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< a name = "l1" > < / a > < span class = cF2 > /*The magic pairs problem:< / span > < span class = cF0 >
< a name = "l2" > < / a >
< a name = "l3" > < / a > < / span > < span class = cF2 > Let SumFact(n) be the sum of factors< / span > < span class = cF0 >
< a name = "l4" > < / a > < / span > < span class = cF2 > of n.< / span > < span class = cF0 >
< a name = "l5" > < / a >
< a name = "l6" > < / a > < / span > < span class = cF2 > Find all n1,n2 in a range such that< / span > < span class = cF0 >
< a name = "l7" > < / a >
< a name = "l8" > < / a > < / span > < span class = cF2 > SumFact(n1)-n1-1 == n2< / span > < span class = cF0 > < / span > < span class = cF2 > and< / span > < span class = cF0 >
< a name = "l9" > < / a > < / span > < span class = cF2 > SumFact(n2)-n2-1 == n1< / span > < span class = cF0 >
< a name = "l10" > < / a >
< a name = "l11" > < / a > < / span > < span class = cF2 > -----------------------------------------------------< / span > < span class = cF0 >
< a name = "l12" > < / a > < / span > < span class = cF2 > To find SumFact(k), start with prime factorization:< / span > < span class = cF0 >
< a name = "l13" > < / a >
< a name = "l14" > < / a > < / span > < span class = cF2 > k=(p1^n1)(p2^n2) ... (pN^nN)< / span > < span class = cF0 >
< a name = "l15" > < / a >
< a name = "l16" > < / a > < / span > < span class = cF2 > THEN,< / span > < span class = cF0 >
< a name = "l17" > < / a >
< a name = "l18" > < / a > < / span > < span class = cF2 > SumFact(k)=(1+p1+p1^2...p1^n1)*(1+p2+p2^2...p2^n2)*< / span > < span class = cF0 >
< a name = "l19" > < / a > < / span > < span class = cF2 > (1+pN+pN^2...pN^nN)< / span > < span class = cF0 >
< a name = "l20" > < / a >
< a name = "l21" > < / a > < / span > < span class = cF2 > PROOF:< / span > < span class = cF0 >
< a name = "l22" > < / a >
< a name = "l23" > < / a > < / span > < span class = cF2 > Do a couple examples -- it's obvious:< / span > < span class = cF0 >
< a name = "l24" > < / a >
< a name = "l25" > < / a > < / span > < span class = cF2 > 48=2^4*3< / span > < span class = cF0 >
< a name = "l26" > < / a >
< a name = "l27" > < / a > < / span > < span class = cF2 > SumFact(48)=(1+2+4+8+16)*(1+3)=1+2+4+8+16+3+6+12+24+48< / span > < span class = cF0 >
< a name = "l28" > < / a >
< a name = "l29" > < / a > < / span > < span class = cF2 > 75=3*5^2< / span > < span class = cF0 >
< a name = "l30" > < / a >
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< a name = "l31" > < / a > < / span > < span class = cF2 > SumFact(75)=(1+3)*(1+5+25)< / span > < span class = cF0 > < / span > < span class = cF2 > =1+5+25+3+15+75< / span > < span class = cF0 >
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< a name = "l32" > < / a >
< a name = "l33" > < / a > < / span > < span class = cF2 > Corollary:< / span > < span class = cF0 >
< a name = "l34" > < / a >
< a name = "l35" > < / a > < / span > < span class = cF2 > SumFact(k)=SumFact(p1^n1)*SumFact(p2^n2)*...*SumFact(pN^nN)< / span > < span class = cF0 >
< a name = "l36" > < / a >
< a name = "l37" > < / a > < / span > < span class = cF2 > */< / span > < span class = cF0 >
< a name = "l38" > < / a >
< a name = "l39" > < / a > < / span > < span class = cF2 > //Primes are needed to sqrt(N). Therefore, we can use U32.< / span > < span class = cF0 >
< a name = "l40" > < / a > < / span > < span class = cF1 > class< / span > < span class = cF0 > PowPrime
< a name = "l41" > < / a > {
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< a name = "l42" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > n;
< a name = "l43" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > sumfact; < / span > < span class = cF2 > //Sumfacts for powers of primes are needed beyond sqrt(N)< / span > < span class = cF0 >
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< a name = "l44" > < / a > };
< a name = "l45" > < / a >
< a name = "l46" > < / a > < / span > < span class = cF1 > class< / span > < span class = cF0 > Prime
< a name = "l47" > < / a > {
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< a name = "l48" > < / a > < / span > < span class = cF9 > U32< / span > < span class = cF0 > prime, pow_count;
< a name = "l49" > < / a > PowPrime *pp;
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< a name = "l50" > < / a > };
< a name = "l51" > < / a >
< a name = "l52" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > *PrimesNew(< / span > < span class = cF9 > I64< / span > < span class = cF0 > N, < / span > < span class = cF9 > I64< / span > < span class = cF0 > *_sqrt_primes, < / span > < span class = cF9 > I64< / span > < span class = cF0 > *_cbrt_primes)
< a name = "l53" > < / a > {
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< a name = "l54" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, j, sqrt = < / span > < span class = cF5 > Ceil< / span > < span class = cF0 > (< / span > < span class = cF5 > Sqrt< / span > < span class = cF7 > (< / span > < span class = cF0 > N< / span > < span class = cF7 > )< / span > < span class = cF0 > ), cbrt = < / span > < span class = cF5 > Ceil< / span > < span class = cF0 > (N ` < / span > < span class = cF7 > (< / span > < span class = cFE > 1< / span > < span class = cF0 > / < / span > < span class = cFE > 3< / span > < span class = cF0 > .< / span > < span class = cFE > 0< / span > < span class = cF7 > )< / span > < span class = cF0 > ),
