1HYPOT(3P)                  POSIX Programmer's Manual                 HYPOT(3P)
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PROLOG

6       This  manual  page is part of the POSIX Programmer's Manual.  The Linux
7       implementation of this interface may differ (consult the  corresponding
8       Linux  manual page for details of Linux behavior), or the interface may
9       not be implemented on Linux.
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NAME

12       hypot, hypotf, hypotl - Euclidean distance function
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SYNOPSIS

15       #include <math.h>
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17       double hypot(double x, double y);
18       float hypotf(float x, float y);
19       long double hypotl(long double x, long double y);
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21

DESCRIPTION

23       These functions shall compute the value of the  square  root  of  x**2+
24       y**2 without undue overflow or underflow.
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26       An  application  wishing to check for error situations should set errno
27       to zero and  call  feclearexcept(FE_ALL_EXCEPT)  before  calling  these
28       functions.   On return, if errno is non-zero or fetestexcept(FE_INVALID
29       | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error  has
30       occurred.
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RETURN VALUE

33       Upon  successful completion, these functions shall return the length of
34       the hypotenuse of a right-angled triangle with sides of length x and y.
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36       If the correct value would cause overflow, a range  error  shall  occur
37       and hypot(), hypotf(), and hypotl() shall return the value of the macro
38       HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.
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40       If x or y is ±Inf, +Inf shall be returned (even if one of  x  or  y  is
41       NaN).
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43       If x or y is NaN, and the other is not ±Inf, a NaN shall be returned.
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45       If  both arguments are subnormal and the correct result is subnormal, a
46       range error may occur and the correct result is returned.
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ERRORS

49       These functions shall fail if:
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51       Range Error
52              The result overflows.
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54       If the integer expression (math_errhandling & MATH_ERRNO) is  non-zero,
55       then  errno  shall  be  set  to  [ERANGE].  If  the  integer expression
56       (math_errhandling & MATH_ERREXCEPT)  is  non-zero,  then  the  overflow
57       floating-point exception shall be raised.
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60       These functions may fail if:
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62       Range Error
63              The result underflows.
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65       If  the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
66       then errno  shall  be  set  to  [ERANGE].  If  the  integer  expression
67       (math_errhandling  &  MATH_ERREXCEPT)  is  non-zero, then the underflow
68       floating-point exception shall be raised.
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71       The following sections are informative.
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EXAMPLES

74       None.
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APPLICATION USAGE

77       hypot(x,y), hypot(y,x), and hypot(x, -y) are equivalent.
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79       hypot(x, ±0) is equivalent to fabs(x).
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81       Underflow only happens when both x and y are subnormal and  the  (inex‐
82       act) result is also subnormal.
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84       These  functions  take precautions against overflow during intermediate
85       steps of the computation.
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87       On  error,  the  expressions  (math_errhandling   &   MATH_ERRNO)   and
88       (math_errhandling  & MATH_ERREXCEPT) are independent of each other, but
89       at least one of them must be non-zero.
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RATIONALE

92       None.
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FUTURE DIRECTIONS

95       None.
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SEE ALSO

98       feclearexcept(), fetestexcept(), isnan(), sqrt(), the Base  Definitions
99       volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Condi‐
100       tions for Mathematical Functions, <math.h>
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103       Portions of this text are reprinted and reproduced in  electronic  form
104       from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
105       -- Portable Operating System Interface (POSIX),  The  Open  Group  Base
106       Specifications  Issue  6,  Copyright  (C) 2001-2003 by the Institute of
107       Electrical and Electronics Engineers, Inc and The Open  Group.  In  the
108       event of any discrepancy between this version and the original IEEE and
109       The Open Group Standard, the original IEEE and The Open Group  Standard
110       is  the  referee document. The original Standard can be obtained online
111       at http://www.opengroup.org/unix/online.html .
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115IEEE/The Open Group                  2003                            HYPOT(3P)
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