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add cas and cis trigonometric functions
Added the following new trigonometric functions:
cas(x [,eps]) trigonometric cosine plus sine
cis(x [,eps]) Euler's formula
This commit is contained in:
Landon Curt Noll
@@ -204,9 +204,9 @@ DETAIL_HELP= abs access acos acosh acot acoth acovercos acoversin \
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ahavercos ahaversin append appr arg argv arrow asec asech asin asinh \
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assign atan atan2 atanh avercos aversin avg base base2 bernoulli bit \
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blk blkcpy blkfree blocks bround btrunc calc_tty calclevel calcpath \
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catalan ceil cfappr cfsim char cmdbuf cmp comb conj cos cosh cot coth \
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count covercos coversin cp crd csc csch ctime d2dm d2dms d2g d2r \
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delete den dereference det digit digits display dms2d dp epsilon \
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cas catalan ceil cfappr cfsim char cis cmdbuf cmp comb conj cos cosh \
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cot coth count covercos coversin cp crd csc csch ctime d2dm d2dms d2g \
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d2r delete den dereference det digit digits display dms2d dp epsilon \
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errcount errmax errno error errsym estr euler eval excsc exp exsec \
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fact factor fclose fcnt feof ferror fflush fgetc fgetfield fgetfile \
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fgetline fgets fgetstr fib files floor fopen forall fpathopen fprintf \
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -54,6 +54,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -54,6 +54,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -51,6 +51,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -58,6 +58,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -60,6 +60,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -57,6 +57,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -57,6 +57,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -57,6 +57,7 @@ SEE ALSO
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ahaversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -58,6 +58,7 @@ SEE ALSO
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ahaversin, hacoversin, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -58,6 +58,7 @@ SEE ALSO
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hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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@@ -55,6 +55,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cas, cis
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epsilon
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EXTERNAL RESOURCES
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86
help/cas
Normal file
86
help/cas
Normal file
@@ -0,0 +1,86 @@
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NAME
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cas - trigonometric cosine plus sine
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SYNOPSIS
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cas(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 trigonometric cosine plus 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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This function is sometimes called cosine and sine, is equivalent to:
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cas(x) = cos(x) + sin(x)
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EXAMPLE
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; print cas(1/2), cas(5/7), cas(42/7)
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1.35700810049457571639 1.41063924387921517267 0.68075478845144014774
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; print cas(1, 1e-5), cas(1, 1e-10), cas(1, 1e-15), cas(1, 1e-20)
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1.38177 1.3817732907 1.381773290676036 1.38177329067603622405
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; print cas(2 + 3i, 1e-5), cas(2 + 3i, 1e-10)
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4.96487-13.27814i 4.9648734559-13.2781348538i
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; pi = pi(1e-20)
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; print cas(pi/6), cas(pi/2), cas(pi)
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1.36602540378443864676 1 -1
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qcas(NUMBER *x, NUMBER *eps)
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COMPLEX *c_cas(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cis
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epsilon
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EXTERNAL RESOURCES
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For general information on trigonometric functions, see:
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https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
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https://en.wikipedia.org/wiki/Versine
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https://en.wikipedia.org/wiki/Exsecant
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https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
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https://en.wikipedia.org/wiki/Chord_(geometry)
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https://en.wikipedia.org/wiki/Secant_line
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https://en.wikipedia.org/wiki/Hartley_transform#cas
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https://en.wikipedia.org/wiki/Cis_(mathematics)
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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
|
||||
## 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
|
||||
## 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: 2023/10/02 23:11:18
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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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92
help/cis
Normal file
92
help/cis
Normal file
@@ -0,0 +1,92 @@
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NAME
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cis - Euler's formula
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SYNOPSIS
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cis(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 Euler's formula value of x to a multiple of eps with error less in
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absolute value than .75 * eps.
