fma-fmaf-fmal.md

title	fma, fmaf, fmal
description	API reference for fma, fmaf, and fmal; which multiplies two values together, adds a third value, and then rounds the result, while only losing a small amount of precision due to intermediary rounding.
ms.date	9/1/2020
api_name	fma fmaf fmal _o_fma _o_fmaf _o_fmal
api_location	msvcrt.dll msvcr80.dll msvcr90.dll msvcr100.dll msvcr100_clr0400.dll msvcr110.dll msvcr110_clr0400.dll msvcr120.dll msvcr120_clr0400.dll ucrtbase.dll api-ms-win-crt-math-l1-1-0.dll
api_type	DLLExport
topic_type	apiref
f1_keywords	fma fmaf fmal math/fma math/fmaf math/fmal
helpviewer_keywords	fma function fmaf function fmal function

fma, fmaf, fmal

Multiplies two values together, adds a third value, and then rounds the result, while only losing a small amount of precision due to intermediary rounding.

Syntax

double fma(
   double x,
   double y,
   double z
);

float fma(
   float  x,
   float  y,
   float z
); //C++ only

long double fma(
   long double  x,
   long double  y,
   long double z
); //C++ only

float fmaf(
   float  x,
   float  y,
   float z
);

long double fmal(
   long double  x,
   long double  y,
   long double z
);

#define fma(X, Y, Z) // Requires C11 or later

Parameters

x
The first value to multiply.

y
The second value to multiply.

z
The value to add.

Return value

Returns approximately (x * y) + z. The return value is then rounded using the current rounding format, although in many cases, it returns incorrectly rounded results and thus the value may be inexact by up to half an ulp from the correct value.

Otherwise, may return one of the following values:

Issue	Return
x = INFINITY, y = 0 or x = 0, y = INFINITY	NaN
x or y = exact ± INFINITY, z = INFINITY with the opposite sign	NaN
x or y = NaN	NaN
not (x = 0, y= indefinite) and z = NaN not (x=indefinite, y=0) and z = NaN	NaN
Overflow range error	±HUGE_VAL, ±HUGE_VALF, or ±HUGE_VALL
Underflow range error	correct value, after rounding.

Errors are reported as specified in _matherr.

Remarks

Because C++ allows overloading, you can call overloads of fma that take and return float and long double types. In a C program, unless you're using the <tgmath.h> macro to call this function, fma always takes and returns a double.

If you use the <tgmath.h> fma() macro, the type of the argument determines which version of the function is selected. See Type-generic math for details.

This function computes the value as though it were taken to infinite precision, and then rounds the final result.

By default, this function's global state is scoped to the application. To change this behavior, see Global state in the CRT.

Requirements

Function	C header	C++ header
fma, fmaf, fmal	<math.h>	<cmath>
fma macro	<tgmath.h>

For more compatibility information, see Compatibility.

See also

Alphabetical function reference
remainder, remainderf, remainderl
remquo, remquof, remquol