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pdclib:floatingpoint [2019/10/17 17:18]
solar [Floating-Point Printout (Dragon2)] 		pdclib:floatingpoint [2019/10/18 14:40]
solar [Fixed Point Fraction Output]
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     * multiply <m>M = 0.015625</m> by <m>B = 10</m> for new <m>M = 0.15625</m>     * multiply <m>M = 0.015625</m> by <m>B = 10</m> for new <m>M = 0.15625</m>
     * Fractional part <m>0.835</m> is larger than mask <m>0.15625</m>, and smaller than <m>1 - 0.15625 = 0.84375</m>, so <m>6</m> is our first (fractional) digit, and the loop continues     * Fractional part <m>0.835</m> is larger than mask <m>0.15625</m>, and smaller than <m>1 - 0.15625 = 0.84375</m>, so <m>6</m> is our first (fractional) digit, and the loop continues
-  * Second (<m>k = 2</m> loop +  * Second (<m>k = 2</m>) loop 
-    * multiply <m>R = 0.835</m> by <m>B = 10</m> for integral part <m>8</m>, fractional part <m>0.35<m> +    * multiply <m>R = 0.835</m> by <m>B = 10</m> for integral part <m>8</m>, fractional part <m>0.35</m> 
-    * multiply <m>M = 0.15625<m> by <m>B = 10</m> for new <m>M = 1.5625</m>+    * multiply <m>M = 0.15625</m> by <m>B = 10</m> for new <m>M = 1.5625</m>
     * Fractional part <m>.35</m> is smaller than mask <m>1.5625</m>, and not smaller than <m>1 - 1.5625 = -0.5625</m>, so the loop terminates     * Fractional part <m>.35</m> is smaller than mask <m>1.5625</m>, and not smaller than <m>1 - 1.5625 = -0.5625</m>, so the loop terminates
   * Post-loop   * Post-loop
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     * We have <m>N = k = 2</m> fractional digits in our result of <m>0.68</m>, which is the smallest <m>N</m> that uniquely identifies our original <m>f = .10110</m>     * We have <m>N = k = 2</m> fractional digits in our result of <m>0.68</m>, which is the smallest <m>N</m> that uniquely identifies our original <m>f = .10110</m>
  
-==== Floating-Point Printout (Dragon2) ====+==== Floating-Point Printout ====
  
 Given: Given:
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   * An approximate representation to base //B//, using exponential notation if the value is very large or very small.   * An approximate representation to base //B//, using exponential notation if the value is very large or very small.
 +
 +Algorithm (Dragon2):
 +
 +   * Compute <m>v prime = v * B ^ {-x}</m>, where <m>x</m> is chosen so that the result either is between 1 / //B// and 1, or between 1 and //B//
 +   * Print the integer part of <m>v prime</m>
 +   * Print a decimal point
 +   * Take the fractional part of <m>v prime</m>, let <m>n = p - floor ( log_ b v prime ) - 1</m>
 +   * Apply algorithm <m>(FP)^3</m> to //f// and //n//
 +   * If <m>x</m> was not zero, append the letter "E" and a representation of the scale factor <m>x</m>
pdclib/floatingpoint.txt · Last modified: 2019/10/21 10:13 by solar

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