crypto/math/math.c - platform/external/srtp - Git at Google

 /*
  * math.c
  *
  * crypto math operations and data types
  *
  * David A. McGrew
  * Cisco Systems, Inc.
  */
 /*
  *
  * Copyright (c) 2001-2006 Cisco Systems, Inc.
  * All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions
  * are met:
  *
  *   Redistributions of source code must retain the above copyright
  *   notice, this list of conditions and the following disclaimer.
  *
  *   Redistributions in binary form must reproduce the above
  *   copyright notice, this list of conditions and the following
  *   disclaimer in the documentation and/or other materials provided
  *   with the distribution.
  *
  *   Neither the name of the Cisco Systems, Inc. nor the names of its
  *   contributors may be used to endorse or promote products derived
  *   from this software without specific prior written permission.
  *
  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  * COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
  * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
  * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
  * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
  * OF THE POSSIBILITY OF SUCH DAMAGE.
  *
  */

 #include "crypto_math.h"

 int
 octet_weight[256] = {
   0, 1, 1, 2, 1, 2, 2, 3,
   1, 2, 2, 3, 2, 3, 3, 4,
   1, 2, 2, 3, 2, 3, 3, 4,
   2, 3, 3, 4, 3, 4, 4, 5,
   1, 2, 2, 3, 2, 3, 3, 4,
   2, 3, 3, 4, 3, 4, 4, 5,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   1, 2, 2, 3, 2, 3, 3, 4,
   2, 3, 3, 4, 3, 4, 4, 5,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   3, 4, 4, 5, 4, 5, 5, 6,
   4, 5, 5, 6, 5, 6, 6, 7,
   1, 2, 2, 3, 2, 3, 3, 4,
   2, 3, 3, 4, 3, 4, 4, 5,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   3, 4, 4, 5, 4, 5, 5, 6,
   4, 5, 5, 6, 5, 6, 6, 7,
   2, 3, 3, 4, 3, 4, 4, 5,
   3, 4, 4, 5, 4, 5, 5, 6,
   3, 4, 4, 5, 4, 5, 5, 6,
   4, 5, 5, 6, 5, 6, 6, 7,
   3, 4, 4, 5, 4, 5, 5, 6,
   4, 5, 5, 6, 5, 6, 6, 7,
   4, 5, 5, 6, 5, 6, 6, 7,
   5, 6, 6, 7, 6, 7, 7, 8
 };

 int
 low_bit[256] = {
   -1, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   5, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   6, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   5, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   7, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   5, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   6, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   5, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0,
   4, 0, 1, 0, 2, 0, 1, 0,
   3, 0, 1, 0, 2, 0, 1, 0
 };


 int
 high_bit[256] = {
   -1, 0, 1, 1, 2, 2, 2, 2,
   3, 3, 3, 3, 3, 3, 3, 3,
   4, 4, 4, 4, 4, 4, 4, 4,
   4, 4, 4, 4, 4, 4, 4, 4,
   5, 5, 5, 5, 5, 5, 5, 5,
   5, 5, 5, 5, 5, 5, 5, 5,
   5, 5, 5, 5, 5, 5, 5, 5,
   5, 5, 5, 5, 5, 5, 5, 5,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   6, 6, 6, 6, 6, 6, 6, 6,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7,
   7, 7, 7, 7, 7, 7, 7, 7
 };

 int
 octet_get_weight(uint8_t octet) {
   extern int octet_weight[256];

   return octet_weight[octet];
 }

 unsigned char
 v32_weight(v32_t a) {
   unsigned int wt = 0;

   wt += octet_weight[a.v8[0]];  /* note: endian-ness makes no difference */
   wt += octet_weight[a.v8[1]];
   wt += octet_weight[a.v8[2]];
   wt += octet_weight[a.v8[3]];

   return wt;
 }

 inline unsigned char
 v32_distance(v32_t x, v32_t y) {
   x.value ^= y.value;
   return v32_weight(x);
 }

 unsigned int
 v32_dot_product(v32_t a, v32_t b) {
   a.value &= b.value;
   return v32_weight(a) & 1;
 }

 /*
  * _bit_string returns a NULL-terminated character string suitable for
  * printing
  */

 #define MAX_STRING_LENGTH 1024

 char bit_string[MAX_STRING_LENGTH];

 char *
 octet_bit_string(uint8_t x) {
   int mask, index;

   for (mask = 1, index = 0; mask < 256; mask <<= 1)
     if ((x & mask) == 0)
       bit_string[index++] = '0';
     else
       bit_string[index++] = '1';

   bit_string[index++] = 0;  /* NULL terminate string */

   return bit_string;
 }

 char *
 v16_bit_string(v16_t x) {
   int i, mask, index;

   for (i = index = 0; i < 2; i++) {
     for (mask = 1; mask < 256; mask <<= 1)
       if ((x.v8[i] & mask) == 0)
 	bit_string[index++] = '0';
       else
 	bit_string[index++] = '1';
   }
   bit_string[index++] = 0;  /* NULL terminate string */
   return bit_string;
 }

