171 lines
3.5 KiB
CoffeeScript
171 lines
3.5 KiB
CoffeeScript
# Sine function of numerical and symbolic arguments
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Eval_sin = ->
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#console.log "sin ---- "
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push(cadr(p1))
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Eval()
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sine()
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#console.log "sin end ---- "
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sine = ->
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#console.log "sine ---- "
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save()
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p1 = pop()
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if (car(p1) == symbol(ADD))
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# sin of a sum can be further decomposed into
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#sin(alpha+beta) = sin(alpha)*cos(beta)+sin(beta)*cos(alpha)
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sine_of_angle_sum()
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else
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sine_of_angle()
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restore()
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#console.log "sine end ---- "
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# Use angle sum formula for special angles.
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#define A p3
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#define B p4
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# decompose sum sin(alpha+beta) into
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# sin(alpha)*cos(beta)+sin(beta)*cos(alpha)
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sine_of_angle_sum = ->
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#console.log "sin of angle sum ---- "
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p2 = cdr(p1)
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while (iscons(p2))
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p4 = car(p2); # p4 is B
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if (isnpi(p4)) # p4 is B
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push(p1)
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push(p4); # p4 is B
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subtract()
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p3 = pop(); # p3 is A
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push(p3); # p3 is A
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sine()
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push(p4); # p4 is B
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cosine()
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multiply()
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push(p3); # p3 is A
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cosine()
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push(p4); # p4 is B
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sine()
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multiply()
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add()
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#console.log "sin of angle sum end ---- "
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return
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p2 = cdr(p2)
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sine_of_angle()
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#console.log "sin of angle sum end ---- "
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sine_of_angle = ->
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if (car(p1) == symbol(ARCSIN))
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push(cadr(p1))
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return
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if isdouble(p1)
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d = Math.sin(p1.d)
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if (Math.abs(d) < 1e-10)
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d = 0.0
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push_double(d)
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return
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# sine function is antisymmetric, sin(-x) = -sin(x)
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if (isnegative(p1))
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push(p1)
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negate()
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sine()
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negate()
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return
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# sin(arctan(x)) = x / sqrt(1 + x^2)
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# see p. 173 of the CRC Handbook of Mathematical Sciences
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if (car(p1) == symbol(ARCTAN))
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push(cadr(p1))
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push_integer(1)
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push(cadr(p1))
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push_integer(2)
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power()
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add()
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push_rational(-1, 2)
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power()
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multiply()
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return
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# multiply by 180/pi to go from radians to degrees.
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# we go from radians to degrees because it's much
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# easier to calculate symbolic results of most (not all) "classic"
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# angles (e.g. 30,45,60...) if we calculate the degrees
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# and the we do a switch on that.
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# Alternatively, we could look at the fraction of pi
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# (e.g. 60 degrees is 1/3 pi) but that's more
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# convoluted as we'd need to look at both numerator and
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# denominator.
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push(p1)
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push_integer(180)
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multiply()
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if evaluatingAsFloats
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push_double(Math.PI)
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else
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push_symbol(PI)
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divide()
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n = pop_integer()
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# most "good" (i.e. compact) trigonometric results
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# happen for a round number of degrees. There are some exceptions
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# though, e.g. 22.5 degrees, which we don't capture here.
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if (n < 0 || isNaN(n))
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push(symbol(SIN))
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push(p1)
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list(2)
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return
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# values of some famous angles. Many more here:
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# https://en.wikipedia.org/wiki/Trigonometric_constants_expressed_in_real_radicals
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switch (n % 360)
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when 0, 180
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push_integer(0)
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when 30, 150
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push_rational(1, 2)
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when 210, 330
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push_rational(-1, 2)
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when 45, 135
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push_rational(1, 2)
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push_integer(2)
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push_rational(1, 2)
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power()
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multiply()
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when 225, 315
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push_rational(-1, 2)
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push_integer(2)
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push_rational(1, 2)
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power()
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multiply()
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when 60, 120
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push_rational(1, 2)
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push_integer(3)
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push_rational(1, 2)
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power()
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multiply()
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when 240, 300
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push_rational(-1, 2)
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push_integer(3)
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push_rational(1, 2)
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power()
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multiply()
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when 90
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push_integer(1)
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when 270
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push_integer(-1)
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else
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push(symbol(SIN))
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push(p1)
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list(2)
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