Legacy Document

expm1

You can use the expm1 function to raise e to some power and subtract 1.

double_t expm1 (double_t x);

x

Any floating-point number.

DESCRIPTION

The expm1 function returns the natural exponential decreased by 1.

$expm1(x)\; =\; ex+-1$

For small numbers, use the function call expm1(x) instead of the expression

exp(x) - 1

The call expm1(x) produces a more exact result because it avoids the roundoff error that might occur when the expression is computed.

EXCEPTIONS

When x is finite and nonzero, the result of $expm1(x)$ might raise the following exceptions:

• inexact (for all finite, nonzero values of x)
• overflow (if the result is outside the range of the data type)
• underflow (if the result is inexact and must be represented as a denormalized number or 0)

SPECIAL CASES

Table 10-9 shows the results when the argument to the expm1 function is a zero, a NaN, or an Infinity.

Special cases for the expm1 function

Operation	Result	Exceptions raised
$expm1(+0)$	+0	None
$expm1(-0)$	-0	None
$expm1(NaN)$	NaN	None[30]
$expm1(+$ )	+	None
$expm1(-$ )	-1	None

EXAMPLES

z = expm1(-2.1);     /* z = e-2.1 - 1 = -0.877544. The inexact
                        exception is raised. */
z = expm1(6);        /* z = e6 - 1 = 402.429. The inexact 
                        exception is raised. */

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[30] If the NaN is a signaling NaN, the invalid exception is raised.