c++ What is the difference between float and double?

As you can see after 0.83, the precision runs down significantly. Find centralized, trusted content and collaborate around the technologies you use most.

Double precision – decimal places

The encoding of a double uses 64 bits (1 bit for the sign, 11 bits for the exponent, 52 explicit significant bits and one implicit bit), which is double the number of bits used to represent a float (32 bits). In essence, if you’re performing a calculation and the result is an irrational number or recurring decimal, then there will be rounding errors when that number is squashed into the finite size data structure you’re using. Since double is twice the size of float then the rounding error will be a lot smaller. Using double to store large integers is dubious; the largest integer that can be stored reliably in double is much smaller than DBL_MAX. You should use long long, and if that’s not enough, you need your own arbitrary-precision code or an existing library. So, because there is no sane or useful interpretation of the bit operators to double values, they are not allowed by the standard.

Floats and Doubles

The IEEE 754 standard (used by most compilers) allocates relatively more bits for the significand than the exponent (23 to 9 for float vs. 52 to 12 for double), which is why the precision is more than doubled. Type long double is nominally 80 bits, though a given compiler/OS pairing may store it as bytes for alignment purposes. The long double has an exponent that just ridiculously huge and should have 19 digits precision. Microsoft, in their infinite wisdom, limits long double to 8 bytes, the same as plain double. Both double and float have 3 sections – a sign bit, an exponent, and the mantissa. In IEEE 754, there’s an implied 1 bit in front of the actual mantissa bits, which also complicates the interpretation.

Finally, financial applications often have to follow specific rounding modes (sometimes mandated by law). A double which is usually implemented with IEEE 754 will be accurate to between 15 and 17 decimal digits. Anything past that can’t be trusted, even if you can make the compiler display it. It’s not exactly double precision because of how IEEE 754 works, and because binary doesn’t really translate well to decimal. Double precision (double) gives you 52 bits of significand, 11 bits of exponent, and 1 sign bit.

Definitely use integer types for your money computations.This cannot be emphasized enough since at first glance it might seem that a floating point type is adequate. Many (most?) debuggers actually look at the contents of the entire register. When the debugger looks at the whole register, it’ll usually find at least one extra digit that’s reasonably accurate — though since that digit won’t have any guard bits, it may not be rounded correctly.

What is the difference between float and double?

The commented out ‘image_print()` function prints an arbitrary set of bytes in hex, with various minor tweaks. A mathematical or comparison operationthat uses a floating-point numbermight not yield the same result if adecimal number is used because thefloating-point number might notexactly approximate the decimalnumber. If you want finite values, then you can use max, which will be greater than or equal to all double top pattern forex strategy other finite values, and lowest, which is less then or equal to all other finite values. In C++ there are two ways to represent/store decimal values.

Answers

You may need to adjust your routine to work on chars, which usually don’t range up to 4096, and there may also be some weirdness with endianness here, but the basic idea should work. It won’t be cross-platform compatible, since machines use different endianness and representations of doubles, so be careful how you use this. The | operator performs a bitwise OR of its two operands (meaning both sides must evaluate to false for it to return false) while the || operator will only evaluate the second operator if it needs to. So to answer the last two questions, I wouldn’t say there are any caveats besides “know the difference between the two operators.” They’re not interchangeable because they do two completely different things.

The environment and the compiler are probably different on you local system and where the final tests are run. I have seen this problem many times before in some TopCoder competitions especially if you try to compare two floating point numbers. The tests may specifically use numbers which would cause this kind of error and therefore tested that you’d used the appropriate type in your code. The size of the numbers involved in the float-point calculations is not the most relevant thing. It’s the calculation that is being performed that is relevant.

Other solution is to get a pointer to the floating point variable and cast it to a pointer to integer type of the same size, and then get value of the integer this pointer points to. Now you have an integer variable with same binary representation as the floating point one and you can use your bitwise operator. Doubles always have 53 significant bits and floats always have 24 significant bits (except for denormals, infinities, and NaN values, but those are subjects for a different question). These are binary formats, and you can only speak clearly about the precision of their representations in terms of binary digits (bits).

If condition1 is true, condition 2 and 3 will NOT be checked. If you need to know these values, the constants FLT_RADIX and FLT_MANT_DIG (and DBL_MANT_DIG / LDBL_MANT_DIG) are defined in float.h. Because of this encoding, many numbers will have small changes to allow them to be stored.

