To: J3                                                     J3/25-143
From: Brandon Cook
Subject: US19 Reqs/specs for additional IEEE-754 math functions
Date: 2025-June-11

#Reference: J3/23-111r1, J3/23-234r2, WG5/N-2239

1. Introduction.
================

Addition of more IEEE-754 math functions was approved for
further work by WG5 at the June 2024 WG5 meeting.

IEEE-754 provides a table of recommended operations that languages
should provide. Specifically it states:

> Language standards should define, to be implemented according to
> this subclause, as many of the operations in Table 9.1 as is
> appropriate to the language.

In an effort to make Fortran as fully compliant with IEEE-754 as
possible, the intrinsic functions listed in this paper are proposed as
additions to the standard. Fortran already has many of the
operations available, and a table is provided to illustrate which are
already available and which are missing. Of note however:

> the names of the operations in Table 9.1 do not necessarily
> correspond to the names that any particular programming language
> would use.

2. Requirements.
================

Fortran shall define intrinsic functions corresponding to each of the
functions that IEEE-754 recommends that a language provide.

3. Specifications.
=================-

The following tables describe the currently available operations and
the required additional operations to be added.

Table of Operations Already Provided
====================================

IEEE-754 Operation | Fortran Operation
----------------------------------
exp(x)             | EXP(X)
exp2(x)            | 2**X
exp10(x)           | 10**X
log(x)             | LOG(X)
log10(x)           | LOG10(X)
hypot(x,y)         | HYPOT(X,Y)
pown(x,n)          | X**N
powr(x,y)          | X**Y
sin(x)             | SIN(X)
cos(x)             | COS(X)
tan(x)             | TAN(X)
sinPi(x)           | SINPI(X)
cosPi(x)           | COSPI(X)
tanPi(x)           | TANPI(X)
asin(x)            | ASIN(X)
acos(x)            | ACOS(X)
atan(x)            | ATAN(X)
atan2(y,x)         | ATAN2(Y,X)
asinPi(X)          | ASINPI(X)
acosPi(X)          | ACOSPI(X)
atanPi(X)          | ATANPI(X)
atan2Pi(y,x)       | ATAN2PI(Y,X)
sinh(x)            | SINH(X)
cosh(x)            | COSH(X)
tanh(x)            | TANH(X)
asinh(x)           | ASINH(X)
acosh(x)           | ACOSH(X)
atanh(x)           | ATANH(X)

Table of Operations Proposed
============================

The Expression column indicates what the proposed function in the
Fortran Operation column will compute mathematically, possibly with
higher precision or performance.

IEEE-754 Operation | Fortran Operation | Expression
--------------------------------------------------
expm1(x)           | EXPM1(X)          | exp(x)-1
exp2m1(x)          | EXP2M1(X)         | 2**x-1
exp10m1(x)         | EXP10M1(X)        | 10**x-1
log2(x)            | LOG2(X)           | log(x)/log(2.)
logp1(x)           | LOGP1(X)          | log(1+x)
log2p1(x)          | LOG2P1(X)         | log2(1+x)
log10p1(x)         | LOG10P1(X)        | log10(1+x)
rsqrt(x)           | RSQRT(X)          | 1/sqrt(x)
compound(x,n)      | COMPOUND(X,N)     | (1+x)**n
rootn(x,n)         | ROOTN(X,N)        | x**(1./n)
pow(x,y)           | POW(x,y)          | x**y