luni/src/main/native/cbigint.cpp - platform/libcore - Git at Google

 /*
  *  Licensed to the Apache Software Foundation (ASF) under one or more
  *  contributor license agreements.  See the NOTICE file distributed with
  *  this work for additional information regarding copyright ownership.
  *  The ASF licenses this file to You under the Apache License, Version 2.0
  *  (the "License"); you may not use this file except in compliance with
  *  the License.  You may obtain a copy of the License at
  *
  *     http://www.apache.org/licenses/LICENSE-2.0
  *
  *  Unless required by applicable law or agreed to in writing, software
  *  distributed under the License is distributed on an "AS IS" BASIS,
  *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  *  See the License for the specific language governing permissions and
  *  limitations under the License.
  */

 #include <string.h>
 #include "cbigint.h"

 #if defined(__linux__) || defined(FREEBSD) || defined(ZOS) || defined(MACOSX) || defined(AIX)
 #define USE_LL
 #endif

 #if __BYTE_ORDER == __LITTLE_ENDIAN
 #define at(i) (i)
 #else
 #define at(i) ((i)^1)
 /* the sequence for halfAt is -1, 2, 1, 4, 3, 6, 5, 8... */
 /* and it should correspond to 0, 1, 2, 3, 4, 5, 6, 7... */
 #define halfAt(i) (-((-(i)) ^ 1))
 #endif

 #define HIGH_IN_U64(u64) ((u64) >> 32)
 #if defined(USE_LL)
 #define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFFLL)
 #else
 #if defined(USE_L)
 #define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFFL)
 #else
 #define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFF)
 #endif /* USE_L */
 #endif /* USE_LL */

 #if defined(USE_LL)
 #define TEN_E1 (0xALL)
 #define TEN_E2 (0x64LL)
 #define TEN_E3 (0x3E8LL)
 #define TEN_E4 (0x2710LL)
 #define TEN_E5 (0x186A0LL)
 #define TEN_E6 (0xF4240LL)
 #define TEN_E7 (0x989680LL)
 #define TEN_E8 (0x5F5E100LL)
 #define TEN_E9 (0x3B9ACA00LL)
 #define TEN_E19 (0x8AC7230489E80000LL)
 #else
 #if defined(USE_L)
 #define TEN_E1 (0xAL)
 #define TEN_E2 (0x64L)
 #define TEN_E3 (0x3E8L)
 #define TEN_E4 (0x2710L)
 #define TEN_E5 (0x186A0L)
 #define TEN_E6 (0xF4240L)
 #define TEN_E7 (0x989680L)
 #define TEN_E8 (0x5F5E100L)
 #define TEN_E9 (0x3B9ACA00L)
 #define TEN_E19 (0x8AC7230489E80000L)
 #else
 #define TEN_E1 (0xA)
 #define TEN_E2 (0x64)
 #define TEN_E3 (0x3E8)
 #define TEN_E4 (0x2710)
 #define TEN_E5 (0x186A0)
 #define TEN_E6 (0xF4240)
 #define TEN_E7 (0x989680)
 #define TEN_E8 (0x5F5E100)
 #define TEN_E9 (0x3B9ACA00)
 #define TEN_E19 (0x8AC7230489E80000)
 #endif /* USE_L */
 #endif /* USE_LL */

 #define TIMES_TEN(x) (((x) << 3) + ((x) << 1))
 #define bitSection(x, mask, shift) (((x) & (mask)) >> (shift))
 #define CREATE_DOUBLE_BITS(normalizedM, e) (((normalizedM) & MANTISSA_MASK) | ((static_cast<uint64_t>((e) + E_OFFSET)) << 52))

 #if defined(USE_LL)
 #define MANTISSA_MASK (0x000FFFFFFFFFFFFFLL)
 #define EXPONENT_MASK (0x7FF0000000000000LL)
 #define NORMAL_MASK (0x0010000000000000LL)
 #define SIGN_MASK (0x8000000000000000LL)
 #else
 #if defined(USE_L)
 #define MANTISSA_MASK (0x000FFFFFFFFFFFFFL)
 #define EXPONENT_MASK (0x7FF0000000000000L)
 #define NORMAL_MASK (0x0010000000000000L)
 #define SIGN_MASK (0x8000000000000000L)
 #else
 #define MANTISSA_MASK (0x000FFFFFFFFFFFFF)
 #define EXPONENT_MASK (0x7FF0000000000000)
 #define NORMAL_MASK (0x0010000000000000)
 #define SIGN_MASK (0x8000000000000000)
 #endif /* USE_L */
 #endif /* USE_LL */

 #define E_OFFSET (1075)

 #define FLOAT_MANTISSA_MASK (0x007FFFFF)
 #define FLOAT_EXPONENT_MASK (0x7F800000)
 #define FLOAT_NORMAL_MASK   (0x00800000)
 #define FLOAT_E_OFFSET (150)

 int32_t
 simpleAddHighPrecision (uint64_t * arg1, int32_t length, uint64_t arg2)
 {
   /* assumes length > 0 */
   int32_t index = 1;

   *arg1 += arg2;
   if (arg2 <= *arg1)
     return 0;
   else if (length == 1)
     return 1;

   while (++arg1[index] == 0 && ++index < length);

   return index == length;
 }

 int32_t
 addHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
 {
   /* addition is limited by length of arg1 as it this function is
    * storing the result in arg1 */
   /* fix for cc (GCC) 3.2 20020903 (Red Hat Linux 8.0 3.2-7): code generated does not
    * do the temp1 + temp2 + carry addition correct.  carry is 64 bit because gcc has
    * subtle issues when you mix 64 / 32 bit maths. */
   uint64_t temp1, temp2, temp3;     /* temporary variables to help the SH-4, and gcc */
   uint64_t carry;
   int32_t index;

   if (length1 == 0 || length2 == 0)
     {
       return 0;
     }
   else if (length1 < length2)
     {
       length2 = length1;
     }

