#include <math.h> double hypot(double x, double y); float hypotf(float x, float y); long double hypotl(long double x, long double y);
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.
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.
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.
If both arguments are subnormal and the correct result is subnormal, a range error may occur and the correct result shall be returned.
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:
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.
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.
The Base Definitions volume of POSIX.1-2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h>
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