Timestamps before 1970 of the form YYYY-MM-DD HH:MM:SS.000X have incorrect seconds

FULL PRODUCT VERSION :
java version "1.8.0_121"
Java(TM) SE Runtime Environment (build 1.8.0_121-b13)
Java HotSpot(TM) 64-Bit Server VM (build 25.121-b13, mixed mode)

ADDITIONAL OS VERSION INFORMATION :
Darwin x.local 17.4.0 Darwin Kernel Version 17.4.0: Sun Dec 17 09:19:54 PST 2017; root:xnu-4570.41.2~1/RELEASE_X86_64 x86_64

A DESCRIPTION OF THE PROBLEM :
For dates before 1970, the Timestamp code only uses the milliseconds to subtract a second. For times with 1,000,000 > nanos > 0 the times will be off by one second.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
  // The current JDK has a bug where values of the form:
  // YYYY-MM-DD HH:MM:SS.000X is off by a second for dates before 1970.
  public static final boolean TIMESTAMP_BUG;
  static {
    Timestamp ts1 = Timestamp.valueOf("1969-12-25 12:34:56.0001");
    Timestamp ts2 = Timestamp.valueOf("1969-12-25 12:34:56.0011");
    // Compare the seconds, which should be the same.
    TIMESTAMP_BUG = ts1.getTime()/1000 != ts2.getTime()/1000;
  }


EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
TIMESTAMP_BUG = false
ACTUAL -
TIMESTAMP_BUG = true

REPRODUCIBILITY :
This bug can be reproduced always.

---------- BEGIN SOURCE ----------
import java.sql.Timestamp;

public class TimestampBug {
  public static void main(String[] args) {
    Timestamp ts1 = Timestamp.valueOf("1969-12-25 12:34:56.0001");
    Timestamp ts2 = Timestamp.valueOf("1969-12-25 12:34:56.0011");
    // Compare the seconds, which should be the same.
    System.out.println("TIMESTAMP_BUG = " +
(ts1.getTime()/1000 != ts2.getTime()/1000));
  }
}
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
Compensating code needs to detect whether the bug is there and add or subtract a second when 1,000,000 > nanos > 1.