## GNU Astronomy Utilities

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#### 10.3.12 Arithmetic on datasets (arithmetic.h)

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 dimensions 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, int 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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