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.
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13 tgamma, tgammaf, tgammal — compute gamma() function
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16 #include <math.h>
17 double tgamma(double x);
19 float tgammaf(float x);
20 long double tgammal(long double x);
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23 The functionality described on this reference page is aligned with the
24 ISO C standard. Any conflict between the requirements described here
25 and the ISO C standard is unintentional. This volume of POSIX.1‐2008
26 defers to the ISO C standard.
27 These functions shall compute the gamma function of x.
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.
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37 Upon successful completion, these functions shall return Gamma(x).
38 If x is a negative integer, a domain error may occur and either a NaN
40 (if supported) or an implementation-defined value shall be returned.
41 On systems that support the IEC 60559 Floating-Point option, a domain
42 error shall occur and a NaN shall be returned.
43 If x is ±0, tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL,
45 ±HUGE_VALF, and ±HUGE_VALL, respectively. On systems that support the
46 IEC 60559 Floating-Point option, a pole error shall occur; otherwise, a
47 pole error may occur.
48 If the correct value would cause overflow, a range error shall occur
50 and tgamma(), tgammaf(), and tgammal() shall return ±HUGE_VAL,
51 ±HUGE_VALF, or ±HUGE_VALL, respectively, with the same sign as the cor‐
52 rect value of the function.
53 If the correct value would cause underflow, and is not representable, a
55 range error may occur, and tgamma(), tgammaf(), and tgammal() shall
56 return 0.0, or (if IEC 60559 Floating-Point is not supported) an imple‐
57 mentation-defined value no greater in magnitude than DBL_MIN, FLT_MIN,
58 and LDBL_MIN, respectively.
59 If the correct value would cause underflow, and is representable, a
61 range error may occur and the correct value shall be returned.
62 If x is NaN, a NaN shall be returned.
64 If x is +Inf, x shall be returned.
66 If x is −Inf, a domain error shall occur, and a NaN shall be returned.
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70 These functions shall fail if:
71 Domain Error
73 The value of x is a negative integer, or x is −Inf.
74 If the integer expression (math_errhandling & MATH_ERRNO)
76 is non-zero, then errno shall be set to [EDOM]. If the
77 integer expression (math_errhandling & MATH_ERREXCEPT) is
78 non-zero, then the invalid floating-point exception shall
79 be raised.
80 Pole Error The value of x is zero.
82 If the integer expression (math_errhandling & MATH_ERRNO)
84 is non-zero, then errno shall be set to [ERANGE]. If the
85 integer expression (math_errhandling & MATH_ERREXCEPT) is
86 non-zero, then the divide-by-zero floating-point exception
87 shall be raised.
88 Range Error The value overflows.
90 If the integer expression (math_errhandling & MATH_ERRNO)
92 is non-zero, then errno shall be set to [ERANGE]. If the
93 integer expression (math_errhandling & MATH_ERREXCEPT) is
94 non-zero, then the overflow floating-point exception shall
95 be raised.
96 These functions may fail if:
98 Domain Error
100 The value of x is a negative integer.
101 If the integer expression (math_errhandling & MATH_ERRNO)
103 is non-zero, then errno shall be set to [EDOM]. If the
104 integer expression (math_errhandling & MATH_ERREXCEPT) is
105 non-zero, then the invalid floating-point exception shall
106 be raised.
107 Pole Error The value of x is zero.
109 If the integer expression (math_errhandling & MATH_ERRNO)
111 is non-zero, then errno shall be set to [ERANGE]. If the
112 integer expression (math_errhandling & MATH_ERREXCEPT) is
113 non-zero, then the divide-by-zero floating-point exception
114 shall be raised.
115 Range Error The result underflows.
117 If the integer expression (math_errhandling & MATH_ERRNO)
119 is non-zero, then errno shall be set to [ERANGE]. If the
120 integer expression (math_errhandling & MATH_ERREXCEPT) is
121 non-zero, then the underflow floating-point exception shall
122 be raised.
123 The following sections are informative.
125
127 None.
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130 For IEEE Std 754‐1985 double, overflow happens when 0 < x < 1/DBL_MAX,
131 and 171.7 < x.
132 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.
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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.1‐2008, Section 4.19, 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, 2013 Edition, Standard for Information Technology
154 -- Portable Operating System Interface (POSIX), The Open Group Base
155 Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri‐
156 cal and Electronics Engineers, Inc and The Open Group. (This is
157 POSIX.1-2008 with the 2013 Technical Corrigendum 1 applied.) In the
158 event of any discrepancy between this version and the original IEEE and
159 The Open Group Standard, the original IEEE and The Open Group Standard
160 is the referee document. The original Standard can be obtained online
161 at http://www.unix.org/online.html .
162 Any typographical or formatting errors that appear in this page are
164 most likely to have been introduced during the conversion of the source
165 files to man page format. To report such errors, see https://www.ker‐
166 nel.org/doc/man-pages/reporting_bugs.html .
167IEEE/The Open Group 2013 TGAMMA(3P)