diff options
Diffstat (limited to 'lib/msun/man')
| -rw-r--r-- | lib/msun/man/acos.3 | 89 | ||||
| -rw-r--r-- | lib/msun/man/acosh.3 | 82 | ||||
| -rw-r--r-- | lib/msun/man/asin.3 | 91 | ||||
| -rw-r--r-- | lib/msun/man/asinh.3 | 70 | ||||
| -rw-r--r-- | lib/msun/man/atan.3 | 75 | ||||
| -rw-r--r-- | lib/msun/man/atan2.3 | 189 | ||||
| -rw-r--r-- | lib/msun/man/atanh.3 | 84 | ||||
| -rw-r--r-- | lib/msun/man/ceil.3 | 63 | ||||
| -rw-r--r-- | lib/msun/man/cos.3 | 74 | ||||
| -rw-r--r-- | lib/msun/man/cosh.3 | 75 | ||||
| -rw-r--r-- | lib/msun/man/erf.3 | 83 | ||||
| -rw-r--r-- | lib/msun/man/exp.3 | 287 | ||||
| -rw-r--r-- | lib/msun/man/fabs.3 | 67 | ||||
| -rw-r--r-- | lib/msun/man/floor.3 | 63 | ||||
| -rw-r--r-- | lib/msun/man/fmod.3 | 76 | ||||
| -rw-r--r-- | lib/msun/man/hypot.3 | 125 | ||||
| -rw-r--r-- | lib/msun/man/ieee.3 | 152 | ||||
| -rw-r--r-- | lib/msun/man/ieee_test.3 | 90 | ||||
| -rw-r--r-- | lib/msun/man/j0.3 | 128 | ||||
| -rw-r--r-- | lib/msun/man/lgamma.3 | 124 | ||||
| -rw-r--r-- | lib/msun/man/math.3 | 633 | ||||
| -rw-r--r-- | lib/msun/man/rint.3 | 63 | ||||
| -rw-r--r-- | lib/msun/man/sin.3 | 73 | ||||
| -rw-r--r-- | lib/msun/man/sinh.3 | 75 | ||||
| -rw-r--r-- | lib/msun/man/sqrt.3 | 121 | ||||
| -rw-r--r-- | lib/msun/man/tan.3 | 74 | ||||
| -rw-r--r-- | lib/msun/man/tanh.3 | 71 |
27 files changed, 3197 insertions, 0 deletions
diff --git a/lib/msun/man/acos.3 b/lib/msun/man/acos.3 new file mode 100644 index 0000000..6961a60 --- /dev/null +++ b/lib/msun/man/acos.3 @@ -0,0 +1,89 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)acos.3 5.1 (Berkeley) 5/2/91 +.\" $Id: acos.3,v 1.4 1993/10/29 22:57:17 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt ACOS 3 +.Os +.Sh NAME +.Nm acos +.Nd arc cosine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn acos "double x" +.Sh DESCRIPTION +The +.Fn acos +function computes the principal value of the arc cosine of +.Fa x . +A domain error occurs for arguments not in the range [-1, +1]. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn acos +function returns the arc cosine in the range +.Bq 0 , \*(Pi +radians. +On the +.Tn VAX +and +.Tn Tahoe , +if: +.Bd -unfilled -offset indent +.Pf \&| Ns Ar x Ns \&| > 1 , +.Ed +.Pp +.Fn acos x +sets the global variable +.Va errno +to +.Dv EDOM +and a reserved operand fault is generated. +.Sh SEE ALSO +.Xr sin 3 , +.Xr cos 3 , +.Xr tan 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr sinh 3 , +.Xr cosh 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn acos +function conforms to +.St -ansiC . diff --git a/lib/msun/man/acosh.3 b/lib/msun/man/acosh.3 new file mode 100644 index 0000000..3b05dd3 --- /dev/null +++ b/lib/msun/man/acosh.3 @@ -0,0 +1,82 @@ +.\" Copyright (c) 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. +.\" +.\" from: @(#)acosh.3 5.2 (Berkeley) 5/6/91 +.\" $Id: acosh.3,v 1.4 1993/10/29 22:57:20 jtc Exp $ +.\" +.Dd May 6, 1991 +.Dt ACOSH 3 +.Os BSD 4.3 +.Sh NAME +.Nm acosh +.Nd inverse hyperbolic cosine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn acosh "double x" +.Sh DESCRIPTION +The +.Fn acosh +function computes the inverse hyperbolic cosine +of the real +argument +.Ar x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn acosh +function +returns the inverse hyperbolic cosine of +.Ar x . +On the +.Tn VAX +and +.Tn Tahoe , +if the argument is less than one +.Fn acosh +sets the global variable +.Va errno +to +.Er EDOM +and +causes a reserved operand fault. +.Sh SEE ALSO +.Xr asinh 3 , +.Xr atanh 3 , +.Xr exp 3 , +.Xr infnan 3 , +.Xr math 3 +.Sh HISTORY +The +.Fn acosh +function appeared in +.Bx 4.3 . diff --git a/lib/msun/man/asin.3 b/lib/msun/man/asin.3 new file mode 100644 index 0000000..3624d78 --- /dev/null +++ b/lib/msun/man/asin.3 @@ -0,0 +1,91 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)asin.3 5.1 (Berkeley) 5/2/91 +.\" $Id: asin.3,v 1.4 1993/10/29 22:57:22 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt ASIN 3 +.Os +.Sh NAME +.Nm asin +.Nd arc sine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn asin "double x" +.Sh DESCRIPTION +The +.Fn asin +function computes the principal value of the arc sine of +.Fa x . +A domain error occurs for arguments not in the range [-1, +1]. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn asin +function returns the arc sine in the range +.Bk -words +.Bq -\*(Pi/2, +\*(Pi/2 +.Ek +radians. +On the +.Tn VAX , +and Tahoe , +if: +.Bd -unfilled -offset indent +.Pf \&| Ns Ar x Ns \&| > 1 +.Ed +.Pp +the +global variable +.Va errno +is set to +.Er EDOM +and +a reserved operand fault generated. +.Sh SEE ALSO +.Xr acos 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn asin +function conforms to +.St -ansiC . diff --git a/lib/msun/man/asinh.3 b/lib/msun/man/asinh.3 new file mode 100644 index 0000000..01b62bf --- /dev/null +++ b/lib/msun/man/asinh.3 @@ -0,0 +1,70 @@ +.\" 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. +.\" +.\" from: @(#)asinh.3 6.4 (Berkeley) 5/6/91 +.\" $Id: asinh.3,v 1.4 1993/10/29 22:57:23 jtc Exp $ +.\" +.Dd May 6, 1991 +.Dt ASINH 3 +.Os BSD 4.3 +.Sh NAME +.Nm asinh +.Nd inverse hyperbolic sine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn asinh "double x" +.Sh DESCRIPTION +The +.Fn asinh +function computes the inverse hyperbolic sine +of the real +argument +.Ar x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn asinh +function +returns the inverse hyperbolic sine of +.Ar x . +.Sh SEE ALSO +.Xr acosh 3 , +.Xr atanh 3 , +.Xr exp 3 , +.Xr infnan 3 , +.Xr math 3 +.Sh HISTORY +The +.Fn asinh +function appeared in +.Bx 4.3 . diff --git a/lib/msun/man/atan.3 b/lib/msun/man/atan.3 new file mode 100644 index 0000000..d698c49 --- /dev/null +++ b/lib/msun/man/atan.3 @@ -0,0 +1,75 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)atan.3 5.1 (Berkeley) 5/2/91 +.\" $Id: atan.3,v 1.4 1993/10/04 18:07:15 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt ATAN 3 +.Os +.Sh NAME +.Nm atan +.Nd arc tangent function of one variable +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn atan "double x" +.Sh DESCRIPTION +The +.Fn atan +function computes the principal value of the arc tangent of +.Fa x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn atan +function returns the arc tangent in the range +.Bk -words +.Bq -\*(Pi/2 , +\*(Pi/2 +.Ek +radians. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn atan +function conforms to +.St -ansiC . diff --git a/lib/msun/man/atan2.3 b/lib/msun/man/atan2.3 new file mode 100644 index 0000000..79b0277 --- /dev/null +++ b/lib/msun/man/atan2.3 @@ -0,0 +1,189 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 +.\" $Id: atan2.3,v 1.3 1993/08/14 13:42:32 mycroft Exp $ +.\" +.Dd May 2, 1991 +.Dt ATAN2 3 +.Os +.Sh NAME +.Nm atan2 +.Nd arc tangent function of two variables +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn atan2 "double y" "double x" +.Sh DESCRIPTION +The +.Xr atan2 +function computes the principal value of the arc tangent of +.Ar y/ Ns Ar x , +using the signs of both arguments to determine the quadrant of +the return value. +.Sh RETURN VALUES +The +.Xr atan2 +function, if successful, +returns the arc tangent of +.Ar y/ Ns Ar x +in the range +.Bk -words +.