From 4784c39e63e0d779fa98850910292bb686a99f29 Mon Sep 17 00:00:00 2001 From: bde Date: Sat, 13 Oct 2001 14:22:08 +0000 Subject: Removed most of the zombie man pages in libm. All relevant parts have been copied to msun/man (most of them long ago without proper history). --- lib/libm/common_source/acos.3 | 91 ------ lib/libm/common_source/acosh.3 | 84 ------ lib/libm/common_source/asin.3 | 93 ------ lib/libm/common_source/asinh.3 | 72 ----- lib/libm/common_source/atan.3 | 77 ----- lib/libm/common_source/atan2.3 | 191 ------------ lib/libm/common_source/atanh.3 | 86 ------ lib/libm/common_source/ceil.3 | 68 ----- lib/libm/common_source/cos.3 | 76 ----- lib/libm/common_source/cosh.3 | 77 ----- lib/libm/common_source/erf.3 | 85 ------ lib/libm/common_source/exp.3 | 290 ------------------ lib/libm/common_source/fabs.3 | 69 ----- lib/libm/common_source/floor.3 | 68 ----- lib/libm/common_source/fmod.3 | 78 ----- lib/libm/common_source/hypot.3 | 127 -------- lib/libm/common_source/ieee.3 | 270 ----------------- lib/libm/common_source/j0.3 | 130 --------- lib/libm/common_source/lgamma.3 | 126 -------- lib/libm/common_source/math.3 | 632 ---------------------------------------- lib/libm/common_source/rint.3 | 118 -------- lib/libm/common_source/sin.3 | 75 ----- lib/libm/common_source/sinh.3 | 78 ----- lib/libm/common_source/sqrt.3 | 123 -------- lib/libm/common_source/tan.3 | 76 ----- lib/libm/common_source/tanh.3 | 73 ----- 26 files changed, 3333 deletions(-) delete mode 100644 lib/libm/common_source/acos.3 delete mode 100644 lib/libm/common_source/acosh.3 delete mode 100644 lib/libm/common_source/asin.3 delete mode 100644 lib/libm/common_source/asinh.3 delete mode 100644 lib/libm/common_source/atan.3 delete mode 100644 lib/libm/common_source/atan2.3 delete mode 100644 lib/libm/common_source/atanh.3 delete mode 100644 lib/libm/common_source/ceil.3 delete mode 100644 lib/libm/common_source/cos.3 delete mode 100644 lib/libm/common_source/cosh.3 delete mode 100644 lib/libm/common_source/erf.3 delete mode 100644 lib/libm/common_source/exp.3 delete mode 100644 lib/libm/common_source/fabs.3 delete mode 100644 lib/libm/common_source/floor.3 delete mode 100644 lib/libm/common_source/fmod.3 delete mode 100644 lib/libm/common_source/hypot.3 delete mode 100644 lib/libm/common_source/ieee.3 delete mode 100644 lib/libm/common_source/j0.3 delete mode 100644 lib/libm/common_source/lgamma.3 delete mode 100644 lib/libm/common_source/math.3 delete mode 100644 lib/libm/common_source/rint.3 delete mode 100644 lib/libm/common_source/sin.3 delete mode 100644 lib/libm/common_source/sinh.3 delete mode 100644 lib/libm/common_source/sqrt.3 delete mode 100644 lib/libm/common_source/tan.3 delete mode 100644 lib/libm/common_source/tanh.3 (limited to 'lib/libm') diff --git a/lib/libm/common_source/acos.3 b/lib/libm/common_source/acos.3 deleted file mode 100644 index 5393247..0000000 --- a/lib/libm/common_source/acos.3 +++ /dev/null @@ -1,91 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)acos.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ACOS 3 -.Os -.Sh NAME -.Nm acos -.Nd arc cosine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 -.Er EDOM -and a reserved operand fault is generated. -.Sh SEE ALSO -.Xr asin 3 , -.Xr atan 3 , -.Xr atan2 3 , -.Xr cos 3 , -.Xr cosh 3 , -.Xr math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn acos -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/acosh.3 b/lib/libm/common_source/acosh.3 deleted file mode 100644 index 597e633..0000000 --- a/lib/libm/common_source/acosh.3 +++ /dev/null @@ -1,84 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)acosh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ACOSH 3 -.Os -.Sh NAME -.Nm acosh -.Nd inverse hyperbolic cosine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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/libm/common_source/asin.3 b/lib/libm/common_source/asin.3 deleted file mode 100644 index c45c3b1..0000000 --- a/lib/libm/common_source/asin.3 +++ /dev/null @@ -1,93 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)asin.