 char *
 v32_bit_string(v32_t x) {
   int i, mask, index;

   for (i = index = 0; i < 4; i++) {
     for (mask = 128; mask > 0; mask >>= 1)
       if ((x.v8[i] & mask) == 0)
 	bit_string[index++] = '0';
       else
 	bit_string[index++] = '1';
   }
   bit_string[index++] = 0;  /* NULL terminate string */
   return bit_string;
 }

 char *
 v64_bit_string(const v64_t *x) {
   int i, mask, index;

   for (i = index = 0; i < 8; i++) {
     for (mask = 1; mask < 256; mask <<= 1)
       if ((x->v8[i] & mask) == 0)
 	bit_string[index++] = '0';
       else
 	bit_string[index++] = '1';
   }
   bit_string[index++] = 0;  /* NULL terminate string */
   return bit_string;
 }

 char *
 v128_bit_string(v128_t *x) {
   int j, index;
   uint32_t mask;

   for (j=index=0; j < 4; j++) {
     for (mask=0x80000000; mask > 0; mask >>= 1) {
       if (x->v32[j] & mask)
 	bit_string[index] = '1';
       else
 	bit_string[index] = '0';
       ++index;
     }
   }
   bit_string[128] = 0; /* null terminate string */

   return bit_string;
 }

 uint8_t
 nibble_to_hex_char(uint8_t nibble) {
   char buf[16] = {'0', '1', '2', '3', '4', '5', '6', '7',
 		  '8', '9', 'a', 'b', 'c', 'd', 'e', 'f' };
   return buf[nibble & 0xF];
 }

 char *
 octet_hex_string(uint8_t x) {

   bit_string[0]  = nibble_to_hex_char(x >> 4);
   bit_string[1]  = nibble_to_hex_char(x & 0xF);

   bit_string[2] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 octet_string_hex_string(const void *str, int length) {
   const uint8_t *s = str;
   int i;

   /* double length, since one octet takes two hex characters */
   length *= 2;

   /* truncate string if it would be too long */
   if (length > MAX_STRING_LENGTH)
     length = MAX_STRING_LENGTH-1;

   for (i=0; i < length; i+=2) {
     bit_string[i]   = nibble_to_hex_char(*s >> 4);
     bit_string[i+1] = nibble_to_hex_char(*s++ & 0xF);
   }
   bit_string[i] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 v16_hex_string(v16_t x) {
   int i, j;

   for (i=j=0; i < 2; i++) {
     bit_string[j++]  = nibble_to_hex_char(x.v8[i] >> 4);
     bit_string[j++]  = nibble_to_hex_char(x.v8[i] & 0xF);
   }

   bit_string[j] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 v32_hex_string(v32_t x) {
   int i, j;

   for (i=j=0; i < 4; i++) {
     bit_string[j++]  = nibble_to_hex_char(x.v8[i] >> 4);
     bit_string[j++]  = nibble_to_hex_char(x.v8[i] & 0xF);
   }

   bit_string[j] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 v64_hex_string(const v64_t *x) {
   int i, j;

   for (i=j=0; i < 8; i++) {
     bit_string[j++]  = nibble_to_hex_char(x->v8[i] >> 4);
     bit_string[j++]  = nibble_to_hex_char(x->v8[i] & 0xF);
   }

   bit_string[j] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 v128_hex_string(v128_t *x) {
   int i, j;

   for (i=j=0; i < 16; i++) {
     bit_string[j++]  = nibble_to_hex_char(x->v8[i] >> 4);
     bit_string[j++]  = nibble_to_hex_char(x->v8[i] & 0xF);
   }

   bit_string[j] = 0; /* null terminate string */
   return bit_string;
 }

 char *
 char_to_hex_string(char *x, int num_char) {
   int i, j;

   if (num_char >= 16)
     num_char = 16;
   for (i=j=0; i < num_char; i++) {
     bit_string[j++]  = nibble_to_hex_char(x[i] >> 4);
     bit_string[j++]  = nibble_to_hex_char(x[i] & 0xF);
   }

   bit_string[j] = 0; /* null terminate string */
   return bit_string;
 }

 int
 hex_char_to_nibble(uint8_t c) {
   switch(c) {
   case ('0'): return 0x0;
   case ('1'): return 0x1;
   case ('2'): return 0x2;
   case ('3'): return 0x3;
   case ('4'): return 0x4;
   case ('5'): return 0x5;
   case ('6'): return 0x6;
   case ('7'): return 0x7;
   case ('8'): return 0x8;
   case ('9'): return 0x9;
   case ('a'): return 0xa;
   case ('A'): return 0xa;
   case ('b'): return 0xb;
   case ('B'): return 0xb;
   case ('c'): return 0xc;
   case ('C'): return 0xc;
   case ('d'): return 0xd;
   case ('D'): return 0xd;
   case ('e'): return 0xe;
   case ('E'): return 0xe;
   case ('f'): return 0xf;
   case ('F'): return 0xf;
   default: return -1;   /* this flags an error */
   }
   /* NOTREACHED */
   return -1;  /* this keeps compilers from complaining */
 }

