Fix precision of BigMath.sin(x,prec) and BigMath.cos(x,prec) for large x (#346)

For large x, sin and cos is calculated:
sin(x) = sin(x % (2*PI))
cos(x) = cos(x % (2*PI))
When x is large, PI(prec) is not precise enough to calculate `x%(2*PI)`. Extra precision is needed.

Author: tompng

lib/bigdecimal/math.rb

@@ -61,7 +61,8 @@ def sin(x, prec)
     one  = BigDecimal("1")
     two  = BigDecimal("2")
     x = -x if neg = x < 0
-    if x > (twopi = two * BigMath.PI(prec))
+    if x > 6
+      twopi = two * BigMath.PI(prec + x.exponent)
       if x > 30
         x %= twopi
       else
@@ -105,7 +106,8 @@ def cos(x, prec)
     one  = BigDecimal("1")
     two  = BigDecimal("2")
     x = -x if x < 0
-    if x > (twopi = two * BigMath.PI(prec))
+    if x > 6
+      twopi = two * BigMath.PI(prec + x.exponent)
       if x > 30
         x %= twopi
       else

test/bigdecimal/test_bigmath.rb

@@ -49,6 +49,7 @@ def test_sin
     assert_in_delta(SQRT3 / 2, sin(PI(100) / 3, 100), BigDecimal("1e-100"))
     assert_in_delta(SQRT2 / 2, sin(PI(100) / 4, 100), BigDecimal("1e-100"))
     assert_fixed_point_precision {|n| sin(BigDecimal("1"), n) }
+    assert_fixed_point_precision {|n| sin(BigDecimal("1e50"), n) }
     assert_fixed_point_precision {|n| sin(BigDecimal("1e-30"), n) }
     assert_fixed_point_precision {|n| sin(BigDecimal(PI(50)), n) }
     assert_fixed_point_precision {|n| sin(BigDecimal(PI(50) * 100), n) }
@@ -70,6 +71,7 @@ def test_cos
     assert_in_delta(SQRT3 / 2, cos(PI(100) / 6, 100), BigDecimal("1e-100"))
     assert_in_delta(SQRT2 / 2, cos(PI(100) / 4, 100), BigDecimal("1e-100"))
     assert_fixed_point_precision {|n| cos(BigDecimal("1"), n) }
+    assert_fixed_point_precision {|n| cos(BigDecimal("1e50"), n) }
     assert_fixed_point_precision {|n| cos(BigDecimal(PI(50) / 2), n) }
     assert_fixed_point_precision {|n| cos(BigDecimal(PI(50) * 201 / 2), n) }
   end