   carry = 0;
   index = 0;
   do
     {
       temp1 = arg1[index];
       temp2 = arg2[index];
       temp3 = temp1 + temp2;
       arg1[index] = temp3 + carry;
       if (arg2[index] < arg1[index])
         carry = 0;
       else if (arg2[index] != arg1[index])
         carry = 1;
     }
   while (++index < length2);
   if (!carry)
     return 0;
   else if (index == length1)
     return 1;

   while (++arg1[index] == 0 && ++index < length1);

   return index == length1;
 }

 void
 subtractHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
 {
   /* assumes arg1 > arg2 */
   int32_t index;
   for (index = 0; index < length1; ++index)
     arg1[index] = ~arg1[index];
   simpleAddHighPrecision (arg1, length1, 1);

   while (length2 > 0 && arg2[length2 - 1] == 0)
     --length2;

   addHighPrecision (arg1, length1, arg2, length2);

   for (index = 0; index < length1; ++index)
     arg1[index] = ~arg1[index];
   simpleAddHighPrecision (arg1, length1, 1);
 }

 static uint32_t simpleMultiplyHighPrecision(uint64_t* arg1, int32_t length, uint64_t arg2) {
   /* assumes arg2 only holds 32 bits of information */
   uint64_t product;
   int32_t index;

   index = 0;
   product = 0;

   do
     {
       product =
         HIGH_IN_U64 (product) + arg2 * LOW_U32_FROM_PTR (arg1 + index);
       LOW_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (product);
       product =
         HIGH_IN_U64 (product) + arg2 * HIGH_U32_FROM_PTR (arg1 + index);
       HIGH_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (product);
     }
   while (++index < length);

   return HIGH_U32_FROM_VAR (product);
 }

 static void
 simpleMultiplyAddHighPrecision (uint64_t * arg1, int32_t length, uint64_t arg2,
                                 uint32_t * result)
 {
   /* Assumes result can hold the product and arg2 only holds 32 bits
      of information */
   uint64_t product;
   int32_t index, resultIndex;

   index = resultIndex = 0;
   product = 0;

   do
     {
       product =
         HIGH_IN_U64 (product) + result[at (resultIndex)] +
         arg2 * LOW_U32_FROM_PTR (arg1 + index);
       result[at (resultIndex)] = LOW_U32_FROM_VAR (product);
       ++resultIndex;
       product =
         HIGH_IN_U64 (product) + result[at (resultIndex)] +
         arg2 * HIGH_U32_FROM_PTR (arg1 + index);
       result[at (resultIndex)] = LOW_U32_FROM_VAR (product);
       ++resultIndex;
     }
   while (++index < length);

   result[at (resultIndex)] += HIGH_U32_FROM_VAR (product);
   if (result[at (resultIndex)] < HIGH_U32_FROM_VAR (product))
     {
       /* must be careful with ++ operator and macro expansion */
       ++resultIndex;
       while (++result[at (resultIndex)] == 0)
         ++resultIndex;
     }
 }

 #if __BYTE_ORDER != __LITTLE_ENDIAN
 void simpleMultiplyAddHighPrecisionBigEndianFix(uint64_t* arg1, int32_t length, uint64_t arg2, uint32_t* result) {
     /* Assumes result can hold the product and arg2 only holds 32 bits of information */
     int32_t index = 0;
     int32_t resultIndex = 0;
     uint64_t product = 0;

     do {
         product = HIGH_IN_U64(product) + result[halfAt(resultIndex)] + arg2 * LOW_U32_FROM_PTR(arg1 + index);
         result[halfAt(resultIndex)] = LOW_U32_FROM_VAR(product);
         ++resultIndex;
         product = HIGH_IN_U64(product) + result[halfAt(resultIndex)] + arg2 * HIGH_U32_FROM_PTR(arg1 + index);
         result[halfAt(resultIndex)] = LOW_U32_FROM_VAR(product);
         ++resultIndex;
     } while (++index < length);

     result[halfAt(resultIndex)] += HIGH_U32_FROM_VAR(product);
     if (result[halfAt(resultIndex)] < HIGH_U32_FROM_VAR(product)) {
         /* must be careful with ++ operator and macro expansion */
         ++resultIndex;
         while (++result[halfAt(resultIndex)] == 0) ++resultIndex;
     }
 }
 #endif

 void
 multiplyHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2,
                        uint64_t * result, int32_t length)
 {
   /* assumes result is large enough to hold product */
   uint64_t* temp;
   uint32_t* resultIn32;
   int32_t count, index;

   if (length1 < length2)
     {
       temp = arg1;
       arg1 = arg2;
       arg2 = temp;
       count = length1;
       length1 = length2;
       length2 = count;
     }

   memset (result, 0, sizeof (uint64_t) * length);

   /* length1 > length2 */
   resultIn32 = reinterpret_cast<uint32_t*>(result);
   index = -1;
   for (count = 0; count < length2; ++count)
     {
       simpleMultiplyAddHighPrecision (arg1, length1, LOW_IN_U64 (arg2[count]),
                                       resultIn32 + (++index));
 #if __BYTE_ORDER == __LITTLE_ENDIAN
       simpleMultiplyAddHighPrecision(arg1, length1, HIGH_IN_U64(arg2[count]), resultIn32 + (++index));
 #else
       simpleMultiplyAddHighPrecisionBigEndianFix(arg1, length1, HIGH_IN_U64(arg2[count]), resultIn32 + (++index));
 #endif
     }
 }

 uint32_t
 simpleAppendDecimalDigitHighPrecision (uint64_t * arg1, int32_t length, uint64_t digit)
 {
   /* assumes digit is less than 32 bits */
   uint64_t arg;
   int32_t index = 0;

   digit <<= 32;
   do
     {
       arg = LOW_IN_U64 (arg1[index]);
       digit = HIGH_IN_U64 (digit) + TIMES_TEN (arg);
       LOW_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (digit);

       arg = HIGH_IN_U64 (arg1[index]);
       digit = HIGH_IN_U64 (digit) + TIMES_TEN (arg);
       HIGH_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (digit);
     }
   while (++index < length);

   return HIGH_U32_FROM_VAR (digit);
 }

 void
 simpleShiftLeftHighPrecision (uint64_t * arg1, int32_t length, int32_t arg2)
 {
   /* assumes length > 0 */
   int32_t index, offset;
   if (arg2 >= 64)
     {
       offset = arg2 >> 6;
       index = length;

       while (--index - offset >= 0)
         arg1[index] = arg1[index - offset];
       do
         {
           arg1[index] = 0;
         }
       while (--index >= 0);

       arg2 &= 0x3F;
     }

   if (arg2 == 0)
     return;
   while (--length > 0)
     {
       arg1[length] = arg1[length] << arg2 | arg1[length - 1] >> (64 - arg2);
     }
   *arg1 <<= arg2;
 }

 int32_t
 highestSetBit (uint64_t * y)
 {
   uint32_t x;
   int32_t result;

   if (*y == 0)
     return 0;

