std::fma
Defined in header <cmath>


float fma( float x, float y, float z ); 
(1)  (since C++11) 
double fma( double x, double y, double z ); 
(2)  (since C++11) 
long double fma( long double x, long double y, long double z ); 
(3)  (since C++11) 
Promoted fma( Arithmetic1 x, Arithmetic2 y, Arithmetic3 z ); 
(4)  (since C++11) 
#define FP_FAST_FMA /* implementationdefined */ 
(5)  (since C++11) 
#define FP_FAST_FMAF /* implementationdefined */ 
(6)  (since C++11) 
#define FP_FAST_FMAL /* implementationdefined */ 
(7)  (since C++11) 
FP_FAST_FMAF
, FP_FAST_FMA
, or FP_FAST_FMAL
are defined, the function std::fma
evaluates faster (in addition to being more precise) than the expression x*y+z for float, double, and long double arguments, respectively. If defined, these macros evaluate to integer 1.Parameters
x, y, z    values of floatingpoint or integral types 
Return value
If successful, returns the value of (x*y) + z as if calculated to infinite precision and rounded once to fit the result type (or, alternatively, calculated as a single ternary floatingpoint operation)
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 value (after rounding) is returned.
Error handling
Errors are reported as specified in math_errhandling
If the implementation supports IEEE floatingpoint arithmetic (IEC 60559),
 If x is zero and y is infinite or if x is infinite and y is zero, and z is not a NaN, then NaN is returned and FE_INVALID is raised
 If x is zero and y is infinite or if x is infinite and y is zero, and z is a NaN, then NaN is returned and FE_INVALID may be raised
 If x*y is an exact infinity and z is an infinity with the opposite sign, NaN is returned and FE_INVALID is raised
 If x or y are NaN, NaN is returned
 If z is NaN, and x*y aren't 0*Inf or Inf*0, then NaN is returned (without FE_INVALID)
Notes
This operation is commonly implemented in hardware as fused multiplyadd CPU instruction. If supported by hardware, the appropriate FP_FAST_FMA*
macros are expected to be defined, but many implementations make use of the CPU instruction even when the macros are not defined.
POSIX additionally specifies that the situations specified to return FE_INVALID are domain errors.
Due to its infinite intermediate precision, fma
is a common building block of other correctlyrounded mathematical operations, such as std::sqrt or even the division (where not provided by the CPU, e.g. Itanium)
As with all floatingpoint expressions, the expression (x*y) + z may be compiled as a fused multiplyadd unless the #pragma STDC FP_CONTRACT is off.
Example
#include <iostream> #include <iomanip> #include <cmath> #include <cfenv> #pragma STDC FENV_ACCESS ON int main() { // demo the difference between fma and builtin operators double in = 0.1; std::cout << "0.1 double is " << std::setprecision(23) << in << " (" << std::hexfloat << in << std::defaultfloat << ")\n" << "0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p3), " << "or 1.0 if rounded to double\n"; double expr_result = 0.1 * 10  1; double fma_result = fma(0.1, 10, 1); std::cout << "0.1 * 10  1 = " << expr_result << " : 1 subtracted after intermediate rounding\n" << "fma(0.1, 10, 1) = " << std::setprecision(6) << fma_result << " (" << std::hexfloat << fma_result << std::defaultfloat << ")\n\n"; // fma is used in doubledouble arithmetic double high = 0.1 * 10; double low = fma(0.1, 10, high); std::cout << "in doubledouble arithmetic, 0.1 * 10 is representable as " << high << " + " << low << "\n\n"; // error handling std::feclearexcept(FE_ALL_EXCEPT); std::cout << "fma(+Inf, 10, Inf) = " << std::fma(INFINITY, 10, INFINITY) << '\n'; if(std::fetestexcept(FE_INVALID)) std::cout << " FE_INVALID raised\n"; }
Possible output:
0.1 double is 0.10000000000000000555112 (0x1.999999999999ap4) 0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p3), or 1.0 if rounded to double 0.1 * 10  1 = 0 : 1 subtracted after intermediate rounding fma(0.1, 10, 1) = 5.55112e17 (0x1p54) in doubledouble arithmetic, 0.1 * 10 is representable as 1 + 5.55112e17 fma(+Inf, 10, Inf) = nan FE_INVALID raised
See also
(C++11) 
signed remainder of the division operation (function) 
(C++11) 
signed remainder as well as the three last bits of the division operation (function) 
C documentation for fma
