Numeric to Yllion

Convert a numeric to text giving the value using Donald Knuth's Yllion naming scheme.

Convert a numeric scalar into text giving the number value using Donald Knuth's Yllion number naming scheme, e.g. 1024e6 -> 'Ten Myllion Twenty-Four Hundred Myriad', or '10;2400,0000' as digits.

Syntax:
txt = num2yllion(num)
txt = num2yllion(num,dgt)
txt = num2yllion(num,dgt,pfx)

The input numeric value is rounded and the output precision is defined to ensure the least-unexpected output: single=6 digits; double=15 digits; while int/uint values are parsed at their full precision. The function implements an efficient algorithm without using recursion and with just one for-loop.

Yllion System

Donald Knuth's Yllion number naming system uses a logarithmic increase in group magnitudes for a much more efficient usage of the group names:

• 10^0 one
• 10^1 ten
• 10^2 hundred
• 10^4 myriad
• 10^8 myllion
• 10^16 byllion
• 10^32 tryllion
• 10^64 quadryllion
• 10^128 quintyllion
• 10^256 sextyllion

Knuth defined the pronunciation as "a myllion (pronounced mile-yun)".

Original Reference: "Supernatural Numbers" by Donald E. Knuth (pp. 310-325 in The Mathematical Gardner, editor David A. Klarner, 1981). Online References:

http://en.wikipedia.org/wiki/-yllion

http://mrob.com/pub/math/largenum-2.html

https://sites.google.com/site/pointlesslargenumberstuff/home/1/knuthyllions

Examples

>> num2yllion(0)
ans = 'Zero'

>> num2yllion(-1e303) % aka one centillion (short scale)
ans = 'Negative Ten Hundred Myriad Myllion Tryllion Sextyllion'

>> num2yllion(9876543210)
ans = 'Ninety-Eight Myllion Seventy-Six Hundred Fifty-Four Myriad Thirty-Two Hundred Ten'
>> num2yllion(9876543210,true)
ans = '98;7654,3210'
>> num2yllion(9876543210,true,true)
ans = '+98;7654,3210'
>> num2yllion(9876543210,false,true)
ans = 'Positive Ninety-Eight Myllion Seventy-Six Hundred Fifty-Four Myriad Thirty-Two Hundred Ten'

>> num2yllion(1e64,false) % default
ans = 'One Quadryllion'
>> num2yllion(1e64,true)
ans = '1::0000,0000;0000,0000:0000,0000;0000,0000;;0000,0000;0000,0000:0000,0000;0000,0000'