 #if defined(USE_LL)
   if (*y & 0xFFFFFFFF00000000LL)
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
   else
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
 #else
 #if defined(USE_L)
   if (*y & 0xFFFFFFFF00000000L)
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
   else
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
 #else
   if (*y & 0xFFFFFFFF00000000)
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
   else
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
 #endif /* USE_L */
 #endif /* USE_LL */

   if (x & 0xFFFF0000)
     {
       x = bitSection (x, 0xFFFF0000, 16);
       result += 16;
     }
   if (x & 0xFF00)
     {
       x = bitSection (x, 0xFF00, 8);
       result += 8;
     }
   if (x & 0xF0)
     {
       x = bitSection (x, 0xF0, 4);
       result += 4;
     }
   if (x > 0x7)
     return result + 4;
   else if (x > 0x3)
     return result + 3;
   else if (x > 0x1)
     return result + 2;
   else
     return result + 1;
 }

 int32_t
 lowestSetBit (uint64_t * y)
 {
   uint32_t x;
   int32_t result;

   if (*y == 0)
     return 0;

 #if defined(USE_LL)
   if (*y & 0x00000000FFFFFFFFLL)
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
   else
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
 #else
 #if defined(USE_L)
   if (*y & 0x00000000FFFFFFFFL)
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
   else
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
 #else
   if (*y & 0x00000000FFFFFFFF)
     {
       x = LOW_U32_FROM_PTR (y);
       result = 0;
     }
   else
     {
       x = HIGH_U32_FROM_PTR (y);
       result = 32;
     }
 #endif /* USE_L */
 #endif /* USE_LL */

   if (!(x & 0xFFFF))
     {
       x = bitSection (x, 0xFFFF0000, 16);
       result += 16;
     }
   if (!(x & 0xFF))
     {
       x = bitSection (x, 0xFF00, 8);
       result += 8;
     }
   if (!(x & 0xF))
     {
       x = bitSection (x, 0xF0, 4);
       result += 4;
     }

   if (x & 0x1)
     return result + 1;
   else if (x & 0x2)
     return result + 2;
   else if (x & 0x4)
     return result + 3;
   else
     return result + 4;
 }

 int32_t
 highestSetBitHighPrecision (uint64_t * arg, int32_t length)
 {
   int32_t highBit;

   while (--length >= 0)
     {
       highBit = highestSetBit (arg + length);
       if (highBit)
         return highBit + 64 * length;
     }

   return 0;
 }

 int32_t
 lowestSetBitHighPrecision (uint64_t * arg, int32_t length)
 {
   int32_t lowBit, index = -1;

   while (++index < length)
     {
       lowBit = lowestSetBit (arg + index);
       if (lowBit)
         return lowBit + 64 * index;
     }

   return 0;
 }

 int32_t
 compareHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
 {
   while (--length1 >= 0 && arg1[length1] == 0);
   while (--length2 >= 0 && arg2[length2] == 0);

   if (length1 > length2)
     return 1;
   else if (length1 < length2)
     return -1;
   else if (length1 > -1)
     {
       do
         {
           if (arg1[length1] > arg2[length1])
             return 1;
           else if (arg1[length1] < arg2[length1])
             return -1;
         }
       while (--length1 >= 0);
     }

   return 0;
 }

 jdouble
 toDoubleHighPrecision (uint64_t * arg, int32_t length)
 {
   int32_t highBit;
   uint64_t mantissa, test64;
   uint32_t test;
   jdouble result;

   while (length > 0 && arg[length - 1] == 0)
     --length;

   if (length == 0)
     result = 0.0;
   else if (length > 16)
     {
       DOUBLE_TO_LONGBITS (result) = EXPONENT_MASK;
     }
   else if (length == 1)
     {
       highBit = highestSetBit (arg);
       if (highBit <= 53)
         {
           highBit = 53 - highBit;
           mantissa = *arg << highBit;
           DOUBLE_TO_LONGBITS (result) =
             CREATE_DOUBLE_BITS (mantissa, -highBit);
         }
       else
         {
           highBit -= 53;
           mantissa = *arg >> highBit;
           DOUBLE_TO_LONGBITS (result) =
             CREATE_DOUBLE_BITS (mantissa, highBit);

           /* perform rounding, round to even in case of tie */
           test = (LOW_U32_FROM_PTR (arg) << (11 - highBit)) & 0x7FF;
           if (test > 0x400 || ((test == 0x400) && (mantissa & 1)))
             DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
         }
     }
   else
     {
       highBit = highestSetBit (arg + (--length));
       if (highBit <= 53)
         {
           highBit = 53 - highBit;
           if (highBit > 0)
             {
               mantissa =
                 (arg[length] << highBit) | (arg[length - 1] >>
                                             (64 - highBit));
             }
           else
             {
               mantissa = arg[length];
             }
           DOUBLE_TO_LONGBITS (result) =
             CREATE_DOUBLE_BITS (mantissa, length * 64 - highBit);

           /* perform rounding, round to even in case of tie */
           test64 = arg[--length] << highBit;
           if (test64 > SIGN_MASK || ((test64 == SIGN_MASK) && (mantissa & 1)))
             DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
           else if (test64 == SIGN_MASK)
             {
               while (--length >= 0)
                 {
                   if (arg[length] != 0)
                     {
                       DOUBLE_TO_LONGBITS (result) =
                         DOUBLE_TO_LONGBITS (result) + 1;
                       break;
                     }
                 }
             }
         }
       else
         {
           highBit -= 53;
           mantissa = arg[length] >> highBit;
           DOUBLE_TO_LONGBITS (result) =
             CREATE_DOUBLE_BITS (mantissa, length * 64 + highBit);

