67 lines
1.9 KiB
Markdown
67 lines
1.9 KiB
Markdown
[sf.cmath.general]
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# 29 Numerics library [[numerics]](./#numerics)
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## 29.7 Mathematical functions for floating-point types [[c.math]](c.math#sf.cmath.general)
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### 29.7.6 Mathematical special functions [[sf.cmath]](sf.cmath#general)
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#### 29.7.6.1 General [sf.cmath.general]
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[1](#1)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L9947)
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If any argument value
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to any of the functions specified in [[sf.cmath]](sf.cmath "29.7.6 Mathematical special functions") is a NaN (Not a Number),
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the function shall return a NaN
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but it shall not report a domain error[.](#1.sentence-1)
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Otherwise,
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the function shall report a domain error
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for just those argument values
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for which:
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- [(1.1)](#1.1)
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the function description's *Returns*: element
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explicitly specifies a domain
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and those argument values fall
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outside the specified domain,
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or
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- [(1.2)](#1.2)
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the corresponding mathematical function value
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has a nonzero imaginary component,
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or
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- [(1.3)](#1.3)
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the corresponding mathematical function
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is not mathematically defined[.](#1.sentence-2)[253](#footnote-253 "A mathematical function is mathematically defined for a given set of argument values (a) if it is explicitly defined for that set of argument values, or (b) if its limiting value exists and does not depend on the direction of approach.")
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[2](#2)
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[#](http://github.com/Eelis/draft/tree/9adde4bc1c62ec234483e63ea3b70a59724c745a/source/numerics.tex#L9989)
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Unless otherwise specified,
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each function is defined
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for all finite values,
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for negative infinity,
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and for positive infinity[.](#2.sentence-1)
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[253)](#footnote-253)[253)](#footnoteref-253)
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A mathematical function
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is mathematically defined
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for a given set of argument values
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(a)
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if it is explicitly defined
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for that set of argument values,
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or
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(b)
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if its limiting value exists
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and does not depend
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on the direction of approach[.](#footnote-253.sentence-1)
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