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This function is sometimes called cosine and sine, is equivalent to:
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cis(x) = cos(x) + 1i*sin(x)
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cis(x) = exp(1i * x)
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EXAMPLE
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; print cis(1/2), cis(5/7)
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0.87758256189037271612+0.47942553860420300027i 0.75556134670069659847+0.6550778971785185742i
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; print cis(42/7)
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0.96017028665036602055-0.27941549819892587281i
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; print cis(1, 1e-5), cis(1, 1e-10), cis(1, 1e-15)
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0.5403+0.84147i 0.5403023059+0.8414709848i 0.54030230586814+0.841470984807896i
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; print cis(1, 1e-20)
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0.5403023058681397174+0.84147098480789650665i
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; print cis(2 + 3i, 1e-5), cis(2 + 3i, 1e-10)
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-0.02072+0.04527i -0.020718731+0.0452712531i
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; pi = pi(1e-20)
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; print cis(pi/6), cis(pi/2), cis(pi)
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0.86602540378443864676+0.5i 1i -1
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LIMITS
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0 < eps < 1
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LINK LIBRARY
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COMPLEX *c_cis(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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cos, tan, cot, sec, csc
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asin, acos, atan, acot, asec, acsc
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versin, coversin, vercos, covercos
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aversin, acoversin, avercos, acovercos
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haversin, hacoversin, havercos, hacovercos
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
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crd, acrd
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cis
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epsilon
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EXTERNAL RESOURCES
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For general information on trigonometric functions, see:
|
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https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
|
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https://en.wikipedia.org/wiki/Versine
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https://en.wikipedia.org/wiki/Exsecant
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https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
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https://en.wikipedia.org/wiki/Chord_(geometry)
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https://en.wikipedia.org/wiki/Secant_line
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https://en.wikipedia.org/wiki/Hartley_transform#cas
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https://en.wikipedia.org/wiki/Cis_(mathematics)
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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
|
||||
## the terms of the version 2.1 of the GNU Lesser General Public License
|
||||
## as published by the Free Software Foundation.
|
||||
##
|
||||
## Calc is distributed in the hope that it will be useful, but WITHOUT
|
||||
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
||||
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
|
||||
## Public License for more details.
|
||||
##
|
||||
## A copy of version 2.1 of the GNU Lesser General Public License is
|
||||
## distributed with calc under the filename COPYING-LGPL. You should have
|
||||
## received a copy with calc; if not, write to Free Software Foundation, Inc.
|
||||
## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
|
||||
##
|
||||
## Under source code control: 2023/10/02 23:11:18
|
||||
## File existed as early as: 2023
|
||||
##
|
||||
## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
|
||||
## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
|
||||
1
help/cos
1
help/cos
@@ -44,6 +44,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
|
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crd, acrd
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cas, cis
|
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epsilon
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||||
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||||
EXTERNAL RESOURCES
|
||||
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1
help/cot
1
help/cot
@@ -50,6 +50,7 @@ SEE ALSO
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ahaversin, hacoversin, havercos, ahacovercos
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exsec, aexsec, excsc, aexcsc
|
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crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
1
help/crd
1
help/crd
@@ -51,6 +51,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
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||||
exsec, aexsec, excsc, aexcsc
|
||||
acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
1
help/csc
1
help/csc
@@ -50,6 +50,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -50,6 +50,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
2
help/exp
2
help/exp
@@ -39,7 +39,7 @@ LINK LIBRARY
|
||||
COMPLEX *c_exp(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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||||
ln, cosh, sinh, tanh
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ln, log, log2, logn, cosh, sinh, tanh
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|
||||
## Copyright (C) 1999,2021,2023 Landon Curt Noll
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||||
##
|
||||
|
||||
@@ -50,6 +50,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
1
help/sec
1
help/sec
@@ -50,6 +50,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
1
help/sin
1
help/sin
@@ -44,6 +44,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
1
help/tan
1
help/tan
@@ -50,6 +50,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
@@ -48,6 +48,7 @@ SEE ALSO
|
||||
ahaversin, hacoversin, havercos, ahacovercos
|
||||
exsec, aexsec, excsc, aexcsc
|
||||
crd, acrd
|
||||
cas, cis
|
||||
epsilon
|
||||
|
||||
EXTERNAL RESOURCES
|
||||
|
||||
Reference in New Issue
Block a user