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arcsin.coffee
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### arcsin =====================================================================
Tags
----
scripting, JS, internal, treenode, general concept
Parameters
----------
x
General description
-------------------
Returns the inverse sine of x.
###
Eval_arcsin = ->
push(cadr(p1))
Eval()
arcsin()
arcsin = ->
n = 0
d = 0
save()
p1 = pop()
if (car(p1) == symbol(SIN))
push(cadr(p1))
restore()
return
if (isdouble(p1))
errno = 0
d = Math.asin(p1.d)
if (errno)
stop("arcsin function argument is not in the interval [-1,1]")
push_double(d)
restore()
return
# if p1 == 1/sqrt(2) then return 1/4*pi (45 degrees)
# second if catches the other way of saying it, sqrt(2)/2
if (isoneoversqrttwo(p1)) or
(car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), 1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))
push_rational(1, 4)
push_symbol(PI)
multiply()
restore()
return
# if p1 == -1/sqrt(2) then return -1/4*pi (-45 degrees)
# second if catches the other way of saying it, -sqrt(2)/2
if (isminusoneoversqrttwo(p1)) or
(car(p1) == symbol(MULTIPLY) && equalq(car(cdr(p1)), -1,2) and car(car(cdr(cdr(p1)))) == symbol(POWER) && equaln(car(cdr(car(cdr(cdr(p1))))),2) && equalq(car(cdr(cdr(car(cdr(cdr(p1)))))), 1, 2))
if evaluatingAsFloats
push_double(-Math.PI / 4.0)
else
push_rational(-1, 4)
push_symbol(PI)
multiply()
restore()
return
if (!isrational(p1))
push_symbol(ARCSIN)
push(p1)
list(2)
restore()
return
push(p1)
push_integer(2)
multiply()
n = pop_integer()
switch (n)
when -2
if evaluatingAsFloats
push_double(-Math.PI / 2.0)
else
push_rational(-1, 2)
push_symbol(PI)
multiply()
when -1
if evaluatingAsFloats
push_double(-Math.PI / 6.0)
else
push_rational(-1, 6)
push_symbol(PI)
multiply()
when 0
if evaluatingAsFloats
push_double(0.0)
else
push(zero)
when 1
if evaluatingAsFloats
push_double(Math.PI / 6.0)
else
push_rational(1, 6)
push_symbol(PI)
multiply()
when 2
if evaluatingAsFloats
push_double(Math.PI / 2.0)
else
push_rational(1, 2)
push_symbol(PI)
multiply()
else
push_symbol(ARCSIN)
push(p1)
list(2)
restore()