Integer root of floating point value

[RonShepard]

@mecej4

A good working solution for the cube root problem would probably require a good way of generating sufficiently close first approximations without resorting to calling exp or log.

When one does these things by hand, the first step is to divide the exponent by 3 for a cube root (2 for a square root, etc). If more accuracy is needed, then extracting maybe the high-order 4 bits of the mantissa and using that in a lookup table would be sufficient.

[FedericoPerini]

@mecej4

A good working solution

Here’s another implementation for those interested in benchmarking:

https://github.com/perazz/fortran-bessels/blob/080119ab8fb296a95579b147aaf234388ffc97be/src/bessels_constants.f90#L878

[PierU]

@kargl

It would only be missing leading to those that do not learn the language. Of course, having provided patches for gfortran for 2+ decades, I can safely say most users seem to have an aversion to documentation.

Fair enough for already existing features/syntax: they are there, and we have to do with them as they are. But when it comes to introduce a new syntax, it can be a good idea to look at what it means elsewhere. ^ is a widely used convention to denote exponentiation/superscript in many languages or math oriented softwares/utilities.

[PierU]

Summary of suggestions for an operator based nth integer root (in order of appearance), with my comments :

x = y ** n     ! reminder of nth power ;)

y = x // n       ! would be possible, although // has a fully different meaning in another context
y = x */ n       ! 2-characters operator, like for the nth power
y = x ^ n        ! denotes the nth power in many other languages rather then the nth root
y = n .throot. x ! reversed order ?
y = x .root. n   ! would make sense if (x .pow. n) was existing
y = x ^/ n       ! could make sense if y^n was adopted as an alternative to y**n

[everythingfunctional]

Not to discourage the exploration, but I’ll just note that this is part of a paper adding the missing operations suggested by IEEE, and ** is the only operator we currently use to support them.

IEEE-754 Operation	Fortran Operation	Status
exp	EXP	available
expm1	EXPM1	proposed
exp2	2**x	available
exp2m1	EXP2M1	proposed
exp10	10**x	available
exp10m1	EXP10M1	proposed
log	LOG	available
log2	LOG2	proposed
log10	LOG10	available
logp1	LOGP1	proposed
log2p1	LOG2P1	proposed
log10p1	LOG10P1	proposed
hypot	HYPOT	available
rsqrt	RSQRT	proposed
compound	COMPOUND	proposed
rootn	ROOTN	proposed
pown	x**n	available
pow	x**y	available
powr	POWR	proposed
sin	SIN	available
cos	COS	available
tan	TAN	available
sinPi	SINPI	available
cosPi	COSPI	available
tanPi	TANPI	available
asin	ASIN	available
acos	ACOS	available
atan	ATAN	available
atan2	ATAN2	available
asinPi	ASINPI	available
acosPi	ACOSPI	available
atanPi	ATANPI	available
atan2Pi	ATAN2PI	available
sinh	SINH	available
cosh	COSH	available
tanh	TANH	available
asinh	ASINH	available
acosh	ACOSH	available
atanh	ATANH	available

[PierU]

@everythingfunctional

Not to discourage the exploration, but I’ll just note that this is part of a paper adding the missing operations suggested by IEEE, and ** is the only operator we currently use to support them.

Got it… Just in case it’s still possible to consider it…