Preserve Rational precision near one in BigMath.log

lib/bigdecimal.rb

@@ -304,7 +304,14 @@ def log(x, prec)
     prec = BigDecimal::Internal.coerce_validate_prec(prec, :log)
     raise Math::DomainError, 'Complex argument for BigMath.log' if Complex === x
 
-    x = BigDecimal::Internal.coerce_to_bigdecimal(x, prec, :log)
+    if Rational === x && x.between?(1/2r, 2r)
+      # Preserve the significant digits of the difference from one.
+      input_prec = [prec + BigDecimal::Internal::EXTRA_PREC, 2 * BigDecimal.double_fig].max
+      difference = BigDecimal(x - 1, input_prec)
+      x = difference.add(1, input_prec + [1 - difference.exponent, 0].max)
+    else
+      x = BigDecimal::Internal.coerce_to_bigdecimal(x, prec, :log)
+    end
     return BigDecimal::Internal.nan_computation_result if x.nan?
     raise Math::DomainError, 'Negative argument for log' if x < 0
     return -BigDecimal::Internal.infinity_computation_result if x.zero?

test/bigdecimal/test_bigdecimal.rb

@@ -2446,6 +2446,7 @@ def test_BigMath_log_with_1
     assert_in_delta(0.0, BigMath.log(1, 20))
     assert_in_delta(0.0, BigMath.log(1.0, 20))
     assert_in_delta(0.0, BigMath.log(BigDecimal(1), 20))
+    assert_positive_zero(BigMath.log(1r, 20))
   end
 
   def test_BigMath_log_with_exp_1
@@ -2488,6 +2489,49 @@ def test_BigMath_log_with_rational
     assert_in_epsilon(BigMath.log(BigDecimal(3 / 7r, 100), 100), BigMath.log(3 / 7r, 100), 1e-99)
   end
 
+  def test_BigMath_log_with_rational_close_to_one
+    n = 12345**9
+    # The first two and three terms of log(1 + 1/n)'s series round to this reference.
+    expected = BigDecimal("1.5016895257722442449503942510970658615421451954590e-37")
+    assert_in_delta(expected, BigMath.log(Rational(n + 1, n), 50), BigDecimal("1e-85"))
+    assert_in_delta(-expected, BigMath.log(Rational(n, n + 1), 50), BigDecimal("1e-85"))
+  end
+
+  def test_BigMath_log_with_rational_close_to_one_at_low_precision
+    n = 12345**9
+    assert_in_delta(BigDecimal("1.5017e-37"), BigMath.log(Rational(n + 1, n), 5), BigDecimal("1e-41"))
+  end
+
+  def test_BigMath_log_with_rational_closer_to_one_than_precision
+    n = 10**100
+    assert_in_delta(BigDecimal("1e-100"), BigMath.log(Rational(n + 1, n), 50), BigDecimal("1e-148"))
+    assert_in_delta(BigDecimal("-1e-100"), BigMath.log(Rational(n, n + 1), 50), BigDecimal("1e-148"))
+  end
+
+  def test_BigMath_log_with_rational_close_to_one_with_limit
+    n = 12345**9
+    expected = BigDecimal("1.5016895257722442449503942510970658615421451954590e-37")
+    BigDecimal.save_rounding_mode do
+      [:half_up, :down, :ceiling, :floor].each do |mode|
+        BigDecimal.mode(BigDecimal::ROUND_MODE, mode)
+        upper, lower = BigDecimal.save_limit do
+          BigDecimal.limit(10)
+          results = [BigMath.log(Rational(n + 1, n), 50), BigMath.log(Rational(n, n + 1), 50)]
+          assert_equal(10, BigDecimal.limit)
+          results
+        end
+        assert_in_delta(expected, upper, BigDecimal("1e-85"), "rounding mode: #{mode}")
+        assert_in_delta(-expected, lower, BigDecimal("1e-85"), "rounding mode: #{mode}")
+      end
+    end
+  end
+
+  def test_BigMath_log_with_exact_rationals
+    [1/4r, 1/2r, 3/2r, 2r, 3r].each do |x|
+      assert_equal(BigMath.log(BigDecimal(x, 50), 50), BigMath.log(x, 50))
+    end
+  end
+
   def test_BigMath_log_under_gc_stress
     paths = $LOAD_PATH.map{|path| "-I#{path}" }
     assert_in_out_err([*paths, "-rbigdecimal", "--disable-gems"], <<-EOS, [], [])