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28 .\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92
48 .Nd log gamma functions, gamma function
59 .Fn lgamma_r "double x" "int *signgamp"
63 .Fn lgammaf_r "float x" "int *signgamp"
65 .Fn lgammal "long double x"
67 .Fn lgammal_r "long double x" "int *signgamp"
71 .Fn gamma_r "double x" "int *signgamp"
75 .Fn gammaf_r "float x" "int *signgamp"
81 .Fn tgammal "long double x"
88 return ln\||\(*G(x)| where
89 .Bd -unfilled -offset indent
90 \(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x > 0 and
91 \(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1.
98 returns the sign of \(*G(x).
100 .Fn lgamma_r x signgamp ,
101 .Fn lgammaf_r x signgamp ,
103 .Fn lgammal_r x signgamp
104 provide the same functionality as
109 but the caller must provide an integer to store the sign of \(*G(x).
116 functions return \(*G(x), with no effect on
124 are deprecated aliases for
132 Do not use the expression
133 .Dq Li signgam\(**exp(lgamma(x))
134 to compute g := \(*G(x).
135 Instead use a program like this (in C):
136 .Bd -literal -offset indent
137 lg = lgamma(x); g = signgam\(**exp(lg);
144 has returned can signgam be correct.
146 For arguments in its range,
148 is preferred, as for positive arguments
149 it is accurate to within one unit in the last place.
152 will lose up to 10 significant bits.
167 return appropriate values unless an argument is out of range.
168 Overflow will occur for sufficiently large positive values, and
169 non-positive integers.
170 For large non-integer negative values,
174 To conform with newer C/C++ standards, a stub implementation for
176 was committed to the math library, where
180 Thus, the numerical accuracy is at most that of the 53-bit double
181 precision implementation.
193 functions are expected to conform to
204 as a function which computed \(*G(x).
205 This version was used in
209 was originally dedicated to the
212 and that usage was restored by switching to Sun's fdlibm in