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi +.Ek +radians. +If both +.Ar x +and +.Ar y +are zero, the global variable +.Va errno +is set to +.Er EDOM . +On the +.Tn VAX : +.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ +.It Fn atan2 y x No := Ta +.Fn atan y/x Ta +if +.Ar x +> 0, +.It Ta sign( Ns Ar y Ns )*(\*(Pi - +.Fn atan "\\*(Bay/x\\*(Ba" ) Ta +if +.Ar x +< 0, +.It Ta +.No 0 Ta +if x = y = 0, or +.It Ta +.Pf sign( Ar y Ns )*\\*(Pi/2 Ta +if +.Ar x += 0 \*(!= +.Ar y . +.El +.Sh NOTES +The function +.Fn atan2 +defines "if x > 0," +.Fn atan2 0 0 += 0 on a +.Tn VAX +despite that previously +.Fn atan2 0 0 +may have generated an error message. +The reasons for assigning a value to +.Fn atan2 0 0 +are these: +.Bl -enum -offset indent +.It +Programs that test arguments to avoid computing +.Fn atan2 0 0 +must be indifferent to its value. +Programs that require it to be invalid are vulnerable +to diverse reactions to that invalidity on diverse computer systems. +.It +The +.Fn atan2 +function is used mostly to convert from rectangular (x,y) +to polar +.if n\ +(r,theta) +.if t\ +(r,\(*h) +coordinates that must satisfy x = +.if n\ +r\(**cos theta +.if t\ +r\(**cos\(*h +and y = +.if n\ +r\(**sin theta. +.if t\ +r\(**sin\(*h. +These equations are satisfied when (x=0,y=0) +is mapped to +.if n \ +(r=0,theta=0) +.if t \ +(r=0,\(*h=0) +on a VAX. In general, conversions to polar coordinates +should be computed thus: +.Bd -unfilled -offset indent +.if n \{\ +r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) +theta := atan2(y,x). +.\} +.if t \{\ +r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) +\(*h := atan2(y,x). +.\} +.Ed +.It +The foregoing formulas need not be altered to cope in a +reasonable way with signed zeros and infinities +on a machine that conforms to +.Tn IEEE 754 ; +the versions of +.Xr hypot 3 +and +.Fn atan2 +provided for +such a machine are designed to handle all cases. +That is why +.Fn atan2 \(+-0 \-0 += \(+-\*(Pi +for instance. +In general the formulas above are equivalent to these: +.Bd -unfilled -offset indent +.if n \ +r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); +.if t \ +r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); +.Ed +.El +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 , +.Sh STANDARDS +The +.Fn atan2 +function conforms to +.St -ansiC . diff --git a/lib/msun/man/atanh.3 b/lib/msun/man/atanh.3 new file mode 100644 index 0000000..51318bc --- /dev/null +++ b/lib/msun/man/atanh.3 @@ -0,0 +1,84 @@ +.\" 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. +.\" +.\" from: @(#)atanh.3 5.2 (Berkeley) 5/6/91 +.\" $Id: atanh.3,v 1.4 1993/10/29 22:57:24 jtc Exp $ +.\" +.Dd May 6, 1991 +.Dt ATANH 3 +.Os BSD 4.3 +.Sh NAME +.Nm atanh +.Nd inverse hyperbolic tangent function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn atanh "double x" +.Sh DESCRIPTION +The +.Fn atanh +function computes the inverse hyperbolic tangent +of the real +argument +.Ar x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn atanh +function +returns the inverse hyperbolic tangent of +.Ar x +if successful. +On the +.Tn VAX +and +.Tn Tahoe , +if the argument has absolute value +bigger than or equal to 1, +.Fn atanh +sets the global variable +.Va errno +to +.Er EDOM +and +a reserved operand fault is generated. +.Sh SEE ALSO +.Xr acosh 3 , +.Xr asinh 3 , +.Xr exp 3 , +.Xr infnan 3 , +.Xr math 3 +.Sh HISTORY +The +.Fn atanh +function appeared in +.Bx 4.3 . diff --git a/lib/msun/man/ceil.3 b/lib/msun/man/ceil.3 new file mode 100644 index 0000000..0cfc7ef --- /dev/null +++ b/lib/msun/man/ceil.3 @@ -0,0 +1,63 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)ceil.3 5.1 (Berkeley) 5/2/91 +.\" $Id: ceil.3,v 1.6 1994/03/11 01:32:08 jtc Exp $ +.\" +.Dd March 10, 1994 +.Dt CEIL 3 +.Os +.Sh NAME +.Nm ceil +.Nd round to smallest integral value not greater than x +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn ceil "double x" +.Sh DESCRIPTION +The +.Fn ceil +function returns the smallest integral value +(represented as a double precision number) +greater than or equal to +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr fabs 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr rint 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn ceil +function conforms to +.St -ansiC . diff --git a/lib/msun/man/cos.3 b/lib/msun/man/cos.3 new file mode 100644 index 0000000..b53c006 --- /dev/null +++ b/lib/msun/man/cos.3 @@ -0,0 +1,74 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)cos.3 5.1 (Berkeley) 5/2/91 +.\" $Id: cos.3,v 1.5 1993/10/29 22:57:25 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt COS 3 +.Os +.Sh NAME +.Nm cos +.Nd cosine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn cos "double x" +.Sh DESCRIPTION +The +.Fn cos +function computes the cosine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little or no +significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn cos +function returns the cosine value. +.Sh SEE ALSO +.Xr sin 3 , +.Xr tan 3 , +.Xr asin 3 , +.Xr acos 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr sinh 3 , +.Xr cosh 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn cos +function conforms to +.St -ansiC . diff --git a/lib/msun/man/cosh.3 b/lib/msun/man/cosh.3 new file mode 100644 index 0000000..33cc949 --- /dev/null +++ b/lib/msun/man/cosh.3 @@ -0,0 +1,75 @@ +.\" Copyright (c) 1989, 1991 The 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. +.\" +.\" from: @(#)cosh.3 5.1 (Berkeley) 5/2/91 +.\" $Id: cosh.3,v 1.4 1993/10/29 22:57:26 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt COSH 3 +.Os +.Sh NAME +.Nm cosh +.Nd hyperbolic cosine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn cosh "double x" +.Sh DESCRIPTION +The +.Fn cosh +function computes the hyperbolic cosine of +.Fa x . +.Sh RETURN VALUES +The +.Fn cosh +function returns the hyperbolic cosine unless the magnitude +of +.Fa x +is too large; in this event, the global variable +.Va errno +is set to +.Er ERANGE . +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn cosh +function conforms to +.St -ansiC . diff --git a/lib/msun/man/erf.3 b/lib/msun/man/erf.3 new file mode 100644 index 0000000..b23dee7 --- /dev/null +++ b/lib/msun/man/erf.3 @@ -0,0 +1,83 @@ +.\" 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. +.\" +.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 +.\" $Id: erf.3,v 1.3 1993/08/14 13:42:38 mycroft Exp $ +.\" +.Dd April 20, 1991 +.Dt ERF 3 +.Os BSD 4.3 +.Sh NAME +.Nm erf , +.Nm erfc +.Nd error function operators +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn erf "double x" +.Ft double +.Fn erfc "double x" +.Sh DESCRIPTION +These functions calculate the error function of +.Fa x . +.Pp +The +.Fn erf +calculates the error function of x; where +.Bd -filled -offset indent +.if n \{\ +erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} +.if t \{\ +erf\|(x) := +(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} +.Ed +.Pp +The +.Fn erfc +function calculates the complementary error function of +.Fa x ; +that is +.Fn erfc +subtracts the result of the error function +.Fn erf x +from 1.0. +This is useful, since for large +.Fa x +places disappear. +.Sh SEE ALSO +.Xr math 3 +.Sh HISTORY +The +.Fn erf +and +.Fn erfc +functions appeared in +.Bx 4.3 . diff --git a/lib/msun/man/exp.3 b/lib/msun/man/exp.3 new file mode 100644 index 0000000..52f64fd --- /dev/null +++ b/lib/msun/man/exp.3 @@ -0,0 +1,287 @@ +.