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When the dataset’s type and other information are already known, any programming language (including C) provides some very good tools for various operations (including arithmetic operations like addition) on the dataset with a simple loop. However, as an author of a program, making assumptions about the type of data, its dimensionality and other basic characteristics will come with a large processing burden.

For example if you always read your data as double precision floating
points for a simple operation like addition with an integer constant, you
will be wasting a lot of CPU and memory when the input dataset is
`int32`

type for example (see Numeric data types). This overhead
may be small for small images, but as you scale your process up and work
with hundred/thousands of files that can be very large, this overhead will
take a significant portion of the processing power. The functions and
macros in this section are designed precisely for this purpose: to allow
you to do any of the defined operations on any dataset with no overhead (in
the native type of the dataset).

Gnuastro’s Arithmetic program uses the functions and macros of this section, so please also have a look at the Arithmetic program and in particular Arithmetic operators for a better description of the operators discussed here.

The main function of this library is `gal_arithmetic`

that is
described below. It can take an arbitrary number of arguments as operands
(depending on the operator, similar to `printf`

). Its first two
arguments are integers specifying the flags and operator. So first we will
review the constants for the recognized flags and operators and discuss
them, then introduce the actual function.

- Macro:
**GAL_ARITHMETIC_INPLACE** - Macro:
**GAL_ARITHMETIC_FREE** - Macro:
**GAL_ARITHMETIC_NUMOK** - Macro:
**GAL_ARITHMETIC_FLAGS_ALL** -
Bit-wise flags to pass onto

`gal_arithmetic`

(see below). To pass multiple flags, use the bitwise-or operator, for example`GAL_ARITHMETIC_INPLACE | GAL_ARITHMETIC_FREE`

.`GAL_ARITHMETIC_FLAGS_ALL`

is a combination of all flags to shorten your code if you want all flags activated. Each flag is described below:`GAL_ARITHMETIC_INPLACE`

Do the operation in-place (in the input dataset, thus modifying it) to improve CPU and memory usage. If this flag is used, after

`gal_arithmetic`

finishes, the input dataset will be modified. It is thus useful if you have no more need for the input after the operation.`GAL_ARITHMETIC_FREE`

Free (all the) input dataset(s) after the operation is done. Hence the inputs are no longer usable after

`gal_arithmetic`

.`GAL_ARITHMETIC_NUMOK`

It is acceptable to use a number and an array together. For example if you want to add all the pixels in an image with a single number you can pass this flag to avoid having to allocate a constant array the size of the image (with all the pixels having the same number).

- Macro:
**GAL_ARITHMETIC_OP_PLUS** - Macro:
**GAL_ARITHMETIC_OP_MINUS** - Macro:
**GAL_ARITHMETIC_OP_MULTIPLY** - Macro:
**GAL_ARITHMETIC_OP_DIVIDE** - Macro:
**GAL_ARITHMETIC_OP_LT** - Macro:
**GAL_ARITHMETIC_OP_LE** - Macro:
**GAL_ARITHMETIC_OP_GT** - Macro:
**GAL_ARITHMETIC_OP_GE** - Macro:
**GAL_ARITHMETIC_OP_EQ** - Macro:
**GAL_ARITHMETIC_OP_NE** - Macro:
**GAL_ARITHMETIC_OP_AND** - Macro:
**GAL_ARITHMETIC_OP_OR** Binary operators (requiring two operands) that accept datasets of any recognized type (see Numeric data types). When

`gal_arithmetic`

is called with any of these operators, it expects two datasets as arguments. For a full description of these operators with the same name, see Arithmetic operators. The first dataset/operand will be put on the left of the operator and the second will be put on the right. The output type of the first four is determined from the input types (largest type of the inputs). The rest (which are all conditional operators) will output a binary`uint8_t`

(or`unsigned char`

) dataset with values of either`0`

(zero) or`1`

(one).

