1TGAMMA(3P) POSIX Programmer's Manual TGAMMA(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 tgamma, tgammaf, tgammal — compute gamma() function
13
15 #include <math.h>
16 double tgamma(double x);
18 float tgammaf(float x);
19 long double tgammal(long double x);
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 Γ(x) where Γ(x) is defined as ∞0∫e^ −tt^
28 x−1dt.
29 An application wishing to check for error situations should set errno
31 to zero and call feclearexcept(FE_ALL_EXCEPT) before calling these
32 functions. On return, if errno is non-zero or fetestexcept(FE_INVALID |
33 FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has
34 occurred.
35
37 Upon successful completion, these functions shall return the gamma of
38 x.
39 If x is a negative integer, a domain error may occur and either a NaN
41 (if supported) or an implementation-defined value shall be returned.
42 On systems that support the IEC 60559 Floating-Point option, a domain
43 error shall occur and a NaN shall be returned.
44 If x is ±0, tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL,
46 ±HUGE_VALF, and ±HUGE_VALL, respectively. On systems that support the
47 IEC 60559 Floating-Point option, a pole error shall occur; otherwise, a
48 pole error may occur.
49 If the correct value would cause overflow, a range error shall occur
51 and tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL,
52 ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same sign as the cor‐
53 rect value of the function.
54 If the correct value would cause underflow, and is not representable, a
56 range error may occur, and tgamma(), tgammaf(), and tgammal() shall
57 return 0.0, or (if IEC 60559 Floating-Point is not supported) an imple‐
58 mentation-defined value no greater in magnitude than DBL_MIN, FLT_MIN,
59 and LDBL_MIN, respectively.
60 If the correct value would cause underflow, and is representable, a
62 range error may occur and the correct value shall be returned.
63 If x is subnormal and 1/x is representable, 1/x should be returned.
65 If x is NaN, a NaN shall be returned.
67 If x is +Inf, x shall be returned.
69 If x is -Inf, a domain error shall occur, and a NaN shall be returned.
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73 These functions shall fail if:
74 Domain Error
76 The value of x is a negative integer, or x is -Inf.
77 If the integer expression (math_errhandling & MATH_ERRNO)
79 is non-zero, then errno shall be set to [EDOM]. If the
80 integer expression (math_errhandling & MATH_ERREXCEPT) is
81 non-zero, then the invalid floating-point exception shall
82 be raised.
83 Pole Error The value of x is zero.
85 If the integer expression (math_errhandling & MATH_ERRNO)
87 is non-zero, then errno shall be set to [ERANGE]. If the
88 integer expression (math_errhandling & MATH_ERREXCEPT) is
89 non-zero, then the divide-by-zero floating-point exception
90 shall be raised.
91 Range Error The value overflows.
93 If the integer expression (math_errhandling & MATH_ERRNO)
95 is non-zero, then errno shall be set to [ERANGE]. If the
96 integer expression (math_errhandling & MATH_ERREXCEPT) is
97 non-zero, then the overflow floating-point exception shall
98 be raised.
99 These functions may fail if:
101 Domain Error
103 The value of x is a negative integer.
104 If the integer expression (math_errhandling & MATH_ERRNO)
106 is non-zero, then errno shall be set to [EDOM]. If the
107 integer expression (math_errhandling & MATH_ERREXCEPT) is
108 non-zero, then the invalid floating-point exception shall
109 be raised.
110 Pole Error The value of x is zero.
112 If the integer expression (math_errhandling & MATH_ERRNO)
114 is non-zero, then errno shall be set to [ERANGE]. If the
115 integer expression (math_errhandling & MATH_ERREXCEPT) is
116 non-zero, then the divide-by-zero floating-point exception
117 shall be raised.
118 Range Error The result underflows.
120 If the integer expression (math_errhandling & MATH_ERRNO)
122 is non-zero, then errno shall be set to [ERANGE]. If the
123 integer expression (math_errhandling & MATH_ERREXCEPT) is
124 non-zero, then the underflow floating-point exception shall
125 be raised.
126 The following sections are informative.
128
130 None.
131
133 On error, the expressions (math_errhandling & MATH_ERRNO) and
134 (math_errhandling & MATH_ERREXCEPT) are independent of each other, but
135 at least one of them must be non-zero.
136
138 This function is named tgamma() in order to avoid conflicts with the
139 historical gamma() and lgamma() functions.
140
142 It is possible that the error response for a negative integer argument
143 may be changed to a pole error and a return value of ±Inf.
144
146 feclearexcept(), fetestexcept(), lgamma()
147 The Base Definitions volume of POSIX.1‐2017, Section 4.20, Treatment of
149 Error Conditions for Mathematical Functions, <math.h>
150
152 Portions of this text are reprinted and reproduced in electronic form
153 from IEEE Std 1003.1-2017, Standard for Information Technology -- Por‐
154 table Operating System Interface (POSIX), The Open Group Base Specifi‐
155 cations Issue 7, 2018 Edition, Copyright (C) 2018 by the Institute of
156 Electrical and Electronics Engineers, Inc and The Open Group. In the
157 event of any discrepancy between this version and the original IEEE and
158 The Open Group Standard, the original IEEE and The Open Group Standard
159 is the referee document. The original Standard can be obtained online
160 at http://www.opengroup.org/unix/online.html .
161 Any typographical or formatting errors that appear in this page are
163 most likely to have been introduced during the conversion of the source
164 files to man page format. To report such errors, see https://www.ker‐
165 nel.org/doc/man-pages/reporting_bugs.html .
166IEEE/The Open Group 2017 TGAMMA(3P)