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Usually, higher programming languages provide a floating point arithmetic without specifying the accuracy of the operations. In contrast, ADA defines the operations by means of model numbers and rounding (see , ). Nevertheless, this definition is not strong enough to satisfy the modern requirement of maximum accuracy in all spaces of scientific computation (see -). By this we mean that no computer representable element lies between the actual and the computer generated result of an operation. The object of this paper is to specify the new arithmetic in ADA for all usual numerical data types. The new arithmetic is made available in a convenient operator form.