1FMA(3P) POSIX Programmer's Manual FMA(3P)
2
6 This manual page is part of the POSIX Programmer's Manual. The Linux
7 implementation of this interface may differ (consult the corresponding
8 Linux manual page for details of Linux behavior), or the interface may
9 not be implemented on Linux.
10
12 fma, fmaf, fmal — floating-point multiply-add
13
15 #include <math.h>
16 double fma(double x, double y, double z);
18 float fmaf(float x, float y, float z);
19 long double fmal(long double x, long double y, long double z);
20
22 The functionality described on this reference page is aligned with the
23 ISO C standard. Any conflict between the requirements described here
24 and the ISO C standard is unintentional. This volume of POSIX.1‐2017
25 defers to the ISO C standard.
26 These functions shall compute (x * y) + z, rounded as one ternary oper‐
28 ation: they shall compute the value (as if) to infinite precision and
29 round once to the result format, according to the rounding mode charac‐
30 terized by the value of FLT_ROUNDS.
31 An application wishing to check for error situations should set errno
33 to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
34 functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
35 FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
36 occurred.
37
39 Upon successful completion, these functions shall return (x * y) + z,
40 rounded as one ternary operation.
41 If the result overflows or underflows, a range error may occur. On
43 systems that support the IEC 60559 Floating-Point option, if the result
44 overflows a range error shall occur.
45 If x or y are NaN, a NaN shall be returned.
47 If x multiplied by y is an exact infinity and z is also an infinity but
49 with the opposite sign, a domain error shall occur, and either a NaN
50 (if supported), or an implementation-defined value shall be returned.
51 If one of x and y is infinite, the other is zero, and z is not a NaN, a
53 domain error shall occur, and either a NaN (if supported), or an imple‐
54 mentation-defined value shall be returned.
55 If one of x and y is infinite, the other is zero, and z is a NaN, a NaN
57 shall be returned and a domain error may occur.
58 If x*y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned.
60
62 These functions shall fail if:
63 Domain Error
65 The value of x*y+z is invalid, or the value x*y is invalid
66 and z is not a NaN.
67 If the integer expression (math_errhandling & MATH_ERRNO)
69 is non-zero, then errno shall be set to [EDOM]. If the
70 integer expression (math_errhandling & MATH_ERREXCEPT) is
71 non-zero, then the invalid floating-point exception shall
72 be raised.
73 Range Error The result overflows.
75 If the integer expression (math_errhandling & MATH_ERRNO)
77 is non-zero, then errno shall be set to [ERANGE]. If the
78 integer expression (math_errhandling & MATH_ERREXCEPT) is
79 non-zero, then the overflow floating-point exception shall
80 be raised.
81 These functions may fail if:
83 Domain Error
85 The value x*y is invalid and z is a NaN.
86 If the integer expression (math_errhandling & MATH_ERRNO)
88 is non-zero, then errno shall be set to [EDOM]. If the
89 integer expression (math_errhandling & MATH_ERREXCEPT) is
90 non-zero, then the invalid floating-point exception shall
91 be raised.
92 Range Error The result underflows.
94 If the integer expression (math_errhandling & MATH_ERRNO)
96 is non-zero, then errno shall be set to [ERANGE]. If the
97 integer expression (math_errhandling & MATH_ERREXCEPT) is
98 non-zero, then the underflow floating-point exception shall
99 be raised.
100 Range Error The result overflows.
102 If the integer expression (math_errhandling & MATH_ERRNO)
104 is non-zero, then errno shall be set to [ERANGE]. If the
105 integer expression (math_errhandling & MATH_ERREXCEPT) is
106 non-zero, then the overflow floating-point exception shall
107 be raised.
108 The following sections are informative.
110
112 None.
113
115 On error, the expressions (math_errhandling & MATH_ERRNO) and
116 (math_errhandling & MATH_ERREXCEPT) are independent of each other, but
117 at least one of them must be non-zero.
118
120 In many cases, clever use of floating (fused) multiply-add leads to
121 much improved code; but its unexpected use by the compiler can under‐
122 mine carefully written code. The FP_CONTRACT macro can be used to dis‐
123 allow use of floating multiply-add; and the fma() function guarantees
124 its use where desired. Many current machines provide hardware floating
125 multiply-add instructions; software implementation can be used for oth‐
126 ers.
127
129 None.
130
132 feclearexcept(), fetestexcept()
133 The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of
135 Error Conditions for Mathematical Functions, <math.h>
136
138 Portions of this text are reprinted and reproduced in electronic form
139 from IEEE Std 1003.1-2017, Standard for Information Technology -- Por‐
140 table Operating System Interface (POSIX), The Open Group Base Specifi‐
141 cations Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of
142 Electrical and Electronics Engineers, Inc and The Open Group. In the
143 event of any discrepancy between this version and the original IEEE and
144 The Open Group Standard, the original IEEE and The Open Group Standard
145 is the referee document. The original Standard can be obtained online
146 at http://www.opengroup.org/unix/online.html .
147 Any typographical or formatting errors that appear in this page are
149 most likely to have been introduced during the conversion of the source
150 files to man page format. To report such errors, see https://www.ker‐
151 nel.org/doc/man-pages/reporting_bugs.html .
152IEEE/The Open Group 2017 FMA(3P)