 int
 is_hex_string(char *s) {
   while(*s != 0)
     if (hex_char_to_nibble(*s++) == -1)
       return 0;
   return 1;
 }

 uint8_t
 hex_string_to_octet(char *s) {
   uint8_t x;

   x = (hex_char_to_nibble(s[0]) << 4)
     | hex_char_to_nibble(s[1] & 0xFF);

   return x;
 }

 /*
  * hex_string_to_octet_string converts a hexadecimal string
  * of length 2 * len to a raw octet string of length len
  */

 int
 hex_string_to_octet_string(char *raw, char *hex, int len) {
   uint8_t x;
   int tmp;
   int hex_len;

   hex_len = 0;
   while (hex_len < len) {
     tmp = hex_char_to_nibble(hex[0]);
     if (tmp == -1)
       return hex_len;
     x = (tmp << 4);
     hex_len++;
     tmp = hex_char_to_nibble(hex[1]);
     if (tmp == -1)
       return hex_len;
     x |= (tmp & 0xff);
     hex_len++;
     *raw++ = x;
     hex += 2;
   }
   return hex_len;
 }

 v16_t
 hex_string_to_v16(char *s) {
   v16_t x;
   int i, j;

   for (i=j=0; i < 4; i += 2, j++) {
     x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
       | hex_char_to_nibble(s[i+1] & 0xFF);
   }
   return x;
 }

 v32_t
 hex_string_to_v32(char *s) {
   v32_t x;
   int i, j;

   for (i=j=0; i < 8; i += 2, j++) {
     x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
       | hex_char_to_nibble(s[i+1] & 0xFF);
   }
   return x;
 }

 v64_t
 hex_string_to_v64(char *s) {
   v64_t x;
   int i, j;

   for (i=j=0; i < 16; i += 2, j++) {
     x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
       | hex_char_to_nibble(s[i+1] & 0xFF);
   }
   return x;
 }

 v128_t
 hex_string_to_v128(char *s) {
   v128_t x;
   int i, j;

   for (i=j=0; i < 32; i += 2, j++) {
     x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
       | hex_char_to_nibble(s[i+1] & 0xFF);
   }
   return x;
 }


 /*
  * the matrix A[] is stored in column format, i.e., A[i] is the ith
  * column of the matrix
  */

 uint8_t
 A_times_x_plus_b(uint8_t A[8], uint8_t x, uint8_t b) {
   int index = 0;
   unsigned mask;

   for (mask=1; mask < 256; mask *= 2) {
     if (x & mask)
       b^= A[index];
     ++index;
   }

   return b;
 }

 inline void
 v16_copy_octet_string(v16_t *x, const uint8_t s[2]) {
   x->v8[0]  = s[0];
   x->v8[1]  = s[1];
 }

 inline void
 v32_copy_octet_string(v32_t *x, const uint8_t s[4]) {
   x->v8[0]  = s[0];
   x->v8[1]  = s[1];
   x->v8[2]  = s[2];
   x->v8[3]  = s[3];
 }

 inline void
 v64_copy_octet_string(v64_t *x, const uint8_t s[8]) {
   x->v8[0]  = s[0];
   x->v8[1]  = s[1];
   x->v8[2]  = s[2];
   x->v8[3]  = s[3];
   x->v8[4]  = s[4];
   x->v8[5]  = s[5];
   x->v8[6]  = s[6];
   x->v8[7]  = s[7];
 }

 void
 v128_copy_octet_string(v128_t *x, const uint8_t s[16]) {
   x->v8[0]  = s[0];
   x->v8[1]  = s[1];
   x->v8[2]  = s[2];
   x->v8[3]  = s[3];
   x->v8[4]  = s[4];
   x->v8[5]  = s[5];
   x->v8[6]  = s[6];
   x->v8[7]  = s[7];
   x->v8[8]  = s[8];
   x->v8[9]  = s[9];
   x->v8[10] = s[10];
   x->v8[11] = s[11];
   x->v8[12] = s[12];
   x->v8[13] = s[13];
   x->v8[14] = s[14];
   x->v8[15] = s[15];

 }

 #ifndef DATATYPES_USE_MACROS /* little functions are not macros */

 void
 v128_set_to_zero(v128_t *x) {
   _v128_set_to_zero(x);
 }

 void
 v128_copy(v128_t *x, const v128_t *y) {
   _v128_copy(x, y);
 }

 void
 v128_xor(v128_t *z, v128_t *x, v128_t *y) {
   _v128_xor(z, x, y);
 }

 void
 v128_and(v128_t *z, v128_t *x, v128_t *y) {
   _v128_and(z, x, y);
 }

 void
 v128_or(v128_t *z, v128_t *x, v128_t *y) {
   _v128_or(z, x, y);
 }

 void
 v128_complement(v128_t *x) {
   _v128_complement(x);
 }

 int
 v128_is_eq(const v128_t *x, const v128_t *y) {
   return _v128_is_eq(x, y);
 }

