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fma, fmaf, fmal

Defined in header <math.h> 
float       fmaf( float x, float y, float z );
-		 (1) (since C99) 
double      fma( double x, double y, double z );
-		 (2) (since C99) 
long double fmal( long double x, long double y, long double z );
-		 (3) (since C99) 
#define FP_FAST_FMA  /* implementation-defined */
-		 (4) (since C99) 
#define FP_FAST_FMAF /* implementation-defined */
-		 (5) (since C99) 
#define FP_FAST_FMAL /* implementation-defined */
-		 (6) (since C99)
Defined in header <tgmath.h> 
#define fma( x, y, z )
-		 (7) (since C99)
-1-3) Computes (x*y) + z as if to infinite precision and rounded only once to fit the result type.
-4-6) If the macro constants FP_FAST_FMA, FP_FAST_FMAF, or FP_FAST_FMAL are defined, the corresponding function fmaf, fma, or fmal 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.
-7) Type-generic macro: If any argument has type long double, fmal is called. Otherwise, if any argument has integer type or has type double, fma is called. Otherwise, fmaf is called.

Parameters

- -
x, y, z - floating point values

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 floating-point 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 floating-point arithmetic (IEC 60559),

-

Notes

This operation is commonly implemented in hardware as fused multiply-add 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 specifies that the situation where the value x*y is invalid and z is a NaN is a domain error.

-

Due to its infinite intermediate precision, fma is a common building block of other correctly-rounded mathematical operations, such as sqrt or even the division (where not provided by the CPU, e.g. Itanium).

-

As with all floating-point expressions, the expression (x*y) + z may be compiled as a fused mutiply-add unless the #pragma STDC FP_CONTRACT is off.

-

Example

#include <stdio.h>
-#include <math.h>
-#include <float.h>
-#include <fenv.h>
-#pragma STDC FENV_ACCESS ON
-int main(void)
-{
-    // demo the difference between fma and built-in operators
-    double in = 0.1;
-    printf("0.1 double is %.23f (%a)\n", in, in);
-    printf("0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3),"
-           " or 1.0 if rounded to double\n");
-    double expr_result = 0.1 * 10 - 1;
-    printf("0.1 * 10 - 1 = %g : 1 subtracted after "
-           "intermediate rounding to 1.0\n", expr_result);
-    double fma_result = fma(0.1, 10, -1);
-    printf("fma(0.1, 10, -1) = %g (%a)\n", fma_result, fma_result);
- 
-    // fma use in double-double arithmetic
-    printf("\nin double-double arithmetic, 0.1 * 10 is representable as ");
-    double high = 0.1 * 10;
-    double low = fma(0.1, 10, -high);
-    printf("%g + %g\n\n", high, low);
- 
-    //error handling
-    feclearexcept(FE_ALL_EXCEPT);
-    printf("fma(+Inf, 10, -Inf) = %f\n", fma(INFINITY, 10, -INFINITY));
-    if(fetestexcept(FE_INVALID)) puts("    FE_INVALID raised");
-}

Possible output:

-
0.1 double is 0.10000000000000000555112 (0x1.999999999999ap-4)
-0.1*10 is 1.0000000000000000555112 (0x8.0000000000002p-3), or 1.0 if rounded to double
-0.1 * 10 - 1 = 0 : 1 subtracted after intermediate rounding to 1.0
-fma(0.1, 10, -1) = 5.55112e-17 (0x1p-54)
- 
-in double-double arithmetic, 0.1 * 10 is representable as 1 + 5.55112e-17
- 
-fma(+Inf, 10, -Inf) = -nan
-    FE_INVALID raised

References

See also

- - -
-
(C99)(C99)(C99)
 computes signed remainder of the floating-point division operation
(function)
-
(C99)(C99)(C99)
 computes signed remainder as well as the three last bits of the division operation
(function)
C++ documentation for fma
-

- © cppreference.com
Licensed under the Creative Commons Attribution-ShareAlike Unported License v3.0.
- https://en.cppreference.com/w/c/numeric/math/fma -

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