Numerical examples 


A second order equationThe roots of the following second order equation are computed: 0.3x^{2}  2.1x + 3.675 = 0.The exact values are: Discriminant d=0, x1=x2=3.5 Without CADNA:d = 3.8146972E06There are two conjugate complex roots: z1 = 0.3499999E+01 + i * 0.9765625E03 z2 = 0.3499999E+01 + i * .9765625E03 With CADNA:CADNA software  University P. et M. Curie  LIP6 Selfvalidation detection: ON Mathematical instabilities detection : ON Branching instabilities detection : ON Intrinsic instabilities detection : ON Cancellation instabilities detection : ON  d = @.0 Discriminant is zero. The double solution is 0.349999E+01  CADNA software  University P. et M. Curie  LIP6 There is 1 numerical instability 0 UNSTABLE DIVISION(S) 0 UNSTABLE POWER FUNCTION(S) 0 UNSTABLE MULTIPLICATION(S) 0 UNSTABLE BRANCHING(S) 0 UNSTABLE MATHEMATICAL FUNCTION(S) 0 UNSTABLE INTRINSIC FUNCTION(S) 1 UNSTABLE CANCELLATION(S) CommentsThe standard floating point arithmetic cannot detect that d=0. The wrong branching is performed and the result is false.The CADNA software takes the accuracy of operands into
account in the order relations or in the equality relation and,
therefore, the good branching is performed and the
exact result is obtained.