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ASIN 3 -.Os -.Sh NAME -.Nm asin -.Nd arc sine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn asin -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/asinh.3 b/lib/libm/common_source/asinh.3 deleted file mode 100644 index e9b50fc..0000000 --- a/lib/libm/common_source/asinh.3 +++ /dev/null @@ -1,72 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)asinh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ASINH 3 -.Os -.Sh NAME -.Nm asinh -.Nd inverse hyperbolic sine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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/libm/common_source/atan.3 b/lib/libm/common_source/atan.3 deleted file mode 100644 index b627190..0000000 --- a/lib/libm/common_source/atan.3 +++ /dev/null @@ -1,77 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)atan.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ATAN 3 -.Os -.Sh NAME -.Nm atan -.Nd arc tangent function of one variable -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn atan -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/atan2.3 b/lib/libm/common_source/atan2.3 deleted file mode 100644 index e4a447c..0000000 --- a/lib/libm/common_source/atan2.3 +++ /dev/null @@ -1,191 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)atan2.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ATAN2 3 -.Os -.Sh NAME -.Nm atan2 -.Nd arc tangent function of two variables -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn atan2 -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/atanh.3 b/lib/libm/common_source/atanh.3 deleted file mode 100644 index 065fd6d..0000000 --- a/lib/libm/common_source/atanh.3 +++ /dev/null @@ -1,86 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)atanh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ATANH 3 -.Os -.Sh NAME -.Nm atanh -.Nd inverse hyperbolic tangent function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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/libm/common_source/ceil.3 b/lib/libm/common_source/ceil.3 deleted file mode 100644 index 031f40f..0000000 --- a/lib/libm/common_source/ceil.3 +++ /dev/null @@ -1,68 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)ceil.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt CEIL 3 -.Os -.Sh NAME -.Nm ceil -.Nd smallest integral value greather than or equal to x -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In math.h -.Ft double -.Fn ceil "double x" -.Sh DESCRIPTION -The -.Fn ceil -function computes the smallest integral value greater than or equal to -.Fa x . -.Sh RETURN VALUES -The -.Fn ceil -function returns the smallest integral value -expressed as a double. -.Sh SEE ALSO -.Xr abs 3 , -.Xr fabs 3 , -.Xr floor 3 , -.Xr ieee 3 , -.Xr math 3 , -.Xr rint 3 -.Sh STANDARDS -The -.Fn ceil -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/cos.3 b/lib/libm/common_source/cos.3 deleted file mode 100644 index af52841..0000000 --- a/lib/libm/common_source/cos.3 +++ /dev/null @@ -1,76 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)cos.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt COS 3 -.Os -.Sh NAME -.Nm cos -.Nd cosine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 acos 3 , -.Xr asin 3 , -.Xr atan 3 , -.Xr atan2 3 , -.Xr cosh 3 , -.Xr math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn acos -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/cosh.3 b/lib/libm/common_source/cosh.3 deleted file mode 100644 index ef97b48..0000000 --- a/lib/libm/common_source/cosh.3 +++ /dev/null @@ -1,77 +0,0 @@ -.