Number to Scientific Prefix

Convert a numeric value to an metric prefixed string (SI/engineering). Bonus: binary prefixes!

The function NUM2SIP converts a numeric scalar into a string with a metric prefix (aka SI prefix, or engineering prefix). For example the value 1000 is converted to '1 k'. The bonus function NUM2BIP converts from numeric to binary-prefixed string, for example the value 1024 is converted to '1 Ki'.

After testing the metric-prefix submissions on MATLAB FEX (see Acknowledgements) and not finding a single one that converted all values correctly and that supported the correct SI spacing, I wrote my own functions. And then exhaustively tested them to confirm that they actually give the correct output.

These functions are particularly useful to help create publications following SI standards, or where control over significant digits and trailing zeros is required, or for including numeric values in figures.

This submission:
* Always includes the space character (required by the SI standard).
* Automatically selects the most suitable prefix.
* Rounds to the requested significant figures (default==5).
* Prefix may be selected as either the full name ('kilo') or the symbol ('k').
* Trailing decimal zeros of the coefficient may be included or removed.
* Rounds up to the next prefix when significant figures require, e.g. '1 M', not '1000 k'.
* Uses simple integer even if precision is less than three (no exponent).

### Reverse Conversion ###

To convert from metric-prefixed string to numeric:

<http://www.mathworks.com/matlabcentral/fileexchange/53886-scientific-prefix-to-number>

### Metric Prefix Examples ###

>> num2sip(10000) OR num2sip(1e4)
ans = '10 k'
>> num2sip(10000,4,true)
ans = '10 kilo'
>> num2sip(10000,4,false,true)
ans = '10.00 k'

>> num2sip(999,3)
ans = '999 '
>> num2sip(999,2)
ans = '1 k'

>> num2sip(0.5e6)
ans = '500 k'
>> num2sip(0.5e6,[],'M')
ans = '0.5 M'

>> ['Power: ',num2sip(200e6,[],true),'watt']
ans = 'Power: 200 megawatt'

>> sprintf('Clock frequency is %shertz.',num2sip(1234567890,3,true))
ans = 'Clock frequency is 1.23 gigahertz.'

>> num2sip(sip2num('9 T')) % 9 tera == 9e12 == 9*1000^4
ans = '9 T'

### Binary Prefix Examples ###

>> num2bip(10240) OR num2bip(1.024e4) OR num2bip(pow2(10,10)) OR num2bip(10*2^10)
ans = '10 Ki'
>> num2bip(10240,4,true)
ans = '10 kibi'
>> num2bip(10240,4,false,true)
ans = '10.00 Ki'

>> num2bip(1023,3)
ans = '1020 '
>> num2bip(1023,2)
ans = '1 Ki'

>> num2bip(pow2(19))
ans = '512 Ki'
>> num2bip(pow2(19),[],'Mi')
ans = '0.5 Mi'

>> ['Memory: ',num2bip(pow2(200,20),[],true),'byte']
ans = 'Memory: 200 mebibyte'

>> sprintf('Data saved in %sbytes.',num2bip(1234567890,3,true))
ans = 'Data saved in 1.15 gibibytes.'

>> num2bip(bip2num('9 Ti')) % 9 tebi == pow2(9,40) == 9*1024^4
ans = '9 Ti'

### Metric Prefixes ###

Magnitude | Symbol / Name
1000^-8 | y / yocto
1000^-7 | z / zepto
1000^-6 | a / atto
1000^-5 | f / femto
1000^-4 | p / pico
1000^-3 | n / nano
1000^-2 | µ / micro
1000^-1 | m / milli
1000^0 |
1000^1 | k / kilo
1000^2 | M / mega
1000^3 | G / giga
1000^4 | T / tera
1000^5 | P / peta
1000^6 | E / exa
1000^7 | Z / zetta
1000^8 | Y / yotta

### Binary Prefixes (IEC 60027-2 A.2 and ISO/IEC 80000-13:2008) ###

Magnitude | Symbol / Name
1024^0 |
1024^1 | Ki / kibi
1024^2 | Mi / mebi
1024^3 | Gi / gibi
1024^4 | Ti / tebi
1024^5 | Pi / pebi
1024^6 | Ei / exbi
1024^7 | Zi / zebi
1024^8 | Yi / yobi

### Notes ###

These functions have been extensively tested against many edge cases, with particular attention to ensuring the correct rounding for all choices of significant figures. Compared to similar submissions available on MATLAB File Exchange, these functions correctly:
* include the space character between the coefficient and the prefix, even if there is no prefix (try 1).
* round to the requested significant figures (try 0.999 or 999e3, with 1 or 2 significant figures).
* return a coefficient without a prefix for zero and values outside the prefix range (try 0, Inf, 1E30).
* return a coefficient without an exponent when the significant digits are less than three (try 1e5 to 1 sigfig).