Manpages - fma.3p

This manual page is part of the POSIX Programmer’s Manual. The Linux implementation of this interface may differ (consult the corresponding Linux manual page for details of Linux behavior), or the interface may not be implemented on Linux.

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

  #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);

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.1‐2017 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.

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. 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.

These functions shall fail if:

Domain Error

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

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

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.

The following sections are informative.

None.

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.

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.

None.

/feclearexcept ( )/, /fetestexcept ( )/

The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of Error Conditions for Mathematical Functions, <math.h>

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1-2017, Standard for Information Technology – Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

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