The Open Group Base Specifications Issue 7, 2018 edition
IEEE Std 1003.1-2017 (Revision of IEEE Std 1003.1-2008)
Copyright © 2001-2018 IEEE and The Open Group


hypot, hypotf, hypotl - Euclidean distance function


#include <math.h>

double hypot(double
x, double y);
float hypotf(float
x, float y);
long double hypotl(long double
x, long double y);


[CX] [Option Start] 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.1-2017 defers to the ISO C standard. [Option End]

These functions shall compute the value of the square root of x2+ y2 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.


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] [Option Start] 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. [Option End]

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


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] [Option Start] 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. [Option End]

The following sections are informative.


See the EXAMPLES section in atan2().


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.






atan2, feclearexcept, fetestexcept, isnan, sqrt

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


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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