The Open Group Base Specifications Issue 7
IEEE Std 1003.1, 2013 Edition
Copyright © 2001-2013 The IEEE and The Open Group

#### NAME

> tan, tanf, tanl - tangent function

#### SYNOPSIS

> ``#include <math.h>
> double tan(double` x`);
> float tanf(float` x`);
> long double tanl(long double` x`);
> ``

#### DESCRIPTION

> [CX] The functionality described on this reference page is aligned with the ISO C standard. Any conflict between the requirements described here and the ISO C standard is unintentional. This volume of POSIX.1-2008 defers to the ISO C standard.

> These functions shall compute the tangent of their argument x, measured in radians.

> An application wishing to check for error situations should set errno to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, if errno is non-zero or fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

#### RETURN VALUE

> Upon successful completion, these functions shall return the tangent of x.

> If the correct value would cause underflow, [MXX] and is not representable, a range error may occur, and tan(), tanf(), and tanl() shall return [MXX] 0.0, or (if IEC 60559 Floating-Point is not supported) an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

> [MX] If x is NaN, a NaN shall be returned.

> If x is ±0, x shall be returned.

> If x is subnormal, a range error may occur
> [MXX] and x should be returned.

> [MX] If x is not returned, tan(), tanf(), and tanl() shall return an implementation-defined value no greater in magnitude than DBL_MIN, FLT_MIN, and LDBL_MIN, respectively.

> If x is ±Inf, a domain error shall occur, and either a NaN (if supported), or an implementation-defined value shall be returned.

> [MXX] If the correct value would cause underflow, and is representable, a range error may occur and the correct value shall be returned.

> [XSI] If the correct value would cause overflow, a range error shall occur and tan(), tanf(), and tanl() shall return ±HUGE_VAL, ±HUGE_VALF, and ±HUGE_VALL, respectively, with the same sign as the correct value of the function.

#### ERRORS

> These functions shall fail if:

> Domain Error
>   [MX] The value of x is ±Inf.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [EDOM]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid floating-point exception shall be raised.

> Range Error
>   [XSI] The result overflows

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

> These functions may fail if:

> Range Error
>   The result underflows, [MX] or the value of x is subnormal.

>   If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errno shall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

The following sections are informative.

#### EXAMPLES

> ##### Taking the Tangent of a 45-Degree Angle

>     #include <math.h>
>     ...
>     double radians = 45.0 * M_PI / 180;
>     double result;
>     ...
>     result = tan (radians);

#### APPLICATION USAGE

> There are no known floating-point representations such that for a normal argument, tan(x) is either overflow or underflow.

> These functions may lose accuracy when their argument is near a multiple of /2 or is far from 0.0.

> On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

#### RATIONALE

> None.

#### FUTURE DIRECTIONS

> None.

#### SEE ALSO

> atan, feclearexcept, fetestexcept, isnan

> XBD Treatment of Error Conditions for Mathematical Functions, <math.h>

#### CHANGE HISTORY

> First released in Issue 1. Derived from Issue 1 of the SVID.

#### Issue 5

> The last two paragraphs of the DESCRIPTION were included as APPLICATION USAGE notes in previous issues.

#### Issue 6

> The tanf() and tanl() functions are added for alignment with the ISO/IEC 9899:1999 standard.

> The DESCRIPTION, RETURN VALUE, ERRORS, and APPLICATION USAGE sections are revised to align with the ISO/IEC 9899:1999 standard.

> IEC 60559:1989 standard floating-point extensions over the ISO/IEC 9899:1999 standard are marked.

> IEEE Std 1003.1-2001/Cor 1-2002, item XSH/TC1/D6/64 is applied, correcting the last paragraph in the RETURN VALUE section.

#### Issue 7

> POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0635 [68], XSH/TC1-2008/0636 [68], and XSH/TC1-2008/0637 [68] are applied.

End of informative text.

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