To: J3 J3/23-105
From: Van Snyder
Subject: Two intrinsic functions EXPM1 and LOGP1
Date: 2023-January-12
13.7.58a EXPM1 (X)
Description. Exponential function of X, less 1.
Class. Elemental function.
Argument. X shall be of type real.
Result characteristics. Same as X.
Result value. The result has a value equal to a processor dependent
approximation to $e^{X}-1$.
Example. EXPM1(1.0E-11) has the value 1.0E-11 (approximately).
NOTE 16.xxx
It is recommended that the result be calculated using a method that
does not incur loss of precision by forming $e^X$ and then
subtracting 1.
Note to J3: EXP(1.0E-11) has the value 1.0 + 1.0E-11 to first order.
This is 1.0 in IEEE single precision, so EXP(1.0E-11)-1.0 has the
value 0.0 in IEEE single precision, not the more correct value 1.0E-11.
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13.7.98a LOGP1 (X)
Description. Natural logarithm of X+1.
Class. Elemental function.
Argument. X shall be of type real.
Result characteristics. Same as X.
Result value. The result has a value equal to a processor dependent
approximation to $\log_e^{X+1}$.
NOTE 16.xxx
It is recommended that the result be calculated using a method that
does not incur loss of precision by forming X+1.
Example. LOGP1(1.0E-11) has the value 1.0e-11 (approximately).
Note to J3: 1.0 + 1.0E-11 has the value 1.0 in IEEE single precision,
so LOG(1.0 + 1.0E-11) has the value 0.0 in IEEE single precision, not
the more correct value 1.0e-11.