Use BigDecimal("1e#{n}") instead of ten**n to make calculation faster

Author: tompng

lib/bigdecimal.rb

@@ -20,21 +20,19 @@ def sqrt(prec)
     raise FloatDomainError, 'sqrt of negative value' if self < 0
     raise FloatDomainError, "sqrt of 'NaN'(Not a Number)" if nan?
 
-    ten = BigDecimal(10)
     n_digits = n_significant_digits
     prec = [prec, n_digits].max
 
     if n_digits < prec / 2
       # Fast path for sqrt(16e100) => 4e50
-      base = ten ** ((n_digits + 1) / 2 - exponent / 2)
-      n = self * base * base
+      ex = (n_digits + 1) / 2 - exponent / 2
+      n = (self * BigDecimal("1e#{2 * ex}")).to_i
       sqrt = Integer.sqrt(n)
-      return BigDecimal(sqrt).div(base, prec) if sqrt * sqrt == n
+      return BigDecimal(sqrt) * BigDecimal("1e#{-ex}") if sqrt * sqrt == n
     end
 
     ex = prec + BigDecimal.double_fig - exponent / 2
-    base = ten ** ex
-    sqrt = Integer.sqrt(self * base * base)
-    BigDecimal(sqrt).div(base, prec + BigDecimal.double_fig)
+    sqrt = Integer.sqrt(self * BigDecimal("1e#{2 * ex}"))
+    BigDecimal(sqrt) * BigDecimal("1e#{-ex}")
   end
 end

test/bigdecimal/test_bigdecimal.rb

@@ -1186,6 +1186,7 @@ def test_sqrt_bigdecimal
     assert_equal(BigDecimal('11.1'), BigDecimal('123.21').sqrt(100))
     assert_equal(BigDecimal('11e20'), BigDecimal('121e40').sqrt(100))
     assert_in_epsilon(Math.sqrt(121e41), BigDecimal('121e41').sqrt(100))
+    assert_in_epsilon(Math.sqrt(2e100), BigDecimal('2e100').sqrt(10))
   end
 
   def test_sqrt_5266