- Macro:
**GAL_ARITHMETIC_OP_NOT** The logical NOT operator. When

`gal_arithmetic`

is called with this operator, it only expects one operand (dataset), since this is a unary operator. The output is`uint8_t`

(or`unsigned char`

) dataset of the same size as the input. Any non-zero element in the input will be`0`

(zero) in the output and any`0`

(zero) will have a value of`1`

(one).

- Macro:
**GAL_ARITHMETIC_OP_ISBLANK** A unary operator with output that is

`1`

for any element in the input that is blank, and`0`

for any non-blank element. When`gal_arithmetic`

is called with this operator, it will only expect one input dataset. The output dataset will have`uint8_t`

(or`unsigned char`

) type.`gal_arithmetic`

with this operator is just a wrapper for the`gal_blank_flag`

function of Library blank values (`blank.h`) and this operator is just included for completeness in arithmetic operations. So in your program, it might be easier to just call`gal_blank_flag`

.

- Macro:
**GAL_ARITHMETIC_OP_WHERE** The three-operand

*where*operator thoroughly discussed in Arithmetic operators. When`gal_arithmetic`

is called with this operator, it will only expect three input datasets: the first (which is the same as the returned dataset) is the array that will be modified. The second is the condition dataset (that must have a`uint8_t`

or`unsigned char`

type), and the third is the value to be used if condition is non-zero.As a result, note that the order of operands when calling

`gal_arithmetic`

with`GAL_ARITHMETIC_OP_WHERE`

is the opposite of running Gnuastro’s Arithmetic program with the`where`

operator (see Arithmetic). This is because the latter uses the reverse-Polish notation which isn’t necessary when calling a function (see Reverse polish notation).

- Macro:
**GAL_ARITHMETIC_OP_SQRT** - Macro:
**GAL_ARITHMETIC_OP_LOG** - Macro:
**GAL_ARITHMETIC_OP_LOG10** Unary operator functions for calculating the square root (\(\sqrt{i}\)), \(ln(i)\) and \(log(i)\) mathematic operators on each element of the input dataset. The output will have the same type as the input, so if your inputs are integer types be careful.

If you want your output to be floating point but your input is an integer type, you can convert the input to a floating point type with

`gal_data_copy_to_new_type`

or`gal_data_copy_to_new_type_free`

(see Copying datasets).

- Macro:
**GAL_ARITHMETIC_OP_MINVAL** - Macro:
**GAL_ARITHMETIC_OP_MAXVAL** - Macro:
**GAL_ARITHMETIC_OP_NUMVAL** - Macro:
**GAL_ARITHMETIC_OP_SUMVAL** - Macro:
**GAL_ARITHMETIC_OP_MEANVAL** - Macro:
**GAL_ARITHMETIC_OP_STDVAL** - Macro:
**GAL_ARITHMETIC_OP_MEDIANVAL** Unary operand statistical operators that will return a single value for datasets of any size. These are just wrappers around similar functions in Statistical operations (

`statistics.h`) and are included in`gal_arithmetic`

only for completeness (to use easily in Arithmetic). In your programs, it will probably be easier if you use those`gal_statistics_`

functions directly.

- Macro:
**GAL_ARITHMETIC_OP_ABS** Unary operand absolute-value operator.

- Macro:
**GAL_ARITHMETIC_OP_MIN** - Macro:
**GAL_ARITHMETIC_OP_MAX** - Macro:
**GAL_ARITHMETIC_OP_NUM** - Macro:
**GAL_ARITHMETIC_OP_SUM** - Macro:
**GAL_ARITHMETIC_OP_MEAN** - Macro:
**GAL_ARITHMETIC_OP_STD** - Macro:
**GAL_ARITHMETIC_OP_MEDIAN** Multi-operand statistical operations. When

`gal_arithmetic`

is called with any of these operators, it will expect only a single operand that will be interpretted as a list of datasets (see List of`gal_data_t`

. The output will be a single dataset with each of its elements replaced by the respective statistical operation on the whole list. See the discussion under the`min`

operator in Arithmetic operators.

