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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 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.

Function	Domain	Range	Pole
`acos(x)`	`-1 <= x && x <= 1`	No	No
`asin(x)`	`-1 <= x && x <= 1`	Yes	No
`atan(x)`	None	Yes	No
`atan2(y, x)`	`x != 0 && y != 0`	No	No
`acosh(x)`	`x >= 1`	Yes	No
`asinh(x)`	None	Yes	No
`atanh(x)`	`-1 < x && x < 1`	Yes	Yes
`cosh(x)`, `sinh(x)`	None	Yes	No
`exp(x)`, `exp2(x)`, `expm1(x)`	None	Yes	No
`ldexp(x, exp)`	None	Yes	No
`log(x)`, `log10(x)`, `log2(x)`	`x >= 0`	No	Yes
`log1p(x)`	`x >= -1`	No	Yes
`ilogb(x)`	`x != 0 && !isinf(x) && !isnan(x)`	Yes	No
`logb(x)`	`x != 0`	Yes	Yes
`scalbn(x, n)`, `scalbln(x, n)`	None	Yes	No
`hypot(x, y)`	None	Yes	No
`pow(x,y)`	`x > 0 \|\| (x == 0 && y > 0) \|\|` (`x < 0 && y` is an integer)	Yes	Yes
`sqrt(x)`	`x >= 0`	No	No
`erf(x)`	None	Yes	No
`erfc(x)`	None	Yes	No
`lgamma(x)`, `tgamma(x)`	`x != 0 &&` `!` (`x < 0 && x` is an integer)	Yes	Yes
`lrint(x)`, `lround(x)`	None	Yes	No
`fmod(x, y)`, `remainder(x, y)`, `remquo(x, y, quo)`	`y != 0`	Yes	No
`nextafter(x, y)`, `nexttoward(x, y)`	None	Yes	No
`fdim(x,y)`	None	Yes	No
`fma(x,y,z)`	None	Yes	No

Domain and Pole Checking

The most reliable way to handle domain and pole errors is to prevent them by checking arguments beforehand, as in the following exemplar:

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Failure to prevent or detect domain and range errors in math functions may cause unexpected results.

Rule	Severity	Likelihood	Remediation Cost	Priority	Level
FLP32-C	Medium	Probable	Medium	P8	L2

Automated Detection

Tool

Version

Checker

Description

Parasoft C/C++test

Include Page

	Parasoft_V
	Parasoft_V

BD-API-VALPARAM

Implemented

Polyspace Bug Finder

R2016a

Invalid use of standard library floating point routine

Wrong arguments to standard library function

PRQA QA-C

9.1

5025

Related Vulnerabilities

Search for vulnerabilities resulting from the violation of this rule on the CERT website.

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Key here (explains table format and definitions)

Taxonomy	Taxonomy item	Relationship
CERT C Secure Coding Standard	FLP03-C. Detect and handle floating-point errors	Prior to 2018-01-12: CERT: Unspecified Relationship
CWE 2.11	CWE-682, Incorrect Calculation	2017-07-07: CERT: Rule subset of CWE

CERT-CWE Mapping Notes

Key here for mapping notes

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Incorrect calculations that do not involve floating-point range errors

Bibliography

[ISO/IEC 9899:2011]	7.3.2, "Conventions" 7.12.1, "Treatment of Error Conditions" F.10.7, "Remainder Functions"
[IEEE 754 2006 ]


[Plum 1985]	Rule 2-2
[Plum 1989]	Topic 2.10, "conv—Conversions and Overflow"
[UNIX 1992]	System V Interface Definition (SVID3)

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Key

Domain and Pole Checking

Automated Detection

Related Vulnerabilities

CERT-CWE Mapping Notes

Bibliography