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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. /** @addtogroup softfloat  
  30.  * @{
  31.  */
  32. /** @file
  33.  */
  34.  
  35. #include "sftypes.h"
  36. #include "conversion.h"
  37. #include "comparison.h"
  38. #include "common.h"
  39.  
  40. float64 convertFloat32ToFloat64(float32 a)
  41. {
  42.     float64 result;
  43.     uint64_t frac;
  44.    
  45.     result.parts.sign = a.parts.sign;
  46.     result.parts.fraction = a.parts.fraction;
  47.     result.parts.fraction <<= (FLOAT64_FRACTION_SIZE - FLOAT32_FRACTION_SIZE );
  48.    
  49.     if ((isFloat32Infinity(a))||(isFloat32NaN(a))) {
  50.         result.parts.exp = 0x7FF;
  51.         /* TODO; check if its correct for SigNaNs*/
  52.         return result;
  53.     };
  54.    
  55.     result.parts.exp = a.parts.exp + ( (int)FLOAT64_BIAS - FLOAT32_BIAS );
  56.     if (a.parts.exp == 0) {
  57.         /* normalize denormalized numbers */
  58.  
  59.         if (result.parts.fraction == 0ll) { /* fix zero */
  60.             result.parts.exp = 0ll;
  61.             return result;
  62.         }
  63.            
  64.         frac = result.parts.fraction;
  65.        
  66.         while (!(frac & (0x10000000000000ll))) {
  67.             frac <<= 1;
  68.             --result.parts.exp;
  69.         };
  70.        
  71.         ++result.parts.exp;
  72.         result.parts.fraction = frac;
  73.     };
  74.    
  75.     return result;
  76.    
  77. }
  78.  
  79. float32 convertFloat64ToFloat32(float64 a)
  80. {
  81.     float32 result;
  82.     int32_t exp;
  83.     uint64_t frac;
  84.    
  85.     result.parts.sign = a.parts.sign;
  86.    
  87.     if (isFloat64NaN(a)) {
  88.        
  89.         result.parts.exp = 0xFF;
  90.        
  91.         if (isFloat64SigNaN(a)) {
  92.             result.parts.fraction = 0x400000; /* set first bit of fraction nonzero */
  93.             return result;
  94.         }
  95.    
  96.         result.parts.fraction = 0x1; /* fraction nonzero but its first bit is zero */
  97.         return result;
  98.     };
  99.  
  100.     if (isFloat64Infinity(a)) {
  101.         result.parts.fraction = 0;
  102.         result.parts.exp = 0xFF;
  103.         return result;
  104.     };
  105.  
  106.     exp = (int)a.parts.exp - FLOAT64_BIAS + FLOAT32_BIAS;
  107.    
  108.     if (exp >= 0xFF) {
  109.         /*FIXME: overflow*/
  110.         result.parts.fraction = 0;
  111.         result.parts.exp = 0xFF;
  112.         return result;
  113.        
  114.     } else if (exp <= 0 ) {
  115.        
  116.         /* underflow or denormalized */
  117.        
  118.         result.parts.exp = 0;
  119.        
  120.         exp *= -1; 
  121.         if (exp > FLOAT32_FRACTION_SIZE ) {
  122.             /* FIXME: underflow */
  123.             result.parts.fraction = 0;
  124.             return result;
  125.         };
  126.        
  127.         /* denormalized */
  128.        
  129.         frac = a.parts.fraction;
  130.         frac |= 0x10000000000000ll; /* denormalize and set hidden bit */
  131.        
  132.         frac >>= (FLOAT64_FRACTION_SIZE - FLOAT32_FRACTION_SIZE + 1);
  133.        
  134.         while (exp > 0) {
  135.             --exp;
  136.             frac >>= 1;
  137.         };
  138.         result.parts.fraction = frac;
  139.        
  140.         return result;
  141.     };
  142.  
  143.     result.parts.exp = exp;
  144.     result.parts.fraction = a.parts.fraction >> (FLOAT64_FRACTION_SIZE - FLOAT32_FRACTION_SIZE);
  145.     return result;
  146. }
  147.  
  148.  
  149. /** Helping procedure for converting float32 to uint32
  150.  * @param a floating point number in normalized form (no NaNs or Inf are checked )
  151.  * @return unsigned integer
  152.  */
  153. static uint32_t _float32_to_uint32_helper(float32 a)
  154. {
  155.     uint32_t frac;
  156.    
  157.     if (a.parts.exp < FLOAT32_BIAS) {
  158.         /*TODO: rounding*/
  159.         return 0;
  160.     }
  161.    
  162.     frac = a.parts.fraction;
  163.    
