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