How to get a correct string representation of double?

oleg63

Hi, I've a problem with the proper conversion of double to it's string representation. For example. If I've in the code some double value: double a = 69000.015; the debugger in debug window will show 69000.014999999999 but not 69000.015 Generally I need the precision and number of significant digits for the conversion. For sprintf(...) I have to specify the precision and specifier. How can I get the correct precision of the double value? Is there any solution/clases for this type of conversion? Thanks.

Luc Pattyn

Hi, there is simply no solution to your problem. Floating point numbers, by their very nature, cannot always represent the intended value. The simplest example is the outcome of 1.0/3.0 humans write it down as 0.333333..., computers perform the division in binary and get a reasonably accurate quotient (say off by no more than 1 of the lowest bit position), which is after all an approximation. The binary approximation of 1/3 is something like 1/4 + 1/16 + 1/64 + 1/256 + ... and it has to stop somewhere since there are only so many bits reserved for the mantissa. Similar things will happen to almost all real numbers; in order to avoid it, the number must happen to be an integer value possibly divided by a power of two. Hence 1.0/4.0, 7.0/4.0, 23.0/256.0 etc can be represented exactly, whereas numbers with a prime factor (other than 2) in the denominator will not be exact, nor will irrational numbers (such as pi, or the square root of 2). If you know how many decimals (i.e. digits behind the decimal point) are required to get an exact representation, then order that number of decimals or fewer. Rounding will occur, and everything will look very natural. If you don't know the number of decimals required and care very much about the correctness of them, say you start your own financial program or business, then you'd better have a look at the decimal type. It offers a smaller range of numbers, but in some sense a better accuracy. :)

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Paul Conrad

No real simple solution due to the way floating point numbers are represented in binary form. You'll always have some odd round off to deal with. You could always try using the Decimal type...

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cp9876

Read this[^]

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oleg63

Thanks Luc for the answer, but unfortunally I'm not a Fortran developer, I do Visual C++ which do not have a decimal type. But the 69000.015 is non preiodical double(not like 1/3=0.333333...) and internal CPU's data register representation will be a particular correspondent binary. I'm not a pro in math, but for me seems like it needs some analysis of the binary representation to get a precision.

CPallini

This page [^]may show the internal representation of a decimal number as double. It comes out, that 69000.015 is represented with 40F0D8803D70A3D, i.e. 1.0528566741943360 as significand and 16 as exponent. If you put the above number in windows calculator then you'll get:

1.0528566741943360 * 2^16 = 1,0528566741943360 * 65536 = 69000.0150000000040960

probably not exactly what is expected by you. :)

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ClementsDan

You won't always have round off to deal with. Binary fractions like 1/2, 1/4, 3/4, 1/8, etc. can be exactly represented as a double. But you're right that most numbers can't (assuming that the word "most" can be used of an infinite set). The reason we put up with the inexactness is that exactness doesn't exist in the physical world. If a piece of wood is "2.4 meters long", it's really "2.4 meters give or take a millimeter" (which would be written as "2.400" to emphasize this). So, then, what difference does it make if your computer represents the length as 2.399999999999999911182158029987476766109466552734375 m, off by a mere 8.88e-17 m, when the physical accuracy is nowhere near that good? The one exception is money. If something costs $3.99, it costs exactly $3.99, not $3.9900000000000002. If the sales tax is 8.25%, it's exactly 8.25%, not 8.2500000000000004%. And, because we use decimal currency, Decimal classes are often used for monetary amounts. You could use it as a general-purpose number class, but: (1) It's not a panacea for rounding error. You still have to deal with 1/3 + 2/3 != 1. (2) Due to the lack of hardware support, it's much slower than binary floats. Therefore, I wouldn't just blindly recommend "use Decimal". If your only complaint with float or double is the string representation, then just use a smaller precision in sprintf or string.Format or the equivalent in your favorite language. (15 digits in the 'g' format will usually get the job done.)

prathapcode

Hi, I have a string with value "111733394601234567094987654321" . Now i want to divide this with 636. I convert it to double , then im getting 1.1173339460123456E+29 . but these both values are differnt finally im getting wrong output. can anyone help me..... Thanks Prathap

oleg63

If you do this for the cryptograpy purposes use any kind of Crypto API, it works with very long integers.