  164.     frac |= FLOAT32_HIDDEN_BIT_MASK;
  165.     /* shift fraction to left so hidden bit will be the most significant bit */
  166.     frac <<= 32 - FLOAT32_FRACTION_SIZE - 1;
  167.  
  168.     frac >>= 32 - (a.parts.exp - FLOAT32_BIAS) - 1;
  169.     if ((a.parts.sign == 1) && (frac != 0)) {
  170.         frac = ~frac;
  171.         ++frac;
  172.     }
  173.    
  174.     return frac;
  175. }
  176.  
  177. /* Convert float to unsigned int32
  178.  * FIXME: Im not sure what to return if overflow/underflow happens
  179.  *  - now its the biggest or the smallest int
  180.  */
  181. uint32_t float32_to_uint32(float32 a)
  182. {
  183.     if (isFloat32NaN(a)) {
  184.         return MAX_UINT32;
  185.     }
  186.    
  187.     if (isFloat32Infinity(a) || (a.parts.exp >= (32 + FLOAT32_BIAS)))  {
  188.         if (a.parts.sign) {
  189.             return MIN_UINT32;
  190.         }
  191.         return MAX_UINT32;
  192.     }
  193.    
  194.     return _float32_to_uint32_helper(a);   
  195. }
  196.  
  197. /* Convert float to signed int32
  198.  * FIXME: Im not sure what to return if overflow/underflow happens
  199.  *  - now its the biggest or the smallest int
  200.  */
  201. int32_t float32_to_int32(float32 a)
  202. {
  203.     if (isFloat32NaN(a)) {
  204.         return MAX_INT32;
  205.     }
  206.    
  207.     if (isFloat32Infinity(a) || (a.parts.exp >= (32 + FLOAT32_BIAS)))  {
  208.         if (a.parts.sign) {
  209.             return MIN_INT32;
  210.         }
  211.         return MAX_INT32;
  212.     }
  213.     return _float32_to_uint32_helper(a);
  214. }  
  215.  
  216.  
  217. /** Helping procedure for converting float64 to uint64
  218.  * @param a floating point number in normalized form (no NaNs or Inf are checked )
  219.  * @return unsigned integer
  220.  */
  221. static uint64_t _float64_to_uint64_helper(float64 a)
  222. {
  223.     uint64_t frac;
  224.    
  225.     if (a.parts.exp < FLOAT64_BIAS) {
  226.         /*TODO: rounding*/
  227.         return 0;
  228.     }
  229.    
  230.     frac = a.parts.fraction;
  231.    
  232.     frac |= FLOAT64_HIDDEN_BIT_MASK;
  233.     /* shift fraction to left so hidden bit will be the most significant bit */
  234.     frac <<= 64 - FLOAT64_FRACTION_SIZE - 1;
  235.  
  236.     frac >>= 64 - (a.parts.exp - FLOAT64_BIAS) - 1;
  237.     if ((a.parts.sign == 1) && (frac != 0)) {
  238.         frac = ~frac;
  239.         ++frac;
  240.     }
  241.    
  242.     return frac;
  243. }
  244.  
  245. /* Convert float to unsigned int64
  246.  * FIXME: Im not sure what to return if overflow/underflow happens
  247.  *  - now its the biggest or the smallest int
  248.  */
  249. uint64_t float64_to_uint64(float64 a)
  250. {
  251.     if (isFloat64NaN(a)) {
  252.         return MAX_UINT64;
  253.     }
  254.    
  255.     if (isFloat64Infinity(a) || (a.parts.exp >= (64 + FLOAT64_BIAS)))  {
  256.         if (a.parts.sign) {
  257.             return MIN_UINT64;
  258.         }
  259.         return MAX_UINT64;
  260.     }
  261.    
  262.     return _float64_to_uint64_helper(a);   
  263. }
  264.  
  265. /* Convert float to signed int64
  266.  * FIXME: Im not sure what to return if overflow/underflow happens
  267.  *  - now its the biggest or the smallest int
  268.  */
  269. int64_t float64_to_int64(float64 a)
  270. {
  271.     if (isFloat64NaN(a)) {
  272.         return MAX_INT64;
  273.     }
  274.    
  275.     if (isFloat64Infinity(a) || (a.parts.exp >= (64 + FLOAT64_BIAS)))  {
  276.         if (a.parts.sign) {
  277.             return MIN_INT64;
  278.         }
  279.         return MAX_INT64;
  280.     }
  281.     return _float64_to_uint64_helper(a);
  282. }  
  283.  
  284.  
  285.  
  286.  
  287.  
  288. /** Helping procedure for converting float32 to uint64
  289.  * @param a floating point number in normalized form (no NaNs or Inf are checked )
  290.  * @return unsigned integer
  291.  */
  292. static uint64_t _float32_to_uint64_helper(float32 a)
  293. {
  294.     uint64_t frac;
  295.    
