NAME

fma, fmaf, fmal — floating-point multiply-add

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);


DESCRIPTION

^[CX] 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.1-2024 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.

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. ^[MX]  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.

ERRORS

These functions shall fail if:

Domain Error

^[MX] 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

^[MX] 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

^[MX] 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.

EXAMPLES

None.

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.

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.

FUTURE DIRECTIONS

None.

SEE ALSO

feclearexcept, fetestexcept

XBD 4.23 Treatment of Error Conditions for Mathematical Functions, <math.h>

CHANGE HISTORY

First released in Issue 6. Derived from the ISO/IEC 9899:1999 standard.

Issue 7

ISO/IEC 9899:1999 standard, Technical Corrigendum 2 #57 (SD5-XSH-ERN-69) is applied, adding a "may fail" range error for non-MX systems.