Updated: 24 October 2020

Page Index

**pamarith**
**-add** | **-subtract** | **-multiply** | **-divide** |
**-difference** |
**-minimum** | **-maximum** | **-mean** |
**-equal** | **-compare** |
**-and** | **-or** | **-nand** | **-nor** | **-xor** |
**-shiftleft** | **-shiftright**
[**-closeness=***N*]
*pamfile1* *pamfile2* ...

All options can be abbreviated to their shortest unique prefix. You may use two hyphens instead of one. You may separate an option name and its value with white space instead of an equals sign.

This program is part of
**Netpbm**(1).

**pamarith** reads two or more PBM, PGM, PPM, or PAM images as input.
It performs the specified binary arithmetic operation on their sample
values and produces an output of a format which is the more general of
the two input formats. The two input images must be of the same width
and height. The arithmetic is performed on each pair of identically
located tuples to generate the identically located tuple of the
output.

For functions that are commutative and associative, **pamarith** applies

the binary function repetitively on as many input images as you supply. For

example, for **-add** , the output is the sum of all the inputs. For

other functions (e.g. **-subtract**), the program fails if you supply

more than two input images. (Before Netpbm 10.93 (December 2020), the

program always failed with more than two input images).

For some other functions, **pamarith** could theoretically compute a

meaningful result for multiple arguments, but it fails nonetheless if you

give more than two input images. **-mean** and **-equal** are in that

category.

Most of what **pamarith** does is not meaningful for visual images. It

works toward Netpbm's secondary purpose of just manipulating arbitrary

matrices of numbers.

For the purpose of the calculation, it assumes any PBM, PGM, or PPM
input image is the equivalent PAM image of tuple type
**BLACKANDWHITE**, **GRAYSCALE**, or **RGB**, respectively,
and if it produces a PBM, PGM, or PPM output, produces the equivalent
of the PAM image which is the result of the calculation.

The first *pamfile* argument identifies the "left"
argument image; the second *pamfile* argument identifies the
"right" one.

If the output is PAM, the tuple type is the same as the tuple type of the left input image.

**pamarith** performs the arithmetic on each pair of identically
located tuples in the two input images.

The arithmetic operation is in all cases fundamentally a function from two
integers to an integer (but see below - the functions are defined in ways that
you can effectively e.g. add real numbers). The operation is performed on two
tuples as follows. The two input images must have the same depth, or one of
them must have depth one. **pamarith** fails if one of these is not the
case.

If they have the same depth, **pamarith** simply carries out the
arithmetic one sample at a time. I.e. if at a particular position the
left input image contains the tuple (s1,s2,...,sN) and the right
input image contains the tuple (t1,t2,...tN), and the function is f,
then the output image contains the tuple
(f(s1,t1),f(s2,t2),...,f(sN,tN)).

If one of the images has depth 1, the arithmetic is performed between the one sample in that image and each of the samples in the other. I.e. if at a particular position the left input image contains the tuple (s) and the right input image contains the tuple (t1,t2,...tN), and the function is f, then the output image contains the tuple (f(s,t1),f(s,t2),...,f(s,tN)).

If you're familiar with the PBM format, you may find **pamarith**'s
operation on PBM images to be nonintuitive. Because in PBM black is
represented as 1 and white as 0, you might be expecting black minus black
to be white.

But the PBM format is irrelevant, because **pamarith** operates on the
numbers found in the PAM equivalent (see above). In a PAM black and white
image, black is 0 and white is 1. So black minus black is black.

The meanings of the samples with respect to the maxval varies according to the function you select.

In PAM images in general, the most usual meaning of a sample (the one that applies when a PAM image represents a visual image), is that it represents a fraction of some maximum. The maxval of the image corresponds to some maximum value (in the case of a visual image, it corresponds to "full intensity."), and a sample value divided by the maxval gives the fraction.

For **pamarith**, this interpretation applies to the regular
arithmetic functions: **-add**, **-subtract**, **-multiply**,
**-divide**,
**-difference**, **-minimum**, **-maximum**, **-mean**,
**-equal**,
and **-compare**. For those, you should think of the arguments and
result as numbers in the range [0,1). For example, if the maxval of
the left argument image is 100 and the maxval of the right argument
image is 200 and the maxval of the output image is 200, and the left
sample value in an **-add** calculation is 50 and the right sample
is 60, the actual calculation is 50/100 + 60/200 = 160/200, and
the output sample value is 160.

For these functions, **pamarith** makes the output image's
maxval the maximum of the two input maxvals, except with
**-equal ** and **-compare**. For **-equal**, the output maxval is
always 1. For **-compare**, it is always 2. (Before Netpbm 10.14
(February 2003), there was no exception for **-compare**; in 10.14, the
exception was just that the maxval was *at least* 2, and sometime
between 10.18 and 10.26 (January 2005), it changed to being exactly 2).

If the result of a calculation falls outside the range [0, 1),
**pamarith** clips it -- i.e. considers it to be zero or 1-.

In many cases, where both your input maxvals are the same, you can
just think of the operation as taking place between the sample values
directly, with no consideration of the maxval except for the clipping.
E.g. an **-add** of sample value 5 to sample value 8 yields sample
value 13.