\" 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. +.\" +.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91 +.\" $Id: exp.3,v 1.7 1994/02/11 18:34:05 jtc Exp $ +.\" +.Dd July 31, 1991 +.Dt EXP 3 +.Os BSD 4 +.Sh NAME +.Nm exp , +.Nm exp2 , +.Nm exp10 , +.Nm expm1 , +.Nm log , +.Nm log2 , +.Nm log10 , +.Nm log1p , +.Nm pow +.Nd exponential, logarithm, power functions +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn exp "double x" +.Ft double +.Fn expm1 "double x" +.Ft double +.Fn log "double x" +.Ft double +.Fn log10 "double x" +.Ft double +.Fn log1p "double x" +.Ft double +.Fn pow "double x" "double y" +.Sh DESCRIPTION +The +.Fn exp +function computes the exponential value of the given argument +.Fa x . +.Pp +The +.Fn expm1 +function computes the value exp(x)\-1 accurately even for tiny argument +.Fa x . +.Pp +The +.Fn log +function computes the value of the natural logarithm of argument +.Fa x. +.Pp +The +.Fn log10 +function computes the value of the logarithm of argument +.Fa x +to base 10. +.Pp +The +.Fn log1p +function computes +the value of log(1+x) accurately even for tiny argument +.Fa x . +.Pp +The +.Fn pow +computes the value +of +.Ar x +to the exponent +.Ar y . +.Sh ERROR (due to Roundoff etc.) +exp(x), log(x), expm1(x) and log1p(x) are accurate to within +an +.Em ulp , +and log10(x) to within about 2 +.Em ulps ; +an +.Em ulp +is one +.Em Unit +in the +.Em Last +.Em Place . +The error in +.Fn pow x y +is below about 2 +.Em ulps +when its +magnitude is moderate, but increases as +.Fn pow x y +approaches +the over/underflow thresholds until almost as many bits could be +lost as are occupied by the floating\-point format's exponent +field; that is 8 bits for +.Tn "VAX D" +and 11 bits for IEEE 754 Double. +No such drastic loss has been exposed by testing; the worst +errors observed have been below 20 +.Em ulps +for +.Tn "VAX D" , +300 +.Em ulps +for +.Tn IEEE +754 Double. +Moderate values of +.Fn pow +are accurate enough that +.Fn pow integer integer +is exact until it is bigger than 2**56 on a +.Tn VAX , +2**53 for +.Tn IEEE +754. +.Sh RETURN VALUES +These functions will return the appropriate computation unless an error +occurs or an argument is out of range. +The functions +.Fn exp , +.Fn expm1 +and +.Fn pow +detect if the computed value will overflow, +set the global variable +.Va errno to +.Er ERANGE +and cause a reserved operand fault on a +.Tn VAX +or +.Tn Tahoe . +The function +.Fn pow x y +checks to see if +.Fa x +< 0 and +.Fa y +is not an integer, in the event this is true, +the global variable +.Va errno +is set to +.Er EDOM +and on the +.Tn VAX +and +.Tn Tahoe +generate a reserved operand fault. +On a +.Tn VAX +and +.Tn Tahoe , +.Va errno +is set to +.Er EDOM +and the reserved operand is returned +by log unless +.Fa x +> 0, by +.Fn log1p +unless +.Fa x +> \-1. +.Sh NOTES +The functions exp(x)\-1 and log(1+x) are called +expm1 and logp1 in +.Tn BASIC +on the Hewlett\-Packard +.Tn HP Ns \-71B +and +.Tn APPLE +Macintosh, +.Tn EXP1 +and +.Tn LN1 +in Pascal, exp1 and log1 in C +on +.Tn 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. +They also provide accurate inverse hyperbolic functions. +.Pp +The function +.Fn pow x 0 +returns x**0 = 1 for all x including x = 0, +.if n \ +Infinity +.if t \ +\(if +(not found on a +.Tn VAX ) , +and +.Em NaN +(the reserved +operand on a +.Tn VAX ) . Previous implementations of pow may +have defined x**0 to be undefined in some or all of these +cases. Here are reasons for returning x**0 = 1 always: +.Bl -enum -width indent +.It +Any program that already tests whether x is zero (or +infinite or \*(Na) before computing x**0 cannot care +whether 0**0 = 1 or not. Any program that depends +upon 0**0 to be invalid is dubious anyway since that +expression's meaning and, if invalid, its consequences +vary from one computer system to another. +.It +Some Algebra texts (e.g. Sigler's) define x**0 = 1 for +all x, including x = 0. +This is compatible with the convention that accepts a[0] +as the value of polynomial +.Bd -literal -offset indent +p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n +.Ed +.Pp +at x = 0 rather than reject a[0]\(**0**0 as invalid. +.It +Analysts will accept 0**0 = 1 despite that x**y can +approach anything or nothing as x and y approach 0 +independently. +The reason for setting 0**0 = 1 anyway is this: +.Bd -filled -offset indent +If x(z) and y(z) are +.Em any +functions analytic (expandable +in power series) in z around z = 0, and if there +x(0) = y(0) = 0, then x(z)**y(z) \(-> 1 as z \(-> 0. +.Ed +.It +If 0**0 = 1, then +.if n \ +infinity**0 = 1/0**0 = 1 too; and +.if t \ +\(if**0 = 1/0**0 = 1 too; and +then \*(Na**0 = 1 too because x**0 = 1 for all finite +and infinite x, i.e., independently of x. +.El +.Sh SEE ALSO +.Xr math 3 , +.Xr infnan 3 +.Sh HISTORY +A +.Fn exp , +.Fn log +and +.Fn pow +functions +appeared in +.At v6 . +A +.Fn log10 +function +appeared in +.At v7 . +The +.Fn log1p +and +.Fn expm1 +functions appeared in +.Bx 4.3 . diff --git a/lib/msun/man/fabs.3 b/lib/msun/man/fabs.3 new file mode 100644 index 0000000..58d4400 --- /dev/null +++ b/lib/msun/man/fabs.3 @@ -0,0 +1,67 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" @(#)fabs.3 5.1 (Berkeley) 5/2/91 +.\" 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. +.\" +.\" from: @(#)fabs.3 5.1 (Berkeley) 5/2/91 +.\" $Id: fabs.3,v 1.4 1993/10/04 18:04:34 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt FABS 3 +.Os +.Sh NAME +.Nm fabs +.Nd floating-point absolute value function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn fabs "double x" +.Sh DESCRIPTION +The +.Fn fabs +function computes the absolute value of a floating-point number +.Fa x . +.Sh RETURN VALUES +The +.Fn fabs +function returns the absolute value of +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr floor 3 , +.Xr rint 3 , +.Xr ieee 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn fabs +function conforms to +.St -ansiC . diff --git a/lib/msun/man/floor.3 b/lib/msun/man/floor.3 new file mode 100644 index 0000000..bda6bf8 --- /dev/null +++ b/lib/msun/man/floor.3 @@ -0,0 +1,63 @@ +.\" Copyright (c) 1985, 1991 The 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. +.\" +.\" from: @(#)floor.3 6.5 (Berkeley) 4/19/91 +.\" $Id: floor.3,v 1.5 1994/03/11 01:32:10 jtc Exp $ +.\" +.Dd March 10, 1994 +.Dt FLOOR 3 +.Os +.Sh NAME +.Nm floor +.Nd round to largest integral value not greater than x +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn floor "double x" +.Sh DESCRIPTION +The +.Fn floor +function returns the largest integral value +(represented as a double precision number) +less than or equal to +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr fabs 3 , +.Xr ieee 3 , +.Xr rint 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn floor +function conforms to +.St -ansiC . diff --git a/lib/msun/man/fmod.3 b/lib/msun/man/fmod.3 new file mode 100644 index 0000000..5152602 --- /dev/null +++ b/lib/msun/man/fmod.3 @@ -0,0 +1,76 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)fmod.3 5.1 (Berkeley) 5/2/91 +.