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    <p>Just to make sure we're on the same page, <code>G</code> is the most significant bit of the three, <code>R</code> comes next and <code>S</code> can be thought of as the least significant bit because its value partially represents the even less significant bits that have been truncated in the calculations. These three bits are only used while doing calculations and aren't stored in the floating-point variable before or after the calculations.</p> <p>This is what you should do in order to round the result to the nearest even number using <code>G</code>, <code>R</code> and <code>S</code>:</p> <p><strong>GRS</strong> - Action<br> <strong>0xx</strong> - round down = do nothing (x means any bit value, 0 or 1)<br> <strong>100</strong> - this is a <strong>tie</strong>: round up if the mantissa's bit just before <strong>G</strong> is 1, else round down=do nothing<br> <strong>101</strong> - round up<br> <strong>110</strong> - round up<br> <strong>111</strong> - round up</p> <p>Rounding up is done by adding 1 to the mantissa in the mantissa's least significant bit position just before <code>G</code>. If the mantissa overflows (its 23 least significant bits that you will store become zeroes), you have to add 1 to the exponent. If the exponent overflows, you set the number to +infinity or -infinity depending on the number's sign.</p> <p>In the case of a tie, you add 1 to the mantissa if the mantissa is odd and you add nothing if it's even. That's what makes the result rounded to the nearest even value.</p>
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    1. POHow to perform round to even with floating point numbers
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    1. POHow to perform round to even with floating point numbers
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    1. CODo you even need the round bit? Can't you just look at the guard bit and the sticky bit becomes the OR of the round and old sticky bit?
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    2. COYou may use none of these bits if you aren't very concerned about rounding. They just help you get a more accurate result.
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    3. COwell I am concerned about rounding, so does my comment "Can't you just look at the guard bit and the sticky bit becomes the OR of the round and old sticky bit?" make sense?
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