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(10 citation statements)

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“…First, we should try to implement our verified algorithms on the virtual computer (for our fix-point arithmetic) available at https://bitbucket.org/ ainoneko/lib_verify/src/ and then test these implementations against selected algebraic values for these functions (for example, sin π 6 = 1 2 , sin π 4 = cos π 4 = √ 2 2 , cos π 6 = √ 3 2 , etc.) in lines with test approach suggested and explained in [12,13]; automatically generated test data computed using Taylor expansions in any language that supports unbounded integer arithmetic; for example, a Lispfunction in Fig. 9 computes approximations for cos in unbounded rational arithmetics with accuracy 10 −8 .…”

confidence: 99%

“…First, we should try to implement our verified algorithms on the virtual computer (for our fix-point arithmetic) available at https://bitbucket.org/ ainoneko/lib_verify/src/ and then test these implementations against selected algebraic values for these functions (for example, sin π 6 = 1 2 , sin π 4 = cos π 4 = √ 2 2 , cos π 6 = √ 3 2 , etc.) in lines with test approach suggested and explained in [12,13]; automatically generated test data computed using Taylor expansions in any language that supports unbounded integer arithmetic; for example, a Lispfunction in Fig. 9 computes approximations for cos in unbounded rational arithmetics with accuracy 10 −8 .…”

confidence: 99%

“…It is worth to remark that a need for better specification and validation of standard functions is recognized (in principle) by industrial and academic professional community, as well as the problem of conformance of their implementation with the specification [3,10,11,13,14].…”

confidence: 99%

“…The next two papers [10,11] address formal specification and testing of standard mathematical functions. The last two cited papers [13,14] present formal specification and verification of some standard memory management and input-output functions.…”

confidence: 99%

“…Another test construction method, not using formal specifications, but based on formal investigation of requirements was used to create conformance tests for mathematical functions working with floating-point numbers in POSIX system libraries [12]. The method uses as test data specific floating point values, including numbers having patterns in mantissa (like 0000FFFFAAAA in hexadecimals), boundaries of domains of specific function behavior (such behaviors include monotonicity, sign preservation, well-known asymptotics), and so-called worst cases, numbers, for which correct function calculations requires much more precision than in average.…”

confidence: 99%