Arithmetic

   Arithmetic is allowed on vectors and scalars in SM, using the
following operators, where expr is a expression and vector the name
of a vector.

     Nonary (?):

PI              Pi

     Unary:

-expr           Change sign             ABS(expr)       Absolute value
ACOS(expr)      Arccosine               ASIN(expr)      Arcsine
ATAN(expr)      Arctangent              COS(expr)       Cosine
CTYPE()         Return CTYPEs           DIMEN(vector)   Dimension of a vector
EXP(expr)       Exponential             FLOAT(expr)     Convert to float
GAMMA(expr,expr) Incomplete gamma fn    INT(expr)       Integral part
LG(expr)        Log_10                  LN(expr)        Log_e
RANDOM(s_expr)  Random numbers          SIN(expr)       Sine
SORT(expr)      Sort                    SQRT(expr)      Square root
STRING(expr)    Convert to a string     SUM(expr)       Sum_i expr_i
TAN(expr)       Tangent                 VECTOR[expr]    Elements of an array
{ list }	Set vector to list      < list >	Set vector to list
( expr )        Raise precedence

     Binary:

expr + expr          Add                expr - expr     Subtract
expr CONCAT expr     Concatenate        expr * expr     Multiply
expr / expr          Divide             expr ** expr    Exponentiate
expr & expr          Bitwise AND        expr | expr     Bitwise OR
expr << expr         Bitshift left      expr >> expr    Bitshift right
expr % expr          Modulus            ATAN2(expr_y,expr_x) Atan2

   There are also some special operators:

HISTOGRAM(expr:expr)            Construct histogram
IMAGE(expr,expr)                Extract cross section (exprs are coordinates)
IMAGE[expr,expr]                Extract cross section (exprs are indices)
expr1 ? expr2 : expr3           expr2 if expr1 is true, else expr3
DO(s_expr, s_expr)              Implicit DO loop
DO(s_expr, s_expr, s_expr)      Implicit DO loop with increment

   `ATAN2' is the same as C's function of the same name, and is
equivalent to `ATAN(y/x)'. It gives a result in the range `-pi -- pi'
dealing correctly with divisions by zero.

   CTYPE returns a vector of red + 256*green + 256*blue values; CTYPE(STRING)
returns their names.

   GAMMA returns an incomplete Gamma function, so GAMMA(a,infty) = 1.

   RANDOM generates a vector of s_expr random numbers in the
range [0,1]. If you don't specify a seed (using `SET RANDOM') one
will be chosen for you based on the current time.

   DO(0,10,2) generates the vector "0 2 4 6 8 10", and may be used as
part of an expression.

   The expression `VECTOR[expr]' results in a vector of the same
dimension as the `expr', with elements taken from `VECTOR' (i.e.
`VECTOR[INT(expr_i)]'). See, for example, the macro `interp'.  You can
also use `WORD([ expr [ , ... ]])' as part of an expression, where
`WORD' is a macro taking zero or more arguments.

   The precedences are what you'd expect, with `**' being highest,
then `*', `/' and `%', then `+' and `-', and then `CONCAT'.  The
logical operators and bitwise all have even lower precedence than
`CONCAT'; ?: has the lowest priority of all. There is NO defined
precedence for bitwise relative to logical operators --- you should
always use parentheses.

   If you have defined an image file with the IMAGE command,
`IMAGE(expr,expr)' is an expression to extract values from your image.
The two expressions give the x and y values where the image is to be
sampled.  For example `SET x=0,1,.01 SET z=IMAGE(x,0.5)' will
extract a horizontal cross section through an image. IMAGE[expr,expr]
interprets the expressions as (0-based) indices into the image. As
a special case, one or other of them may be '*' meaning, "all values".

   `HISTOGRAM(expr1:expr2)' constructs a histogram from a vector, where the
data is in `expr1', and `expr2' (which must be sorted) gives the location
of the bins.  If the values of `expr2' are equally spaced, the `location' of
the bin means the centre; if they are not, a bin is defined by saying that
points with value (e2[i-1] + e2[i])/2 <= x < (e2[i] + e2[i+1])/2 go into
the ith bin.  Note that values on bin boundaries go into the higher bin.

See `Logical' for the logical operators, `Strings' for string
operators, and `whatis' for finding out if strings are numbers,
words, vectors, or whatever.