точка умножить-добавить (point multiply-add)
Пролог (Prolog)
This manual page is part of the POSIX Programmer's Manual. The
Linux implementation of this interface may differ (consult the
corresponding Linux manual page for details of Linux behavior),
or the interface may not be implemented on Linux.
Имя (Name)
fma, fmaf, fmal — floating-point multiply-add
Синопсис (Synopsis)
#include <math.h>
double fma(double x, double y, double z);
float fmaf(float x, float y, float z);
long double fmal(long double x, long double y, long double z);
Описание (Description)
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 (x * y) + z, rounded as one ternary
operation: they shall compute the value (as if) to infinite
precision and round once to the result format, according to the
rounding mode characterized by the value of FLT_ROUNDS.
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.
Возвращаемое значение (Return value)
Upon successful completion, these functions shall return
(x * y) + z, rounded as one ternary operation.
If the result overflows or underflows, a range error may occur.
On systems that support the IEC 60559 Floating-Point option, if
the result overflows a range error shall occur.
If x or y are NaN, a NaN shall be returned.
If x multiplied by y is an exact infinity and z is also an
infinity but with the opposite sign, a domain error shall occur,
and either a NaN (if supported), or an implementation-defined
value shall be returned.
If one of x and y is infinite, the other is zero, and z is not a
NaN, a domain error shall occur, and either a NaN (if supported),
or an implementation-defined value shall be returned.
If one of x and y is infinite, the other is zero, and z is a NaN,
a NaN shall be returned and a domain error may occur.
If x*y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be
returned.
Ошибки (Error)
These functions shall fail if:
Domain Error
The value of x*y+z is invalid, or the value x*y is
invalid and z is not a NaN.
If the integer expression (math_errhandling &
MATH_ERRNO) is non-zero, then errno shall be set to
[EDOM]. If the integer expression (math_errhandling
& MATH_ERREXCEPT) is non-zero, then the invalid
floating-point exception shall be raised.
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:
Domain Error
The value x*y is invalid and z is a NaN.
If the integer expression (math_errhandling &
MATH_ERRNO) is non-zero, then errno shall be set to
[EDOM]. If the integer expression (math_errhandling
& MATH_ERREXCEPT) is non-zero, then the invalid
floating-point exception shall be raised.
Range Error 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.
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.
The following sections are informative.
Примеры (Examples)
None.
Использование в приложениях (Application usage)
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.
Обоснование (Rationale)
In many cases, clever use of floating (fused) multiply-add leads
to much improved code; but its unexpected use by the compiler can
undermine carefully written code. The FP_CONTRACT macro can be
used to disallow use of floating multiply-add; and the fma()
function guarantees its use where desired. Many current machines
provide hardware floating multiply-add instructions; software
implementation can be used for others.
Будущие направления (Future directions)
None.
Смотри также (See also)
feclearexcept(3p), fetestexcept(3p)
The Base Definitions volume of POSIX.1‐2017, Section 4.20,
Treatment of Error Conditions for Mathematical Functions,
math.h(0p)
