Make tan depend only on sin

lib/bigdecimal/math.rb

@@ -148,7 +148,37 @@ def cos(x, prec)
   #   #=> "0.999999999999999999999955588155008544487055622030633191403625599381672572e0"
   #
   def tan(x, prec)
-    sin(x, prec) / cos(x, prec)
+    sine = sin(x, prec)
+
+    n    = prec + BigDecimal.double_fig
+    one  = BigDecimal("1")
+    two  = BigDecimal("2")
+    x = -x if x < 0
+    if x > (twopi = two * BigMath.PI(prec))
+      if x > 30
+        x %= twopi
+      else
+        x -= twopi while x > twopi
+      end
+    end
+    x1 = one
+    x2 = x.mult(x,n)
+    sign = 1
+    cosine = one
+    d = cosine
+    i = BigDecimal("0")
+    z = one
+    while d.nonzero? && ((m = n - (cosine.exponent - d.exponent).abs) > 0)
+      m = BigDecimal.double_fig if m < BigDecimal.double_fig
+      sign = -sign
+      x1  = x2.mult(x1,n)
+      i  += two
+      z  *= (i-one) * i
+      d   = sign * x1.div(z,m)
+      cosine += d
+    end
+
+    sine / cosine
   end
 
   # call-seq: