diff --git a/lib/bigdecimal/math.rb b/lib/bigdecimal/math.rb
index 16e095df..a98ca84f 100644
--- a/lib/bigdecimal/math.rb
+++ b/lib/bigdecimal/math.rb
@@ -24,6 +24,8 @@
 #   log10(x, prec)
 #   log1p(x, prec)
 #   expm1(x, prec)
+#   frexp(x)
+#   ldexp(x, exponent)
 #   PI  (prec)
 #   E   (prec) == exp(1.0,prec)
 #
@@ -568,6 +570,35 @@ def expm1(x, prec)
     exp_prec > 0 ? BigMath.exp(x, exp_prec).sub(1, prec) : BigDecimal(-1)
   end
 
+  # call-seq:
+  #   frexp(x) -> [BigDecimal, Integer]
+  #
+  # Decomposes +x+ into a normalized fraction and an integral power of ten.
+  #
+  #   BigMath.frexp(BigDecimal(123.456))
+  #   #=> [0.123456e0, 3]
+  #
+  def frexp(x)
+    x = BigDecimal::Internal.coerce_to_bigdecimal(x, 0, :frexp)
+    return [x, 0] unless x.finite?
+
+    exponent = x.exponent
+    [x._decimal_shift(-exponent), exponent]
+  end
+
+  # call-seq:
+  #   ldexp(fraction, exponent) -> BigDecimal
+  #
+  # Inverse of +frexp+.
+  # Returns the value of fraction * 10**exponent.
+  #
+  #   BigMath.ldexp(BigDecimal("0.123456e0"), 3)
+  #   #=> 0.123456e3
+  #
+  def ldexp(x, exponent)
+    x = BigDecimal::Internal.coerce_to_bigdecimal(x, 0, :frexp)
+    x.finite? ? x._decimal_shift(exponent) : x
+  end
 
   # call-seq:
   #   PI(numeric) -> BigDecimal
diff --git a/test/bigdecimal/test_bigmath.rb b/test/bigdecimal/test_bigmath.rb
index 1147a337..9f0edb60 100644
--- a/test/bigdecimal/test_bigmath.rb
+++ b/test/bigdecimal/test_bigmath.rb
@@ -469,4 +469,28 @@ def test_expm1
     assert_in_exact_precision(BigMath.exp(BigDecimal("1.23e-10"), 120) - 1, expm1(BigDecimal("1.23e-10"), 100), 100)
     assert_in_exact_precision(BigMath.exp(123, 120) - 1, expm1(BigDecimal("123"), 100), 100)
   end
+
+  def test_frexp
+    BigDecimal.save_limit do
+      BigDecimal.limit(3)
+      assert_equal([BigDecimal("-0.123456"), 10], BigMath.frexp(BigDecimal("-0.123456e10")))
+      assert_equal([BigDecimal("0.123456"), -10], BigMath.frexp(BigDecimal("0.123456e-10")))
+      assert_equal([BigDecimal("0.123456789"), 9], BigMath.frexp(123456789))
+      assert_equal([BigDecimal(0), 0], BigMath.frexp(BigDecimal(0)))
+      assert_equal([BigDecimal::NAN, 0], BigMath.frexp(BigDecimal::NAN))
+      assert_equal([BigDecimal::INFINITY, 0], BigMath.frexp(BigDecimal::INFINITY))
+    end
+  end
+
+  def test_ldexp
+    BigDecimal.save_limit do
+      BigDecimal.limit(3)
+      assert_equal(BigDecimal("-0.123456e10"), BigMath.ldexp(BigDecimal("-0.123456"), 10))
+      assert_equal(BigDecimal("0.123456e20"), BigMath.ldexp(BigDecimal("0.123456e10"), 10.9))
+      assert_equal(BigDecimal("0.123456e-10"), BigMath.ldexp(BigDecimal("0.123456"), -10))
+      assert_equal(BigDecimal("0.123456789e19"), BigMath.ldexp(123456789, 10))
+      assert(BigMath.ldexp(BigDecimal::NAN, 10).nan?)
+      assert_equal(BigDecimal::INFINITY, BigMath.ldexp(BigDecimal::INFINITY, 10))
+    end
+  end
 end