20121008, 06:52  #100 
Einyen
Dec 2003
Denmark
3,253 Posts 
Code:
LL: 43112609 (FFT 2240K) PRP=2,2,43112610,3 (FFT 2560K) PRP=3,2,43112610,5 (FFT 2688K) PRP=4,2,43112610,7 (FFT 2688K) PRP=5,2,43112610,9 (FFT 2880K) PRP=6,2,43112610,11 (FFT 2880K) PRP=7,2,43112610,13 (FFT 3000K) PRP=8,2,43112610,15 (FFT 2800K) PRP=9,2,43112610,17 (FFT 3200K) PRP=10,2,43112610,19 (FFT 3000K) PRP=20,2,43112610,39 (FFT 3360K) PRP=30,2,43112610,59 (FFT 3840K) PRP=40,2,43112610,79 (FFT 3584K) PRP=50,2,43112610,99 (FFT 4000K) PRP=60,2,43112610,119 (FFT 4000K) PRP=70,2,43112610,139 (FFT 4480K) PRP=80,2,43112610,159 (FFT 3840K) PRP=90,2,43112610,179 (FFT 4480K) PRP=100,2,43112610,199 (FFT 4480K) PRP=110,2,43112610,219 (FFT 4608K) PRP=120,2,43112610,239 (FFT 4480K) PRP=130,2,43112610,259 (FFT 4608K) PRP=140,2,43112610,279 (FFT 4608K) PRP=150,2,43112610,299 (FFT 4608K) PRP=160,2,43112610,319 (FFT 4000K) PRP=170,2,43112610,339 (FFT 4608K) PRP=180,2,43112610,359 (FFT 4608K) PRP=190,2,43112610,379 (FFT 4608K) PRP=200,2,43112610,399 (FFT 4608K) 
20121008, 08:43  #101 
Banned
"Luigi"
Aug 2002
Team Italia
2·41·59 Posts 
MM47 sieved up to 1T (except for 185).
Luigi 
20121008, 18:33  #102 
∂^{2}ω=0
Sep 2002
República de California
2^{3}×3×487 Posts 

20121008, 18:56  #103  
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 
Quote:
The columns read as follows: id, exponent_id, k, sieve_level, factor. Luigi Last fiddled with by ET_ on 20121008 at 18:57 

20121009, 01:37  #104  
∂^{2}ω=0
Sep 2002
República de California
26650_{8} Posts 
Quote:
The wordsizes are as for DWT modulo 2^p1, but with p replaced by (n + log2 k) = 89 + 7.53... = 96.53... This translates to 24 bits per word for words 02, and with the high word (word 3) having as many as 24.53... bits? And what are the 4 weight factors for this case? (For p = 96 and n = 4, the straight Mersennemod DWT weights are all unity). 

20121009, 02:17  #105  
P90 years forever!
Aug 2002
Yeehaw, FL
2·13^{2}·23 Posts 
Quote:
Quote:
// The FFT weight for the jth FFT word doing a b^n+c weighted transform is // b ^ (ceil (j*n/FFTLEN)  j*n/FFTLEN) * abs(c) ^ j/FFTLEN In your case b = 2, n = 96.53...., c = 1, FFTLEN=4. 

20121009, 02:22  #106 
P90 years forever!
Aug 2002
Yeehaw, FL
2×13^{2}×23 Posts 
Correction. FFT word 0 has 25 bits. FFT words 1,2 have 24 bits. FFT word 3 has 23.53... bits.
From the code: // The FFT base for the jth FFT word doing a b^n+c weighted transform is // ceil (j*n/FFTLEN) To calc whether the ith word is a big word (25 bits): /* Compute the number of b in this word. It is a big word if */ /* the number of b is more than NUM_B_PER_SMALL_WORD. */ base = gwfft_base (gwdata>dd_data, i); next_base = gwfft_base (gwdata>dd_data, i+1); return ((next_base  base) > gwdata>NUM_B_PER_SMALL_WORD); 
20121009, 19:47  #107  
∂^{2}ω=0
Sep 2002
República de California
2^{3}×3×487 Posts 
Quote:
Code:
j ceil[n.j/N] n.j/N w_j     0 0 0 2^0 = 1 1 25 24.13... 1.82406... 2 49 48.26... 1.66360... 3 73 72.39... 1.51725... 

