The C Standard, 7.12.1 [ISO/IEC 9899:2011], defines three types of errors that relate specifically to math functions in <math.h>. Paragraph 2 states:
A domain error occurs if an input argument is outside the domain over which the mathematical function is defined.
Paragraph 3 states:
A pole error (also known as a singularity or infinitary) occurs if the mathematical function has an exact infinite result as the finite input argument(s) are approached in the limit.
Paragraph 4 states:
A range error occurs if the mathematical result of the function cannot be represented in an object of the specified type, due to extreme magnitude.
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The following table lists the double forms of standard mathematical functions, along with checks that should be performed to ensure a proper input domain, and indicates whether they can also result in range or pole errors, as reported by the C Standard. Both float and long double forms of these function functions also exist but are omitted from the table for brevity. If a function has a specific domain over which it is defined, the programmer must check its input values. The programmer must also check for range errors , where they might occur. The standard math functions not listed in this table, such as fabs(), have no domain restrictions and cannot result in range or pole errors.
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A subnormal number is a nonzero number that does not use all of its precision bits [IEEE 754 2006]. They These numbers can be used to represent values that are closer to 0 than the smallest normal number (one that uses all of its precision bits). However, the asin(), asinh(), atan(), atanh(), and erf() functions may produce range errors, specifically when passed a subnormal number. When evaluated with a subnormal number, these functions can produce an inexact, subnormal value, which is an underflow error. The C Standard, 7.12.1, paragraph 6 [ISO/IEC 9899:2011], defines the following behavior for floating-point underflow:
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