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	1	.\" Copyright (c) 1985, 1991 Regents of the University of California.
	2	.\" All rights reserved.
	3	.\"
	4	.\" Redistribution and use in source and binary forms, with or without
	5	.\" modification, are permitted provided that the following conditions
	6	.\" are met:
	7	.\" 1. Redistributions of source code must retain the above copyright
	8	.\" notice, this list of conditions and the following disclaimer.
	9	.\" 2. Redistributions in binary form must reproduce the above copyright
	10	.\" notice, this list of conditions and the following disclaimer in the
	11	.\" documentation and/or other materials provided with the distribution.
	12	.\" 3. Neither the name of the University nor the names of its contributors
	13	.\" may be used to endorse or promote products derived from this software
	14	.\" without specific prior written permission.
	15	.\"
	16	.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	17	.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	18	.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	19	.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	20	.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	21	.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	22	.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	23	.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	24	.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	25	.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	26	.\" SUCH DAMAGE.
	27	.\"
	28	.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91
	29	.\" $FreeBSD: head/lib/msun/man/exp.3 251343 2013-06-03 19:51:32Z kargl $
	30	.\"
	31	.Dd June 11, 2013
	32	.Dt EXP 3
	33	.Os
	34	.Sh NAME
	35	.Nm exp ,
	36	.Nm expf ,
	37	.Nm expl ,
	38	.\" The sorting error is intentional. exp, expf, and expl should be adjacent.
	39	.Nm exp2 ,
	40	.Nm exp2f ,
	41	.Nm exp2l ,
	42	.Nm expm1 ,
	43	.Nm expm1f ,
	44	.Nm expm1l ,
	45	.Nm pow ,
	46	.Nm powf
	47	.Nd exponential and power functions
	48	.Sh LIBRARY
	49	.Lb libm
	50	.Sh SYNOPSIS
	51	.In math.h
	52	.Ft double
	53	.Fn exp "double x"
	54	.Ft float
	55	.Fn expf "float x"
	56	.Ft long double
	57	.Fn expl "long double x"
	58	.Ft double
	59	.Fn exp2 "double x"
	60	.Ft float
	61	.Fn exp2f "float x"
	62	.Ft long double
	63	.Fn exp2l "long double x"
	64	.Ft double
	65	.Fn expm1 "double x"
	66	.Ft float
	67	.Fn expm1f "float x"
	68	.Ft long double
	69	.Fn expm1l "long double x"
	70	.Ft double
	71	.Fn pow "double x" "double y"
	72	.Ft float
	73	.Fn powf "float x" "float y"
	74	.Sh DESCRIPTION
	75	The
	76	.Fn exp ,
	77	.Fn expf ,
	78	and
	79	.Fn expl
	80	functions compute the base
	81	.Ms e
	82	exponential value of the given argument
	83	.Fa x .
	84	.Pp
	85	The
	86	.Fn exp2 ,
	87	.Fn exp2f ,
	88	and
	89	.Fn exp2l
	90	functions compute the base 2 exponential of the given argument
	91	.Fa x .
	92	.Pp
	93	The
	94	.Fn expm1 ,
	95	.Fn expm1f ,
	96	and the
	97	.Fn expm1l
	98	functions compute the value exp(x)\-1 accurately even for tiny argument
	99	.Fa x .
	100	.Pp
	101	The
	102	.Fn pow
	103	and the
	104	.Fn powf
	105	functions compute the value
	106	of
	107	.Ar x
	108	to the exponent
	109	.Ar y .
	110	.Sh ERROR (due to Roundoff etc.)
	111	The values of
	112	.Fn exp 0 ,
	113	.Fn expm1 0 ,
	114	.Fn exp2 integer ,
	115	and
	116	.Fn pow integer integer
	117	are exact provided that they are representable.
	118	.\" XXX Is this really true for pow()?
	119	Otherwise the error in these functions is generally below one
	120	.Em ulp .
	121	.Sh RETURN VALUES
	122	These functions will return the appropriate computation unless an error
	123	occurs or an argument is out of range.
	124	The functions
	125	.Fn pow x y
	126	and
	127	.Fn powf x y
	128	raise an invalid exception and return an \*(Na if
	129	.Fa x
	130	< 0 and
	131	.Fa y
	132	is not an integer.
	133	.Sh NOTES
	134	The function
	135	.Fn pow x 0
	136	returns x*0 = 1 for all x including x = 0, \(If, and \*(Na .
	137	Previous implementations of pow may
	138	have defined x**0 to be undefined in some or all of these
	139	cases.
	140	Here are reasons for returning x**0 = 1 always:
	141	.Bl -enum -width indent
	142	.It
	143	Any program that already tests whether x is zero (or
	144	infinite or \(Na) before computing x*0 cannot care
	145	whether 0**0 = 1 or not.
	146	Any program that depends
	147	upon 0**0 to be invalid is dubious anyway since that
	148	expression's meaning and, if invalid, its consequences
	149	vary from one computer system to another.
	150	.It
	151	Some Algebra texts (e.g.\& Sigler's) define x**0 = 1 for
	152	all x, including x = 0.
	153	This is compatible with the convention that accepts a[0]
	154	as the value of polynomial
	155	.Bd -literal -offset indent
	156	p(x) = a[0]\(x0 + a[1]\(x1 + a[2]\(x2 +...+ a[n]\(xn
	157	.Ed
	158	.Pp
	159	at x = 0 rather than reject a[0]\(00 as invalid.
	160	.It
	161	Analysts will accept 00 = 1 despite that xy can
	162	approach anything or nothing as x and y approach 0
	163	independently.
	164	The reason for setting 0**0 = 1 anyway is this:
	165	.Bd -ragged -offset indent
	166	If x(z) and y(z) are
	167	.Em any
	168	functions analytic (expandable
	169	in power series) in z around z = 0, and if there
	170	x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0.
	171	.Ed
	172	.It
	173	If 0**0 = 1, then
	174	\(If0 = 1/0*0 = 1 too; and
	175	then \(Na0 = 1 too because x*0 = 1 for all finite
	176	and infinite x, i.e., independently of x.
	177	.El
	178	.Sh SEE ALSO
	179	.Xr fenv 3 ,
	180	.Xr ldexp 3 ,
	181	.Xr log 3 ,
	182	.Xr math 3
	183	.Sh STANDARDS
	184	These functions conform to
	185	.St -isoC-99 .