\" $Id: fmod.3,v 1.3 1993/08/14 13:42:46 mycroft Exp $ +.\" +.Dd May 2, 1991 +.Dt FMOD 3 +.Os +.Sh NAME +.Nm fmod +.Nd floating-point remainder function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn fmod "double x" "double y" +.Sh DESCRIPTION +The +.Fn fmod +function computes the floating-point remainder of +.Fa x Ns / Fa y . +.Sh RETURN VALUES +The +.Fn fmod +function returns the value +.Sm off +.Fa x - Em i * Fa y , +.Sm on +for some integer +.Em i +such that, if +.Fa y +is non-zero, the result has the same sign as +.Fa x +and magnitude less than the magnitude of +.Fa y . +If +.Fa y +is zero, whether a domain error occurs or the +.Fn fmod +function returns zero is implementation-defined. +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +The +.Fn fmod +function conforms to +.St -ansiC . diff --git a/lib/msun/man/hypot.3 b/lib/msun/man/hypot.3 new file mode 100644 index 0000000..0098170 --- /dev/null +++ b/lib/msun/man/hypot.3 @@ -0,0 +1,125 @@ +.\" 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. +.\" +.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 +.\" $Id: hypot.3,v 1.3 1993/08/14 13:42:48 mycroft Exp $ +.\" +.Dd May 6, 1991 +.Dt HYPOT 3 +.Os BSD 4 +.Sh NAME +.Nm hypot , +.Nm cabs +.Nd euclidean distance and complex absolute value functions +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn hypot "double x" "double y" +.Fd struct {double x, y;} z; +.Ft double +.Fn cabs z +.Sh DESCRIPTION +The +.Fn hypot +and +.Fn cabs +functions +computes the +sqrt(x*x+y*y) +in such a way that underflow will not happen, and overflow +occurs only if the final result deserves it. +.Pp +.Fn hypot "\*(If" "v" += +.Fn hypot "v" "\*(If" += +\*(If for all +.Ar v , +including \*(Na. +.Sh ERROR (due to Roundoff, etc.) +Below 0.97 +.Em ulps . +Consequently +.Fn hypot "5.0" "12.0" += 13.0 +exactly; +in general, hypot and cabs return an integer whenever an +integer might be expected. +.Pp +The same cannot be said for the shorter and faster version of hypot +and cabs that is provided in the comments in cabs.c; its error can +exceed 1.2 +.Em ulps . +.Sh NOTES +As might be expected, +.Fn hypot "v" "\*(Na" +and +.Fn hypot "\*(Na" "v" +are \*(Na for all +.Em finite +.Ar v ; +with "reserved operand" in place of "\*(Na", the +same is true on a +.Tn VAX . +But programmers on machines other than a +.Tn VAX +(if has no \*(If) +might be surprised at first to discover that +.Fn hypot "\(+-\*(If" "\*(Na" += +\*(If. +This is intentional; it happens because +.Fn hypot "\*(If" "v" += +\*(If +for +.Em all +.Ar v , +finite or infinite. +Hence +.Fn hypot "\*(If" "v" +is independent of +.Ar v . +Unlike the reserved operand fault on a +.Tn VAX , +the +.Tn IEEE +\*(Na is designed to +disappear when it turns out to be irrelevant, as it does in +.Fn hypot "\*(If" "\*(Na" . +.Sh SEE ALSO +.Xr math 3 , +.Xr sqrt 3 +.Sh HISTORY +Both a +.Fn hypot +function and a +.Fn cabs +function +appeared in +.At v7 . diff --git a/lib/msun/man/ieee.3 b/lib/msun/man/ieee.3 new file mode 100644 index 0000000..e8b1583 --- /dev/null +++ b/lib/msun/man/ieee.3 @@ -0,0 +1,152 @@ +.\" 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. +.\" +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $Id: ieee.3,v 1.7 1994/03/10 18:15:07 jtc Exp $ +.\" +.Dd Feb 25, 1994 +.Dt IEEE 3 +.Os +.Sh NAME +.Nm copysign , +.Nm finite , +.Nm ilogb , +.Nm nextafter , +.Nm remainder , +.Nm scalbn +.Nd Functions for IEEE arithmetic +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn copysign "double x" "double y" +.Ft int +.Fn finite "double x" +.Ft int +.Fn ilogb "double x" +.Ft double +.Fn nextafter "double x" "double y" +.Ft double +.Fn remainder "double x" "double y" +.Ft double +.Fn scalbn "double x" "int n" +.Sh DESCRIPTION +These functions are required or recommended by +.St -ieee754 . +.Pp +.Fn copysign +returns +.Fa x +with its sign changed to +.Fa y Ns 's. +.Pp +.Fn finite +returns the value 1 just when +\-\*(If \*(Lt +.Fa x +\*(Lt +\*(If; +otherwise a +zero is returned +(when +.Pf \\*(Ba Ns Fa x Ns \\*(Ba += \*(If or +.Fa x +is \*(Na +.Pp +.Fn ilogb +returns +.Fa x Ns 's exponent +.Fa n , +in integer format. +.Fn ilogb \*(Pm\*(If +returns +.Dv INT_MAX +and +.Fn ilogb 0 +returns +.Dv INT_MIN . +.Pp +.Fn nextafter +returns the next machine representable number from +.Fa x +in direction +.Fa y . +.Pp +.Fn remainder +returns the remainder +.Fa r +:= +.Fa x +\- +.Fa n\(**y +where +.Fa n +is the integer nearest the exact value of +.Bk -words +.Fa x Ns / Ns Fa y ; +.Ek +moreover if +.Pf \\*(Ba Fa n +\- +.Sm off +.Fa x No / Fa y No \\*(Ba +.Sm on += +1/2 +then +.Fa n +is even. Consequently +the remainder is computed exactly and +.Sm off +.Pf \\*(Ba Fa r No \\*(Ba +.Sm on +\*(Le +.Sm off +.Pf \\*(Ba Fa y No \\*(Ba/2. +.Sm on +But +.Fn remainder x 0 +and +.Fn remainder \*(If 0 +are invalid operations that produce a \*(Na. +.Pp +.Fn scalbn +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Sh SEE ALSO +.Xr math 3 +.Sh HISTORY +The +.Nm ieee +functions appeared in +.Bx 4.3 . +.Sh STANDARDS +.St -ieee754 diff --git a/lib/msun/man/ieee_test.3 b/lib/msun/man/ieee_test.3 new file mode 100644 index 0000000..e1311ca --- /dev/null +++ b/lib/msun/man/ieee_test.3 @@ -0,0 +1,90 @@ +.\" 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. +.\" +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $Id: ieee_test.3,v 1.1 1994/03/11 17:19:01 jtc Exp $ +.\" +.Dd March 10, 1994 +.Dt IEEE_TEST 3 +.Os +.Sh NAME +.Nm logb , +.Nm scalb , +.Nm significand +.Nd IEEE test functions +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn logb "double x" +.Ft double +.Fn scalb "double x" "double n" +.Ft double +.Fn significand "double x" +.Sh DESCRIPTION +These functions allow users to test conformance to +.St -ieee754 . +Their use is not otherwise recommended. +.Pp +.Fn logb x +returns +.Fa x Ns 's exponent +.Fa n , +a signed integer converted to double\-precision floating\-point. +.Fn logb \*(Pm\*(If += +\*(If; +.Fn logb 0 += -\*(If with a division by zero exception. +.Pp +.Fn scalbn x n +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Pp +.Fn significand x +returns +.Fa sig , +where +.Fa x +:= +.Fa sig No \(** 2** Ns Fa n +with 1 \(<= +.Fa sig +< 2. +.Fn significand x +is not defined when +.Fa x +is 0, \*(Pm\*(If, or \*(Na. +.Sh SEE ALSO +.Xr ieee 3 , +.Xr math 3 + +.Sh STANDARDS +.St -ieee754 diff --git a/lib/msun/man/j0.3 b/lib/msun/man/j0.3 new file mode 100644 index 0000000..4b18e85 --- /dev/null +++ b/lib/msun/man/j0.3 @@ -0,0 +1,128 @@ +.\" 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. +.\" +.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 +.\" $Id: j0.3,v 1.5 1994/01/11 00:46:54 jtc Exp $ +.