--- ais/ai-00156.txt 2000/07/13 04:31:29 1.7 +++ ais/ai-00156.txt 2000/08/01 05:39:34 1.8 @@ -1,4 +1,4 @@ -!standard G.1.1 (55) 00-06-19 AI95-00156/06 +!standard G.1.1 (55) 00-07-31 AI95-00156/07 !class binding interpretation 96-09-04 !status Corrigendum 2000 99-05-27 !status WG9 approved 98-06-12 @@ -48,16 +48,15 @@ Here is a proof by example that the given method is incorrect: -Assume that the method described in the standard is correct. Let a -complex number X=0+I. Let an integer n=-1 +Assume that the method described in the standard is correct. Let a +complex number X = 0+I. Let an integer n = -1. Then -X**n=1/i=-i +X**n = 1/i = -i -argument(X)=pi/2 and n is negative. So, according to G.1.1(55), -argument(X**n)=(pi/2)/|-1|=pi/2 +argument(X) = pi/2 and n is negative. So, according to G.1.1(55), +argument(X**n) = (pi/2)/|-1| = pi/2, +but argument(X**n) = argument(-i) = -pi/2 -but, argument(X**n)=argument(-i)=-pi/2 - Obviously, pi/2 is not equal to -pi/2 (even as an angle); i.e. a contradiction has been found. No zero-valued complex numbers were involved (they can mess things up). @@ -70,7 +69,7 @@ Implementations may obtain the result of exponentiation of a complex or pure-imaginary operand by repeated complex multiplication, with arbitrary association of the factors and with a possible final complex reciprocation -(when the exponent is negative). Implementations are also permitted to +(when the exponent is negative). Implementations are also permitted to obtain the result of exponentiation of a complex operand, but not of a pure-imaginary operand, by converting the left operand to a polar representation; exponentiating the modulus by the given exponent; multiplying @@ -89,7 +88,7 @@ pure-imaginary operand, by converting the left operand to a polar representation, exponentiating the modulus by the given exponent, multiplying the argument by the given exponent, and reconverting to a -Cartesian representation. Because of this implementation freedom, no +cartesian representation. Because of this implementation freedom, no accuracy requirement is imposed on complex exponentiation (except for the prescribed results given above, which apply regardless of the implementation method chosen).

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