But with **-multiply**, this doesn't work. Say your two input
images have maxval 255, which means the output image also has maxval
255. Consider a location in the image where the input sample values
are 5 and 10. You might think the multiplicative product of those
would yield 50 in the output. But **pamarith** carries out the
arithmetic on the fractions 5/255 and 10/255. It multiplies those
together and then rescales to the output maxval, giving a sample value
in the output PAM of 50/255 rounded to the nearest integer: 0.

With the bit string operations, the maxval has a whole different
meaning. The operations in question are: **-and**, **-or**,
**-nand**, **-nor**, **-xor**, and **-shiftleft**,
**-shiftright**.

With these, each sample value in one or both input images, and in
the output image, represents a bit string, not a number. The maxval
tells how wide the bit string is. The maxval must be a full binary
count (a power of two minus one, such as 0xff) and the number of ones
in it is the width of the bit string. For the dyadic bit string
operations (that's everything but the shift functions), the maxvals of
the input images must be the same and **pamarith** makes the maxval
of the output image the same.

For the bit shift operations, the output maxval is the same as the left input maxval. The right input image (which contains the shift counts) can have any maxval and the maxval is irrelevant to the interpretation of the samples. The sample value is the actual shift count. But it's still required that no sample value exceed the maxval.

**pamarith** applies only binary functions. If you want to apply a
unary function, e.g. "halve", to a single image, use **pamfunc**.

In addition to the options common to all programs based on libnetpbm
(most notably **-quiet**, see

Common Options
), **pamarith** recognizes the following
command line options:

These options select the function that **pamarith** applies.

You must specify one of these, and cannot specify more than one.

**-add**-
Adds the two values. If the result is larger than maxval, it is
clipped.
**-subtract**-
Subtracts a value in the right input image from a value in the left input
image.
**-minimum**-
Chooses the smaller value of the two.
**-maximum**-
Chooses the larger value of the two.
**-difference**-
Calculates the absolute value of the difference.
**-multiply**-
Does an ordinary arithmetic multiplication, but tends to produce
nonobvious results because of the way
**pamarith**interprets sample values. See Maxval . **-divide**-
Divides a value in the left input image by the value in the right
input image. But like
**-multiply**, it tends to produce nonobvious results. Note that**pamarith**clipping behavior makes this of little use when the left argument (dividend) is greater than the right argument (divisor) -- the result in that case is always the maxval. If the divisor is 0, the result is the maxval.**-divide**was new in Netpbm 10.30 (October 2005). **-equal**-
Produces maxval when the values in the two images are equal and
zero when they are not. Note that the output maxval is always 1 for
**-equal**.If the maxvals of the input images are not identical,

**pamarith**may claim two values are not equal when in fact they are, because of the precision with which it does the arithmetic. However, it will never say A is greater than B if A is less than B.You can make the equality test approximate with the

**-closeness**option. This gives the percentage of maxval by which the samples can differ and still be considered equal.**-equal**was new in Netpbm 10.93 (December 2020). **-compare**-
Produces the value
**0**when the value in the left input image is less than the value in the right input image,**1**when the values are equal, and**2**when the left is greater than the right.If the maxvals of the input images are not identical,

**pamarith**may claim two values are not equal when in fact they are, because of the precision with which it does the arithmetic. However, it will never say A is greater than B if A is less than B.**-compare**was new in Netpbm 10.13 (December 2002). **-and**,**-nand**,**-or**,**-nor**,**-xor**-
These consider the input and output images to contain bit strings;
they compute bitwise logic operations. Note that if the maxval is 1,
you can also look at these as logic operations on boolean input values.
See section
Maxval
for the special meaning of
maxval with respect to bit string operations such as these.
**-shiftleft**,**-shiftright**-
These consider the left input image and output image to contain
bit strings. They compute a bit shift operation, with bits falling
off the left or right end and zeroes shifting in, as opposed to bits
off one end to the other. The right input image sample value is the
number of bit positions to shift.
Note that the maxval (see Maxval ) determines the width of the frame within which you are shifting.

**-closeness**-
This changes the meaning of
**-equal**. It is not valid with any other function. See the description of**-equal**.

**pamarith** replaced **pnmarith** in Netpbm 10.3 (June 2002).

In Netpbm 10.3 through 10.8, though, **pamarith** was not
backward compatible because it required the input images to be of the
same depth, so you could not multiply a PBM by a PPM as is often done
for masking. (It was not intended at the time that **pnmarith**
would be removed from Netpbm -- the plan was just to rewrite it to use
**pamarith**; it was removed by mistake).

But starting with Netpbm 10.9 (September 2002), **pamarith** allows
the images to have different depths as long as one of them has depth 1, and
that made it backward compatible with **pnmarith**.

The original **pnmarith** did not have the **-mean** option.

The **-compare** option was added in Netpbm 10.13 (December 2002).

The bit string operations were added in Netpbm 10.27 (March 2005).

The **-divide** option was added in Netpbm 10.30 (October 2005).

The ability to have more than one input (operand) was added in Netpbm 10.93 (December 2020).

The **-equal** option was added in Netpbm 10.93 (December 2020).