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POarray: convert index of one dimensional array to a vector index of a multidimensional array
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copied!<p>It will be a long question, please, take a deep breath before reading.</p> <p>I want to understand what would be the fastest algorithm to convert index of one dimensional array to a vector index of a multidimensional array.</p> <p>Let's proceed with an example to understand why do I need it:</p> <blockquote> <p>I have a 2 dimensional array: Array[i1][i2]</p> <p>i1 runs from i1_b=0 to i1_e=2</p> <p>i2 runs from i2_b=0 to i2_e=1</p> </blockquote> <p>So this array is outputted into the file line by line:</p> <blockquote> <p>Array[0][0]</p> <p>Array[0][1]</p> <p>Array[0][2]</p> <p>Array[1][0]</p> <p>Array[1][1]</p> <p>Array[1][2]</p> </blockquote> <p>Now I read the file line by line and index k is the number of the line being read last. </p> <blockquote> <p>I read the first line which is Array[0][0] and k=0</p> <p>I read the second line which is Array[0][1] and k=1</p> <p>...</p> </blockquote> <p>One can notice that k will run from k_b=0 to k_e=5 and </p> <blockquote> <p>k=0 will correspond to i1=0, i2=0</p> <p>k=1 will correspond to i1=0, i2=1</p> <p>...</p> </blockquote> <p>Problem: So my problem is how to convert k into i1 and i2 the fastest way possible? (I don't need it while reading the file, but later in my program)</p> <p>In this example, one of the solutions would be</p> <blockquote> <p>i1=k/(i1_e - i1_b + 1);</p> <p>i2=k%(i1_e - i1_b + 1);</p> </blockquote> <p>Question 1: Is it the fastest possible solution in term of cycles and computer time?</p> <p>OK. Question 2: How can we generalize this algorithm to multidimensional arrays?</p> <blockquote> <p>Array[i1][i2][i3][i4]</p> <p>i1=k/(i1_e - i1_b + 1);</p> <p>i2=k%(i1_e - i1_b + 1);</p> <p>i3=i2/(i1_e - i1_b + 1);</p> <p>i4=i2%(i1_e - i1_b + 1);</p> </blockquote> <p>Question 3: Is it the fastest way to do it?</p> <p>Question 4: related question would be what is the latency for modular division, integer division, adding integers and multiplying integers? If these numbers depend on the architecture, please, also let me know.</p> <p>Thanks in advance!</p> <p>P.S. It may be easier for someone to think about this problem as the fastest algorithm to convert seconds into days-hours-minutes-seconds.</p>

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