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_FMAF`

, `FP_FAST_FMA`

, 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.x, y, z | - | floating point values |

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.

Errors are reported as specified in math_errhandling.

If the implementation supports IEEE floating-point 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)

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.

#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

- C11 standard (ISO/IEC 9899:2011):
- 7.12.13.1 The fma functions (p: 258)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- F.10.10.1 The fma functions (p: 530)
- C99 standard (ISO/IEC 9899:1999):
- 7.12.13.1 The fma functions (p: 239)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- F.9.10.1 The fma functions (p: 466)

(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) |

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