\" +.Dd April 19, 1991 +.Dt J0 3 +.Os BSD 4 +.Sh NAME +.Nm j0 , +.Nm j1 , +.Nm jn , +.Nm y0 , +.Nm y1 , +.Nm yn +.Nd bessel functions of first and second kind +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn j0 "double x" +.Ft double +.Fn j1 "double x" +.Ft double +.Fn jn "int n" "double x" +.Ft double +.Fn y0 "double x" +.Ft double +.Fn y1 "double x" +.Ft double +.Fn yn "int n" "double x" +.Sh DESCRIPTION +The functions +.Fn j0 +and +.Fn j1 +compute the +.Em Bessel function of the first kind of the order +0 and the +.Em order +1, respectively, +for the +real value +.Fa x ; +the function +.Fn jn +computes the +.Em Bessel function of the first kind of the integer order +.Fa n +for the real value +.Fa x . +.Pp +The functions +.Fn y0 +and +.Fn y1 +compute the linearly independent +.Em Bessel function of the second kind of the order +0 and the +.Em order +1, respectively, +for the +positive +.Em integer +value +.Fa x +(expressed as a double); +the function +.Fn yn +computes the +.Em Bessel function of the second kind for the integer order +.Fa n +for the positive +.Em integer +value +.Fa x +(expressed as a double). +.Sh RETURN VALUES +If these functions are successful, +the computed value is returned. On the +.Tn VAX +and +.Tn Tahoe +architectures, +a negative +.Fa x +value +results in an error; the global +variable +.Va errno +is set to +.Er EDOM +and a reserve operand fault is generated. +.Sh SEE ALSO +.Xr math 3 , +.Xr infnan 3 +.Sh HISTORY +This set of functions +appeared in +.At v7 . diff --git a/lib/msun/man/lgamma.3 b/lib/msun/man/lgamma.3 new file mode 100644 index 0000000..02bd1ad --- /dev/null +++ b/lib/msun/man/lgamma.3 @@ -0,0 +1,124 @@ +.\" 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. +.\" +.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 +.\" $Id: lgamma.3,v 1.6 1994/01/11 00:46:56 jtc Exp $ +.\" +.Dd December 3, 1992 +.Dt LGAMMA 3 +.Os BSD 4.3 +.Sh NAME +.Nm lgamma , +.Nm gamma +.Nd log gamma function, gamma function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft extern int +.Fa signgam ; +.sp +.Ft double +.Fn lgamma "double x" +.Ft double +.Fn gamma "double x" +.Sh DESCRIPTION +.Fn Lgamma x +.if t \{\ +returns ln\||\(*G(x)| where +.Bd -unfilled -offset indent +\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x > 0 and +.br +\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x < 1. +.Ed +.\} +.if n \ +returns ln\||\(*G(x)|. +.Pp +The external integer +.Fa signgam +returns the sign of \(*G(x). +.Pp +.Fn Gamma x +returns \(*G(x), with no effect on +.Fa signgam . +.Sh IDIOSYNCRASIES +Do not use the expression +.Dq Li signgam\(**exp(lgamma(x)) +to compute g := \(*G(x). +Instead use a program like this (in C): +.Bd -literal -offset indent +lg = lgamma(x); g = signgam\(**exp(lg); +.Ed +.Pp +Only after +.Fn lgamma +has returned can signgam be correct. +.Pp +For arguments in its range, +.Fn gamma +is preferred, as for positive arguments +it is accurate to within one unit in the last place. +Exponentiation of +.Fn lgamma +will lose up to 10 significant bits. +.Sh RETURN VALUES +.Fn Gamma +and +.Fn lgamma +return appropriate values unless an argument is out of range. +Overflow will occur for sufficiently large positive values, and +non-positive integers. +On the +.Tn VAX, +the reserved operator is returned, +and +.Va errno +is set to +.Er ERANGE +For large non-integer negative values, +.Fn gamma +will underflow. +.Sh SEE ALSO +.Xr math 3 , +.Xr infnan 3 +.Sh HISTORY +The +.Nm lgamma +function appeared in +.Bx 4.3 . +The +.Nm gamma +function appeared in +.Bx 4.4 . +The name +.Fn gamma +was originally dedicated to the +.Fn lgamma +function, so some old code may no longer be compatible. diff --git a/lib/msun/man/math.3 b/lib/msun/man/math.3 new file mode 100644 index 0000000..b49a510 --- /dev/null +++ b/lib/msun/man/math.3 @@ -0,0 +1,633 @@ +.\" Copyright (c) 1985 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. +.\" +.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91 +.\" $Id: math.3,v 1.4 1994/02/25 19:43:56 jtc Exp $ +.\" +.TH MATH 3M "May 6, 1991" +.UC 4 +.ds up \fIulp\fR +.ds nn \fINaN\fR +.de If +.if n \\ +\\$1Infinity\\$2 +.if t \\ +\\$1\\(if\\$2 +.. +.SH NAME +math \- introduction to mathematical library functions +.SH DESCRIPTION +These functions constitute the C math library, +.I libm. +The link editor searches this library under the \*(lq\-lm\*(rq option. +Declarations for these functions may be obtained from the include file +.RI < math.h >. +The Fortran math library is described in ``man 3f intro''. +.SH "LIST OF FUNCTIONS" +.sp 2 +.nf +.ta \w'copysign'u+2n +\w'infnan.3m'u+10n +\w'inverse trigonometric func'u +\fIName\fP \fIAppears on Page\fP \fIDescription\fP \fIError Bound (ULPs)\fP +.ta \w'copysign'u+4n +\w'infnan.3m'u+4n +\w'inverse trigonometric function'u+6nC +.sp 5p +acos sin.3m inverse trigonometric function 3 +acosh asinh.3m inverse hyperbolic function 3 +asin sin.3m inverse trigonometric function 3 +asinh asinh.3m inverse hyperbolic function 3 +atan sin.3m inverse trigonometric function 1 +atanh asinh.3m inverse hyperbolic function 3 +atan2 sin.3m inverse trigonometric function 2 +cabs hypot.3m complex absolute value 1 +cbrt sqrt.3m cube root 1 +ceil floor.3m integer no less than 0 +copysign ieee.3m copy sign bit 0 +cos sin.3m trigonometric function 1 +cosh sinh.3m hyperbolic function 3 +erf erf.3m error function ??? +erfc erf.3m complementary error function ??? +exp exp.3m exponential 1 +expm1 exp.3m exp(x)\-1 1 +fabs floor.3m absolute value 0 +floor floor.3m integer no greater than 0 +hypot hypot.3m Euclidean distance 1 +ilogb ieee.3m exponent extraction 0 +infnan infnan.3m signals exceptions +j0 j0.3m bessel function ??? +j1 j0.3m bessel function ??? +jn j0.3m bessel function ??? +lgamma lgamma.3m log gamma function; (formerly gamma.3m) +log exp.3m natural logarithm 1 +log10 exp.3m logarithm to base 10 3 +log1p exp.3m log(1+x) 1 +pow exp.3m exponential x**y 60\-500 +remainder ieee.3m remainder 0 +rint floor.3m round to nearest integer 0 +scalbn ieee.3m exponent adjustment 0 +sin sin.3m trigonometric function 1 +sinh sinh.3m hyperbolic function 3 +sqrt sqrt.3m square root 1 +tan sin.3m trigonometric function 3 +tanh sinh.3m hyperbolic function 3 +y0 j0.3m bessel function ??? +y1 j0.3m bessel function ??? +yn j0.3m bessel function ??? +.ta +.fi +.SH NOTES +In 4.3 BSD, distributed from the University of California +in late 1985, most of the foregoing functions come in two +versions, one for the double\-precision "D" format in the +DEC VAX\-11 family of computers, another for double\-precision +arithmetic conforming to the IEEE Standard 754 for Binary +Floating\-Point Arithmetic. The two versions behave very +similarly, as should be expected from programs more accurate +and robust than was the norm when UNIX was born. For +instance, the programs are accurate to within the numbers +of \*(ups tabulated above; an \*(up is one \fIU\fRnit in the \fIL\fRast +\fIP\fRlace. And the programs have been cured of anomalies that +afflicted the older math library \fIlibm\fR in which incidents like +the following had been reported: +.RS +sqrt(\-1.0) = 0.0 and log(\-1.0) = \-1.7e38. +.br +cos(1.0e\-11) > cos(0.0) > 1.0. +.br +pow(x,1.0) +.if n \ +!= +.if t \ +\(!