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expm1, expm1f, expm1l - compute exponential functions

#include <math.h>

double expm1(doublex);

float expm1f(floatx);

long double expm1l(long doublex);

These functions shall compute

e**x-1.0.An application wishing to check for error situations should set

errnoto zero and callfeclearexcept(FE_ALL_EXCEPT) before calling these functions. On return, iferrnois non-zero orfetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW) is non-zero, an error has occurred.

Upon successful completion, these functions return

e**x-1.0.If the correct value would cause overflow, a range error shall occur and

expm1(),expm1f(), andexpm1l() shall return the value of the macro HUGE_VAL, HUGE_VALF, and HUGE_VALL, respectively.If

xis NaN, a NaN shall be returned.If

xis ±0, ±0 shall be returned.If

xis -Inf, -1 shall be returned.If

xis +Inf,xshall be returned.If

xis subnormal, a range error may occur andxshould be returned.

These functions shall fail if:

If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then

Range Error The result overflows. If the integer expression (math_errhandling & MATH_ERRNO) is non-zero, then errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the overflow floating-point exception shall be raised.

These functions may fail if: Range Error The value of xis subnormal.errnoshall be set to [ERANGE]. If the integer expression (math_errhandling & MATH_ERREXCEPT) is non-zero, then the underflow floating-point exception shall be raised.

The following sections are informative.

None.

The value of

expm1(x) may be more accurate thanexp(x)-1.0 for small values ofx.The

expm1() andlog1p() functions are useful for financial calculations of ((1+x)**n-1)/x, namely:

expm1(n* log1p(x))/xwhen

xis very small (for example, when calculating small daily interest rates). These functions also simplify writing accurate inverse hyperbolic functions.For IEEE Std 754-1985

double, 709.8 <ximpliesexpm1(x) has overflowed.On error, the expressions (math_errhandling & MATH_ERRNO) and (math_errhandling & MATH_ERREXCEPT) are independent of each other, but at least one of them must be non-zero.

None.

None.

exp() ,feclearexcept() ,fetestexcept() ,ilogb() ,log1p() , the Base Definitions volume of IEEE Std 1003.1-2001, Section 4.18, Treatment of Error Conditions for Mathematical Functions,<math.h>

Portions of this text are reprinted and reproduced in electronic form from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology -- Portable Operating System Interface (POSIX), The Open Group Base Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of Electrical and Electronics Engineers, Inc and The Open Group. In the event of any discrepancy between this version and the original IEEE and The Open Group Standard, the original IEEE and The Open Group Standard is the referee document. The original Standard can be obtained online at http://www.opengroup.org/unix/online.html .

IEEE/The Open Group |
EXPM1 (P) | 2003 |