## GNU Astronomy Utilities

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### 4.4 Numeric data types

At the lowest level, the computer stores everything in terms of 1 or 0. For example, each program in Gnuastro, or each astronomical image you take with the telescope is actually a string of millions of these zeros and ones. The space required to keep a zero or one is the smallest unit of storage, and is known as a bit. However, understanding and manipulating this string of bits is extremely hard for most people. Therefore, we define packages of these bits along with a standard on how to interpret the bits in each package as a type.

The most basic standard for reading the bits is integer numbers ($$..., -2, -1, 0, 1, 2, ...$$, more bits will give larger limits). The common integer types are 8, 16, 32, and 64 bits wide. For each width, there are two standards for reading the bits: signed and unsigned integers. In the former, negative numbers are allowed and in the latter, they aren’t. The unsigned types thus have larger positive limits (one extra bit), but no negative value. When the context of your work doesn’t involve negative numbers (for example counting, where negative is not defined), it is best to use the unsigned types. For full numerical range of all integer types, see below.

Another standard of converting a given number of bits to numbers is the floating point standard, this standard can approximately store any real number with a given precision. There are two common floating point types: 32-bit and 64-bit, for single and double precision floating point numbers respectively. The former is sufficient for data with less than 8 significant decimal digits (most astronomical data), while the latter is good for less than 16 significant decimal digits. The representation of real numbers as bits is much more complex than integers. If you are interested, you can start with the Wikipedia article.

With the conversion operators in Gnuastro’s Arithmetic, you can change the types of data to each other, which is necessary in some contexts. For example the program/library, that you intend to feed the data into, only accepts floating point values, but you have an integer image. Another situation that conversion can be helpful is when you know that your data only has values that fit within int8 or uint16. However it is currently formatted in the float64 type. Operations involving floating point or larger integer types are significantly slower than integer or smaller-width types respectively. In the latter case, it also requires much more (by 8 or 4 times in the example above) storage space. So when you confront such situations and want to store/archive/transfter the data, it is best convert them to the most efficient type.

The short and long names for the recognized numeric data types in Gnuastro are listed below. Both short and long names can be used when you want to specify a type. For example, as a value to the common option --type (see Input/Output options), or in the information comment lines of Gnuastro text table format. The ranges listed below are inclusive.

u8
uint8

8-bit un-signed integers, range:
$$[0\rm{\ to\ }2^8-1]$$ or $$[0\rm{\ to\ }255]$$.

i8
int8

8-bit signed integers, range:
$$[-2^7\rm{\ to\ }2^7-1]$$ or $$[-128\rm{\ to\ }127]$$.

u16
uint16

16-bit un-signed integers, range:
$$[0\rm{\ to\ }2^{16}-1]$$ or $$[0\rm{\ to\ }65535]$$.

i16
int16

16-bit signed integers, range:
$$[-2^{15}\rm{\ to\ }2^{15}-1]$$ or $$[-32768\rm{\ to\ }32767]$$.

u32
uint32

32-bit un-signed integers, range:
$$[0\rm{\ to\ }2^{32}-1]$$ or $$[0\rm{\ to\ }4294967295]$$.

i32
int32

32-bit signed integers, range:
$$[-2^{31}\rm{\ to\ }2^{31}-1]$$ or $$[-2147483648\rm{\ to\ }2147483647]$$.

u64
uint64

64-bit un-signed integers, range
$$[0\rm{\ to\ }2^{64}-1]$$ or $$[0\rm{\ to\ }18446744073709551615]$$.

i64
int64

64-bit signed integers, range:
$$[-2^{63}\rm{\ to\ }2^{63}-1]$$ or $$[-9223372036854775808\rm{\ to\ }9223372036854775807]$$.

f32
float32

32-bit (single-precision) floating point types. The maximum (minimum is its negative) possible value is $$3.402823\times10^{38}$$. Single-precision floating points can accurately represent a floating point number up to $$\sim7.2$$ significant decimals. Given the heavy noise in astronomical data, this is usually more than sufficient for storing results.

f64
float64

64-bit (double-precision) floating point types. The maximum (minimum is its negative) possible value is $$\sim10^{308}$$. Double-precision floating points can accurately represent a floating point number $$\sim15.9$$ significant decimals. This is usually good for processing (mixing) the data internally, for example a sum of single precision data (and later storing the result as float32).

 Some file formats don’t recognize all types. Some file formats don’t recognize all the types, for example the FITS standard (see Fits) does not define uint64 in binary tables or images. When a type is not acceptable for output into a given file format, the respective Gnuastro program or library will let you know and abort. On the command-line, you can use the Arithmetic program to convert the numerical type of a dataset, in the libraries, you can call gal_data_copy_to_new_type.

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