= +x when x = 2.0, 3.0, 4.0, ..., 9.0. +.br +pow(\-1.0,1.0e10) trapped on Integer Overflow. +.br +sqrt(1.0e30) and sqrt(1.0e\-30) were very slow. +.RE +However the two versions do differ in ways that have to be +explained, to which end the following notes are provided. +.PP +\fBDEC VAX\-11 D_floating\-point:\fR +.PP +This is the format for which the original math library \fIlibm\fR +was developed, and to which this manual is still principally +dedicated. It is \fIthe\fR double\-precision format for the PDP\-11 +and the earlier VAX\-11 machines; VAX\-11s after 1983 were +provided with an optional "G" format closer to the IEEE +double\-precision format. The earlier DEC MicroVAXs have no +D format, only G double\-precision. (Why? Why not?) +.PP +Properties of D_floating\-point: +.RS +Wordsize: 64 bits, 8 bytes. Radix: Binary. +.br +Precision: 56 +.if n \ +sig. +.if t \ +significant +bits, roughly like 17 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive D_floating\-point +numbers (they differ by 1 \*(up), then +.br +1.3e\-17 < 0.5**56 < (x'\-x)/x \(<= 0.5**55 < 2.8e\-17. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**127'u+1n +Range: Overflow threshold = 2.0**127 = 1.7e38. + Underflow threshold = 0.5**128 = 2.9e\-39. + NOTE: THIS RANGE IS COMPARATIVELY NARROW. +.ta +.fi +.RS +Overflow customarily stops computation. +.br +Underflow is customarily flushed quietly to zero. +.br +CAUTION: +.RS +It is possible to have x +.if n \ +!= +.if t \ +\(!= +y and yet +x\-y = 0 because of underflow. Similarly +x > y > 0 cannot prevent either x\(**y = 0 +or y/x = 0 from happening without warning. +.RE +.RE +Zero is represented ambiguously. +.RS +Although 2**55 different representations of zero are accepted by +the hardware, only the obvious representation is ever produced. +There is no \-0 on a VAX. +.RE +.If +is not part of the VAX architecture. +.br +Reserved operands: +.RS +of the 2**55 that the hardware +recognizes, only one of them is ever produced. +Any floating\-point operation upon a reserved +operand, even a MOVF or MOVD, customarily stops +computation, so they are not much used. +.RE +Exceptions: +.RS +Divisions by zero and operations that +overflow are invalid operations that customarily +stop computation or, in earlier machines, produce +reserved operands that will stop computation. +.RE +Rounding: +.RS +Every rational operation (+, \-, \(**, /) on a +VAX (but not necessarily on a PDP\-11), if not an +over/underflow nor division by zero, is rounded to +within half an \*(up, and when the rounding error is +exactly half an \*(up then rounding is away from 0. +.RE +.RE +.PP +Except for its narrow range, D_floating\-point is one of the +better computer arithmetics designed in the 1960's. +Its properties are reflected fairly faithfully in the elementary +functions for a VAX distributed in 4.3 BSD. +They over/underflow only if their results have to lie out of range +or very nearly so, and then they behave much as any rational +arithmetic operation that over/underflowed would behave. +Similarly, expressions like log(0) and atanh(1) behave +like 1/0; and sqrt(\-3) and acos(3) behave like 0/0; +they all produce reserved operands and/or stop computation! +The situation is described in more detail in manual pages. +.RS +.ll -0.5i +\fIThis response seems excessively punitive, so it is destined +to be replaced at some time in the foreseeable future by a +more flexible but still uniform scheme being developed to +handle all floating\-point arithmetic exceptions neatly. +See infnan(3M) for the present state of affairs.\fR +.ll +0.5i +.RE +.PP +How do the functions in 4.3 BSD's new \fIlibm\fR for UNIX +compare with their counterparts in DEC's VAX/VMS library? +Some of the VMS functions are a little faster, some are +a little more accurate, some are more puritanical about +exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), +and most occupy much more memory than their counterparts in +\fIlibm\fR. +The VMS codes interpolate in large table to achieve +speed and accuracy; the \fIlibm\fR codes use tricky formulas +compact enough that all of them may some day fit into a ROM. +.PP +More important, DEC regards the VMS codes as proprietary +and guards them zealously against unauthorized use. But the +\fIlibm\fR codes in 4.3 BSD are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine whose arithmetic resembles +VAX D_floating\-point need use anything worse than the new \fIlibm\fR. +.PP +\fBIEEE STANDARD 754 Floating\-Point Arithmetic:\fR +.PP +This standard is on its way to becoming more widely adopted +than any other design for computer arithmetic. +VLSI chips that conform to some version of that standard have been +produced by a host of manufacturers, among them ... +.nf +.ta 0.5i +\w'Intel i8070, i80287'u+6n + Intel i8087, i80287 National Semiconductor 32081 + Motorola 68881 Weitek WTL-1032, ... , -1165 + Zilog Z8070 Western Electric (AT&T) WE32106. +.ta +.fi +Other implementations range from software, done thoroughly +in the Apple Macintosh, through VLSI in the Hewlett\-Packard +9000 series, to the ELXSI 6400 running ECL at 3 Megaflops. +Several other companies have adopted the formats +of IEEE 754 without, alas, adhering to the standard's way +of handling rounding and exceptions like over/underflow. +The DEC VAX G_floating\-point format is very similar to the IEEE +754 Double format, so similar that the C programs for the +IEEE versions of most of the elementary functions listed +above could easily be converted to run on a MicroVAX, though +nobody has volunteered to do that yet. +.PP +The codes in 4.3 BSD's \fIlibm\fR for machines that conform to +IEEE 754 are intended primarily for the National Semi. 32081 +and WTL 1164/65. To use these codes with the Intel or Zilog +chips, or with the Apple Macintosh or ELXSI 6400, is to +forego the use of better codes provided (perhaps freely) by +those companies and designed by some of the authors of the +codes above. +Except for \fIatan\fR, \fIcabs\fR, \fIcbrt\fR, \fIerf\fR, +\fIerfc\fR, \fIhypot\fR, \fIj0\-jn\fR, \fIlgamma\fR, \fIpow\fR +and \fIy0\-yn\fR, +the Motorola 68881 has all the functions in \fIlibm\fR on chip, +and faster and more accurate; +it, Apple, the i8087, Z8070 and WE32106 all use 64 +.if n \ +sig. +.if t \ +significant +bits. +The main virtue of 4.3 BSD's +\fIlibm\fR codes is that they are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine that conforms to +IEEE 754 need use anything worse than the new \fIlibm\fR. +.PP +Properties of IEEE 754 Double\-Precision: +.RS +Wordsize: 64 bits, 8 bytes. Radix: Binary. +.br +Precision: 53 +.if n \ +sig. +.if t \ +significant +bits, roughly like 16 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive Double\-Precision +numbers (they differ by 1 \*(up), then +.br +1.1e\-16 < 0.5**53 < (x'\-x)/x \(<= 0.5**52 < 2.3e\-16. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**1024'u+1n +Range: Overflow threshold = 2.0**1024 = 1.8e308 + Underflow threshold = 0.5**1022 = 2.2e\-308 +.ta +.fi +.RS +Overflow goes by default to a signed +.If "" . +.br +Underflow is \fIGradual,\fR rounding to the nearest +integer multiple of 0.5**1074 = 4.9e\-324. +.RE +Zero is represented ambiguously as +0 or \-0. +.RS +Its sign transforms correctly through multiplication or +division, and is preserved by addition of zeros +with like signs; but x\-x yields +0 for every +finite x. The only operations that reveal zero's +sign are division by zero and copysign(x,\(+-0). +In particular, comparison (x > y, x \(>= y, etc.) +cannot be affected by the sign of zero; but if +finite x = y then +.If +\&= 1/(x\-y) +.if n \ +!