           /* perform rounding, round to even in case of tie */
           test = (LOW_U32_FROM_PTR (arg + length) << (11 - highBit)) & 0x7FF;
           if (test > 0x400 || ((test == 0x400) && (mantissa & 1)))
             DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
           else if (test == 0x400)
             {
               do
                 {
                   if (arg[--length] != 0)
                     {
                       DOUBLE_TO_LONGBITS (result) =
                         DOUBLE_TO_LONGBITS (result) + 1;
                       break;
                     }
                 }
               while (length > 0);
             }
         }
     }

   return result;
 }

 static uint64_t simpleMultiplyHighPrecision64(uint64_t* arg1, int32_t length, uint64_t arg2);

 int32_t
 timesTenToTheEHighPrecision (uint64_t * result, int32_t length, jint e)
 {
   /* assumes result can hold value */
   uint64_t overflow;
   int exp10 = e;

   if (e == 0)
     return length;

   /* bad O(n) way of doing it, but simple */
   /*
      do {
      overflow = simpleAppendDecimalDigitHighPrecision(result, length, 0);
      if (overflow)
      result[length++] = overflow;
      } while (--e);
    */
   /* Replace the current implementaion which performs a
    * "multiplication" by 10 e number of times with an actual
    * multiplication. 10e19 is the largest exponent to the power of ten
    * that will fit in a 64-bit integer, and 10e9 is the largest exponent to
    * the power of ten that will fit in a 64-bit integer. Not sure where the
    * break-even point is between an actual multiplication and a
    * simpleAappendDecimalDigit() so just pick 10e3 as that point for
    * now.
    */
   while (exp10 >= 19)
     {
       overflow = simpleMultiplyHighPrecision64 (result, length, TEN_E19);
       if (overflow)
         result[length++] = overflow;
       exp10 -= 19;
     }
   while (exp10 >= 9)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E9);
       if (overflow)
         result[length++] = overflow;
       exp10 -= 9;
     }
   if (exp10 == 0)
     return length;
   else if (exp10 == 1)
     {
       overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 2)
     {
       overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
       if (overflow)
         result[length++] = overflow;
       overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 3)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E3);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 4)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E4);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 5)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E5);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 6)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E6);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 7)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E7);
       if (overflow)
         result[length++] = overflow;
     }
   else if (exp10 == 8)
     {
       overflow = simpleMultiplyHighPrecision (result, length, TEN_E8);
       if (overflow)
         result[length++] = overflow;
     }
   return length;
 }

 uint64_t
 doubleMantissa (jdouble z)
 {
   uint64_t m = DOUBLE_TO_LONGBITS (z);

   if ((m & EXPONENT_MASK) != 0)
     m = (m & MANTISSA_MASK) | NORMAL_MASK;
   else
     m = (m & MANTISSA_MASK);

   return m;
 }

 int32_t
 doubleExponent (jdouble z)
 {
   /* assumes positive double */
   int32_t k = HIGH_U32_FROM_VAR (z) >> 20;

   if (k)
     k -= E_OFFSET;
   else
     k = 1 - E_OFFSET;

   return k;
 }

 uint32_t floatMantissa(jfloat z) {
   uint32_t m = FLOAT_TO_INTBITS (z);

   if ((m & FLOAT_EXPONENT_MASK) != 0)
     m = (m & FLOAT_MANTISSA_MASK) | FLOAT_NORMAL_MASK;
   else
     m = (m & FLOAT_MANTISSA_MASK);

   return m;
 }

 int32_t
 floatExponent (jfloat z)
 {
   /* assumes positive float */
   int32_t k = FLOAT_TO_INTBITS (z) >> 23;
   if (k)
     k -= FLOAT_E_OFFSET;
   else
     k = 1 - FLOAT_E_OFFSET;

   return k;
 }

 /* Allow a 64-bit value in arg2 */
 uint64_t
 simpleMultiplyHighPrecision64 (uint64_t * arg1, int32_t length, uint64_t arg2)
 {
   uint64_t intermediate, carry1, carry2, prod1, prod2, sum;
   uint64_t* pArg1;
   int32_t index;
   uint32_t buf32;

   index = 0;
   intermediate = 0;
   pArg1 = arg1 + index;
   carry1 = carry2 = 0;

   do
     {
       if ((*pArg1 != 0) || (intermediate != 0))
         {
           prod1 =
             static_cast<uint64_t>(LOW_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(LOW_U32_FROM_PTR (pArg1));
           sum = intermediate + prod1;
           if ((sum < prod1) || (sum < intermediate))
             {
               carry1 = 1;
             }
           else
             {
               carry1 = 0;
             }
           prod1 =
             static_cast<uint64_t>(LOW_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(HIGH_U32_FROM_PTR (pArg1));
           prod2 =
             static_cast<uint64_t>(HIGH_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(LOW_U32_FROM_PTR (pArg1));
           intermediate = carry2 + HIGH_IN_U64 (sum) + prod1 + prod2;
           if ((intermediate < prod1) || (intermediate < prod2))
             {
               carry2 = 1;
             }
           else
             {
               carry2 = 0;
             }
           LOW_U32_FROM_PTR (pArg1) = LOW_U32_FROM_VAR (sum);
           buf32 = HIGH_U32_FROM_PTR (pArg1);
           HIGH_U32_FROM_PTR (pArg1) = LOW_U32_FROM_VAR (intermediate);
           intermediate = carry1 + HIGH_IN_U64 (intermediate)
             + static_cast<uint64_t>(HIGH_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(buf32);
         }
       pArg1++;
     }
   while (++index < length);
   return intermediate;
 }
	/*
	* Licensed to the Apache Software Foundation (ASF) under one or more
	* contributor license agreements. See the NOTICE file distributed with
	* this work for additional information regarding copyright ownership.
	* The ASF licenses this file to You under the Apache License, Version 2.0
	* (the "License"); you may not use this file except in compliance with
	* the License. You may obtain a copy of the License at
	*
	* http://www.apache.org/licenses/LICENSE-2.0
	*
	* Unless required by applicable law or agreed to in writing, software
	* distributed under the License is distributed on an "AS IS" BASIS,
	* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	* See the License for the specific language governing permissions and
	* limitations under the License.
	*/