 int
 v128_get_bit(const v128_t *x, int i) {
   return _v128_get_bit(x, i);
 }

 void
 v128_set_bit(v128_t *x, int i) {
   _v128_set_bit(x, i);
 }

 void
 v128_clear_bit(v128_t *x, int i){
   _v128_clear_bit(x, i);
 }

 void
 v128_set_bit_to(v128_t *x, int i, int y){
   _v128_set_bit_to(x, i, y);
 }


 #endif /* DATATYPES_USE_MACROS */


 inline void
 v128_left_shift2(v128_t *x, int num_bits) {
   int i;
   int word_shift = num_bits >> 5;
   int bit_shift  = num_bits & 31;

   for (i=0; i < (4-word_shift); i++) {
     x->v32[i] = x->v32[i+word_shift] << bit_shift;
   }

   for (   ; i < word_shift; i++) {
     x->v32[i] = 0;
   }

 }

 void
 v128_right_shift(v128_t *x, int index) {
   const int base_index = index >> 5;
   const int bit_index = index & 31;
   int i, from;
   uint32_t b;

   if (index > 127) {
     v128_set_to_zero(x);
     return;
   }

   if (bit_index == 0) {

     /* copy each word from left size to right side */
     x->v32[4-1] = x->v32[4-1-base_index];
     for (i=4-1; i > base_index; i--)
       x->v32[i-1] = x->v32[i-1-base_index];

   } else {

     /* set each word to the "or" of the two bit-shifted words */
     for (i = 4; i > base_index; i--) {
       from = i-1 - base_index;
       b = x->v32[from] << bit_index;
       if (from > 0)
         b |= x->v32[from-1] >> (32-bit_index);
       x->v32[i-1] = b;
     }

   }

   /* now wrap up the final portion */
   for (i=0; i < base_index; i++)
     x->v32[i] = 0;

 }

 void
 v128_left_shift(v128_t *x, int index) {
   int i;
   const int base_index = index >> 5;
   const int bit_index = index & 31;

   if (index > 127) {
     v128_set_to_zero(x);
     return;
   }

   if (bit_index == 0) {
     for (i=0; i < 4 - base_index; i++)
       x->v32[i] = x->v32[i+base_index];
   } else {
     for (i=0; i < 4 - base_index - 1; i++)
       x->v32[i] = (x->v32[i+base_index] << bit_index) ^
 	(x->v32[i+base_index+1] >> (32 - bit_index));
     x->v32[4 - base_index-1] = x->v32[4-1] << bit_index;
   }

   /* now wrap up the final portion */
   for (i = 4 - base_index; i < 4; i++)
     x->v32[i] = 0;

 }


 #if 0
 void
 v128_add(v128_t *z, v128_t *x, v128_t *y) {
   /* integer addition modulo 2^128    */

 #ifdef WORDS_BIGENDIAN
   uint64_t tmp;

   tmp = x->v32[3] + y->v32[3];
   z->v32[3] = (uint32_t) tmp;

   tmp =  x->v32[2] + y->v32[2] + (tmp >> 32);
   z->v32[2] = (uint32_t) tmp;

   tmp =  x->v32[1] + y->v32[1] + (tmp >> 32);
   z->v32[1] = (uint32_t) tmp;

   tmp =  x->v32[0] + y->v32[0] + (tmp >> 32);
   z->v32[0] = (uint32_t) tmp;

 #else /* assume little endian architecture */
   uint64_t tmp;

   tmp = htonl(x->v32[3]) + htonl(y->v32[3]);
   z->v32[3] = ntohl((uint32_t) tmp);

   tmp =  htonl(x->v32[2]) + htonl(y->v32[2]) + htonl(tmp >> 32);
   z->v32[2] = ntohl((uint32_t) tmp);

   tmp =  htonl(x->v32[1]) + htonl(y->v32[1]) + htonl(tmp >> 32);
   z->v32[1] = ntohl((uint32_t) tmp);

   tmp =  htonl(x->v32[0]) + htonl(y->v32[0]) + htonl(tmp >> 32);
   z->v32[0] = ntohl((uint32_t) tmp);

 #endif /* WORDS_BIGENDIAN */

 }
 #endif

 int
 octet_string_is_eq(uint8_t *a, uint8_t *b, int len) {
   uint8_t *end = b + len;
   while (b < end)
     if (*a++ != *b++)
       return 1;
   return 0;
 }

 void
 octet_string_set_to_zero(uint8_t *s, int len) {
   uint8_t *end = s + len;

   do {
     *s = 0;
   } while (++s < end);

 }


 /* functions below not yet tested! */

 int
 v32_low_bit(v32_t *w) {
   int value;

   value = low_bit[w->v8[0]];
   if (value != -1)
     return value;
   value = low_bit[w->v8[1]];
   if (value != -1)
     return value + 8;
   value = low_bit[w->v8[2]];
   if (value != -1)
     return value + 16;
   value = low_bit[w->v8[3]];
   if (value == -1)
     return -1;
   return value + 24;
 }