= +.if t \ +\(!= +\-1/(y\-x) = +.If \- . +.RE +.If +is signed. +.RS +it persists when added to itself +or to any finite number. Its sign transforms +correctly through multiplication and division, and +.If (finite)/\(+- \0=\0\(+-0 +(nonzero)/0 = +.If \(+- . +But +.if n \ +Infinity\-Infinity, Infinity\(**0 and Infinity/Infinity +.if t \ +\(if\-\(if, \(if\(**0 and \(if/\(if +are, like 0/0 and sqrt(\-3), +invalid operations that produce \*(nn. ... +.RE +Reserved operands: +.RS +there are 2**53\-2 of them, all +called \*(nn (\fIN\fRot \fIa N\fRumber). +Some, called Signaling \*(nns, trap any floating\-point operation +performed upon them; they are used to mark missing +or uninitialized values, or nonexistent elements +of arrays. The rest are Quiet \*(nns; they are +the default results of Invalid Operations, and +propagate through subsequent arithmetic operations. +If x +.if n \ +!= +.if t \ +\(!= +x then x is \*(nn; every other predicate +(x > y, x = y, x < y, ...) is FALSE if \*(nn is involved. +.br +NOTE: Trichotomy is violated by \*(nn. +.RS +Besides being FALSE, predicates that entail ordered +comparison, rather than mere (in)equality, +signal Invalid Operation when \*(nn is involved. +.RE +.RE +Rounding: +.RS +Every algebraic operation (+, \-, \(**, /, +.if n \ +sqrt) +.if t \ +\(sr) +is rounded by default to within half an \*(up, and +when the rounding error is exactly half an \*(up then +the rounded value's least significant bit is zero. +This kind of rounding is usually the best kind, +sometimes provably so; for instance, for every +x = 1.0, 2.0, 3.0, 4.0, ..., 2.0**52, we find +(x/3.0)\(**3.0 == x and (x/10.0)\(**10.0 == x and ... +despite that both the quotients and the products +have been rounded. Only rounding like IEEE 754 +can do that. But no single kind of rounding can be +proved best for every circumstance, so IEEE 754 +provides rounding towards zero or towards +.If + +or towards +.If \- +at the programmer's option. And the +same kinds of rounding are specified for +Binary\-Decimal Conversions, at least for magnitudes +between roughly 1.0e\-10 and 1.0e37. +.RE +Exceptions: +.RS +IEEE 754 recognizes five kinds of floating\-point exceptions, +listed below in declining order of probable importance. +.RS +.nf +.ta \w'Invalid Operation'u+6n +\w'Gradual Underflow'u+2n +Exception Default Result +.tc \(ru + +.tc +Invalid Operation \*(nn, or FALSE +.if n \{\ +Overflow \(+-Infinity +Divide by Zero \(+-Infinity \} +.if t \{\ +Overflow \(+-\(if +Divide by Zero \(+-\(if \} +Underflow Gradual Underflow +Inexact Rounded value +.ta +.fi +.RE +NOTE: An Exception is not an Error unless handled +badly. What makes a class of exceptions exceptional +is that no single default response can be satisfactory +in every instance. On the other hand, if a default +response will serve most instances satisfactorily, +the unsatisfactory instances cannot justify aborting +computation every time the exception occurs. +.RE +.PP +For each kind of floating\-point exception, IEEE 754 +provides a Flag that is raised each time its exception +is signaled, and stays raised until the program resets +it. Programs may also test, save and restore a flag. +Thus, IEEE 754 provides three ways by which programs +may cope with exceptions for which the default result +might be unsatisfactory: +.IP 1) \w'\0\0\0\0'u +Test for a condition that might cause an exception +later, and branch to avoid the exception. +.IP 2) \w'\0\0\0\0'u +Test a flag to see whether an exception has occurred +since the program last reset its flag. +.IP 3) \w'\0\0\0\0'u +Test a result to see whether it is a value that only +an exception could have produced. +.RS +CAUTION: The only reliable ways to discover +whether Underflow has occurred are to test whether +products or quotients lie closer to zero than the +underflow threshold, or to test the Underflow +flag. (Sums and differences cannot underflow in +IEEE 754; if x +.if n \ +!= +.if t \ +\(!= +y then x\-y is correct to +full precision and certainly nonzero regardless of +how tiny it may be.) Products and quotients that +underflow gradually can lose accuracy gradually +without vanishing, so comparing them with zero +(as one might on a VAX) will not reveal the loss. +Fortunately, if a gradually underflowed value is +destined to be added to something bigger than the +underflow threshold, as is almost always the case, +digits lost to gradual underflow will not be missed +because they would have been rounded off anyway. +So gradual underflows are usually \fIprovably\fR ignorable. +The same cannot be said of underflows flushed to 0. +.RE +.PP +At the option of an implementor conforming to IEEE 754, +other ways to cope with exceptions may be provided: +.IP 4) \w'\0\0\0\0'u +ABORT. This mechanism classifies an exception in +advance as an incident to be handled by means +traditionally associated with error\-handling +statements like "ON ERROR GO TO ...". Different +languages offer different forms of this statement, +but most share the following characteristics: +.IP \(em \w'\0\0\0\0'u +No means is provided to substitute a value for +the offending operation's result and resume +computation from what may be the middle of an +expression. An exceptional result is abandoned. +.IP \(em \w'\0\0\0\0'u +In a subprogram that lacks an error\-handling +statement, an exception causes the subprogram to +abort within whatever program called it, and so +on back up the chain of calling subprograms until +an error\-handling statement is encountered or the +whole task is aborted and memory is dumped. +.IP 5) \w'\0\0\0\0'u +STOP. This mechanism, requiring an interactive +debugging environment, is more for the programmer +than the program. It classifies an exception in +advance as a symptom of a programmer's error; the +exception suspends execution as near as it can to +the offending operation so that the programmer can +look around to see how it happened. Quite often +the first several exceptions turn out to be quite +unexceptionable, so the programmer ought ideally +to be able to resume execution after each one as if +execution had not been stopped. +.IP 6) \w'\0\0\0\0'u +\&... Other ways lie beyond the scope of this document. +.RE +.PP +The crucial problem for exception handling is the problem of +Scope, and the problem's solution is understood, but not +enough manpower was available to implement it fully in time +to be distributed in 4.3 BSD's \fIlibm\fR. Ideally, each +elementary function should act as if it were indivisible, or +atomic, in the sense that ... +.IP i) \w'iii)'u+2n +No exception should be signaled that is not deserved by +the data supplied to that function. +.IP ii) \w'iii)'u+2n +Any exception signaled should be identified with that +function rather than with one of its subroutines. +.IP iii) \w'iii)'u+2n +The internal behavior of an atomic function