mirror of
https://github.com/lcn2/calc.git
synced 2025-08-19 01:13:27 +03:00
57 lines
1.6 KiB
Plaintext
57 lines
1.6 KiB
Plaintext
NAME
|
|
power - evaluate a numerical power to specified accuracy
|
|
|
|
SYNOPSIS
|
|
power(x, y, [, eps])
|
|
|
|
TYPES
|
|
x number
|
|
x number
|
|
eps nonzero real, defaults to epsilon()
|
|
|
|
return number
|
|
|
|
DESCRIPTION
|
|
For real or complex x and y, power(x,y,eps) returns a real or
|
|
complex number for which the real and imaginary parts are multiples
|
|
of epsilon differing from the true real and imaginary parts of the
|
|
principal y-th power of x by less than 0.75 * abs(eps), usually by
|
|
less than 0.5 * abs(eps). If the principal y-th power of x is a
|
|
multiple of eps, it will be returned exactly.
|
|
|
|
If y is a large integer but x^y is not large, and accuracy
|
|
represented by eps is all that is required, power(x,y,eps) may be
|
|
considerably faster than appr(x^y, eps, 24), the difference between
|
|
the two results being probably at most abs(eps).
|
|
|
|
EXAMPLE
|
|
> print power(1.2345, 10, 1e-5), power(1.2345, 10, 1e-10)
|
|
8.22074 8.2207405646
|
|
|
|
> print power(1+3i, 3, 1e-5), power(1 + 3i, 2+ 1i, 1e-5)
|
|
-26-18i -2.50593-1.39445i
|
|
|
|
> print power(1+ 1e-30, 1e30, 1e-20)
|
|
2.71828182845904523536
|
|
|
|
> print power(1i, 1i, 1e-20)
|
|
.20787957635076190855
|
|
|
|
> print power(exp(1, 1e-20), pi(1e-20) * 1i/2, 1e-20)
|
|
1i
|
|
|
|
LIMITS
|
|
If x = 0, y in power(x,y,eps) has to have positive real part,
|
|
except in the case of y = 0; power(0, 0, eps) is the multiple of
|
|
eps nearest 1.
|
|
|
|
eps > 0
|
|
|
|
LIBRARY
|
|
void powervalue(VALUE *x, VALUE *y, VALUE *eps, VALUE *result)
|
|
NUMBER *qpower(NUMBER *x, NUMBER *y, NUMBER *eps)
|
|
COMPLEX *cpower(COMPLEX *x, COMPLEX *y, NUMBER *eps)
|
|
|
|
SEE ALSO
|
|
root
|