Add support for tangent function (#231)

* Add support for tangent function

* Apply review comments for tests

* Make tan depend only on sin

* Use Ziv's loop method suggested in review

* Test failing test

* Use first implementation based on sin and cos

* Remove unused code

Author: rhannequin

lib/bigdecimal/math.rb

@@ -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)
@@ -124,6 +125,24 @@ def cos(x, prec)
     sign * sin(x, prec)
   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
+  #   #=> "0.99999999999999999999419869652481995799388629632650769e0"
+  #
+  def tan(x, prec)
+    sin(x, prec) / cos(x, prec)
+  end
+
   # call-seq:
   #   atan(decimal, numeric) -> BigDecimal
   #

test/bigdecimal/test_bigmath.rb

@@ -91,6 +91,17 @@ def test_cos
     assert_operator(cos(PI(30) * 2, 30), :<=, 1)
   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))
+  end
+
   def test_atan
     assert_equal(0.0, atan(BigDecimal("0.0"), N))
     assert_in_delta(Math::PI/4, atan(BigDecimal("1.0"), N))