should not +be disrupted when a calling program changes from +one to another of the five or so ways of handling +exceptions listed above, although the definition +of the function may be correlated intentionally +with exception handling. +.PP +Ideally, every programmer should be able \fIconveniently\fR to +turn a debugged subprogram into one that appears atomic to +its users. But simulating all three characteristics of an +atomic function is still a tedious affair, entailing hosts +of tests and saves\-restores; work is under way to ameliorate +the inconvenience. +.PP +Meanwhile, the functions in \fIlibm\fR are only approximately +atomic. They signal no inappropriate exception except +possibly ... +.RS +Over/Underflow +.RS +when a result, if properly computed, might have lain barely within range, and +.RE +Inexact in \fIcabs\fR, \fIcbrt\fR, \fIhypot\fR, \fIlog10\fR and \fIpow\fR +.RS +when it happens to be exact, thanks to fortuitous cancellation of errors. +.RE +.RE +Otherwise, ... +.RS +Invalid Operation is signaled only when +.RS +any result but \*(nn would probably be misleading. +.RE +Overflow is signaled only when +.RS +the exact result would be finite but beyond the overflow threshold. +.RE +Divide\-by\-Zero is signaled only when +.RS +a function takes exactly infinite values at finite operands. +.RE +Underflow is signaled only when +.RS +the exact result would be nonzero but tinier than the underflow threshold. +.RE +Inexact is signaled only when +.RS +greater range or precision would be needed to represent the exact result. +.RE +.RE +.SH BUGS +When signals are appropriate, they are emitted by certain +operations within the codes, so a subroutine\-trace may be +needed to identify the function with its signal in case +method 5) above is in use. And the codes all take the +IEEE 754 defaults for granted; this means that a decision to +trap all divisions by zero could disrupt a code that would +otherwise get correct results despite division by zero. +.SH SEE ALSO +An explanation of IEEE 754 and its proposed extension p854 +was published in the IEEE magazine MICRO in August 1984 under +the title "A Proposed Radix\- and Word\-length\-independent +Standard for Floating\-point Arithmetic" by W. J. Cody et al. +The manuals for Pascal, C and BASIC on the Apple Macintosh +document the features of IEEE 754 pretty well. +Articles in the IEEE magazine COMPUTER vol. 14 no. 3 (Mar. +1981), and in the ACM SIGNUM Newsletter Special Issue of +Oct. 1979, may be helpful although they pertain to +superseded drafts of the standard. diff --git a/lib/msun/man/rint.3 b/lib/msun/man/rint.3 new file mode 100644 index 0000000..13132e6 --- /dev/null +++ b/lib/msun/man/rint.3 @@ -0,0 +1,63 @@ +.\" 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. +.\" +.\" from: @(#)rint.3 5.1 (Berkeley) 5/2/91 +.\" $Id: rint.3,v 1.4 1994/03/11 01:32:11 jtc Exp $ +.\" +.Dd March 10, 1994 +.Dt RINT 3 +.Os +.Sh NAME +.Nm rint +.Nd round to integral value in floating-point format +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn rint "double x" +.Sh DESCRIPTION +The +.Fn rint +function returns the integral value (represented as a double precision number) +nearest to +.Fa x +according to the prevailing rounding mode. +.Sh SEE ALSO +.Xr abs 3 , +.Xr fabs 3 , +.Xr ceil 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 +.Sh HISTORY +A +.Fn rint +function appeared in +.At v6 . diff --git a/lib/msun/man/sin.3 b/lib/msun/man/sin.3 new file mode 100644 index 0000000..4274a0f --- /dev/null +++ b/lib/msun/man/sin.3 @@ -0,0 +1,73 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" @(#)sin.3 6.7 (Berkeley) 4/19/91 +.\" 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. +.\" +.\" from: @(#)sin.3 6.7 (Berkeley) 4/19/91 +.\" $Id: sin.3,v 1.4 1993/10/29 22:57:28 jtc Exp $ +.\" +.Dd April 19, 1991 +.Dt SIN 3 +.Os +.Sh NAME +.Nm sin +.Nd sine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn sin "double x" +.Sh DESCRIPTION +The +.Fn sin +function computes the sine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little +or no significance. +.Sh RETURN VALUES +The +.Fn sin +function returns the sine value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn sin +function conforms to +.St -ansiC . diff --git a/lib/msun/man/sinh.3 b/lib/msun/man/sinh.3 new file mode 100644 index 0000000..39e0a1f --- /dev/null +++ b/lib/msun/man/sinh.3 @@ -0,0 +1,75 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)sinh.3 6.6 (Berkeley) 4/19/91 +.\" $Id: sinh.3,v 1.4 1993/10/29 22:57:30 jtc Exp $ +.Dd April 19, 1991 +.Dt SINH 3 +.Os +.Sh NAME +.Nm sinh +.Nd hyperbolic sine function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn sinh "double x" +.Sh DESCRIPTION +The +.Fn sinh +function computes the hyperbolic sine of +.Fa x . +.Sh RETURN VALUES +The +.Fn sinh +function returns the hyperbolic sine value unless +the magnitude +of +.Fa x +is too large; in this event, the global variable +.Va errno +is set to +.Er ERANGE . +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr tan 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn sinh +function conforms to +.St -ansiC . diff --git a/lib/msun/man/sqrt.3 b/lib/msun/man/sqrt.3 new file mode 100644 index 0000000..dbe3bfe --- /dev/null +++ b/lib/msun/man/sqrt.3 @@ -0,0 +1,121 @@ +.\" 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. +.\" +.\" from: @(#)sqrt.3 6.4 (Berkeley) 5/6/91 +.\" $Id: sqrt.3,v 1.3 1993/08/14 13:43:05 mycroft Exp $ +.\" +.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 . diff --git a/lib/msun/man/tan.3 b/lib/msun/man/tan.3 new file mode 100644 index 0000000..c1acb48 --- /dev/null +++ b/lib/msun/man/tan.3 @@ -0,0 +1,74 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)tan.3 5.1 (Berkeley) 5/2/91 +.\" $Id: tan.3,v 1.4 1993/10/05 16:33:47 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt TAN 3 +.Os +.Sh NAME +.Nm tan +.Nd tangent function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn tan "double x" +.Sh DESCRIPTION +The +.Fn tan +function computes the tangent of +.Fa x +(measured in radians). +A large magnitude argument may yield a result +with little or no significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tan +function returns the tangent value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tanh 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn tan +function conforms to +.St -ansiC . diff --git a/lib/msun/man/tanh.3 b/lib/msun/man/tanh.3 new file mode 100644 index 0000000..2f1e27f --- /dev/null +++ b/lib/msun/man/tanh.3 @@ -0,0 +1,71 @@ +.\" Copyright (c) 1991 The 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. +.\" +.\" from: @(#)tanh.3 5.1 (Berkeley) 5/2/91 +.\" $Id: tanh.3,v 1.4 1993/10/05 16:33:49 jtc Exp $ +.\" +.Dd May 2, 1991 +.Dt TANH 3 +.Os +.Sh NAME +.Nm tanh +.Nd hyperbolic tangent function +.Sh SYNOPSIS +.Fd #include <math.h> +.Ft double +.Fn tanh "double x" +.Sh DESCRIPTION +The +.Fn tanh +function computes the hyperbolic tangent of +.Fa x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tanh +function returns the hyperbolic tangent value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn tanh +function conforms to +.St -ansiC . |