If the exact value of numbers is not important, use double for speed. This includes graphics, physics or other physical sciences computations where there is already a “number of significant digits”. The upshot, which is not nearly as well known as it should be, is that you should almost always use type double.

It took me five hours to realize this minor error, which ruined my program. I just ran into a error that took me forever to figure out and potentially can give you a good example of float precision. During testing, maybe a few test cases contain these huge numbers, which may cause your programs to fail if you use floats.

No one ever uses the single & or | operators though, unless you have a design where each condition is a function that HAS to be executed. Sounds like a design smell, but sometimes (rarely) it’s a clean way to do stuff. The & operator does “run these 3 functions, and if one of them returns false, execute the else block”, while the | does “only run the else block if none return false” – can be useful, but as said, often it’s a design smell.

|| and && alter the properties of the OR and AND operators by stopping them when the LHS condition isn’t fulfilled. By their mathematical definition, OR and AND are binary operators; they verify the LHS and RHS conditions regardless, similarly to | and &. But perhaps even more important is the qualitative difference. Type float has good precision, which will often be good enough for whatever you’re doing. Type double, on the other hand, has excellent precision, which will almost always be good enough for whatever you’re doing.

Floats and Doubles

The program fails when I try to instantiate the template using a “double” or a “float”. Using double instead of decimal for monetary applications is a micro-optimization – that’s the simplest way I look at it. This includes any financial storage or calculations, scores, or other numbers that people might do by hand. Somewhat confusingly, min actually gives you the smallest positive normalized value, which is completely out of sync with what it gives with integer types (thanks @JiveDadson for pointing this out). This will check conditions 2 and 3, even if 1 is already true.

• The size of the numbers involved in the float-point calculations is not the most relevant thing.
• Although you already know, read What WE Should Know About Floating-Point Arithmetic for better understanding.
• This isn’t officially included in C++98 or C++03, but is part of C99 and C++11, so all reasonably current compilers support it.

Single precision (float) gives you 23 bits of significand, 8 bits of exponent, and 1 sign bit. Also, the number of significant digits can change slightly since it is a binary representation, not a decimal one. So if the precision of a float is enough to handle the needs, the program will execute some times faster with float then double. Generally speaking, just use type double when you need a floating point value/variable. Literal floating point values used in expressions will be treated as doubles by default, and most of the math functions that return floating point values return doubles. You’ll save yourself many headaches and typecastings if you just use double.

If you’re using Intel (little-endian), you’ll probably need to tweak the code to deal with the reverse bit order. If has_infinity is true (which it will for basically any platform nowadays), then you can use infinity to get the value which is greater than or equal to all other values (except NaNs). Its negation will give a negative infinity, and be less than or equal to all other values (except NaNs again). Notice how I changed the last digit, but it printed out the same number anyway. Evaluates to true if either condition1 OR condition2 is true.

• Generally speaking, just use type double when you need a floating point value/variable.
• No one ever uses the single & or
• Type double, on the other hand, has excellent precision, which will almost always be good enough for whatever you’re doing.
• Microsoft, in their infinite wisdom, limits long double to 8 bytes, the same as plain double.

Although you already know, read What WE Should Know About Floating-Point Arithmetic for better understanding. This precision loss could lead to greater truncation errors being accumulated when repeated calculations are done, e.g. As to your original question, if you want a larger integer type than long, you should probably consider long long. This isn’t officially included in C++98 or C++03, but is part of C99 and C++11, so all reasonably current compilers support it.

Also, note that there’s no guarantee in the C Standard that a long double has more precision than a double. The built-in comparison operations differ as in when you compare 2 numbers with floating point, the difference in data type (i.e. float or double) may result in different outcomes. I would suggest having a look at the excellent What Every Computer Scientist Should Know About Floating-Point Arithmetic that covers the IEEE floating-point standard in depth. You’ll learn about the representation details and you’ll realize there is a tradeoff between magnitude and precision. The precision of the floating point representation increases as the magnitude decreases, hence floating point numbers between -1 and 1 are those with the most precision.

As your conditions can be quite expensive functions, you can get a good performance boost by using them. Create the double first, add the numbers to it, and add that array to the List. By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy. When using floating point numbers you cannot trust that your local tests will be exactly the same as the tests that are done on the server side.