	#include <string.h>
	#include "cbigint.h"

	#if defined(__linux__) \|\| defined(FREEBSD) \|\| defined(ZOS) \|\| defined(MACOSX) \|\| defined(AIX)
	#define USE_LL
	#endif

	#if __BYTE_ORDER == __LITTLE_ENDIAN
	#define at(i) (i)
	#else
	#define at(i) ((i)^1)
	/* the sequence for halfAt is -1, 2, 1, 4, 3, 6, 5, 8... */
	/* and it should correspond to 0, 1, 2, 3, 4, 5, 6, 7... */
	#define halfAt(i) (-((-(i)) ^ 1))
	#endif

	#define HIGH_IN_U64(u64) ((u64) >> 32)
	#if defined(USE_LL)
	#define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFFLL)
	#else
	#if defined(USE_L)
	#define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFFL)
	#else
	#define LOW_IN_U64(u64) ((u64) & 0x00000000FFFFFFFF)
	#endif /* USE_L */
	#endif /* USE_LL */

	#if defined(USE_LL)
	#define TEN_E1 (0xALL)
	#define TEN_E2 (0x64LL)
	#define TEN_E3 (0x3E8LL)
	#define TEN_E4 (0x2710LL)
	#define TEN_E5 (0x186A0LL)
	#define TEN_E6 (0xF4240LL)
	#define TEN_E7 (0x989680LL)
	#define TEN_E8 (0x5F5E100LL)
	#define TEN_E9 (0x3B9ACA00LL)
	#define TEN_E19 (0x8AC7230489E80000LL)
	#else
	#if defined(USE_L)
	#define TEN_E1 (0xAL)
	#define TEN_E2 (0x64L)
	#define TEN_E3 (0x3E8L)
	#define TEN_E4 (0x2710L)
	#define TEN_E5 (0x186A0L)
	#define TEN_E6 (0xF4240L)
	#define TEN_E7 (0x989680L)
	#define TEN_E8 (0x5F5E100L)
	#define TEN_E9 (0x3B9ACA00L)
	#define TEN_E19 (0x8AC7230489E80000L)
	#else
	#define TEN_E1 (0xA)
	#define TEN_E2 (0x64)
	#define TEN_E3 (0x3E8)
	#define TEN_E4 (0x2710)
	#define TEN_E5 (0x186A0)
	#define TEN_E6 (0xF4240)
	#define TEN_E7 (0x989680)
	#define TEN_E8 (0x5F5E100)
	#define TEN_E9 (0x3B9ACA00)
	#define TEN_E19 (0x8AC7230489E80000)
	#endif /* USE_L */
	#endif /* USE_LL */

	#define TIMES_TEN(x) (((x) << 3) + ((x) << 1))
	#define bitSection(x, mask, shift) (((x) & (mask)) >> (shift))
	#define CREATE_DOUBLE_BITS(normalizedM, e) (((normalizedM) & MANTISSA_MASK) \| ((static_cast<uint64_t>((e) + E_OFFSET)) << 52))

	#if defined(USE_LL)
	#define MANTISSA_MASK (0x000FFFFFFFFFFFFFLL)
	#define EXPONENT_MASK (0x7FF0000000000000LL)
	#define NORMAL_MASK (0x0010000000000000LL)
	#define SIGN_MASK (0x8000000000000000LL)
	#else
	#if defined(USE_L)
	#define MANTISSA_MASK (0x000FFFFFFFFFFFFFL)
	#define EXPONENT_MASK (0x7FF0000000000000L)
	#define NORMAL_MASK (0x0010000000000000L)
	#define SIGN_MASK (0x8000000000000000L)
	#else
	#define MANTISSA_MASK (0x000FFFFFFFFFFFFF)
	#define EXPONENT_MASK (0x7FF0000000000000)
	#define NORMAL_MASK (0x0010000000000000)
	#define SIGN_MASK (0x8000000000000000)
	#endif /* USE_L */
	#endif /* USE_LL */

	#define E_OFFSET (1075)

	#define FLOAT_MANTISSA_MASK (0x007FFFFF)
	#define FLOAT_EXPONENT_MASK (0x7F800000)
	#define FLOAT_NORMAL_MASK (0x00800000)
	#define FLOAT_E_OFFSET (150)

	int32_t
	simpleAddHighPrecision (uint64_t * arg1, int32_t length, uint64_t arg2)
	{
	/* assumes length > 0 */
	int32_t index = 1;

	*arg1 += arg2;
	if (arg2 <= *arg1)
	return 0;
	else if (length == 1)
	return 1;

	while (++arg1[index] == 0 && ++index < length);

	return index == length;
	}

	int32_t
	addHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
	{
	/* addition is limited by length of arg1 as it this function is
	* storing the result in arg1 */
	/* fix for cc (GCC) 3.2 20020903 (Red Hat Linux 8.0 3.2-7): code generated does not
	* do the temp1 + temp2 + carry addition correct. carry is 64 bit because gcc has
	* subtle issues when you mix 64 / 32 bit maths. */
	uint64_t temp1, temp2, temp3; /* temporary variables to help the SH-4, and gcc */
	uint64_t carry;
	int32_t index;

	if (length1 == 0 \|\| length2 == 0)
	{
	return 0;
	}
	else if (length1 < length2)
	{
	length2 = length1;
	}

	carry = 0;
	index = 0;
	do
	{
	temp1 = arg1[index];
	temp2 = arg2[index];
	temp3 = temp1 + temp2;
	arg1[index] = temp3 + carry;
	if (arg2[index] < arg1[index])
	carry = 0;
	else if (arg2[index] != arg1[index])
	carry = 1;
	}
	while (++index < length2);
	if (!carry)
	return 0;
	else if (index == length1)
	return 1;

