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. ---------------------------------------------------------------------- 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.