Alright. Using what I learned from here (thanks everyone) and the other parts of the web I wrote a neat little summary of the two just in case I run into another issue like this.
In C++ there are two ways to represent/store decimal values.
Floats and Doubles
A float can store values from:
- -340282346638528859811704183484516925440.0000000000000000 Float lowest
- 340282346638528859811704183484516925440.0000000000000000 Float max
A double can store values from:
-179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.0000000000000000 Double lowest
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.0000000000000000 Double max
Float's precision allows it to store a value of up to 9 digits (7 real digits, +2 from decimal to binary conversion)
Double, like the name suggests can store twice as much precision as a float. It can store up to 17 digits. (15 real digits, +2 from decimal to binary conversion)
e.g.
float x = 1.426;
double y = 8.739437;
Decimals & Math
Due to a float being able to carry 7 real decimals, and a double being able to carry 15 real decimals, to print them out when performing calculations a proper method must be used.
e.g
include
typedef std::numeric_limits<double> dbl;
cout.precision(dbl::max_digits10-2); // sets the precision to the *proper* amount of digits.
cout << dbl::max_digits10 <<endl; // prints 17.
double x = 12345678.312;
double a = 12345678.244;
// these calculations won't perform correctly be printed correctly without setting the precision.
cout << endl << x+a <<endl;
example 2:
typedef std::numeric_limits< float> flt;
cout.precision(flt::max_digits10-2);
cout << flt::max_digits10 <<endl;
float x = 54.122111;
float a = 11.323111;
cout << endl << x+a <<endl; /* without setting precison this outputs a different value, as well as making sure we're *limited* to 7 digits. If we were to enter another digit before the decimal point, the digits on the right would be one less, as there can only be 7. Doubles work in the same way */
Roughly how accurate is this description? Can it be used as a standard when confused?
Answer from user9318444 on Stack OverflowJust started learning C. so forigve me if this is a dumb question.
For int and long, the maximum number we can assign them is 2^32 and 2^64 respectively. how about for float and double? I know that double has higher precision of about 15 decimal points while float is 7.
i also know that float is 32 bit while double is 64 bit. So does that mean the highest we can store them (2^32)and (2^64) but with decimal points in between their numbers? i aslo learnt that these data type cant have unsigned value so does that value doubles?
variables - What are the actual min/max values for float and double (C++) - Stack Overflow
c - Limits for floating point types? - Stack Overflow
floating point - Understanding the maximum values that can be stored in floats in C - Stack Overflow
Maximum whole number a float can represe - C++ Forum
Alright. Using what I learned from here (thanks everyone) and the other parts of the web I wrote a neat little summary of the two just in case I run into another issue like this.
In C++ there are two ways to represent/store decimal values.
Floats and Doubles
A float can store values from:
- -340282346638528859811704183484516925440.0000000000000000 Float lowest
- 340282346638528859811704183484516925440.0000000000000000 Float max
A double can store values from:
-179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.0000000000000000 Double lowest
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.0000000000000000 Double max
Float's precision allows it to store a value of up to 9 digits (7 real digits, +2 from decimal to binary conversion)
Double, like the name suggests can store twice as much precision as a float. It can store up to 17 digits. (15 real digits, +2 from decimal to binary conversion)
e.g.
float x = 1.426;
double y = 8.739437;
Decimals & Math
Due to a float being able to carry 7 real decimals, and a double being able to carry 15 real decimals, to print them out when performing calculations a proper method must be used.
e.g
include
typedef std::numeric_limits<double> dbl;
cout.precision(dbl::max_digits10-2); // sets the precision to the *proper* amount of digits.
cout << dbl::max_digits10 <<endl; // prints 17.
double x = 12345678.312;
double a = 12345678.244;
// these calculations won't perform correctly be printed correctly without setting the precision.
cout << endl << x+a <<endl;
example 2:
typedef std::numeric_limits< float> flt;
cout.precision(flt::max_digits10-2);
cout << flt::max_digits10 <<endl;
float x = 54.122111;
float a = 11.323111;
cout << endl << x+a <<endl; /* without setting precison this outputs a different value, as well as making sure we're *limited* to 7 digits. If we were to enter another digit before the decimal point, the digits on the right would be one less, as there can only be 7. Doubles work in the same way */
Roughly how accurate is this description? Can it be used as a standard when confused?
The std::numerics_limits class in the <limits> header provides information about the characteristics of numeric types.
For a floating-point type T, here are the greatest and least values representable in the type, in various senses of “greatest” and “least.” I also include the values for the common IEEE 754 64-bit binary type, which is called double in this answer. These are in decreasing order:
std::numeric_limits<T>::infinity()is the largest representable value, ifTsupports infinity. It is, of course, infinity. Whether the typeTsupports infinity is indicated bystd::numeric_limits<T>::has_infinity.std::numeric_limits<T>::max()is the largest finite value. Fordouble, this is 21024−2971, approximately 1.79769•10308.std::numeric_limits<T>::min()is the smallest positive normal value. Floating-point formats often have an interval where the exponent cannot get any smaller, but the significand (fraction portion of the number) is allowed to get smaller until it reaches zero. This comes at the expense of precision but has some desirable mathematical-computing properties.min()is the point where this precision loss starts. Fordouble, this is 2−1022, approximately 2.22507•10−308.std::numeric_limits<T>::denorm_min()is the smallest positive value. In types which have subnormal values, it is subnormal. Otherwise, it equalsstd::numeric_limits<T>::min(). Fordouble, this is 2−1074, approximately 4.94066•10−324.std::numeric_limits<T>::lowest()is the least finite value. It is usually a negative number large in magnitude. Fordouble, this is −(21024−2971), approximately −1.79769•10308.If
std::numeric_limits<T>::has_infinityandstd::numeric_limits<T>::is_signedare true, then-std::numeric_limits<T>::infinity()is the least value. It is, of course, negative infinity.
Another characteristic you may be interested in is:
std::numeric_limits<T>::digits10is the greatest number of decimal digits such that converting any decimal number with that many digits toTand then converting back to the same number of decimal digits will yield the original number. Fordouble, this is 15.
The problem here isn't the range of values but the precision.
Assuming a 32-bit IEEE754 float, this datatype has a maximum of 24 bits of precision. This means that not all integers larger than 16777216 can be represented exactly.
So when your sum reaches 16777216, adding 1 to it is outside the precision of what the datatype can store, so the number doesn't get any bigger.
A (presumably) 64-bit double has 53 bits of precision. This is enough bits to hold all integer values up to your sum of 134217728, so it gives you an accurate result.
A float can precisely represent any integer between -16777215 and +16777215, inclusive. It can also represent all even integers between -2*16777215 and +2*16777215 (including +/- 2*8388608, i.e. 16777216), all multiples of 4 between -4*16777215 and +4*16777215, and likewise for all power-of-two scaling factors up to 2^104 (roughly 2.028E+31). Additionally, it can represent multiples of 1/2 from -16777215/2 to +16777215/2, multiples of 1/4 from -16777215/4 to +16777215/4, etc. down to multiples of 1/2^149 from -167777215/(2^149) to +16777215/(2^149).