 /* high_bit not done yet */
	/*
	* math.c
	*
	* crypto math operations and data types
	*
	* David A. McGrew
	* Cisco Systems, Inc.
	*/
	/*
	*
	* Copyright (c) 2001-2006 Cisco Systems, Inc.
	* All rights reserved.
	*
	* Redistribution and use in source and binary forms, with or without
	* modification, are permitted provided that the following conditions
	* are met:
	*
	* Redistributions of source code must retain the above copyright
	* notice, this list of conditions and the following disclaimer.
	*
	* Redistributions in binary form must reproduce the above
	* copyright notice, this list of conditions and the following
	* disclaimer in the documentation and/or other materials provided
	* with the distribution.
	*
	* Neither the name of the Cisco Systems, Inc. nor the names of its
	* contributors may be used to endorse or promote products derived
	* from this software without specific prior written permission.
	*
	* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
	* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
	* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
	* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
	* COPYRIGHT HOLDERS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
	* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
	* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
	* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
	* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
	* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
	* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
	* OF THE POSSIBILITY OF SUCH DAMAGE.
	*
	*/

	#include "crypto_math.h"

	int
	octet_weight[256] = {
	0, 1, 1, 2, 1, 2, 2, 3,
	1, 2, 2, 3, 2, 3, 3, 4,
	1, 2, 2, 3, 2, 3, 3, 4,
	2, 3, 3, 4, 3, 4, 4, 5,
	1, 2, 2, 3, 2, 3, 3, 4,
	2, 3, 3, 4, 3, 4, 4, 5,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	1, 2, 2, 3, 2, 3, 3, 4,
	2, 3, 3, 4, 3, 4, 4, 5,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	3, 4, 4, 5, 4, 5, 5, 6,
	4, 5, 5, 6, 5, 6, 6, 7,
	1, 2, 2, 3, 2, 3, 3, 4,
	2, 3, 3, 4, 3, 4, 4, 5,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	3, 4, 4, 5, 4, 5, 5, 6,
	4, 5, 5, 6, 5, 6, 6, 7,
	2, 3, 3, 4, 3, 4, 4, 5,
	3, 4, 4, 5, 4, 5, 5, 6,
	3, 4, 4, 5, 4, 5, 5, 6,
	4, 5, 5, 6, 5, 6, 6, 7,
	3, 4, 4, 5, 4, 5, 5, 6,
	4, 5, 5, 6, 5, 6, 6, 7,
	4, 5, 5, 6, 5, 6, 6, 7,
	5, 6, 6, 7, 6, 7, 7, 8
	};

	int
	low_bit[256] = {
	-1, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	5, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	6, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	5, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	7, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	5, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	6, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	5, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0,
	4, 0, 1, 0, 2, 0, 1, 0,
	3, 0, 1, 0, 2, 0, 1, 0
	};


	int
	high_bit[256] = {
	-1, 0, 1, 1, 2, 2, 2, 2,
	3, 3, 3, 3, 3, 3, 3, 3,
	4, 4, 4, 4, 4, 4, 4, 4,
	4, 4, 4, 4, 4, 4, 4, 4,
	5, 5, 5, 5, 5, 5, 5, 5,
	5, 5, 5, 5, 5, 5, 5, 5,
	5, 5, 5, 5, 5, 5, 5, 5,
	5, 5, 5, 5, 5, 5, 5, 5,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	6, 6, 6, 6, 6, 6, 6, 6,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7,
	7, 7, 7, 7, 7, 7, 7, 7
	};

	int
	octet_get_weight(uint8_t octet) {
	extern int octet_weight[256];

	return octet_weight[octet];
	}

	unsigned char
	v32_weight(v32_t a) {
	unsigned int wt = 0;

	wt += octet_weight[a.v8[0]]; /* note: endian-ness makes no difference */
	wt += octet_weight[a.v8[1]];
	wt += octet_weight[a.v8[2]];
	wt += octet_weight[a.v8[3]];

	return wt;
	}

	inline unsigned char
	v32_distance(v32_t x, v32_t y) {
	x.value ^= y.value;
	return v32_weight(x);
	}

	unsigned int
	v32_dot_product(v32_t a, v32_t b) {
	a.value &= b.value;
	return v32_weight(a) & 1;
	}

	/*
	* _bit_string returns a NULL-terminated character string suitable for
	* printing
	*/