\" Copyright (c) 1989, 1991, 1993 -.\" 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. -.\" -.\" @(#)cosh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt COSH 3 -.Os -.Sh NAME -.Nm cosh -.Nd hyperbolic cosine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn cosh -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/erf.3 b/lib/libm/common_source/erf.3 deleted file mode 100644 index a76815a..0000000 --- a/lib/libm/common_source/erf.3 +++ /dev/null @@ -1,85 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)erf.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt ERF 3 -.Os -.Sh NAME -.Nm erf , -.Nm erfc -.Nd error function operators -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 -ragged -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/libm/common_source/exp.3 b/lib/libm/common_source/exp.3 deleted file mode 100644 index fa31db8..0000000 --- a/lib/libm/common_source/exp.3 +++ /dev/null @@ -1,290 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)exp.3 8.2 (Berkeley) 4/19/94 -.\" $FreeBSD$ -.\" -.Dd April 19, 1994 -.Dt EXP 3 -.Os -.Sh NAME -.Nm exp , -.Nm expm1 , -.Nm log , -.Nm log10 , -.Nm log1p , -.Nm pow -.Nd exponential, logarithm, power functions -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 for the natural logarithm of -the argument x. -.Pp -The -.Fn log10 -function computes the value for 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 up , -and log10(x) to within about 2 -.Em ups ; -an -.Em up -is one -.Em Unit -in the -.Em Last -.Em Place . -The error in -.Fn pow x y -is below about 2 -.Em ups -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 ups -for -.Tn "VAX D" , -300 -.Em ups -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 -ragged -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 infnan 3 , -.Xr math 3 -.Sh HISTORY -A -.Fn exp , -.Fn log -and -.Fn pow -function -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/libm/common_source/fabs.3 b/lib/libm/common_source/fabs.3 deleted file mode 100644 index 9a5533c..0000000 --- a/lib/libm/common_source/fabs.3 +++ /dev/null @@ -1,69 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. -.\" -.\" @(#)fabs.3 8.1 (Berkeley) 6/4/93 -.\" 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. -.\" -.\" @(#)fabs.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt FABS 3 -.Os -.Sh NAME -.Nm fabs -.Nd floating-point absolute value function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 ieee 3 , -.Xr math 3 , -.Xr rint 3 -.Sh STANDARDS -The -.Fn fabs -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/floor.3 b/lib/libm/common_source/floor.3 deleted file mode 100644 index 1751f81..0000000 --- a/lib/libm/common_source/floor.3 +++ /dev/null @@ -1,68 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)floor.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt FLOOR 3 -.Os -.Sh NAME -.Nm floor -.Nd largest integral value less than or equal to x -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In math.h -.Ft double -.Fn floor "double x" -.Sh DESCRIPTION -The -.Fn floor -function computes the largest integral value less than or equal to -.Fa x . -.Sh RETURN VALUES -The -.Fn floor -function returns the largest integral value -expressed as a double. -.Sh SEE ALSO -.Xr abs 3 , -.Xr fabs 3 , -.Xr floor 3 , -.Xr ieee 3 , -.Xr math 3 , -.Xr rint 3 -.Sh STANDARDS -The -.Fn floor -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/fmod.3 b/lib/libm/common_source/fmod.3 deleted file mode 100644 index 9f5b206..0000000 --- a/lib/libm/common_source/fmod.3 +++ /dev/null @@ -1,78 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)fmod.