	while (++arg1[index] == 0 && ++index < length1);

	return index == length1;
	}

	void
	subtractHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
	{
	/* assumes arg1 > arg2 */
	int32_t index;
	for (index = 0; index < length1; ++index)
	arg1[index] = ~arg1[index];
	simpleAddHighPrecision (arg1, length1, 1);

	while (length2 > 0 && arg2[length2 - 1] == 0)
	--length2;

	addHighPrecision (arg1, length1, arg2, length2);

	for (index = 0; index < length1; ++index)
	arg1[index] = ~arg1[index];
	simpleAddHighPrecision (arg1, length1, 1);
	}

	static uint32_t simpleMultiplyHighPrecision(uint64_t* arg1, int32_t length, uint64_t arg2) {
	/* assumes arg2 only holds 32 bits of information */
	uint64_t product;
	int32_t index;

	index = 0;
	product = 0;

	do
	{
	product =
	HIGH_IN_U64 (product) + arg2 * LOW_U32_FROM_PTR (arg1 + index);
	LOW_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (product);
	product =
	HIGH_IN_U64 (product) + arg2 * HIGH_U32_FROM_PTR (arg1 + index);
	HIGH_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (product);
	}
	while (++index < length);

	return HIGH_U32_FROM_VAR (product);
	}

	static void
	simpleMultiplyAddHighPrecision (uint64_t * arg1, int32_t length, uint64_t arg2,
	uint32_t * result)
	{
	/* Assumes result can hold the product and arg2 only holds 32 bits
	of information */
	uint64_t product;
	int32_t index, resultIndex;

	index = resultIndex = 0;
	product = 0;

	do
	{
	product =
	HIGH_IN_U64 (product) + result[at (resultIndex)] +
	arg2 * LOW_U32_FROM_PTR (arg1 + index);
	result[at (resultIndex)] = LOW_U32_FROM_VAR (product);
	++resultIndex;
	product =
	HIGH_IN_U64 (product) + result[at (resultIndex)] +
	arg2 * HIGH_U32_FROM_PTR (arg1 + index);
	result[at (resultIndex)] = LOW_U32_FROM_VAR (product);
	++resultIndex;
	}
	while (++index < length);

	result[at (resultIndex)] += HIGH_U32_FROM_VAR (product);
	if (result[at (resultIndex)] < HIGH_U32_FROM_VAR (product))
	{
	/* must be careful with ++ operator and macro expansion */
	++resultIndex;
	while (++result[at (resultIndex)] == 0)
	++resultIndex;
	}
	}

	#if __BYTE_ORDER != __LITTLE_ENDIAN
	void simpleMultiplyAddHighPrecisionBigEndianFix(uint64_t* arg1, int32_t length, uint64_t arg2, uint32_t* result) {
	/* Assumes result can hold the product and arg2 only holds 32 bits of information */
	int32_t index = 0;
	int32_t resultIndex = 0;
	uint64_t product = 0;

	do {
	product = HIGH_IN_U64(product) + result[halfAt(resultIndex)] + arg2 * LOW_U32_FROM_PTR(arg1 + index);
	result[halfAt(resultIndex)] = LOW_U32_FROM_VAR(product);
	++resultIndex;
	product = HIGH_IN_U64(product) + result[halfAt(resultIndex)] + arg2 * HIGH_U32_FROM_PTR(arg1 + index);
	result[halfAt(resultIndex)] = LOW_U32_FROM_VAR(product);
	++resultIndex;
	} while (++index < length);

	result[halfAt(resultIndex)] += HIGH_U32_FROM_VAR(product);
	if (result[halfAt(resultIndex)] < HIGH_U32_FROM_VAR(product)) {
	/* must be careful with ++ operator and macro expansion */
	++resultIndex;
	while (++result[halfAt(resultIndex)] == 0) ++resultIndex;
	}
	}
	#endif

	void
	multiplyHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2,
	uint64_t * result, int32_t length)
	{
	/* assumes result is large enough to hold product */
	uint64_t* temp;
	uint32_t* resultIn32;
	int32_t count, index;

	if (length1 < length2)
	{
	temp = arg1;
	arg1 = arg2;
	arg2 = temp;
	count = length1;
	length1 = length2;
	length2 = count;
	}

	memset (result, 0, sizeof (uint64_t) * length);

	/* length1 > length2 */
	resultIn32 = reinterpret_cast<uint32_t*>(result);
	index = -1;
	for (count = 0; count < length2; ++count)
	{
	simpleMultiplyAddHighPrecision (arg1, length1, LOW_IN_U64 (arg2[count]),
	resultIn32 + (++index));
	#if __BYTE_ORDER == __LITTLE_ENDIAN
	simpleMultiplyAddHighPrecision(arg1, length1, HIGH_IN_U64(arg2[count]), resultIn32 + (++index));
	#else
	simpleMultiplyAddHighPrecisionBigEndianFix(arg1, length1, HIGH_IN_U64(arg2[count]), resultIn32 + (++index));
	#endif
	}
	}

	uint32_t
	simpleAppendDecimalDigitHighPrecision (uint64_t * arg1, int32_t length, uint64_t digit)
	{
	/* assumes digit is less than 32 bits */
	uint64_t arg;
	int32_t index = 0;

	digit <<= 32;
	do
	{
	arg = LOW_IN_U64 (arg1[index]);
	digit = HIGH_IN_U64 (digit) + TIMES_TEN (arg);
	LOW_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (digit);

	arg = HIGH_IN_U64 (arg1[index]);
	digit = HIGH_IN_U64 (digit) + TIMES_TEN (arg);
	HIGH_U32_FROM_PTR (arg1 + index) = LOW_U32_FROM_VAR (digit);
	}
	while (++index < length);

	return HIGH_U32_FROM_VAR (digit);
	}

	void
	simpleShiftLeftHighPrecision (uint64_t * arg1, int32_t length, int32_t arg2)
	{
	/* assumes length > 0 */
	int32_t index, offset;
	if (arg2 >= 64)
	{
	offset = arg2 >> 6;
	index = length;

	while (--index - offset >= 0)
	arg1[index] = arg1[index - offset];
	do
	{
	arg1[index] = 0;
	}
	while (--index >= 0);

	arg2 &= 0x3F;
	}

	if (arg2 == 0)
	return;
	while (--length > 0)
	{
	arg1[length] = arg1[length] << arg2 \| arg1[length - 1] >> (64 - arg2);
	}
	*arg1 <<= arg2;
	}

	int32_t
	highestSetBit (uint64_t * y)
	{
	uint32_t x;
	int32_t result;

	if (*y == 0)
	return 0;

