1FMA(P) POSIX Programmer's Manual FMA(P)
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6 fma, fmaf, fmal - floating-point multiply-add
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9 #include <math.h>
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11 double fma(double x, double y, double z);
12 float fmaf(float x, float y, float z);
13 long double fmal(long double x, long double y, long double z);
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17 These functions shall compute (x * y) + z, rounded as one ternary oper‐
18 ation: they shall compute the value (as if) to infinite precision and
19 round once to the result format, according to the rounding mode charac‐
20 terized by the value of FLT_ROUNDS.
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22 An application wishing to check for error situations should set errno
23 to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
24 functions. On return, if errno is non-zero or fetestexcept(FE_INVALID
25 | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
26 occurred.
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29 Upon successful completion, these functions shall return (x * y) + z,
30 rounded as one ternary operation.
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32 If x or y are NaN, a NaN shall be returned.
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34 If x multiplied by y is an exact infinity and z is also an infinity but
35 with the opposite sign, a domain error shall occur, and either a NaN
36 (if supported), or an implementation-defined value shall be returned.
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38 If one of x and y is infinite, the other is zero, and z is not a NaN, a
39 domain error shall occur, and either a NaN (if supported), or an imple‐
40 mentation-defined value shall be returned.
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42 If one of x and y is infinite, the other is zero, and z is a NaN, a NaN
43 shall be returned and a domain error may occur.
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45 If x* y is not 0*Inf nor Inf*0 and z is a NaN, a NaN shall be returned.
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48 These functions shall fail if:
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50 Domain Error
51 The value of x* y+ z is invalid, or the value x* y is invalid
52 and z is not a NaN.
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54 If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
55 then errno shall be set to [EDOM]. If the integer expression
56 (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid
57 floating-point exception shall be raised.
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59 Range Error
60 The result overflows.
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62 If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
63 then errno shall be set to [ERANGE]. If the integer expression
64 (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow
65 floating-point exception shall be raised.
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68 These functions may fail if:
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70 Domain Error
71 The value x* y is invalid and z is a NaN.
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73 If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
74 then errno shall be set to [EDOM]. If the integer expression
75 (math_errhandling & MATH_ERREXCEPT) is non-zero, then the invalid
76 floating-point exception shall be raised.
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78 Range Error
79 The result underflows.
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81 If the integer expression (math_errhandling & MATH_ERRNO) is non-zero,
82 then errno shall be set to [ERANGE]. If the integer expression
83 (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow
84 floating-point exception shall be raised.
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87 The following sections are informative.
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90 None.
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93 On error, the expressions (math_errhandling & MATH_ERRNO) and
94 (math_errhandling & MATH_ERREXCEPT) are independent of each other, but
95 at least one of them must be non-zero.
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98 In many cases, clever use of floating (fused) multiply-add leads to
99 much improved code; but its unexpected use by the compiler can under‐
100 mine carefully written code. The FP_CONTRACT macro can be used to dis‐
101 allow use of floating multiply-add; and the fma() function guarantees
102 its use where desired. Many current machines provide hardware floating
103 multiply-add instructions; software implementation can be used for oth‐
104 ers.
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107 None.
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110 feclearexcept() , fetestexcept() , the Base Definitions volume of
111 IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for
112 Mathematical Functions, <math.h>
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115 Portions of this text are reprinted and reproduced in electronic form
116 from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology
117 -- Portable Operating System Interface (POSIX), The Open Group Base
118 Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of
119 Electrical and Electronics Engineers, Inc and The Open Group. In the
120 event of any discrepancy between this version and the original IEEE and
121 The Open Group Standard, the original IEEE and The Open Group Standard
122 is the referee document. The original Standard can be obtained online
123 at http://www.opengroup.org/unix/online.html .
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127IEEE/The Open Group 2003 FMA(P)