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89 lines
4.1 KiB
Text
89 lines
4.1 KiB
Text
COMMENT(!MOD!zsh/mathfunc
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Standard scientific functions for use in mathematical evaluations.
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!MOD!)
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cindex(functions, mathematical)
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cindex(mathematical functions)
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The tt(zsh/mathfunc) module provides standard
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mathematical functions for use when
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evaluating mathematical formulae. The syntax agrees with normal C and
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FORTRAN conventions, for example,
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example((( f = sin+LPAR()0.3+RPAR() )))
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assigns the sine of 0.3 to the parameter f.
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Most functions take floating point arguments and return a floating point
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value. However, any necessary conversions from or to integer type will be
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performed automatically by the shell. Apart from tt(atan) with a second
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argument and the tt(abs), tt(int) and tt(float) functions, all functions
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behave as noted in the manual page for the corresponding C function,
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except that any arguments out of range for the function in question will be
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detected by the shell and an error reported.
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The following functions take a single floating point argument: tt(acos),
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tt(acosh), tt(asin), tt(asinh), tt(atan), tt(atanh), tt(cbrt), tt(ceil),
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tt(cos), tt(cosh), tt(erf), tt(erfc), tt(exp), tt(expm1), tt(fabs),
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tt(floor), tt(gamma), tt(j0), tt(j1), tt(lgamma), tt(log), tt(log10),
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tt(log1p), tt(logb), tt(sin), tt(sinh), tt(sqrt), tt(tan), tt(tanh),
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tt(y0), tt(y1). The tt(atan) function can optionally take a second
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argument, in which case it behaves like the C function tt(atan2).
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The tt(ilogb) function takes a single floating point argument, but
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returns an integer.
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The function tt(signgam) takes no arguments, and returns an integer, which
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is the C variable of the same name, as described in manref(gamma)(3). Note
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that it is therefore only useful immediately after a call to tt(gamma) or
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tt(lgamma). Note also that `tt(signgam+LPAR()RPAR)' and `tt(signgam)' are
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distinct expressions.
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The following functions take two floating point arguments: tt(copysign),
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tt(fmod), tt(hypot), tt(nextafter).
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The following take an integer first argument and a floating point second
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argument: tt(jn), tt(yn).
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The following take a floating point first argument and an integer second
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argument: tt(ldexp), tt(scalb).
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The function tt(abs) does not convert the type of its single argument; it
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returns the absolute value of either a floating point number or an
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integer. The functions tt(float) and tt(int) convert their arguments into
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a floating point or integer value (by truncation) respectively.
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Note that the C tt(pow) function is available in ordinary math evaluation
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as the `tt(**)' operator and is not provided here.
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The function tt(rand48) is available if your system's mathematical library
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has the function tt(erand48(3)). It returns a pseudo-random floating point
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number between 0 and 1. It takes a single string optional argument.
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If the argument is not present, the random number seed is initialised by
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three calls to the tt(rand+LPAR()3+RPAR()) function --- this produces the
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same random
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numbers as the next three values of tt($RANDOM).
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If the argument is present, it gives the name of a scalar parameter where
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the current random number seed will be stored. On the first call, the
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value must contain at least twelve hexadecimal digits (the remainder of the
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string is ignored), or the seed will be initialised in the same manner as
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for a call to tt(rand48) with no argument. Subsequent calls to
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tt(rand48)LPAR()var(param)RPAR() will then maintain the seed in the
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parameter var(param) as a string of twelve hexadecimal digits, with no base
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signifier. The random number sequences for different parameters are
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completely independent, and are also independent from that used by calls to
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tt(rand48) with no argument.
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For example, consider
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example(print $(( rand48(seed) ))
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print $(( rand48() ))
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print $(( rand48(seed) )))
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Assuming tt($seed) does not exist, it will be initialised by the first
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call. In the second call, the default seed is initialised; note, however,
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that because of the properties of tt(rand+LPAR()RPAR()) there is a
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correlation between
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the seeds used for the two initialisations, so for more secure uses, you
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should generate your own 12-byte seed. The third call returns to the same
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sequence of random numbers used in the first call, unaffected by the
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intervening tt(rand48()).
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