	#if defined(USE_LL)
	if (*y & 0xFFFFFFFF00000000LL)
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	else
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	#else
	#if defined(USE_L)
	if (*y & 0xFFFFFFFF00000000L)
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	else
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	#else
	if (*y & 0xFFFFFFFF00000000)
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	else
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	#endif /* USE_L */
	#endif /* USE_LL */

	if (x & 0xFFFF0000)
	{
	x = bitSection (x, 0xFFFF0000, 16);
	result += 16;
	}
	if (x & 0xFF00)
	{
	x = bitSection (x, 0xFF00, 8);
	result += 8;
	}
	if (x & 0xF0)
	{
	x = bitSection (x, 0xF0, 4);
	result += 4;
	}
	if (x > 0x7)
	return result + 4;
	else if (x > 0x3)
	return result + 3;
	else if (x > 0x1)
	return result + 2;
	else
	return result + 1;
	}

	int32_t
	lowestSetBit (uint64_t * y)
	{
	uint32_t x;
	int32_t result;

	if (*y == 0)
	return 0;

	#if defined(USE_LL)
	if (*y & 0x00000000FFFFFFFFLL)
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	else
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	#else
	#if defined(USE_L)
	if (*y & 0x00000000FFFFFFFFL)
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	else
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	#else
	if (*y & 0x00000000FFFFFFFF)
	{
	x = LOW_U32_FROM_PTR (y);
	result = 0;
	}
	else
	{
	x = HIGH_U32_FROM_PTR (y);
	result = 32;
	}
	#endif /* USE_L */
	#endif /* USE_LL */

	if (!(x & 0xFFFF))
	{
	x = bitSection (x, 0xFFFF0000, 16);
	result += 16;
	}
	if (!(x & 0xFF))
	{
	x = bitSection (x, 0xFF00, 8);
	result += 8;
	}
	if (!(x & 0xF))
	{
	x = bitSection (x, 0xF0, 4);
	result += 4;
	}

	if (x & 0x1)
	return result + 1;
	else if (x & 0x2)
	return result + 2;
	else if (x & 0x4)
	return result + 3;
	else
	return result + 4;
	}

	int32_t
	highestSetBitHighPrecision (uint64_t * arg, int32_t length)
	{
	int32_t highBit;

	while (--length >= 0)
	{
	highBit = highestSetBit (arg + length);
	if (highBit)
	return highBit + 64 * length;
	}

	return 0;
	}

	int32_t
	lowestSetBitHighPrecision (uint64_t * arg, int32_t length)
	{
	int32_t lowBit, index = -1;

	while (++index < length)
	{
	lowBit = lowestSetBit (arg + index);
	if (lowBit)
	return lowBit + 64 * index;
	}

	return 0;
	}

	int32_t
	compareHighPrecision (uint64_t * arg1, int32_t length1, uint64_t * arg2, int32_t length2)
	{
	while (--length1 >= 0 && arg1[length1] == 0);
	while (--length2 >= 0 && arg2[length2] == 0);

	if (length1 > length2)
	return 1;
	else if (length1 < length2)
	return -1;
	else if (length1 > -1)
	{
	do
	{
	if (arg1[length1] > arg2[length1])
	return 1;
	else if (arg1[length1] < arg2[length1])
	return -1;
	}
	while (--length1 >= 0);
	}

	return 0;
	}

	jdouble
	toDoubleHighPrecision (uint64_t * arg, int32_t length)
	{
	int32_t highBit;
	uint64_t mantissa, test64;
	uint32_t test;
	jdouble result;

	while (length > 0 && arg[length - 1] == 0)
	--length;

	if (length == 0)
	result = 0.0;
	else if (length > 16)
	{
	DOUBLE_TO_LONGBITS (result) = EXPONENT_MASK;
	}
	else if (length == 1)
	{
	highBit = highestSetBit (arg);
	if (highBit <= 53)
	{
	highBit = 53 - highBit;
	mantissa = *arg << highBit;
	DOUBLE_TO_LONGBITS (result) =
	CREATE_DOUBLE_BITS (mantissa, -highBit);
	}
	else
	{
	highBit -= 53;
	mantissa = *arg >> highBit;
	DOUBLE_TO_LONGBITS (result) =
	CREATE_DOUBLE_BITS (mantissa, highBit);

	/* perform rounding, round to even in case of tie */
	test = (LOW_U32_FROM_PTR (arg) << (11 - highBit)) & 0x7FF;
	if (test > 0x400 \|\| ((test == 0x400) && (mantissa & 1)))
	DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
	}
	}
	else
	{
	highBit = highestSetBit (arg + (--length));
	if (highBit <= 53)
	{
	highBit = 53 - highBit;
	if (highBit > 0)
	{
	mantissa =
	(arg[length] << highBit) \| (arg[length - 1] >>
	(64 - highBit));
	}
	else
	{
	mantissa = arg[length];
	}
	DOUBLE_TO_LONGBITS (result) =
	CREATE_DOUBLE_BITS (mantissa, length * 64 - highBit);

	/* perform rounding, round to even in case of tie */
	test64 = arg[--length] << highBit;
	if (test64 > SIGN_MASK \|\| ((test64 == SIGN_MASK) && (mantissa & 1)))
	DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
	else if (test64 == SIGN_MASK)
	{
	while (--length >= 0)
	{
	if (arg[length] != 0)
	{
	DOUBLE_TO_LONGBITS (result) =
	DOUBLE_TO_LONGBITS (result) + 1;
	break;
	}
	}
	}
	}
	else
	{
	highBit -= 53;
	mantissa = arg[length] >> highBit;
	DOUBLE_TO_LONGBITS (result) =
	CREATE_DOUBLE_BITS (mantissa, length * 64 + highBit);

