Legacy Document

log1p

You can use the log1p function to compute the natural logarithm of 1 plus a real number.

double_t log1p (double_t x);

x

Any floating-point number greater than -1.

DESCRIPTION

The log1p function computes the natural logarithm of 1 plus its argument.

$log1p(x)\; =\; log$_e(x+1) = ln(x+1) = y such that $1+x\; =\; 10y$

For small numbers, use the function call log1p(x) instead of the function call log(1 + x). The call log1p(x) produces a more exact result because it avoids the roundoff error that might occur when the expression 1 + x is computed.

EXCEPTIONS

When x is finite and nonzero, the result of $log1p(x)$ might raise one of the following exceptions:

• inexact (for all finite, nonzero values of x > -1)
• invalid (when x is less than -1)
• divide-by-zero (when x is -1)

SPECIAL CASES

Table 10-16 shows the results when the argument to the log1p function is a zero, a NaN, or an Infinity, plus other special cases for the log1p function.

Special cases for the log1p function

Operation	Result	Exceptions raised
$log1p(x)$ for x < -1	NaN	Invalid
$log1p(-1)$	-	Divide-by-zero
$log1p(+0)$	+0	None
$log1p(-0)$	-0	None
$log1p(NaN)$	NaN	None[37]
$log1p(+$ )	+	None
$log1p(-$ )	NaN	Invalid

EXAMPLES

z = log1p(-1.0);  /* z = log(0) = -INFINITY. The divide-by-zero 
                     and inexact exceptions are raised. */
z = log1p(0.0);   /* z = log(1) = 0.0 because e0 = 1. */
z = log1p(-2.0);  /* z = log(-1) = NAN because logarithms of 
                     negative numbers are not allowed. The 
                     invalid exception is raised. */

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