  296.     if (a.parts.exp < FLOAT32_BIAS) {
  297.         /*TODO: rounding*/
  298.         return 0;
  299.     }
  300.    
  301.     frac = a.parts.fraction;
  302.    
  303.     frac |= FLOAT32_HIDDEN_BIT_MASK;
  304.     /* shift fraction to left so hidden bit will be the most significant bit */
  305.     frac <<= 64 - FLOAT32_FRACTION_SIZE - 1;
  306.  
  307.     frac >>= 64 - (a.parts.exp - FLOAT32_BIAS) - 1;
  308.     if ((a.parts.sign == 1) && (frac != 0)) {
  309.         frac = ~frac;
  310.         ++frac;
  311.     }
  312.    
  313.     return frac;
  314. }
  315.  
  316. /* Convert float to unsigned int64
  317.  * FIXME: Im not sure what to return if overflow/underflow happens
  318.  *  - now its the biggest or the smallest int
  319.  */
  320. uint64_t float32_to_uint64(float32 a)
  321. {
  322.     if (isFloat32NaN(a)) {
  323.         return MAX_UINT64;
  324.     }
  325.    
  326.     if (isFloat32Infinity(a) || (a.parts.exp >= (64 + FLOAT32_BIAS)))  {
  327.         if (a.parts.sign) {
  328.             return MIN_UINT64;
  329.         }
  330.         return MAX_UINT64;
  331.     }
  332.    
  333.     return _float32_to_uint64_helper(a);   
  334. }
  335.  
  336. /* Convert float to signed int64
  337.  * FIXME: Im not sure what to return if overflow/underflow happens
  338.  *  - now its the biggest or the smallest int
  339.  */
  340. int64_t float32_to_int64(float32 a)
  341. {
  342.     if (isFloat32NaN(a)) {
  343.         return MAX_INT64;
  344.     }
  345.    
  346.     if (isFloat32Infinity(a) || (a.parts.exp >= (64 + FLOAT32_BIAS)))  {
  347.         if (a.parts.sign) {
  348.             return (MIN_INT64);
  349.         }
  350.         return MAX_INT64;
  351.     }
  352.     return _float32_to_uint64_helper(a);
  353. }  
  354.  
  355.  
  356. /* Convert float64 to unsigned int32
  357.  * FIXME: Im not sure what to return if overflow/underflow happens
  358.  *  - now its the biggest or the smallest int
  359.  */
  360. uint32_t float64_to_uint32(float64 a)
  361. {
  362.     if (isFloat64NaN(a)) {
  363.         return MAX_UINT32;
  364.     }
  365.    
  366.     if (isFloat64Infinity(a) || (a.parts.exp >= (32 + FLOAT64_BIAS)))  {
  367.         if (a.parts.sign) {
  368.             return MIN_UINT32;
  369.         }
  370.         return MAX_UINT32;
  371.     }
  372.    
  373.     return (uint32_t)_float64_to_uint64_helper(a); 
  374. }
  375.  
  376. /* Convert float64 to signed int32
  377.  * FIXME: Im not sure what to return if overflow/underflow happens
  378.  *  - now its the biggest or the smallest int
  379.  */
  380. int32_t float64_to_int32(float64 a)
  381. {
  382.     if (isFloat64NaN(a)) {
  383.         return MAX_INT32;
  384.     }
  385.    
  386.     if (isFloat64Infinity(a) || (a.parts.exp >= (32 + FLOAT64_BIAS)))  {
  387.         if (a.parts.sign) {
  388.             return MIN_INT32;
  389.         }
  390.         return MAX_INT32;
  391.     }
  392.     return (int32_t)_float64_to_uint64_helper(a);
  393. }  
  394.  
  395. /** Convert unsigned integer to float32
  396.  *
  397.  *
  398.  */
  399. float32 uint32_to_float32(uint32_t i)
  400. {
  401.     int counter;
  402.     int32_t exp;
  403.     float32 result;
  404.    
  405.     result.parts.sign = 0;
  406.     result.parts.fraction = 0;
  407.  
  408.     counter = countZeroes32(i);
  409.  
  410.     exp = FLOAT32_BIAS + 32 - counter - 1;
  411.    
  412.     if (counter == 32) {
  413.         result.binary = 0;
  414.         return result;
  415.     }
  416.    
  417.     if (counter > 0) {
  418.         i <<= counter - 1;
  419.     } else {
  420.         i >>= 1;
  421.     }
  422.  
  423.     roundFloat32(&exp, &i);
  424.  
