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 /*

  * 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;

 }

 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;

 }

 void

 v16_copy_octet_string(v16_t *x, const uint8_t s[2]) {

   x->v8[0]  = s[0];

   x->v8[1]  = s[1];

 }

 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];

 }

 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 */

 static 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 */