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

#### NAME

> hypot, hypotf, hypotl - Euclidean distance function

#### SYNOPSIS

> ``#include <math.h>
> double hypot(double` x`, double` y`);
> float hypotf(float` x`, float` y`);
> long double hypotl(long double` x`, long double` y`);
> ``

#### 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 value of the square root of x 2+ y 2 without undue overflow or underflow.

> 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 length of the hypotenuse of a right-angled triangle with sides of length x and y.

> If the correct value would cause overflow, a range error shall occur and hypot(), hypotf(), and hypotl() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.

> [MX] If x or y is ±Inf, +Inf shall be returned (even if one of x or y is NaN).

> If x or y is NaN, and the other is not ±Inf, a NaN shall be returned.

> [MXX] If both arguments are subnormal and the correct result is subnormal, a range error may occur and the correct result shall be returned.

#### ERRORS

> These functions shall fail if:

> Range Error
>   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
>   [MX] The result underflows.

>   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

> See the EXAMPLES section in atan2().

#### APPLICATION USAGE

> hypot(x,y), hypot(y,x), and hypot(x, -y) are equivalent.

> hypot(x, ±0) is equivalent to fabs(x).

> Underflow only happens when both x and y are subnormal and the (inexact) result is also subnormal.

> These functions take precautions against overflow during intermediate steps of the computation.

> 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

> atan2, feclearexcept, fetestexcept, isnan, sqrt

> 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 DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.

#### Issue 6

> The hypot() function is no longer marked as an extension.

> The hypotf() and hypotl() 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 2-2004, item XSH/TC2/D6/49 is applied, updating the EXAMPLES section.

#### Issue 7

> POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0273 [68] is applied.

End of informative text.

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