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt FMOD 3 -.Os -.Sh NAME -.Nm fmod -.Nd floating-point remainder function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 -isoC . diff --git a/lib/libm/common_source/hypot.3 b/lib/libm/common_source/hypot.3 deleted file mode 100644 index 1c53d7d..0000000 --- a/lib/libm/common_source/hypot.3 +++ /dev/null @@ -1,127 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)hypot.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt HYPOT 3 -.Os -.Sh NAME -.Nm hypot , -.Nm cabs -.Nd euclidean distance and complex absolute value functions -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In math.h -.Ft double -.Fn hypot "double x" "double y" -.Vt 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/libm/common_source/ieee.3 b/lib/libm/common_source/ieee.3 deleted file mode 100644 index a906ba1..0000000 --- a/lib/libm/common_source/ieee.3 +++ /dev/null @@ -1,270 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)ieee.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt IEEE 3 -.Os -.Sh NAME -.Nm copysign , -.Nm drem , -.Nm finite , -.Nm logb , -.Nm scalb -.Nd "IEEE 754 floating point support -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In math.h -.Ft double -.Fn copysign "double x" "double y" -.Ft double -.Fn drem "double x" "double y" -.Ft int -.Fn finite "double x" -.Ft double -.Fn logb "double x" -.Ft double -.Fn scalb "double x" "int n" -.Sh DESCRIPTION -These functions are required for, or recommended by the -.Tn IEEE -standard -754 for floating\-point arithmetic. -.Pp -The -.Fn copysign -function -returns -.Fa x -with its sign changed to -.Fa y Ns 's . -.Pp -The -.Fn drem -function -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 drem x 0 -is exceptional. -(See below under -.Sx DIAGNOSTICS . ) -.Pp -The -.Fn finite -function 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 or -is the -.Tn VAX Ns 's -reserved operand). -.Pp -The -.Fn logb -function returns -.Fa x Ns 's exponent -.Fa n , -a signed integer converted to double\-precision floating\-point and so -chosen that -1 (<= -.Pf \\*(Ba Ns Fa x Ns \\*(Ba2** Ns Fa n -< 2 -unless -.Fa x -= 0 or -(only on machines that conform to -.Tn IEEE -754) -.Pf \\*(Ba Fa x Ns \\*(Ba -= \*(If -or -.Fa x -lies between 0 and the Underflow Threshold. -(See below under -.Sx BUGS . ) -.Pp -The -.Fn scalb -function returns -.Fa x Ns \(**(2** Ns Fa n ) -computed, for integer n, without first computing -.Pf 2\(** Fa n . -.Sh RETURN VALUES -The -.Tn IEEE -standard -754 defines -.Fn drem x 0 -and -.Fn drem \\*(If y -to be invalid operations that produce a \*(Na. -On the -.Tn VAX , -.Fn drem x 0 -generates a reserved operand fault. No \*(If -exists on a -.Tn VAX . -.Pp -.Tn IEEE -754 defines -.if n \ -.Fn logb \(+-\\*(If -= \*(If and -.Fn logb 0 -= \-\*(If, and -requires the latter to signal Division\-by\-Zero. -But on a -.Tn VAX , -.Fn logb 0 -= 1.0 \- 2.0**31 = \-2,147,483,647.0. -And if the correct value of -.Fn scalb -would overflow on a -.Tn VAX , -it generates a reserved operand fault and sets the global variable -.Va errno -to -.Er ERANGE . -.Sh SEE ALSO -.Xr floor 3 , -.Xr infnan 3 , -.Xr math 3 -.Sh HISTORY -The -.Nm ieee -functions appeared in -.Bx 4.3 . -.Sh BUGS -Should -.Fn drem x 0 -and -.Fn logb 0 -on a -.Tn VAX -signal invalidity -by setting -.Va errno No = Er EDOM ? -Should -.Fn logb 0 -return \-1.7e38? -.Pp -.Tn IEEE -754 currently specifies that -.Fn logb "denormalized no.