1EXPM1(3P)                  POSIX Programmer's Manual                 EXPM1(3P)
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PROLOG

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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11

NAME

13       expm1, expm1f, expm1l — compute exponential functions
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SYNOPSIS

16       #include <math.h>
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18       double expm1(double x);
19       float expm1f(float x);
20       long double expm1l(long double x);
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DESCRIPTION

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.
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28       These functions shall compute ex−1.0.
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30       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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RETURN VALUE

37       Upon successful completion, these functions return ex−1.0.
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39       If  the  correct  value would cause overflow, a range error shall occur
40       and expm1(), expm1f(), and expm1l() shall return the value of the macro
41       HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.
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43       If x is NaN, a NaN shall be returned.
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45       If x is ±0, ±0 shall be returned.
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47       If x is −Inf, −1 shall be returned.
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49       If x is +Inf, x shall be returned.
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51       If x is subnormal, a range error may occur
52       and x should be returned.
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54       If  x  is not returned, expm1(), expm1f(), and expm1l() shall return an
55       implementation-defined value no  greater  in  magnitude  than  DBL_MIN,
56       FLT_MIN, and LDBL_MIN, respectively.
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ERRORS

59       These functions shall fail if:
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61       Range Error The result overflows.
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63                   If  the  integer expression (math_errhandling & MATH_ERRNO)
64                   is non-zero, then errno shall be set to [ERANGE].   If  the
65                   integer  expression  (math_errhandling & MATH_ERREXCEPT) is
66                   non-zero, then the overflow floating-point exception  shall
67                   be raised.
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69       These functions may fail if:
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71       Range Error The value of x is subnormal.
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73                   If  the  integer expression (math_errhandling & MATH_ERRNO)
74                   is non-zero, then errno shall be set to [ERANGE].   If  the
75                   integer  expression  (math_errhandling & MATH_ERREXCEPT) is
76                   non-zero, then the underflow floating-point exception shall
77                   be raised.
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79       The following sections are informative.
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EXAMPLES

82       None.
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APPLICATION USAGE

85       The  value  of  expm1(x) may be more accurate than exp(x)−1.0 for small
86       values of x.
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88       The expm1() and log1p() functions are useful for financial calculations
89       of ((1+x)n−1)/x, namely:
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91           expm1(n * log1p(x))/x
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93       when  x is very small (for example, when calculating small daily inter‐
94       est rates). These functions  also  simplify  writing  accurate  inverse
95       hyperbolic functions.
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97       For  IEEE Std 754‐1985  double,  709.8  <  x implies expm1(x) has over‐
98       flowed.
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100       On  error,  the  expressions  (math_errhandling   &   MATH_ERRNO)   and
101       (math_errhandling  & MATH_ERREXCEPT) are independent of each other, but
102       at least one of them must be non-zero.
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RATIONALE

105       None.
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FUTURE DIRECTIONS

108       None.
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SEE ALSO

111       exp(), feclearexcept(), fetestexcept(), ilogb(), log1p()
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113       The Base Definitions volume of POSIX.1‐2008, Section 4.19, Treatment of
114       Error Conditions for Mathematical Functions, <math.h>
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117       Portions  of  this text are reprinted and reproduced in electronic form
118       from IEEE Std 1003.1, 2013 Edition, Standard for Information Technology
119       --  Portable  Operating  System  Interface (POSIX), The Open Group Base
120       Specifications Issue 7, Copyright (C) 2013 by the Institute of Electri‐
121       cal  and  Electronics  Engineers,  Inc  and  The  Open Group.  (This is
122       POSIX.1-2008 with the 2013 Technical Corrigendum  1  applied.)  In  the
123       event of any discrepancy between this version and the original IEEE and
124       The Open Group Standard, the original IEEE and The Open Group  Standard
125       is  the  referee document. The original Standard can be obtained online
126       at http://www.unix.org/online.html .
127
128       Any typographical or formatting errors that appear  in  this  page  are
129       most likely to have been introduced during the conversion of the source
130       files to man page format. To report such errors,  see  https://www.ker‐
131       nel.org/doc/man-pages/reporting_bugs.html .
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135IEEE/The Open Group                  2013                            EXPM1(3P)
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