	#define MAX_STRING_LENGTH 1024

	char bit_string[MAX_STRING_LENGTH];

	char *
	octet_bit_string(uint8_t x) {
	int mask, index;

	for (mask = 1, index = 0; mask < 256; mask <<= 1)
	if ((x & mask) == 0)
	bit_string[index++] = '0';
	else
	bit_string[index++] = '1';

	bit_string[index++] = 0; /* NULL terminate string */

	return bit_string;
	}

	char *
	v16_bit_string(v16_t x) {
	int i, mask, index;

	for (i = index = 0; i < 2; i++) {
	for (mask = 1; mask < 256; mask <<= 1)
	if ((x.v8[i] & mask) == 0)
	bit_string[index++] = '0';
	else
	bit_string[index++] = '1';
	}
	bit_string[index++] = 0; /* NULL terminate string */
	return bit_string;
	}

	char *
	v32_bit_string(v32_t x) {
	int i, mask, index;

	for (i = index = 0; i < 4; i++) {
	for (mask = 128; mask > 0; mask >>= 1)
	if ((x.v8[i] & mask) == 0)
	bit_string[index++] = '0';
	else
	bit_string[index++] = '1';
	}
	bit_string[index++] = 0; /* NULL terminate string */
	return bit_string;
	}

	char *
	v64_bit_string(const v64_t *x) {
	int i, mask, index;

	for (i = index = 0; i < 8; i++) {
	for (mask = 1; mask < 256; mask <<= 1)
	if ((x->v8[i] & mask) == 0)
	bit_string[index++] = '0';
	else
	bit_string[index++] = '1';
	}
	bit_string[index++] = 0; /* NULL terminate string */
	return bit_string;
	}

	char *
	v128_bit_string(v128_t *x) {
	int j, index;
	uint32_t mask;

	for (j=index=0; j < 4; j++) {
	for (mask=0x80000000; mask > 0; mask >>= 1) {
	if (x->v32[j] & mask)
	bit_string[index] = '1';
	else
	bit_string[index] = '0';
	++index;
	}
	}
	bit_string[128] = 0; /* null terminate string */

	return bit_string;
	}

	uint8_t
	nibble_to_hex_char(uint8_t nibble) {
	char buf[16] = {'0', '1', '2', '3', '4', '5', '6', '7',
	'8', '9', 'a', 'b', 'c', 'd', 'e', 'f' };
	return buf[nibble & 0xF];
	}

	char *
	octet_hex_string(uint8_t x) {

	bit_string[0] = nibble_to_hex_char(x >> 4);
	bit_string[1] = nibble_to_hex_char(x & 0xF);

	bit_string[2] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	octet_string_hex_string(const void *str, int length) {
	const uint8_t *s = str;
	int i;

	/* double length, since one octet takes two hex characters */
	length *= 2;

	/* truncate string if it would be too long */
	if (length > MAX_STRING_LENGTH)
	length = MAX_STRING_LENGTH-1;

	for (i=0; i < length; i+=2) {
	bit_string[i] = nibble_to_hex_char(*s >> 4);
	bit_string[i+1] = nibble_to_hex_char(*s++ & 0xF);
	}
	bit_string[i] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	v16_hex_string(v16_t x) {
	int i, j;

	for (i=j=0; i < 2; i++) {
	bit_string[j++] = nibble_to_hex_char(x.v8[i] >> 4);
	bit_string[j++] = nibble_to_hex_char(x.v8[i] & 0xF);
	}

	bit_string[j] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	v32_hex_string(v32_t x) {
	int i, j;

	for (i=j=0; i < 4; i++) {
	bit_string[j++] = nibble_to_hex_char(x.v8[i] >> 4);
	bit_string[j++] = nibble_to_hex_char(x.v8[i] & 0xF);
	}

	bit_string[j] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	v64_hex_string(const v64_t *x) {
	int i, j;

	for (i=j=0; i < 8; i++) {
	bit_string[j++] = nibble_to_hex_char(x->v8[i] >> 4);
	bit_string[j++] = nibble_to_hex_char(x->v8[i] & 0xF);
	}

	bit_string[j] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	v128_hex_string(v128_t *x) {
	int i, j;

	for (i=j=0; i < 16; i++) {
	bit_string[j++] = nibble_to_hex_char(x->v8[i] >> 4);
	bit_string[j++] = nibble_to_hex_char(x->v8[i] & 0xF);
	}

	bit_string[j] = 0; /* null terminate string */
	return bit_string;
	}

	char *
	char_to_hex_string(char *x, int num_char) {
	int i, j;

	if (num_char >= 16)
	num_char = 16;
	for (i=j=0; i < num_char; i++) {
	bit_string[j++] = nibble_to_hex_char(x[i] >> 4);
	bit_string[j++] = nibble_to_hex_char(x[i] & 0xF);
	}

	bit_string[j] = 0; /* null terminate string */
	return bit_string;
	}

	int
	hex_char_to_nibble(uint8_t c) {
	switch(c) {
	case ('0'): return 0x0;
	case ('1'): return 0x1;
	case ('2'): return 0x2;
	case ('3'): return 0x3;
	case ('4'): return 0x4;
	case ('5'): return 0x5;
	case ('6'): return 0x6;
	case ('7'): return 0x7;
	case ('8'): return 0x8;
	case ('9'): return 0x9;
	case ('a'): return 0xa;
	case ('A'): return 0xa;
	case ('b'): return 0xb;
	case ('B'): return 0xb;
	case ('c'): return 0xc;
	case ('C'): return 0xc;
	case ('d'): return 0xd;
	case ('D'): return 0xd;
	case ('e'): return 0xe;
	case ('E'): return 0xe;
	case ('f'): return 0xf;
	case ('F'): return 0xf;
	default: return -1; /* this flags an error */
	}
	/* NOTREACHED */
	return -1; /* this keeps compilers from complaining */
	}