\&" -= -.Fn logb "tiniest normalized no. > 0" -but the consensus has changed to the specification in the new -proposed -.Tn IEEE -standard p854, namely that -.Fn logb x -satisfy -.Bd -ragged -offset indent -1 \(<= -.Fn scalb \\*(Bax\\*(Ba \-logb(x) -< -Radix\0 ... = 2 -for -.Tn IEEE -754 -.Ed -.Pp -for every x except 0, -\*(If -and \*(Na. -Almost every program that assumes 754's specification will work -correctly if -.Fn logb -follows 854's specification instead. -.Pp -.Tn IEEE -754 requires -.Fn copysign x \\*(Na) -= -.Pf \(+- Ns Fa x -but says nothing -else about the sign of a \*(Na. A \*(Na -.Em (N Ns ot -.Em a -.Em N Ns umber ) -is -similar in spirit to the -.Tn VAX Ns 's -reserved operand, but very -different in important details. Since the sign bit of a -reserved operand makes it look negative, -.Bd -ragged -offset indent -.Fn copysign x "reserved operand" -= -.Pf \- Fa x ; -.Ed -.Pp -should this return the reserved operand instead? diff --git a/lib/libm/common_source/j0.3 b/lib/libm/common_source/j0.3 deleted file mode 100644 index dbc603d..0000000 --- a/lib/libm/common_source/j0.3 +++ /dev/null @@ -1,130 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)j0.3 8.2 (Berkeley) 4/19/94 -.\" $FreeBSD$ -.\" -.Dd April 19, 1994 -.Dt J0 3 -.Os -.Sh NAME -.Nm j0 , -.Nm j1 , -.Nm jn , -.Nm y0 , -.Nm y1 , -.Nm yn -.Nd bessel functions of first and second kind -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 infnan 3 , -.Xr math 3 -.Sh HISTORY -A set of these functions -function appeared in -.At v7 . diff --git a/lib/libm/common_source/lgamma.3 b/lib/libm/common_source/lgamma.3 deleted file mode 100644 index 13dcee9..0000000 --- a/lib/libm/common_source/lgamma.3 +++ /dev/null @@ -1,126 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)lgamma.3 8.2 (Berkeley) 12/11/93 -.\" $FreeBSD$ -.\" -.Dd December 11, 1993 -.Dt LGAMMA 3 -.Os -.Sh NAME -.Nm lgamma -.Nm gamma -.Nd log gamma function, gamma function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 infnan 3 , -.Xr math 3 -.Sh HISTORY -The -.Fn lgamma -function appeared in -.Bx 4.3 . -The -.Fn 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/libm/common_source/math.3 b/lib/libm/common_source/math.3 deleted file mode 100644 index 4bc1ff3..0000000 --- a/lib/libm/common_source/math.3 +++ /dev/null @@ -1,632 +0,0 @@ -.\" Copyright (c) 1985, 1993 -.\" 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. -.\" -.\" @(#)math.3 8.2 (Berkeley) 5/5/94 -.\" $FreeBSD$ -.\" -.TH MATH 3 "May 5, 1994" -.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 -drem ieee.3m remainder 0 -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 -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 -logb ieee.3m exponent extraction 0 -log10 exp.3m logarithm to base 10 3 -log1p exp.3m log(1+x) 1 -pow exp.3m exponential x**y 60\-500 -rint floor.3m round to nearest integer 0 -scalb 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 -.sp 0.5 -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/libm/common_source/rint.3 b/lib/libm/common_source/rint.3 deleted file mode 100644 index 599851c..0000000 --- a/lib/libm/common_source/rint.3 +++ /dev/null @@ -1,118 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)rint.3 8.2 (Berkeley) 12/11/93 -.\" $FreeBSD$ -.\" -.Dd December 11, 1993 -.Dt RINT 3 -.Os -.Sh NAME -.Nm rint -.Nd round-to-closest integer functions -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In math.h -.Ft double -.Fn rint "double x" -.Sh DESCRIPTION -The -.Fn rint -function finds the integer (represented as a double precision number) -nearest to -.Fa x -in the direction of the prevailing rounding mode. -.Sh NOTES -On a -.Tn VAX , -.Fn rint x -is equivalent to adding half to the magnitude -and then rounding towards zero. -.Pp -In the default rounding mode, to nearest, -on a machine that conforms to -.Tn IEEE -754, -.Fn rint x -is the integer nearest -.Fa x -with the additional stipulation -that if -.Li |rint(x)\-x|=1/2 -then -.Fn