gammal_r(3m)

1lgamma(3M)              Mathematical Library Functions              lgamma(3M)
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NAME

6       lgamma,  lgammaf,  lgammal, lgamma_r, lgammaf_r, lgammal_r, gamma, gam‐
7       maf, gammal, gamma_r, gammaf_r, gammal_r - log gamma function
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SYNOPSIS

10       c99 [ flag... ] file... -lm [ library... ]
11       #include <math.h>
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13       extern int signgam;
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15       double lgamma(double x);
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18       float lgammaf(float x);
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21       long double lgammal(long double x);
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24       double gamma(double x);
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27       float gammaf(float x);
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30       long double gammal(long double x);
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33       double lgamma_r(double x, int *signgamp);
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36       float lgammaf_r(float x, int *signgamp);
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39       long double lgammal_r(long double x, int *signgamp);
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42       double gamma_r(double x, int *signgamp);
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44
45       float gammaf_r(float x, int *signgamp);
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48       long double gammal_r(long double x, int *signgamp);
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50

DESCRIPTION

52       These functions return
53
54       ln||~(x)|
55
56
57       where
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59       |~(x) = integral from 0 to +Infinity of pow(t,x-1)*exp(-t) dt
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61
62       for x > 0 and
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64       |~(x) = n/(|~(1-x)sin(nx))
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66
67       for x < 1.
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70       These functions use the external integer signgam to return the sign  of
71       |~(x)  while  lgamma_r()  and  gamma_r()  use  the user-allocated space
72       addressed by signgamp.
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RETURN VALUES

75       Upon successful completion,  these  functions  return  the  logarithmic
76       gamma of x.
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79       If x is a non-positive integer, a pole error occurs and these functions
80       return +HUGE_VAL, +HUGE_VALF, and +HUGE_VALL, respectively.
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82
83       If x is NaN, a NaN is returned.
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85
86       If x is 1 or 2, +0 shall be returned.
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88
89       If x is ±Inf, +Inf is returned.
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ERRORS

92       These functions will fail if:
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94       Pole Error    The x argument is a negative integer or 0.
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96                     If the integer expression (math_errhandling & MATH_ERREX‐
97                     CEPT) is non-zero, then the divide-by-zero floating-point
98                     exception is raised.
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100

USAGE

102       An application wanting to check for exceptions should  call  feclearex‐
103       cept(FE_ALL_EXCEPT)  before  calling  these  functions.  On  return, if
104       fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is
105       non-zero,  an  exception  has been raised. An application should either
106       examine the return value or check the floating point exception flags to
107       detect exceptions.
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109
110       In    the    case    of   lgamma(),   do   not   use   the   expression
111       signgam*exp(lgamma(x)) to compute
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113       `g  := |~(x)'
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115
116       Instead compute lgamma() first:
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118
119       lg = lgamma(x); g = signgam*exp(lg);
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121
122       only after lgamma() has returned can  signgam  be  correct.  Note  that
123       |~(x)  must overflow when x is large enough, underflow when −x is large
124       enough, and generate a division by 0 exception at the singularities x a
125       nonpositive integer.
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ATTRIBUTES

128       See attributes(5) for descriptions of the following attributes:
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133       ┌─────────────────────────────┬─────────────────────────────┐
134       │      ATTRIBUTE TYPE         │      ATTRIBUTE VALUE        │
135       ├─────────────────────────────┼─────────────────────────────┤
136       │Interface Stability          │See below.                   │
137       ├─────────────────────────────┼─────────────────────────────┤
138       │MT-Level                     │See below.                   │
139       └─────────────────────────────┴─────────────────────────────┘
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141
142       The lgamma(), lgammaf(), lgammal(), and gamma() functions are Standard.
143       The lgamma_r(), lgammaf_r(), lgammal_r(),  gamma_r(),  gammaf_r(),  and
144       gammal_r(), functions are Stable.
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146
147       The  lgamma(),  lgammaf(),  lgammal(),  gamma(), gammaf(), and gammal()
148       functions are Unsafe in  multithreaded  applications.  The  lgamma_r(),
149       lgammaf_r(),  lgammal_r(),  gamma_r(), gammaf_r(), and gammal_r() func‐
150       tions are MT-Safe and should be used instead.
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NOTES

157       When  compiling multithreaded applications, the _REENTRANT flag must be
158       defined on the compile line.  This flag should only be used  in  multi‐
159       threaded applications.
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163SunOS 5.11                        12 Jul 2006                       lgamma(3M)