  425.     result.parts.fraction = i >> 7;
  426.     result.parts.exp = exp;
  427.  
  428.     return result;
  429. }
  430.  
  431. float32 int32_to_float32(int32_t i)
  432. {
  433.     float32 result;
  434.  
  435.     if (i < 0) {
  436.         result = uint32_to_float32((uint32_t)(-i));
  437.     } else {
  438.         result = uint32_to_float32((uint32_t)i);
  439.     }
  440.    
  441.     result.parts.sign = i < 0;
  442.  
  443.     return result;
  444. }
  445.  
  446.  
  447. float32 uint64_to_float32(uint64_t i)
  448. {
  449.     int counter;
  450.     int32_t exp;
  451.     uint32_t j;
  452.     float32 result;
  453.    
  454.     result.parts.sign = 0;
  455.     result.parts.fraction = 0;
  456.  
  457.     counter = countZeroes64(i);
  458.  
  459.     exp = FLOAT32_BIAS + 64 - counter - 1;
  460.    
  461.     if (counter == 64) {
  462.         result.binary = 0;
  463.         return result;
  464.     }
  465.    
  466.     /* Shift all to the first 31 bits (31. will be hidden 1)*/
  467.     if (counter > 33) {
  468.         i <<= counter - 1 - 32;
  469.     } else {
  470.         i >>= 1 + 32 - counter;
  471.     }
  472.    
  473.     j = (uint32_t)i;
  474.     roundFloat32(&exp, &j);
  475.  
  476.     result.parts.fraction = j >> 7;
  477.     result.parts.exp = exp;
  478.     return result;
  479. }
  480.  
  481. float32 int64_to_float32(int64_t i)
  482. {
  483.     float32 result;
  484.  
  485.     if (i < 0) {
  486.         result = uint64_to_float32((uint64_t)(-i));
  487.     } else {
  488.         result = uint64_to_float32((uint64_t)i);
  489.     }
  490.    
  491.     result.parts.sign = i < 0;
  492.  
  493.     return result;
  494. }
  495.  
  496. /** Convert unsigned integer to float64
  497.  *
  498.  *
  499.  */
  500. float64 uint32_to_float64(uint32_t i)
  501. {
  502.     int counter;
  503.     int32_t exp;
  504.     float64 result;
  505.     uint64_t frac;
  506.    
  507.     result.parts.sign = 0;
  508.     result.parts.fraction = 0;
  509.  
  510.     counter = countZeroes32(i);
  511.  
  512.     exp = FLOAT64_BIAS + 32 - counter - 1;
  513.    
  514.     if (counter == 32) {
  515.         result.binary = 0;
  516.         return result;
  517.     }
  518.    
  519.     frac = i;
  520.     frac <<= counter + 32 - 1;
  521.  
  522.     roundFloat64(&exp, &frac);
  523.  
  524.     result.parts.fraction = frac >> 10;
  525.     result.parts.exp = exp;
  526.  
  527.     return result;
  528. }
  529.  
  530. float64 int32_to_float64(int32_t i)
  531. {
  532.     float64 result;
  533.  
  534.     if (i < 0) {
  535.         result = uint32_to_float64((uint32_t)(-i));
  536.     } else {
  537.         result = uint32_to_float64((uint32_t)i);
  538.     }
  539.    
  540.     result.parts.sign = i < 0;
  541.  
  542.     return result;
  543. }
  544.  
  545.  
  546. float64 uint64_to_float64(uint64_t i)
  547. {
  548.     int counter;
  549.     int32_t exp;
  550.     float64 result;
  551.    
  552.     result.parts.sign = 0;
  553.     result.parts.fraction = 0;
  554.  
  555.     counter = countZeroes64(i);
  556.  
  557.     exp = FLOAT64_BIAS + 64 - counter - 1;
  558.    
  559.     if (counter == 64) {
  560.         result.binary = 0;
  561.         return result;
  562.     }
  563.    
  564.     if (counter > 0) {
  565.         i <<= counter - 1;
  566.     } else {
  567.         i >>= 1;
  568.     }
  569.  
  570.     roundFloat64(&exp, &i);
  571.  
  572.     result.parts.fraction = i >> 10;
  573.     result.parts.exp = exp;
  574.     return result;
  575. }
  576.  
  577. float64 int64_to_float64(int64_t i)
  578. {
  579.     float64 result;
  580.  
  581.     if (i < 0) {
  582.         result = uint64_to_float64((uint64_t)(-i));
  583.     } else {
  584.         result = uint64_to_float64((uint64_t)i);
  585.     }
  586.    
  587.     result.parts.sign = i < 0;
  588.  
  589.     return result;
  590. }
  591.  
  592. /** @}
  593.  */
  594.