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add new versin and vercos builtin functions
Added new versin(x, [,eps]) for versed sine and vercos(x, [,eps]) for versed cosine. Updated trig help files.
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Landon Curt Noll
@@ -228,8 +228,8 @@ DETAIL_HELP= abs access acos acosh acot acoth acsc acsch address agd \
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sin sinh size sizeof sleep sort sqrt srand srandom ssq stoponerror str \
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strcasecmp strcat strcmp strcpy strerror strlen strncasecmp strncmp \
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strncpy strpos strprintf strscan strscanf strtolower strtoupper substr \
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sum swap system systime tail tan tanh test time trunc usertime version \
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xor
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sum swap system systime tail tan tanh test time trunc usertime vercos \
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versin version xor
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# This list is of files that are clones of DETAIL_HELP files. They are
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# built from DETAIL_HELP files.
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1
help/cos
1
help/cos
@@ -34,6 +34,7 @@ LINK LIBRARY
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SEE ALSO
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sin, tan, sec, csc, cot, epsilon
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versin, vercos
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## Copyright (C) 1999,2021,2023 Landon Curt Noll
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##
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2
help/cot
2
help/cot
@@ -23,9 +23,11 @@ LIMITS
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LINK LIBRARY
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NUMBER *qcot(NUMBER *x, NUMBER *eps)
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COMPLEX *c_acot(COMPLEX *c, NUMBER *eps);
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SEE ALSO
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sin, cos, tan, sec, csc, epsilon
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versin, vercos
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## Copyright (C) 1999,2021,2023 Landon Curt Noll
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##
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1
help/csc
1
help/csc
@@ -26,6 +26,7 @@ LINK LIBRARY
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SEE ALSO
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sin, cos, tan, sec, cot, epsilon
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versin, vercos
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## Copyright (C) 1999,2023 Landon Curt Noll
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##
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1
help/sec
1
help/sec
@@ -27,6 +27,7 @@ LINK LIBRARY
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SEE ALSO
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sin, cos, tan, csc, cot, epsilon
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versin, vercos
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## Copyright (C) 1999,2023 Landon Curt Noll
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##
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1
help/sin
1
help/sin
@@ -34,6 +34,7 @@ LINK LIBRARY
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SEE ALSO
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cos, tan, sec, csc, cot, epsilon
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versin, vercos
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## Copyright (C) 1999,2021,2023 Landon Curt Noll
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##
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2
help/tan
2
help/tan
@@ -24,9 +24,11 @@ LIMITS
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LINK LIBRARY
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NUMBER *qtan(NUMBER *x, NUMBER *eps)
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COMPLEX *c_atan(COMPLEX *c, NUMBER *eps);
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SEE ALSO
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sin, cos, sec, csc, cot, epsilon
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versin, vercos
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## Copyright (C) 1999,2023 Landon Curt Noll
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##
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67
help/vercos
Normal file
67
help/vercos
Normal file
@@ -0,0 +1,67 @@
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NAME
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vercos - versed cosine
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SYNOPSIS
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vercos(x [,eps])
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TYPES
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x number (real or complex)
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eps 0 < real < 1, defaults to epsilon()
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return number
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DESCRIPTION
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Calculate the versed cosine of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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The versed cosine function is sometimes called coversin, sometimes called cvs,
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may be defined as:
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vercos(x) = 1 - sin(x)
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EXAMPLE
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; print vercos(0.2), vercos(3/7), vercos(-31)
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0.80133066920493878454 0.58442814500694799193 0.59596235467693499395
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; print vercos(1, 1e-5), vercos(1, 1e-10), vercos(1, 1e-15), vercos(1, 1e-20)
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0.15853 0.1585290152 0.158529015192104 0.15852901519210349335
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; print vercos(2 + 3i, 1e-5), vercos(2 + 3i, 1e-10)
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-8.1545+4.16891i -8.1544991469+4.16890696i
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; pi = pi(1e-20)
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; print vercos(pi/6, 1e-10), vercos(pi/2, 1e-10), vercos(pi, 1e-10), vercos(3*pi/2, 1e-10)
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0.5 0 1 2
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qvercos(NUMBER *x, NUMBER *eps)
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COMPLEX *c_vercos(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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sin, cos, tan, sec, csc, cot, epsilon
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versin
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## Copyright (C) 2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2023/08/31 23:07:08
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## File existed as early as: 2023
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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67
help/versin
Normal file
67
help/versin
Normal file
@@ -0,0 +1,67 @@
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NAME
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versin - versed sine
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SYNOPSIS
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versin(x [,eps])
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TYPES
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x number (real or complex)
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eps 0 < real < 1, defaults to epsilon()
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return number
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DESCRIPTION
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Calculate the versed sine of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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The versed sine function is sometimes called vers, sometimes called ver,
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may be defined as:
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versin(x) = 1 - cos(x)
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EXAMPLE
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; print versin(0.2), versin(3/7), versin(-31)
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0.01993342215875836888 0.09043964832583332597 0.08525764219546872104
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; print versin(1, 1e-5), versin(1, 1e-10), versin(1, 1e-15), versin(1, 1e-20)
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0.4597 0.4596976941 0.45969769413186 0.4596976941318602826
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; print versin(2 + 3i, 1e-5), versin(2 + 3i, 1e-10)
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5.18963+9.10923i 5.189625691+9.1092278938i
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; pi = pi(1e-20)
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; print versin(pi/3, 1e-10), versin(pi/2, 1e-10), versin(pi, 1e-10), versin(3*pi/2, 1e-10)
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0.5 1 2 1
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qversin(NUMBER *x, NUMBER *eps)
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COMPLEX *c_versin(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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sin, cos, tan, sec, csc, cot, epsilon
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vercos
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## Copyright (C) 2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2023/08/31 23:05:28
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## File existed as early as: 2023
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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