Add a precision assertion to BigMath test (#316)

* Add a precision assertion to BigMath test

* Move precision assertion methods to test helper

* Assert precision with multiple precision values: [50, 100, 150]

Author: tompng

test/bigdecimal/helper.rb

@@ -36,4 +36,31 @@ def under_gc_stress
   ensure
     GC.stress = stress
   end
+
+  # Asserts that the calculation of the given block converges to some value
+  # with precision specified by block parameter.
+
+  def assert_fixed_point_precision(&block)
+    _assert_precision(:fixed_point, &block)
+  end
+
+  def assert_relative_precision(&block)
+    _assert_precision(:relative, &block)
+  end
+
+  def _assert_precision(mode)
+    expected = yield(200)
+    [50, 100, 150].each do |n|
+      value = yield(n)
+      if mode == :fixed_point
+        precision = -(value - expected).exponent
+      elsif mode == :relative
+        precision = -(value.div(expected, expected.precision) - 1).exponent
+      else
+        raise ArgumentError, "Unknown mode: #{mode}"
+      end
+      assert(value != expected, "Unable to estimate precision for exact value")
+      assert(precision >= n, "Precision is not enough: #{precision} < #{n}")
+    end
+  end
 end

test/bigdecimal/test_bigmath.rb

@@ -6,6 +6,9 @@ class TestBigMath < Test::Unit::TestCase
   include TestBigDecimalBase
   include BigMath
   N = 20
+  # SQRT in 116 (= 100 + double_fig) digits
+  SQRT2 = BigDecimal("1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309123")
+  SQRT3 = BigDecimal("1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067")
   PINF = BigDecimal("+Infinity")
   MINF = BigDecimal("-Infinity")
   NAN = BigDecimal("NaN")
@@ -23,6 +26,11 @@ def test_sqrt
     assert_raise(FloatDomainError) {sqrt(BigDecimal("-1.0"), N)}
     assert_raise(FloatDomainError) {sqrt(NAN, N)}
     assert_raise(FloatDomainError) {sqrt(PINF, N)}
+    assert_in_delta(SQRT2, sqrt(BigDecimal("2"), 100), BigDecimal("1e-100"))
+    assert_in_delta(SQRT3, sqrt(BigDecimal("3"), 100), BigDecimal("1e-100"))
+    assert_relative_precision {|n| sqrt(BigDecimal("2"), n) }
+    assert_relative_precision {|n| sqrt(BigDecimal("2e-50"), n) }
+    assert_relative_precision {|n| sqrt(BigDecimal("2e50"), n) }
   end
 
   def test_sin
@@ -37,6 +45,13 @@ def test_sin
     assert_in_delta(0.0, sin(PI(N) * 21, N))
     assert_in_delta(0.0, sin(PI(N) * 30, N))
     assert_in_delta(-1.0, sin(PI(N) * BigDecimal("301.5"), N))
+    assert_in_delta(BigDecimal('0.5'), sin(PI(100) / 6, 100), BigDecimal("1e-100"))
+    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("1e-30"), n) }
+    assert_fixed_point_precision {|n| sin(BigDecimal(PI(50)), n) }
+    assert_fixed_point_precision {|n| sin(BigDecimal(PI(50) * 100), n) }
   end
 
   def test_cos
@@ -51,20 +66,36 @@ def test_cos
     assert_in_delta(-1.0, cos(PI(N) * 21, N))
     assert_in_delta(1.0, cos(PI(N) * 30, N))
     assert_in_delta(0.0, cos(PI(N) * BigDecimal("301.5"), N))
+    assert_in_delta(BigDecimal('0.5'), cos(PI(100) / 3, 100), BigDecimal("1e-100"))
+    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(PI(50) / 2), n) }
+    assert_fixed_point_precision {|n| cos(BigDecimal(PI(50) * 201 / 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))
     assert_in_delta(Math::PI/6, atan(sqrt(BigDecimal("3.0"), N) / 3, N))
     assert_in_delta(Math::PI/2, atan(PINF, N))
+    assert_in_delta(PI(100) / 3, atan(SQRT3, 100), BigDecimal("1e-100"))
     assert_equal(BigDecimal("0.823840753418636291769355073102514088959345624027952954058347023122539489"),
                  atan(BigDecimal("1.08"), 72).round(72), '[ruby-dev:41257]')
+    assert_relative_precision {|n| atan(BigDecimal("2"), n)}
+    assert_relative_precision {|n| atan(BigDecimal("1e-30"), n)}
+    assert_relative_precision {|n| atan(BigDecimal("1e30"), n)}
   end
 
   def test_log
     assert_equal(0, BigMath.log(BigDecimal("1.0"), 10))
     assert_in_epsilon(Math.log(10)*1000, BigMath.log(BigDecimal("1e1000"), 10))
+    assert_in_epsilon(BigDecimal("2.3025850929940456840179914546843642076011014886287729760333279009675726096773524802359972050895982983419677840422862"),
+                      BigMath.log(BigDecimal("10"), 100), BigDecimal("1e-100"))
+    assert_relative_precision {|n| BigMath.log(BigDecimal("2"), n) }
+    assert_relative_precision {|n| BigMath.log(BigDecimal("1e-30") + 1, n) }
+    assert_relative_precision {|n| BigMath.log(BigDecimal("1e-30"), n) }
+    assert_relative_precision {|n| BigMath.log(BigDecimal("1e30"), n) }
     assert_raise(Math::DomainError) {BigMath.log(BigDecimal("0"), 10)}
     assert_raise(Math::DomainError) {BigMath.log(BigDecimal("-1"), 10)}
     assert_separately(%w[-rbigdecimal], <<-SRC)