It may be somewhat interesting to mention why expm1(x) = exp(x) - 1 and log1p(x) = log(1 + x) are provided and what their historical purpose is. However, as mlarkin@ put it: are any of our users of exp(3) going to seriously be asking themselves "hmm, is OpenBSD's exp compatible with BASIC on the HP-71B?"
I suggest to keep a little bit of the historical background but strip away the extra verbiage. While there, use \(mi instead of - for the mathematical minus sign, as mandoc_char(7) recommends. I'd also like to add some spaces surrounding the arithmetic operations. I think this makes the formulas much easier to parse: I had to think for a second to be sure whether (1+x)**n-1 means (1+x)**(n-1) or ((1+x)**n)-1, while (1 + x)**n - 1 is hard to misinterpret at first glance. Index: exp.3 =================================================================== RCS file: /var/cvs/src/lib/libm/man/exp.3,v retrieving revision 1.33 diff -u -p -r1.33 exp.3 --- exp.3 26 Apr 2016 19:49:22 -0000 1.33 +++ exp.3 30 May 2016 12:02:21 -0000 @@ -139,7 +139,7 @@ function is an extended precision versio .Pp The .Fn expm1 -function computes the value exp(x)\-1 accurately even for tiny argument +function computes the value exp(x) \(mi 1 accurately even for tiny argument .Fa x . The .Fn expm1f @@ -194,7 +194,7 @@ function is an extended precision versio The .Fn log1p function computes -the value of log(1+x) accurately even for tiny argument +the value of log(1 + x) accurately even for tiny argument .Fa x . The .Fn log1pf @@ -277,12 +277,9 @@ are accurate enough that .Fn pow integer integer is exact until it is bigger than 2**53 for IEEE 754. .Sh NOTES -The functions exp(x)\-1 and log(1+x) are called -expm1 and logp1 in BASIC on the Hewlett\-Packard HP-71B -and APPLE Macintosh, EXP1 and LN1 in Pascal, exp1 and log1 in C -on APPLE Macintoshes, where they have been provided to make -sure financial calculations of ((1+x)**n\-1)/x, namely -expm1(n*log1p(x))/x, will be accurate when x is tiny. +The historical use of expm1(x) = exp(x) \(mi 1 and log1p(x) = log(1 + x) +is to make sure financial calculations of ((1 + x)**n \(mi 1) / x, +namely expm1(n * log1p(x)) / x, will be accurate when x is tiny. They also provide accurate inverse hyperbolic functions. .Pp The function