	int
	is_hex_string(char *s) {
	while(*s != 0)
	if (hex_char_to_nibble(*s++) == -1)
	return 0;
	return 1;
	}

	uint8_t
	hex_string_to_octet(char *s) {
	uint8_t x;

	x = (hex_char_to_nibble(s[0]) << 4)
	\| hex_char_to_nibble(s[1] & 0xFF);

	return x;
	}

	/*
	* hex_string_to_octet_string converts a hexadecimal string
	* of length 2 * len to a raw octet string of length len
	*/

	int
	hex_string_to_octet_string(char raw, char hex, int len) {
	uint8_t x;
	int tmp;
	int hex_len;

	hex_len = 0;
	while (hex_len < len) {
	tmp = hex_char_to_nibble(hex[0]);
	if (tmp == -1)
	return hex_len;
	x = (tmp << 4);
	hex_len++;
	tmp = hex_char_to_nibble(hex[1]);
	if (tmp == -1)
	return hex_len;
	x \|= (tmp & 0xff);
	hex_len++;
	*raw++ = x;
	hex += 2;
	}
	return hex_len;
	}

	v16_t
	hex_string_to_v16(char *s) {
	v16_t x;
	int i, j;

	for (i=j=0; i < 4; i += 2, j++) {
	x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
	\| hex_char_to_nibble(s[i+1] & 0xFF);
	}
	return x;
	}

	v32_t
	hex_string_to_v32(char *s) {
	v32_t x;
	int i, j;

	for (i=j=0; i < 8; i += 2, j++) {
	x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
	\| hex_char_to_nibble(s[i+1] & 0xFF);
	}
	return x;
	}

	v64_t
	hex_string_to_v64(char *s) {
	v64_t x;
	int i, j;

	for (i=j=0; i < 16; i += 2, j++) {
	x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
	\| hex_char_to_nibble(s[i+1] & 0xFF);
	}
	return x;
	}

	v128_t
	hex_string_to_v128(char *s) {
	v128_t x;
	int i, j;

	for (i=j=0; i < 32; i += 2, j++) {
	x.v8[j] = (hex_char_to_nibble(s[i]) << 4)
	\| hex_char_to_nibble(s[i+1] & 0xFF);
	}
	return x;
	}



	/*
	* the matrix A[] is stored in column format, i.e., A[i] is the ith
	* column of the matrix
	*/

	uint8_t
	A_times_x_plus_b(uint8_t A[8], uint8_t x, uint8_t b) {
	int index = 0;
	unsigned mask;

	for (mask=1; mask < 256; mask *= 2) {
	if (x & mask)
	b^= A[index];
	++index;
	}

	return b;
	}

	inline void
	v16_copy_octet_string(v16_t *x, const uint8_t s[2]) {
	x->v8[0] = s[0];
	x->v8[1] = s[1];
	}

	inline void
	v32_copy_octet_string(v32_t *x, const uint8_t s[4]) {
	x->v8[0] = s[0];
	x->v8[1] = s[1];
	x->v8[2] = s[2];
	x->v8[3] = s[3];
	}

	inline void
	v64_copy_octet_string(v64_t *x, const uint8_t s[8]) {
	x->v8[0] = s[0];
	x->v8[1] = s[1];
	x->v8[2] = s[2];
	x->v8[3] = s[3];
	x->v8[4] = s[4];
	x->v8[5] = s[5];
	x->v8[6] = s[6];
	x->v8[7] = s[7];
	}

	void
	v128_copy_octet_string(v128_t *x, const uint8_t s[16]) {
	x->v8[0] = s[0];
	x->v8[1] = s[1];
	x->v8[2] = s[2];
	x->v8[3] = s[3];
	x->v8[4] = s[4];
	x->v8[5] = s[5];
	x->v8[6] = s[6];
	x->v8[7] = s[7];
	x->v8[8] = s[8];
	x->v8[9] = s[9];
	x->v8[10] = s[10];
	x->v8[11] = s[11];
	x->v8[12] = s[12];
	x->v8[13] = s[13];
	x->v8[14] = s[14];
	x->v8[15] = s[15];

	}

	#ifndef DATATYPES_USE_MACROS /* little functions are not macros */

	void
	v128_set_to_zero(v128_t *x) {
	_v128_set_to_zero(x);
	}

	void
	v128_copy(v128_t x, const v128_t y) {
	_v128_copy(x, y);
	}

	void
	v128_xor(v128_t z, v128_t x, v128_t *y) {
	_v128_xor(z, x, y);
	}

	void
	v128_and(v128_t z, v128_t x, v128_t *y) {
	_v128_and(z, x, y);
	}

	void
	v128_or(v128_t z, v128_t x, v128_t *y) {
	_v128_or(z, x, y);
	}

	void
	v128_complement(v128_t *x) {
	_v128_complement(x);
	}

	int
	v128_is_eq(const v128_t x, const v128_t y) {
	return _v128_is_eq(x, y);
	}

	int
	v128_get_bit(const v128_t *x, int i) {
	return _v128_get_bit(x, i);
	}

	void
	v128_set_bit(v128_t *x, int i) {
	_v128_set_bit(x, i);
	}

	void
	v128_clear_bit(v128_t *x, int i){
	_v128_clear_bit(x, i);
	}

	void
	v128_set_bit_to(v128_t *x, int i, int y){
	_v128_set_bit_to(x, i, y);
	}


	#endif /* DATATYPES_USE_MACROS */


	inline void
	v128_left_shift2(v128_t *x, int num_bits) {
	int i;
	int word_shift = num_bits >> 5;
	int bit_shift = num_bits & 31;

