Implement BigMath.tan

Calculate `tan(x, prec)` by `sin(x, prec) / cos(x, denominator_prec)`.
If the precision of cos is not enough, increase denominator_prec and recalculate cos again.

Author: tompng

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)
@@ -134,6 +135,32 @@ def cos(x, prec)
     y < -1 ? BigDecimal("-1") : y > 1 ? BigDecimal("1") : 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(BigMath.PI(16) / 3, 16).to_s
+  #   #=> "0.17320508075688772935274463415059e1"
+  #
+  def tan(x, prec)
+    denominator_prec = prec + BigDecimal.double_fig
+    while true
+      cos = cos(x, denominator_prec)
+      break if prec - cos.exponent <= denominator_prec
+
+      if cos.exponent == 0 || denominator_prec < -cos.exponent
+        denominator_prec = denominator_prec * 3 / 2
+      else
+        denominator_prec = prec - cos.exponent + BigDecimal.double_fig
+      end
+    end
+    sin(x, prec).div(cos, prec + BigDecimal.double_fig)
+  end
+
   # call-seq:
   #   atan(decimal, numeric) -> BigDecimal
   #

test/bigdecimal/test_bigmath.rb

@@ -80,6 +80,26 @@ def test_cos
     assert_operator(cos(PI(30) * 2, 30), :<=, 1)
   end
 
+  def test_tan
+    assert_in_delta(0.0, tan(-PI(N), N))
+    assert_in_delta(0.0, tan(BigDecimal(0), N))
+    assert_in_delta(0.0, tan(PI(N), N))
+    assert_in_delta(1.0, tan(PI(N) / 4, N))
+    assert_in_delta(-1.0, tan(-PI(N) / 4, N))
+    assert_in_delta(-1.0, tan(PI(N) * 3 / 4, N))
+    assert_in_delta(1.0, tan(-PI(N) * 3 / 4, N))
+    assert_in_delta(0.0, tan(PI(N) * 100, N))
+    assert_in_delta(1.0, tan(PI(N) * 101 / 4, N))
+    assert_in_delta(-1.0, tan(PI(N) * 103 / 4, N))
+    assert_in_delta(BigDecimal("1").div(SQRT3, 100), tan(PI(100) / 6, 100), BigDecimal("1e-100"))
+    assert_in_delta(SQRT3, tan(PI(100) / 3, 100), BigDecimal("1e-100"))
+    assert_relative_precision {|n| tan(BigDecimal("0.5"), n) }
+    assert_relative_precision {|n| tan(BigDecimal("1e-30"), n) }
+    assert_relative_precision {|n| tan(BigDecimal("1.5"), n) }
+    assert_relative_precision {|n| tan(PI(100) / 2, n) }
+    assert_relative_precision {|n| tan(PI(200) * 101 / 2, 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))