20121009, 22:01  #108 
P90 years forever!
Aug 2002
Yeehaw, FL
1111001011110_{2} Posts 

20121009, 22:35  #109 
∂^{2}ω=0
Sep 2002
República de California
2^{3}·3·487 Posts 
I wanted to wait for your reply before commenting on the results. Here is annotated Pari code (code in italics)  note that in the sample below I am so far only using the multiplier k to compute "equivalent power of 2" for the modified DWT; according to what you've noted so far k would appear again in the postiFFT normalize/carry step.
n = 89; k = 185; l2k = log(k)/log(2); p = n+l2k; Do modsquare of the 97bit (but < 2^p) input x = 114159265358979323846264338327 below: N = 4; ninv = 1.0/N; j = 1; w0 = 2^(ceil(p*j/N)  (p*j/N)); j++; w1 = 2^(ceil(p*j/N)  (p*j/N)); j++; w2 = 2^(ceil(p*j/N)  (p*j/N)); j++; w3 = 2^(ceil(p*j/N)  (p*j/N)); j++; Here are the 2 bases and the components of the input x w.r.to the mixedbase representation: b0 = 2^24;b1=2*b0; x0=x%b1;x1=(x>>25)%b0;x2=(x>>49)%b0;x3=(x>>73); Checksum: x0+b1*(x1+b0*(x2+b0*x3))  x gives 0, as expected. Now do a length4 realinput weighted FFT/dyadicsquare/iFFT: x0 *= w0; x1 *= w1; x2 *= w2; x3 *= w3; y0 = x0+x1+x2+x3; y1 = x0+I*x1x2I*x3; y2 = x0x1+x2x3; y3 = x0I*x1x2+I*x3; y0 *= y0; y1 *= y1; y2 *= y2; y3 *= y3; x0 = y0+y1+y2+y3; x1 = y0I*y1y2+I*y3; x2 = y0y1+y2y3; x3 = y0+I*y1y2I*y3; x0 *= ninv/w0 x1 *= ninv/w1 x2 *= ninv/w2 x3 *= ninv/w3 Gives unnormalized outputs x0 = 703887643638004.71907792172553111306890 + 0.E43*I x1 = 204197471363853.84715648872049568720197 + 0.E43*I x2 = 616272238041294.96214451135558685583677 + 0.E43*I x3 = 835670265851967.92537464503288200734149 + 0.E43*I which are not the expected "very close to a whole number". What went wrong? (Note that I tried the above Pari DWTtesting code on a classic Mersennemod DWT for modulus 2^891, to verify that the results are as expected.) Last fiddled with by ewmayer on 20121009 at 22:36 
20121009, 23:49  #110 
∂^{2}ω=0
Sep 2002
República de California
2^{3}×3×487 Posts 
Aha  found the bug: In my Pari code above, the computation of the weights w0w3 should begin with index j = 0, not 1. (I computed these individually in nonloopstyle fashion when I first posted them).
Using the corrected weights, we get unnormalized outputs x0 = 476933840021096.17837837837837837837838 + 0.E43*I x1 = 216945451434081.81621621621621621621622 + 0.E44*I x2 = 438974751056908.94054054054054054054054 + 0.E43*I x3 = 460450104164716.00000000000000000000000 + 0.E44*I which looks more promising, since if I multiply each of these by 185 (dropping the negligible imaginary part resulting from roundoff error), I get 185*x0 = 88232760403902793.000000000000000000000 185*x1 = 40134908515305136.000000000000000000000 185*x2 = 81210328945528153.999999999999999999999 185*x3 = 85183269270472460.000000000000000000000 . Very nice! So now one just needs to do the normalize/carry step  that will allow me to work out the details of the wraparound carry  and divide every resulting word by 185 before the next squaring? 
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