[unix-history] / lib / libm / common_source / sqrt.3

.\" Copyright (c) 1985, 1991 Regents of the University of California.
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\"    notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\"    notice, this list of conditions and the following disclaimer in the
.\"    documentation and/or other materials provided with the distribution.
.\" 3. All advertising materials mentioning features or use of this software
.\"    must display the following acknowledgement:
.\"	This product includes software developed by the University of
.\"	California, Berkeley and its contributors.
.\" 4. Neither the name of the University nor the names of its contributors
.\"    may be used to endorse or promote products derived from this software
.\"    without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\"     @(#)sqrt.3	6.4 (Berkeley) 5/6/91
.\"
.Dd May 6, 1991
.Dt SQRT 3
.Os
.Sh NAME
.Nm cbrt ,
.Nm sqrt
.Nd cube root and square root functions
.Sh SYNOPSIS
.Fd #include <math.h>
.Ft double
.Fn cbrt "double x"
.Ft double
.Fn sqrt "double x"
.Sh DESCRIPTION
The
.Fn cbrt
function computes
the cube root of
.Ar x .
.Pp
The
.Fn sqrt
computes the
non-negative square root of x.
.Sh RETURN VALUES
The
.Fn cbrt
function returns the requested cube root.
The
.Fn sqrt
function returns the requested square root
unless an error occurs.
On the
.Tn VAX
or
.Tn Tahoe
processor an attempt to take the
.Fn sqrt
of negative
.Fa x
causes an error; in this event,
the global variable
.Va errno
is set to
.Dv EDOM
and a reserved operand fault is generated.
.Sh ERROR (due to Roundoff etc.)
The
.Fn cbrt
function
is accurate to within 0.7
.Em ulps .
.Pp
The
.Fn sqrt
function on a
.Tn VAX
is accurate to within 0.501
.Em ulps .
Sqrt on a machine that conforms to
.Tn IEEE
754 is correctly rounded
in accordance with the rounding mode in force; the error is less than
half an
.Em ulp
in the default mode (round\-to\-nearest).
An
.Em ulp
is one
.Em U Ns nit
in the
.Em L Ns ast
.Em P Ns lace
carried.
.Sh SEE ALSO
.Xr math 3 ,
.Xr infnan 3
.Sh STANDARDS
The
.Nm sqrt
function conforms to
.St -ansiC .
.Sh HISTORY
The
.Nm cbrt
function appeared in
.Bx 4.3 .
Commit	Line	Data
15637ed4 RG	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. All advertising materials mentioning features or use of this software
	13	.\" must display the following acknowledgement:
	14	.\" This product includes software developed by the University of
	15	.\" California, Berkeley and its contributors.
	16	.\" 4. Neither the name of the University nor the names of its contributors
	17	.\" may be used to endorse or promote products derived from this software
	18	.\" without specific prior written permission.
	19	.\"
	20	.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
	21	.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
	22	.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
	23	.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
	24	.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
	25	.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
	26	.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	27	.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
	28	.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
	29	.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
	30	.\" SUCH DAMAGE.
	31	.\"
	32	.\" @(#)sqrt.3 6.4 (Berkeley) 5/6/91
	33	.\"
	34	.Dd May 6, 1991
	35	.Dt SQRT 3
	36	.Os
	37	.Sh NAME
	38	.Nm cbrt ,
	39	.Nm sqrt
	40	.Nd cube root and square root functions
	41	.Sh SYNOPSIS
	42	.Fd #include <math.h>
	43	.Ft double
	44	.Fn cbrt "double x"
	45	.Ft double
	46	.Fn sqrt "double x"
	47	.Sh DESCRIPTION
	48	The
	49	.Fn cbrt
	50	function computes
	51	the cube root of
	52	.Ar x .
	53	.Pp
	54	The
	55	.Fn sqrt
	56	computes the
	57	non-negative square root of x.
	58	.Sh RETURN VALUES
	59	The
	60	.Fn cbrt
	61	function returns the requested cube root.
	62	The
	63	.Fn sqrt
	64	function returns the requested square root
65	unless an error occurs.
66	On the
67	.Tn VAX
68	or
69	.Tn Tahoe
70	processor an attempt to take the
71	.Fn sqrt
72	of negative
73	.Fa x
74	causes an error; in this event,
75	the global variable
76	.Va errno
77	is set to
78	.Dv EDOM
79	and a reserved operand fault is generated.
80	.Sh ERROR (due to Roundoff etc.)
81	The
82	.Fn cbrt
83	function
84	is accurate to within 0.7
85	.Em ulps .
86	.Pp
87	The
88	.Fn sqrt
89	function on a
90	.Tn VAX
91	is accurate to within 0.501
92	.Em ulps .
93	Sqrt on a machine that conforms to
94	.Tn IEEE
95	754 is correctly rounded
96	in accordance with the rounding mode in force; the error is less than
97	half an
98	.Em ulp
99	in the default mode (round\-to\-nearest).
100	An
101	.Em ulp
102	is one
103	.Em U Ns nit
104	in the
105	.Em L Ns ast
106	.Em P Ns lace
107	carried.
108	.Sh SEE ALSO
109	.Xr math 3 ,
110	.Xr infnan 3
111	.Sh STANDARDS
112	The
113	.Nm sqrt
114	function conforms to
115	.St -ansiC .
116	.Sh HISTORY
117	The
118	.Nm cbrt
119	function appeared in
120	.Bx 4.3 .