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  1. /*
  2.  * Copyright (C) 2005 Josef Cejka
  3.  * All rights reserved.
  4.  *
  5.  * Redistribution and use in source and binary forms, with or without
  6.  * modification, are permitted provided that the following conditions
  7.  * are met:
  8.  *
  9.  * - Redistributions of source code must retain the above copyright
  10.  *   notice, this list of conditions and the following disclaimer.
  11.  * - Redistributions in binary form must reproduce the above copyright
  12.  *   notice, this list of conditions and the following disclaimer in the
  13.  *   documentation and/or other materials provided with the distribution.
  14.  * - The name of the author may not be used to endorse or promote products
  15.  *   derived from this software without specific prior written permission.
  16.  *
  17.  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  18.  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  19.  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  20.  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  21.  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  22.  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  23.  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  24.  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  25.  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  26.  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  27.  */
  28.  
  29. #include<sftypes.h>
  30. #include<common.h>
  31.  
  32. /* Table for fast leading zeroes counting */
  33. char zeroTable[256] = {
  34.     8, 7, 7, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, 4, 4, \
  35.     3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, \
  36.     2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
  37.     2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, \
  38.     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
  39.     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
  40.     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
  41.     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, \
  42.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  43.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  44.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  45.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  46.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  47.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  48.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
  49.     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
  50. };
  51.  
  52.  
  53.  
  54. /** Take fraction shifted by 10 bits to left, round it, normalize it and detect exceptions
  55.  * @param exp exponent with bias
  56.  * @param cfrac fraction shifted 10 places left with added hidden bit
  57.  * @return valied float64
  58.  */
  59. float64 finishFloat64(int32_t cexp, uint64_t cfrac, char sign)
  60. {
  61.     float64 result;
  62.  
  63.     result.parts.sign = sign;
  64.  
  65.     /* find first nonzero digit and shift result and detect possibly underflow */
  66.     while ((cexp > 0) && (cfrac) && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ) )))) {
  67.         cexp--;
  68.         cfrac <<= 1;
  69.             /* TODO: fix underflow */
  70.     };
  71.    
  72.     if ((cexp < 0) || ( cexp == 0 && (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))))) {
  73.         /* FIXME: underflow */
  74.         result.parts.exp = 0;
  75.         if ((cexp + FLOAT64_FRACTION_SIZE + 1) < 0) { /* +1 is place for rounding */
  76.             result.parts.fraction = 0;
  77.             return result;
  78.         }
  79.        
  80.         while (cexp < 0) {
  81.             cexp++;
  82.             cfrac >>= 1;
  83.         }
  84.    
  85.         cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
  86.        
  87.         if (!(cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1)))) {
  88.            
  89.             result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2) ) & (~FLOAT64_HIDDEN_BIT_MASK));
  90.             return result;
  91.         }  
  92.     } else {
  93.         cfrac += (0x1 << (64 - FLOAT64_FRACTION_SIZE - 3));
  94.     }
  95.    
  96.     ++cexp;
  97.  
  98.     if (cfrac & (FLOAT64_HIDDEN_BIT_MASK << (64 - FLOAT64_FRACTION_SIZE - 1 ))) {
  99.         ++cexp;
  100.         cfrac >>= 1;
  101.     }  
  102.  
  103.     /* check overflow */
  104.     if (cexp >= FLOAT64_MAX_EXPONENT ) {
  105.         /* FIXME: overflow, return infinity */
  106.         result.parts.exp = FLOAT64_MAX_EXPONENT;
  107.         result.parts.fraction = 0;
  108.         return result;
  109.     }
  110.  
  111.     result.parts.exp = (uint32_t)cexp;
  112.    
  113.     result.parts.fraction = ((cfrac >>(64 - FLOAT64_FRACTION_SIZE - 2 ) ) & (~FLOAT64_HIDDEN_BIT_MASK));
  114.    
  115.     return result; 
  116. }
  117.  
  118. /** Counts leading zeroes in 64bit unsigned integer
  119.  * @param i
  120.  */
  121. int countZeroes64(uint64_t i)
  122. {
  123.     int j;
  124.     for (j =0; j < 64; j += 8) {
  125.         if ( i & (0xFFll << (56 - j))) {
  126.             return (j + countZeroes8(i >> (56 - j)));
  127.         }
  128.     }
  129.  
  130.     return 64;
  131. }
  132.  
  133. /** Counts leading zeroes in 32bit unsigned integer
  134.  * @param i
  135.  */
  136. int countZeroes32(uint32_t i)
  137. {
  138.     int j;
  139.     for (j =0; j < 32; j += 8) {
  140.         if ( i & (0xFF << (24 - j))) {
  141.             return (j + countZeroes8(i >> (24 - j)));
  142.         }
  143.     }
  144.  
  145.     return 32;
  146. }
  147.  
  148. /** Counts leading zeroes in byte
  149.  * @param i
  150.  */
  151. int countZeroes8(uint8_t i)
  152. {
  153.     return zeroTable[i];
  154. }
  155.  
  156. /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 30. bit
  157.  * @param exp exponent
  158.  * @param fraction part with hidden bit shifted to 30. bit
  159.  */
  160. void roundFloat32(int32_t *exp, uint32_t *fraction)
  161. {
  162.     /* rounding - if first bit after fraction is set then round up */
  163.     (*fraction) += (0x1 << 6);
  164.    
  165.     if ((*fraction) & (FLOAT32_HIDDEN_BIT_MASK << 8)) {
  166.         /* rounding overflow */
  167.         ++(*exp);
  168.         (*fraction) >>= 1;
  169.     };
  170.    
  171.     if (((*exp) >= FLOAT32_MAX_EXPONENT ) || ((*exp) < 0)) {
  172.         /* overflow - set infinity as result */
  173.         (*exp) = FLOAT32_MAX_EXPONENT;
  174.         (*fraction) = 0;
  175.         return;
  176.     }
  177.  
  178.     return;
  179. }
  180.  
  181. /** Round and normalize number expressed by exponent and fraction with first bit (equal to hidden bit) at 62. bit
  182.  * @param exp exponent
  183.  * @param fraction part with hidden bit shifted to 62. bit
  184.  */
  185. void roundFloat64(int32_t *exp, uint64_t *fraction)
  186. {
  187.     /* rounding - if first bit after fraction is set then round up */
  188.     (*fraction) += (0x1 << 9);
  189.    
  190.     if ((*fraction) & (FLOAT64_HIDDEN_BIT_MASK << 11)) {
  191.         /* rounding overflow */
  192.         ++(*exp);
  193.         (*fraction) >>= 1;
  194.     };
  195.    
  196.     if (((*exp) >= FLOAT64_MAX_EXPONENT ) || ((*exp) < 0)) {
  197.         /* overflow - set infinity as result */
  198.         (*exp) = FLOAT64_MAX_EXPONENT;
  199.         (*fraction) = 0;
  200.         return;
  201.     }
  202.  
  203.     return;
  204. }
  205.  
  206.