	/* perform rounding, round to even in case of tie */
	test = (LOW_U32_FROM_PTR (arg + length) << (11 - highBit)) & 0x7FF;
	if (test > 0x400 \|\| ((test == 0x400) && (mantissa & 1)))
	DOUBLE_TO_LONGBITS (result) = DOUBLE_TO_LONGBITS (result) + 1;
	else if (test == 0x400)
	{
	do
	{
	if (arg[--length] != 0)
	{
	DOUBLE_TO_LONGBITS (result) =
	DOUBLE_TO_LONGBITS (result) + 1;
	break;
	}
	}
	while (length > 0);
	}
	}
	}

	return result;
	}

	static uint64_t simpleMultiplyHighPrecision64(uint64_t* arg1, int32_t length, uint64_t arg2);

	int32_t
	timesTenToTheEHighPrecision (uint64_t * result, int32_t length, jint e)
	{
	/* assumes result can hold value */
	uint64_t overflow;
	int exp10 = e;

	if (e == 0)
	return length;

	/* bad O(n) way of doing it, but simple */
	/*
	do {
	overflow = simpleAppendDecimalDigitHighPrecision(result, length, 0);
	if (overflow)
	result[length++] = overflow;
	} while (--e);
	*/
	/* Replace the current implementaion which performs a
	* "multiplication" by 10 e number of times with an actual
	* multiplication. 10e19 is the largest exponent to the power of ten
	* that will fit in a 64-bit integer, and 10e9 is the largest exponent to
	* the power of ten that will fit in a 64-bit integer. Not sure where the
	* break-even point is between an actual multiplication and a
	* simpleAappendDecimalDigit() so just pick 10e3 as that point for
	* now.
	*/
	while (exp10 >= 19)
	{
	overflow = simpleMultiplyHighPrecision64 (result, length, TEN_E19);
	if (overflow)
	result[length++] = overflow;
	exp10 -= 19;
	}
	while (exp10 >= 9)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E9);
	if (overflow)
	result[length++] = overflow;
	exp10 -= 9;
	}
	if (exp10 == 0)
	return length;
	else if (exp10 == 1)
	{
	overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 2)
	{
	overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
	if (overflow)
	result[length++] = overflow;
	overflow = simpleAppendDecimalDigitHighPrecision (result, length, 0);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 3)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E3);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 4)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E4);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 5)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E5);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 6)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E6);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 7)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E7);
	if (overflow)
	result[length++] = overflow;
	}
	else if (exp10 == 8)
	{
	overflow = simpleMultiplyHighPrecision (result, length, TEN_E8);
	if (overflow)
	result[length++] = overflow;
	}
	return length;
	}

	uint64_t
	doubleMantissa (jdouble z)
	{
	uint64_t m = DOUBLE_TO_LONGBITS (z);

	if ((m & EXPONENT_MASK) != 0)
	m = (m & MANTISSA_MASK) \| NORMAL_MASK;
	else
	m = (m & MANTISSA_MASK);

	return m;
	}

	int32_t
	doubleExponent (jdouble z)
	{
	/* assumes positive double */
	int32_t k = HIGH_U32_FROM_VAR (z) >> 20;

	if (k)
	k -= E_OFFSET;
	else
	k = 1 - E_OFFSET;

	return k;
	}

	uint32_t floatMantissa(jfloat z) {
	uint32_t m = FLOAT_TO_INTBITS (z);

	if ((m & FLOAT_EXPONENT_MASK) != 0)
	m = (m & FLOAT_MANTISSA_MASK) \| FLOAT_NORMAL_MASK;
	else
	m = (m & FLOAT_MANTISSA_MASK);

	return m;
	}

	int32_t
	floatExponent (jfloat z)
	{
	/* assumes positive float */
	int32_t k = FLOAT_TO_INTBITS (z) >> 23;
	if (k)
	k -= FLOAT_E_OFFSET;
	else
	k = 1 - FLOAT_E_OFFSET;

	return k;
	}

	/* Allow a 64-bit value in arg2 */
	uint64_t
	simpleMultiplyHighPrecision64 (uint64_t * arg1, int32_t length, uint64_t arg2)
	{
	uint64_t intermediate, carry1, carry2, prod1, prod2, sum;
	uint64_t* pArg1;
	int32_t index;
	uint32_t buf32;

	index = 0;
	intermediate = 0;
	pArg1 = arg1 + index;
	carry1 = carry2 = 0;

	do
	{
	if ((*pArg1 != 0) \|\| (intermediate != 0))
	{
	prod1 =
	static_cast<uint64_t>(LOW_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(LOW_U32_FROM_PTR (pArg1));
	sum = intermediate + prod1;
	if ((sum < prod1) \|\| (sum < intermediate))
	{
	carry1 = 1;
	}
	else
	{
	carry1 = 0;
	}
	prod1 =
	static_cast<uint64_t>(LOW_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(HIGH_U32_FROM_PTR (pArg1));
	prod2 =
	static_cast<uint64_t>(HIGH_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(LOW_U32_FROM_PTR (pArg1));
	intermediate = carry2 + HIGH_IN_U64 (sum) + prod1 + prod2;
	if ((intermediate < prod1) \|\| (intermediate < prod2))
	{
	carry2 = 1;
	}
	else
	{
	carry2 = 0;
	}
	LOW_U32_FROM_PTR (pArg1) = LOW_U32_FROM_VAR (sum);
	buf32 = HIGH_U32_FROM_PTR (pArg1);
	HIGH_U32_FROM_PTR (pArg1) = LOW_U32_FROM_VAR (intermediate);
	intermediate = carry1 + HIGH_IN_U64 (intermediate)
	+ static_cast<uint64_t>(HIGH_U32_FROM_VAR (arg2)) * static_cast<uint64_t>(buf32);
	}
	pArg1++;
	}
	while (++index < length);
	return intermediate;
	}