0,102,255)#000099
(0,0,153)#3333CC
(51,51,204)#3333FF
(51,51,255)
#0033CC
(0,51,204)#0033FF
(0,51,255)#0000CC
(0,0,204)#0000FF
(0,0,255)
#3300FF
(51,0,255)#3300CC
(51,0,204)#6600FF
(102,0,255)#330099
(51,0,153)
#6600CC
(102,0,204)#6633FF
(102,51,255)#6633CC
(102,51,204)#660099
(102,0,153)
#663399
(102,51,153)#9900FF
(153,0,255)#330066
(51,0,102)#9900CC
(153,0,204)
#9933FF
(153,51,255)#9933CC
(153,51,204)#9966FF
(153,102,255)#9966CC
(153,102,204)
#CC00FF
(204,0,255)#CC33FF
(204,51,255)#CC66FF
(204,102,255)#CC99FF
(204,153,255)

```

## Sunday, November 11, 2012

### "How do I love thee? Let me count the ways..."

I was reading a post by CodeBuddy via reddit on brute force techniques in Python and it was getting a lot of grief in the reddit comments.

It turns out that the author was learning Python and blogging to help him remember. He wrote a lot but with very little meat so I guess the redditers were justified in one sense as they may have expected more, but as soon as I heard that the guy was learning Python I thought back to some small thing I did the week before that I think may interest both him and the redditers in providing a little (and only a little), more meat on the table.

So, I was on Youtube which now insists on giving me more of what I liked before and I got to watching an episode of Numberphile called "One to One Million" in which they posed the question:

"What is the sum of the digits of all the numbers one to one million"

Now, I new they would go on to give some fiendishly clever way of doing it (so clever it is simple). But I had my engineers hat on, and I quickly worked out that a brute-force direct approach in Python would not take long to write or run. Indeed, a few minutes later I had something like the following:

>>> x = ''.join(str(i) for i in range(1, 1000000+1))
>>> sum(int(digit) * x.count(digit) for digit in '123456789')
27000001
>>>

The Python code just concatenates all the string representations of all numbers in the range together, (that's only 5888896 digits); it then sums the digits by finding out how many of each there are multiplied by the digits value.

Not a brainy solution but I had time to pay attention to their solution which was to take numbers in pairs from the ...

... Best to watch the video.

P.s. In searching for the title I reacquainted myself with this poem by Elizabeth Barrett Browning:

How do I love thee? Let me count the ways.
I love thee to the depth and breadth and height
My soul can reach, when feeling out of sight
For the ends of being and ideal grace.
I love thee to the level of every day's
Most quiet need, by sun and candle-light.
I love thee freely, as men strive for right.
I love thee purely, as they turn from praise.
I love thee with the passion put to use
In my old griefs, and with my childhood's faith.
I love thee with a love I seemed to lose
With my lost saints. I love thee with the breath,
Smiles, tears, of all my life; and, if God choose,
I shall but love thee better after death.