Difference between revisions of "cpp/numeric/math/hypot"
From cppreference.com
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(return values, explanation for 4), POSIX requirement on subnormals) |
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@1-3@ Computes the square root of the sum of the squares of {{tt|x}} and {{tt|y}}, without undue overflow or underflow at intermediate stages of the computation. | @1-3@ Computes the square root of the sum of the squares of {{tt|x}} and {{tt|y}}, without undue overflow or underflow at intermediate stages of the computation. | ||
| − | @4@ If any argument has [[cpp/types/is_integral|integral type]], it is cast to {{c|double}}. If any other argument is {{c|long double}}, then the return type is {{c|long double}}, otherwise it is {{c|double}}. | + | @4@ A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has [[cpp/types/is_integral|integral type]], it is cast to {{c|double}}. If any other argument is {{c|long double}}, then the return type is {{c|long double}}, otherwise it is {{c|double}}. |
The value computed by this function is the length of the hypotenuse of a right-angled triangle with sides of length {{tt|x}} and {{tt|y}}, or the distance of the point {{tt|(x,y)}} from the origin {{tt|(0,0)}}, or the magnitude of a complex number {{tt|x+''i''y}} | The value computed by this function is the length of the hypotenuse of a right-angled triangle with sides of length {{tt|x}} and {{tt|y}}, or the distance of the point {{tt|(x,y)}} from the origin {{tt|(0,0)}}, or the magnitude of a complex number {{tt|x+''i''y}} | ||
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===Return value=== | ===Return value=== | ||
| − | + | If no errors occur, the hypotenuse of a right-angled triangle, {{math|{{mrad|x{{su|p=2}}+y{{su|p=2}}}}}}, is returned. | |
| − | === | + | If a range error due to overflow occurs, {{tt|±HUGE_VAL}}, {{tt|±HUGE_VALF}}, or {{tt|±HUGE_VALL}} is returned. |
| + | |||
| + | If a range error due to underflow occurs, the correct result (after rounding) is returned. | ||
| + | |||
| + | ===Error handling=== | ||
Errors are reported as specified in {{lc|math_errhandling}} | Errors are reported as specified in {{lc|math_errhandling}} | ||
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{{c|std::hypot(x, y)}} is equivalent to {{c|std::abs(std::complex<double>(x,y))}} | {{c|std::hypot(x, y)}} is equivalent to {{c|std::abs(std::complex<double>(x,y))}} | ||
| + | [http://pubs.opengroup.org/onlinepubs/9699919799/functions/hypot.html POSIX specifies] that underflow may only occur when both arguments are subnormal and the correct result is also subnormal (this forbids naive implementations) | ||
===Example=== | ===Example=== | ||
{{example | {{example | ||
Revision as of 07:21, 22 May 2014
| Defined in header <cmath>
|
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| float hypot( float x, float y ); |
(1) | (since C++11) |
| double hypot( double x, double y ); |
(2) | (since C++11) |
| long double hypot( long double x, long double y ); |
(3) | (since C++11) |
| Promoted hypot( Arithmetic1 x, Arithmetic2 y ); |
(4) | (since C++11) |
1-3) Computes the square root of the sum of the squares of
x and y, without undue overflow or underflow at intermediate stages of the computation.4) A set of overloads or a function template for all combinations of arguments of arithmetic type not covered by 1-3). If any argument has integral type, it is cast to double. If any other argument is long double, then the return type is long double, otherwise it is double.
The value computed by this function is the length of the hypotenuse of a right-angled triangle with sides of length x and y, or the distance of the point (x,y) from the origin (0,0), or the magnitude of a complex number x+iy
Contents |
Parameters
| x, y | - | values of floating-point or integral types |
Return value
If no errors occur, the hypotenuse of a right-angled triangle, √x2+y2, is returned.
If a range error due to overflow occurs, ±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL is returned.
If a range error due to underflow occurs, the correct result (after rounding) is returned.
Error handling
Errors are reported as specified in math_errhandling
If the implementation supports IEEE floating-point arithmetic (IEC 60559),
- hypot(x, y), hypot(y, x), and hypot(x, -y) are equivalent
- if one of the arguments is ±0,
hypotis equivalent to fabs called with the non-zero argument - if one of the arguments is ±∞,
hypotreturns +∞ even if the other argument is NaN - otherwise, if any of the arguments is NaN, NaN is returned
Notes
Implementations usually guarantee precision of less than 1 ulp (units in the last place): GNU, BSD, Open64
std::hypot(x, y) is equivalent to std::abs(std::complex<double>(x,y))
POSIX specifies that underflow may only occur when both arguments are subnormal and the correct result is also subnormal (this forbids naive implementations)
Example
Run this code
#include <iostream> #include <cmath> #include <cerrno> #include <cfenv> #include <cfloat> #include <cstring> #pragma STDC FENV_ACCESS ON int main() { // typical usage std::cout << "(1,1) cartesian is (" << std::hypot(1,1) << ',' << std::atan2(1,1) << ") polar\n"; // special values std::cout << "hypot(NAN,INFINITY) = " << std::hypot(NAN,INFINITY) << '\n'; // error handling errno = 0; std::feclearexcept(FE_ALL_EXCEPT); std::cout << "hypot(DBL_MAX,DBL_MAX) = " << std::hypot(DBL_MAX,DBL_MAX) << '\n'; if(errno == ERANGE) std::cout << " errno = ERANGE " << std::strerror(errno) << '\n'; if(fetestexcept(FE_OVERFLOW)) std::cout << " FE_OVERFLOW raised\n"; }
Output:
(1,1) cartesian is (1.41421,0.785398) polar
hypot(NAN,INFINITY) = inf
hypot(DBL_MAX,DBL_MAX) = inf
errno = ERANGE Numerical result out of range
FE_OVERFLOW raisedSee also
| (C++11)(C++11) |
computes square root (√x) (function) |
| (C++11)(C++11) |
raises a number to the given power (xy) (function) |
| returns the magnitude of a complex number (function template) | |
| C documentation for hypot
| |
