abandoned idea: base80 asciilification

[buhman]

This implements a base80 symbol set using a 41/32 encoding.

After implementing this, I realized my original math was incorrect:

(256^32 / 80^41) means only 10.89% of the possible 41-character base80 values are used for a given 32-byte input. I did more math, and came up with this table for all idealized baseN encoding schemes between 64 and 85, for all <=256-bit encodings:

symbols: 85 5/4=1.250 96.798%
symbols: 83 39/31=1.258 64.773%
symbols: 82 34/27=1.259 89.703%
symbols: 82 29/23=1.261 77.431%
symbols: 81 24/19=1.263 89.726%
symbols: 80 19/15=1.267 92.234%
symbols: 79 33/26=1.269 98.298%
symbols: 79 14/11=1.273 83.919%
symbols: 78 37/29=1.276 67.836%
symbols: 77 23/18=1.278 90.998%
symbols: 77 32/25=1.280 68.912%
symbols: 76 41/32=1.281 89.191%
symbols: 75 9/7=1.286 95.968%
symbols: 74 40/31=1.290 76.943%
symbols: 74 31/24=1.292 71.052%
symbols: 73 22/17=1.294 88.507%
symbols: 73 35/27=1.296 64.000%
symbols: 72 13/10=1.300 86.512%
symbols: 71 30/23=1.304 71.083%
symbols: 70 17/13=1.308 87.187%
symbols: 69 38/29=1.310 91.768%
symbols: 69 21/16=1.312 82.415%
symbols: 68 25/19=1.316 87.869%
symbols: 68 29/22=1.318 68.948%
symbols: 67 33/25=1.320 88.213%
symbols: 67 37/28=1.321 73.443%
symbols: 67 41/31=1.323 61.147%
symbols: 64 4/3=1.333 100.000%

base75 at seems like a clear winner:

• 9/7 is implementable with 64-bit integer math
• a base75 value of length 6 has 2.49x more entropy than a base64 value of length 6
• has at least one symbol set plausibly usable as a URL, unlike base85

Note base66 is not present in this table--despite the additional 2 symbols, it doesn't actually have more possible values than base64 in a 4/3 encoding scheme.

[buhman]

4b0512a