	for (i=0; i < (4-word_shift); i++) {
	x->v32[i] = x->v32[i+word_shift] << bit_shift;
	}

	for ( ; i < word_shift; i++) {
	x->v32[i] = 0;
	}

	}

	void
	v128_right_shift(v128_t *x, int index) {
	const int base_index = index >> 5;
	const int bit_index = index & 31;
	int i, from;
	uint32_t b;

	if (index > 127) {
	v128_set_to_zero(x);
	return;
	}

	if (bit_index == 0) {

	/* copy each word from left size to right side */
	x->v32[4-1] = x->v32[4-1-base_index];
	for (i=4-1; i > base_index; i--)
	x->v32[i-1] = x->v32[i-1-base_index];

	} else {

	/* set each word to the "or" of the two bit-shifted words */
	for (i = 4; i > base_index; i--) {
	from = i-1 - base_index;
	b = x->v32[from] << bit_index;
	if (from > 0)
	b \|= x->v32[from-1] >> (32-bit_index);
	x->v32[i-1] = b;
	}

	}

	/* now wrap up the final portion */
	for (i=0; i < base_index; i++)
	x->v32[i] = 0;

	}

	void
	v128_left_shift(v128_t *x, int index) {
	int i;
	const int base_index = index >> 5;
	const int bit_index = index & 31;

	if (index > 127) {
	v128_set_to_zero(x);
	return;
	}

	if (bit_index == 0) {
	for (i=0; i < 4 - base_index; i++)
	x->v32[i] = x->v32[i+base_index];
	} else {
	for (i=0; i < 4 - base_index - 1; i++)
	x->v32[i] = (x->v32[i+base_index] << bit_index) ^
	(x->v32[i+base_index+1] >> (32 - bit_index));
	x->v32[4 - base_index-1] = x->v32[4-1] << bit_index;
	}

	/* now wrap up the final portion */
	for (i = 4 - base_index; i < 4; i++)
	x->v32[i] = 0;

	}


	#if 0
	void
	v128_add(v128_t z, v128_t x, v128_t *y) {
	/* integer addition modulo 2^128 */

	#ifdef WORDS_BIGENDIAN
	uint64_t tmp;

	tmp = x->v32[3] + y->v32[3];
	z->v32[3] = (uint32_t) tmp;

	tmp = x->v32[2] + y->v32[2] + (tmp >> 32);
	z->v32[2] = (uint32_t) tmp;

	tmp = x->v32[1] + y->v32[1] + (tmp >> 32);
	z->v32[1] = (uint32_t) tmp;

	tmp = x->v32[0] + y->v32[0] + (tmp >> 32);
	z->v32[0] = (uint32_t) tmp;

	#else /* assume little endian architecture */
	uint64_t tmp;

	tmp = htonl(x->v32[3]) + htonl(y->v32[3]);
	z->v32[3] = ntohl((uint32_t) tmp);

	tmp = htonl(x->v32[2]) + htonl(y->v32[2]) + htonl(tmp >> 32);
	z->v32[2] = ntohl((uint32_t) tmp);

	tmp = htonl(x->v32[1]) + htonl(y->v32[1]) + htonl(tmp >> 32);
	z->v32[1] = ntohl((uint32_t) tmp);

	tmp = htonl(x->v32[0]) + htonl(y->v32[0]) + htonl(tmp >> 32);
	z->v32[0] = ntohl((uint32_t) tmp);

	#endif /* WORDS_BIGENDIAN */

	}
	#endif

	int
	octet_string_is_eq(uint8_t a, uint8_t b, int len) {
	uint8_t *end = b + len;
	while (b < end)
	if (a++ != b++)
	return 1;
	return 0;
	}

	void
	octet_string_set_to_zero(uint8_t *s, int len) {
	uint8_t *end = s + len;

	do {
	*s = 0;
	} while (++s < end);

	}


	/* functions below not yet tested! */

	int
	v32_low_bit(v32_t *w) {
	int value;

	value = low_bit[w->v8[0]];
	if (value != -1)
	return value;
	value = low_bit[w->v8[1]];
	if (value != -1)
	return value + 8;
	value = low_bit[w->v8[2]];
	if (value != -1)
	return value + 16;
	value = low_bit[w->v8[3]];
	if (value == -1)
	return -1;
	return value + 24;
	}

	/* high_bit not done yet */