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Ontario Technoblog

Ontario Emperor technology blog.

This blog has been superseded by the mrontemp blog
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Location: Ontario, California, United States

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Thursday, August 17, 2006

You'd think that a Bill Gates application would be able to handle large numbers

Some people can wiggle their ears. I can recite powers of 2 up to about 8,192 or so. I can't necessarily tell you that 4,096 is 2 to the twelfth power, but I can multiply the numbers. (I used to be able to go up to 65,536, but I can't do that any more. Age, I guess.)

As a result of a drunken bet with Catherine Zeta-Jones on the deck of the Edmund Fitzgerald -

Strike that. It's not true, but it sounds better that way.

As a result of an inane conversation with co-workers, I was going to multiply powers of two all the way up to two to the 8,192nd power. Using Microsoft Excel, I got all the way to two to the 49th power:

2
4
8
16
32
64
128
256
512
1,024
2,048
4,096
8,192
16,384
32,768
65,536
131,072
262,144
524,288
1,048,576
2,097,152
4,194,304
8,388,608
16,777,216
33,554,432
67,108,864
134,217,728
268,435,456
536,870,912
1,073,741,824
2,147,483,648
4,294,967,296
8,589,934,592
17,179,869,184
34,359,738,368
68,719,476,736
137,438,953,472
274,877,906,944
549,755,813,888
1,099,511,627,776
2,199,023,255,552
4,398,046,511,104
8,796,093,022,208
17,592,186,044,416
35,184,372,088,832
70,368,744,177,664
140,737,488,355,328
281,474,976,710,656
562,949,953,421,312


But then I looked at the number for two to the 50th power:

1,125,899,906,842,620

As Devo would say, It's Not Right. But Excel was not meant to be a high-powered scientific calculator:

Numeric Precision
Microsoft Excel [was] developed to compete in the business software market where precision is probably not important for simple calculations. However many of the real-world calculations used in computational science require many digits of precision to the right of the decimal point.

Excel's maintains an internal numeric precision of 15 digits. By comparison a typical scientific calculator displays 10 digits but probably stores 12 digits while a CRAY 1 supercomputer has 15 digits in single-precision, floating point number. Excel stores 15 digits internally, but rounds the value for the screen display according to the format of the cell.

Numeric Range

Numeric range determines the sensitivity of the spreadsheet to overflow and underflow errors. Excel stores numbers between -1.798 x10 +308 and 1.798 x 10+308 for a numeric range of ±10+308. A scientific calculator handles a range of 10±99 and the CRAY 1 has a range of 10±2500. Although the largest number that Excel can store is 1.798 x 10+308, the largest number that you can type is 9.999 x 10+307. If you type in a larger number, Excel will treat it as a character string.

Most computational science calculations have reasonable results somewhere in the range of 10-40 to 10+40. When these numbers are used in an equation, the intermediate results are often quite large. If the intermediate results exceed the range of the computer then an overflow condition will return an error.


Returning to the title of this post, the precision in Excel is good enough for Bill and Melinda to maintain their household budget. I don't think they'll become quadrillionaires any time soon.

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