Underflow is a condition which occurs in a computer or similar device when a mathematical operation results in a number which is smaller than what the device is capable of storing.

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Roundoff errors play a key role in many fields of computational and applied mathematics, mathematical physics and computer science applications. :����kg��߂���)P�J8љ(�s�@i(������� 393 0 obj <>stream Although A*B can appear to be a common subexpression, it is not because the rounding mode is different at the two evaluation sites. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. On the variance of a centered random value roundoff error. Despite these … Roundoff errors arise because digital computers cannot represent some quantities exactly.

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endstream endobj 164 0 obj <>stream The check digit is calculated and added to the barcode, packaging, product code etc at the point of manufacture; A …

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Three final examples: x = x cannot be replaced by the boolean constant true, because it fails when x is a NaN; -x = 0 - x fails for x = +0; and x < y is not the opposite of x y, because NaNs are neither greater than nor less than ordinary floating-point numbers. From Wikibooks, open books for an open world < Numerical MethodsNumerical Methods. %%EOF endstream endobj 165 0 obj <>stream 0 endstream endobj 336 0 obj <>/Metadata 44 0 R/Names 361 0 R/Outlines 82 0 R/PageLayout/OneColumn/Pages 331 0 R/StructTreeRoot 105 0 R/Type/Catalog>> endobj 337 0 obj <>/ExtGState<>/Font<>/Shading<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 338 0 obj <>stream h޴SMo�0��W��0#���P�$���nzz�'q�؍����� �[�)>>Rz�>!h!16G��

We find the means and variances of the roundoff errors for a centered random variable in a given range.

335 0 obj <> endobj We derive two expressions for roundoff error variance, one for a rounded off random value with a zero mean and a given variance under uniform distribution and another for such a value under a normal. M��2 %Y6 AD0�)H����>� ���9�sHP�\�#�38a%��ZB{��R���͈RXO\Q�F����S�֯�毯�ԣQ=:O�0F�E����d08��v��r�ˤ.��?���ɢ�N��U5��Bf���߽�߽?*�f~S���j�_̟�����:��y3l���ϫ�ų�v���vM*��R��%_������!���z>�^�8��f�ܾ�?��E3�}�?�}�_�Û��I}�a! Indeed, any usual computational process in the real numbers domain can lead to errors caused by a finite accuracy rate of its operands and results representation. ���E"�3��iN ��� https://doi.org/10.1016/j.sigpro.2014.06.022. ��e�����`?��/��e�f-z]F�w�eU���cn+ch{��ۻz����֑iz�X��7��5&w�PI8�$4��gYc6�U�MAUn�3j\�DH(�l)���%?��1�YN�i'F+��e��/{s��V{g�L vڬM�Δ��pM#v�le��cK]�7��"�6ķ��f�s2�s2���P�>tj��l�/��u��[����!������Y+� j��������,���t!�Ț��6���^W�.+���u�3F�6+����:�Z���=q�:߷UmG�Q}�b��@���Y!����y��n ��}��wf�7m �m�sA����0;�� C\]��U��}]�8��iC�ۈA���b��ػ8N@�/ �����׉��T�VR:�R�K$ci P"�M�V:Q�4'� W�@�2� M�X685 ^Fd!�R��sutu��������ww�l�D=��)����7$����" Y�W�����4���"w�.+/�D�0X�m4�U�f�ô�Ӹ�����M�K��3�@���l��릝?f5�ğ�qW�kֹp_ᯟLܟCG�|�>6�����C(>HL���Jg���� WK(���{̀�{!�ծ�^q�n���cɬ~���,��p��3�7[�|��W���V������Ct� l�z7ڙ�/}�9� �sH�1��\)�{ʋ��0F��=���s; ���e��o��%����}���d�^1Y��0�^��;{����^�m*�w~EK����f�$NlG��ݸJ� �J�g

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