zsh: The zsh/mathfunc Module

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### 22.17 The zsh/mathfunc Module

The `zsh/mathfunc` module provides standard mathematical functions for use when evaluating mathematical formulae. The syntax agrees with normal C and FORTRAN conventions, for example,

    (( f = sin(0.3) ))

assigns the sine of 0.3 to the parameter f.

Most functions take floating point arguments and return a floating point value. However, any necessary conversions from or to integer type will be performed automatically by the shell. Apart from `atan` with a second argument and the `abs`, `int` and `float` functions, all functions behave as noted in the manual page for the corresponding C function, except that any arguments out of range for the function in question will be detected by the shell and an error reported.

The following functions take a single floating point argument: `acos`, `acosh`, `asin`, `asinh`, `atan`, `atanh`, `cbrt`, `ceil`, `cos`, `cosh`, `erf`, `erfc`, `exp`, `expm1`, `fabs`, `floor`, `gamma`, `j0`, `j1`, `lgamma`, `log`, `log10`, `log1p`, `logb`, `sin`, `sinh`, `sqrt`, `tan`, `tanh`, `y0`, `y1`. The `atan` function can optionally take a second argument, in which case it behaves like the C function `atan2`. The `ilogb` function takes a single floating point argument, but returns an integer.

The function `signgam` takes no arguments, and returns an integer, which is the C variable of the same name, as described in man page gamma(3). Note that it is therefore only useful immediately after a call to `gamma` or `lgamma`. Note also that ‘`signgam()`’ and ‘`signgam`’ are distinct expressions.

The following functions take two floating point arguments: `copysign`, `fmod`, `hypot`, `nextafter`.

The following take an integer first argument and a floating point second argument: `jn`, `yn`.

The following take a floating point first argument and an integer second argument: `ldexp`, `scalb`.

The function `abs` does not convert the type of its single argument; it returns the absolute value of either a floating point number or an integer. The functions `float` and `int` convert their arguments into a floating point or integer value (by truncation) respectively.

Note that the C `pow` function is available in ordinary math evaluation as the ‘`**`’ operator and is not provided here.

The function `rand48` is available if your system’s mathematical library has the function `erand48(3)`. It returns a pseudo-random floating point number between 0 and 1. It takes a single string optional argument.

If the argument is not present, the random number seed is initialised by three calls to the `rand(3)` function — this produces the same random numbers as the next three values of `$RANDOM`.

If the argument is present, it gives the name of a scalar parameter where the current random number seed will be stored. On the first call, the value must contain at least twelve hexadecimal digits (the remainder of the string is ignored), or the seed will be initialised in the same manner as for a call to `rand48` with no argument. Subsequent calls to `rand48`(param) will then maintain the seed in the parameter param as a string of twelve hexadecimal digits, with no base signifier. The random number sequences for different parameters are completely independent, and are also independent from that used by calls to `rand48` with no argument.

For example, consider

    print $(( rand48(seed) ))
    print $(( rand48() ))
    print $(( rand48(seed) ))

Assuming `$seed` does not exist, it will be initialised by the first call. In the second call, the default seed is initialised; note, however, that because of the properties of `rand()` there is a correlation between the seeds used for the two initialisations, so for more secure uses, you should generate your own 12-byte seed. The third call returns to the same sequence of random numbers used in the first call, unaffected by the intervening `rand48()`.

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