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Add support for tangent function #231

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fc016a6
Add support for tangent function
rhannequin Jun 28, 2022
83c2723
Apply review comments for tests
rhannequin Jul 28, 2022
46dca76
Make tan depend only on sin
rhannequin Oct 30, 2022
ffa10b2
Merge branch 'master' into add_bigmath_tan
mrkn May 15, 2025
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21 changes: 21 additions & 0 deletions lib/bigdecimal/math.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@
# sqrt(x, prec)
# sin (x, prec)
# cos (x, prec)
# tan (x, prec)
# atan(x, prec)
# PI (prec)
# E (prec) == exp(1.0,prec)
Expand Down Expand Up @@ -131,6 +132,26 @@ def cos(x, prec)
y
end

# call-seq:
# tan(decimal, numeric) -> BigDecimal
#
# Computes the tangent of +decimal+ to the specified number of digits of
# precision, +numeric+.
#
# If +decimal+ is Infinity or NaN, returns NaN.
#
# BigMath.tan(BigDecimal("0.0"), 4).to_s
# #=> "0.0"
#
# BigMath.tan(BigMath.PI(4) / 4, 4).to_s
# #=> "0.999999999999999999999955588155008544487055622030633191403625599381672572e0"
#
def tan(x, prec)
sine = sin(x, prec)
cosine = sqrt(1 - sine**2, prec)
sine / cosine
Comment on lines +150 to +152
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As I wrote in #319, I want to redefine sin by $\sin x = \sqrt{1 - \cos^2 x}$ for $|x| \le \pi$.
So I want to rewrite these lines as follow:

    x, sign = adjust_x_and_detect_sgin_of_tangent(x)
    t = guarantee_precision(prec) do |n|
      c = cos(x, n)
      s = sqrt(1 - c**2, n)
      s.div(c, n)
    end
    sign >= 0 ? t : -t

The adjust_x_and_detect_sign_of_tangent method adjusts $x$ within the range $[-\pi, \pi]$ and calculates the result sign from the original $x$.
The guarantee_precision method performs Ziv's loop to ensure the result of the block has the desired precision.

end
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@mrkn mrkn Oct 31, 2022 •
edited
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@rhannequin Could you please mention the origin such as the paper reference of this algorithm in the comment?
And, I want to know how this algorithm is better than just doing sine/(1 - sine**2). Could you explain?

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@mrkn I don't believe tanθ is defined as sinθ / (1 - sin2θ), but should be sinθ / cosθ and cosθ is √(1 - sin2θ).

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@nobu The current code was updated against my comment above. Please compare the commit timestamp and the comment timestamp.

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sqrt(1 - sine**2, prec) is not cosine. It is cosine.abs
Test case of x around -PI/4, 3*PI/4, -3*PI/4 are missing.


# call-seq:
# atan(decimal, numeric) -> BigDecimal
#
Expand Down
11 changes: 11 additions & 0 deletions test/bigdecimal/test_bigmath.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -53,6 +53,17 @@ def test_cos
assert_in_delta(0.0, cos(PI(N) * BigDecimal("301.5"), N))
end

def test_tan
assert_in_delta(0.0, tan(BigDecimal("0.0"), N))
assert_in_delta(0.0, tan(PI(N), N))
assert_in_delta(1.0, tan(PI(N) / 4, N))
assert_in_delta(sqrt(BigDecimal(3), N), tan(PI(N) / 3, N))
assert_in_delta(sqrt(BigDecimal(3), 10 * N), tan(PI(10 * N) / 3, 10 * N))
assert_in_delta(0.0, tan(-PI(N), N))
assert_in_delta(-1.0, tan(-PI(N) / 4, N))
assert_in_delta(-sqrt(BigDecimal(3), N), tan(-PI(N) / 3, N))
Comment on lines +57 to +64
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We need to specify an appropriate BigDecimal for the delta parameter in each assertion.
I'll rewrite them later.

end

def test_atan
assert_equal(0.0, atan(BigDecimal("0.0"), N))
assert_in_delta(Math::PI/4, atan(BigDecimal("1.0"), N))
Expand Down
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