rint x -is even. -Other rounding modes can make -.Fn rint -act like -.Fn floor , -or like -.Fn ceil , -or round towards zero. -.Pp -Another way to obtain an integer near -.Fa x -is to declare (in C) -.Bd -literal -offset indent -double x;\0\0\0\0 int k;\0\0\0\0k\0=\0x; -.Ed -.Pp -Most C compilers round -.Fa x -towards 0 to get the integer -.Fa k , -but -some do otherwise. -If in doubt, use -.Fn floor , -.Fn ceil , -or -.Fn rint -first, whichever you intend. -Also note that, if x is larger than -.Fa k -can accommodate, the value of -.Fa k -and the presence or absence of an integer overflow are hard to -predict. -.Sh SEE ALSO -.Xr abs 3 , -.Xr ceil 3 , -.Xr fabs 3 , -.Xr floor 3 , -.Xr ieee 3 , -.Xr math 3 -.Sh HISTORY -A -.Fn rint -function appeared in -.At v6 . diff --git a/lib/libm/common_source/sin.3 b/lib/libm/common_source/sin.3 deleted file mode 100644 index fba0476..0000000 --- a/lib/libm/common_source/sin.3 +++ /dev/null @@ -1,75 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" The Regents of the University of California. All rights reserved. -.\" -.\" @(#)sin.3 8.1 (Berkeley) 6/4/93 -.\" 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. -.\" -.\" @(#)sin.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt SIN 3 -.Os -.Sh NAME -.Nm sin -.Nd sine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sinh 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn sin -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/sinh.3 b/lib/libm/common_source/sinh.3 deleted file mode 100644 index 2b1c0d7..0000000 --- a/lib/libm/common_source/sinh.3 +++ /dev/null @@ -1,78 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)sinh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt SINH 3 -.Os -.Sh NAME -.Nm sinh -.Nd hyperbolic sine function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr tan 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn sinh -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/sqrt.3 b/lib/libm/common_source/sqrt.3 deleted file mode 100644 index 36c4287..0000000 --- a/lib/libm/common_source/sqrt.3 +++ /dev/null @@ -1,123 +0,0 @@ -.\" Copyright (c) 1985, 1991, 1993 -.\" 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. -.\" -.\" @(#)sqrt.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt SQRT 3 -.Os -.Sh NAME -.Nm cbrt , -.Nm sqrt -.Nd cube root and square root functions -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 -.Er 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 infnan 3 , -.Xr math 3 -.Sh STANDARDS -The -.Fn sqrt -function conforms to -.St -isoC . -.Sh HISTORY -The -.Fn cbrt -function appeared in -.Bx 4.3 . diff --git a/lib/libm/common_source/tan.3 b/lib/libm/common_source/tan.3 deleted file mode 100644 index 3365dc6..0000000 --- a/lib/libm/common_source/tan.3 +++ /dev/null @@ -1,76 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)tan.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt TAN 3 -.Os -.Sh NAME -.Nm tan -.Nd tangent function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tanh 3 -.Sh STANDARDS -The -.Fn tan -function conforms to -.St -isoC . diff --git a/lib/libm/common_source/tanh.3 b/lib/libm/common_source/tanh.3 deleted file mode 100644 index ab181a4..0000000 --- a/lib/libm/common_source/tanh.3 +++ /dev/null @@ -1,73 +0,0 @@ -.\" Copyright (c) 1991, 1993 -.\" 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. -.\" -.\" @(#)tanh.3 8.1 (Berkeley) 6/4/93 -.\" $FreeBSD$ -.\" -.Dd June 4, 1993 -.Dt TANH 3 -.Os -.Sh NAME -.Nm tanh -.Nd hyperbolic tangent function -.Sh LIBRARY -.Lb libm -.Sh SYNOPSIS -.In 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 math 3 , -.Xr sin 3 , -.Xr sinh 3 , -.Xr tan 3 -.Sh STANDARDS -The -.Fn tanh -function conforms to -.St -isoC . -- cgit v1.1