- Macro:
**GAL_ARITHMETIC_OP_POW** Binary operator to-power operator. When

`gal_arithmetic`

is called with any of these operators, it will expect two operands: raising the first by the second. This operator only accepts floating point inputs and the output is also floating point.

- Macro:
**GAL_ARITHMETIC_OP_BITAND** - Macro:
**GAL_ARITHMETIC_OP_BITOR** - Macro:
**GAL_ARITHMETIC_OP_BITXOR** - Macro:
**GAL_ARITHMETIC_OP_BITLSH** - Macro:
**GAL_ARITHMETIC_OP_BITRSH** - Macro:
**GAL_ARITHMETIC_OP_MODULO** Binary integer-only operand operators. These operators are only defined on integer data types. When

`gal_arithmetic`

is called with any of these operators, it will expect two operands: the first is put on the left of the operator and the second on the right. The ones starting with`BIT`

are the respective bit-wise operators in C and`MODULO`

is the modulo/remainder operator. For a discussion on these operators, please see Arithmetic operators.The output type is determined from the input types and C’s internal conversions: it is strongly recommended that both inputs have the same type (any integer type), otherwise the bit-wise behavior will be determined by your compiler.

- Macro:
**GAL_ARITHMETIC_OP_BITNOT** The unary bit-wise NOT operator. When

`gal_arithmetic`

is called with any of these operators, it will expect one operand of an integer type and preform the bitwise-NOT operation on it. The output will have the same type as the input.

- Macro:
**GAL_ARITHMETIC_OP_TO_UINT8** - Macro:
**GAL_ARITHMETIC_OP_TO_INT8** - Macro:
**GAL_ARITHMETIC_OP_TO_UINT16** - Macro:
**GAL_ARITHMETIC_OP_TO_INT16** - Macro:
**GAL_ARITHMETIC_OP_TO_UINT32** - Macro:
**GAL_ARITHMETIC_OP_TO_INT32** - Macro:
**GAL_ARITHMETIC_OP_TO_UINT64** - Macro:
**GAL_ARITHMETIC_OP_TO_INT64** - Macro:
**GAL_ARITHMETIC_OP_TO_FLOAT32** - Macro:
**GAL_ARITHMETIC_OP_TO_FLOAT64** Unary type-conversion operators. When

`gal_arithmetic`

is called with any of these operators, it will expect one operand and convert it to the requested type. Note that with these operators,`gal_arithmetic`

is just a wrapper over the`gal_data_copy_to_new_type`

or`gal_data_copy_to_new_type_free`

that are discussed in`Copying datasets`

. It accepts these operators only for completeness and easy usage in Arithmetic. So in your programs, it might be preferable to directly use those functions.

- Function:

*gal_data_t **

**gal_arithmetic***(int operator, unsigned char flags, ...)* Do the arithmetic operation of

`operator`

on the given operands (the third argument and any further argument). Certain special conditions can also be specified with the`flag`

operator. The acceptable values for`operator`

are defined in the macros above.`gal_arithmetic`

is a multi-argument function (like C’s`printf`

). In other words, the number of necessary arguments is not fixed and depends on the value to`operator`

. Here are a few examples showing this variability:out_1=gal_arithmetic(GAL_ARITHMETIC_OP_LOG, 0, in_1); out_2=gal_arithmetic(GAL_ARITHMETIC_OP_PLUS, 0, in_1, in_2); out_3=gal_arithmetic(GAL_ARITHMETIC_OP_WHERE, 0, in_1, in_2, in_3);

The number of necessary operands for each operator (and thus the number of necessary arguments to

`gal_arithmetic`

) are described above under each operator.

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GNU Astronomy Utilities 0.4 manual, September 2017.