hypot, hypotf, hypotl - Euclidean distance function
double hypot(double x, double y);
float hypotf(float x, float y);
long double hypotl(long double x, long double y);
[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.1-2017 defers to the ISO C standard.
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] 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.
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.
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.
The DESCRIPTION is updated to indicate how an application should check for an error. This text was previously published in the APPLICATION USAGE section.
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.
POSIX.1-2008, Technical Corrigendum 1, XSH/TC1-2008/0273  is applied.
return to top of page