< a name = "l55" > < / a > sqrt_sqrt = < / span > < span class = cF5 > Ceil< / span > < span class = cF0 > (< / span > < span class = cF5 > Sqrt< / span > < span class = cF7 > (< / span > < span class = cF0 > sqrt< / span > < span class = cF7 > )< / span > < span class = cF0 > ), sqrt_primes = < / span > < span class = cFE > 0< / span > < span class = cF0 > , cbrt_primes = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l56" > < / a > < / span > < span class = cF1 > U8< / span > < span class = cF0 > *s = < / span > < span class = cF5 > CAlloc< / span > < span class = cF0 > (< / span > < span class = cF7 > (< / span > < span class = cF0 > sqrt + < / span > < span class = cFE > 1< / span > < span class = cF0 > + < / span > < span class = cFE > 7< / span > < span class = cF7 > )< / span > < span class = cF0 > / < / span > < span class = cFE > 8< / span > < span class = cF0 > );
< a name = "l57" > < / a > Prime *primes, *p;
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< a name = "l58" > < / a >
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< a name = "l59" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 2< / span > < span class = cF0 > ; i < = sqrt_sqrt; i++)
< a name = "l60" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l61" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (!< / span > < span class = cF5 > Bt< / span > < span class = cF7 > (< / span > < span class = cF0 > s, i< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l62" > < / a > {
< a name = "l63" > < / a > j = i * < / span > < span class = cFE > 2< / span > < span class = cF0 > ;
< a name = "l64" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (j < = sqrt)
< a name = "l65" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l66" > < / a > < / span > < span class = cF5 > Bts< / span > < span class = cF0 > (s, j);
< a name = "l67" > < / a > j += i;
< a name = "l68" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l69" > < / a > }
< a name = "l70" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l71" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 2< / span > < span class = cF0 > ; i < = sqrt; i++)
< a name = "l72" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (!< / span > < span class = cF5 > Bt< / span > < span class = cF7 > (< / span > < span class = cF0 > s, i< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l73" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l74" > < / a > sqrt_primes++; < / span > < span class = cF2 > //Count primes< / span > < span class = cF0 >
< a name = "l75" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (i < = cbrt)
< a name = "l76" > < / a > cbrt_primes++;
< a name = "l77" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l78" > < / a >
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< a name = "l79" > < / a > p = primes = < / span > < span class = cF5 > CAlloc< / span > < span class = cF0 > (sqrt_primes * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF0 > Prime< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l80" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 2< / span > < span class = cF0 > ; i < = sqrt; i++)
< a name = "l81" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (!< / span > < span class = cF5 > Bt< / span > < span class = cF7 > (< / span > < span class = cF0 > s, i< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l82" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l83" > < / a > p-> prime = i;
< a name = "l84" > < / a > p++;
< a name = "l85" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l86" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (s);
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< a name = "l87" > < / a >
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< a name = "l88" > < / a > *_sqrt_primes = sqrt_primes;
< a name = "l89" > < / a > *_cbrt_primes = cbrt_primes;
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< a name = "l90" > < / a >
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< a name = "l91" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > primes;
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< a name = "l92" > < / a > }
< a name = "l93" > < / a >
< a name = "l94" > < / a > PowPrime *PowPrimesNew(< / span > < span class = cF9 > I64< / span > < span class = cF0 > N, < / span > < span class = cF9 > I64< / span > < span class = cF0 > sqrt_primes, Prime *primes, < / span > < span class = cF9 > I64< / span > < span class = cF0 > *_num_powprimes)
< a name = "l95" > < / a > {
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< a name = "l96" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, j, k, sf, num_powprimes = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l97" > < / a > Prime *p;
< a name = "l98" > < / a > PowPrime *powprimes, *pp;
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< a name = "l99" > < / a >
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< a name = "l100" > < / a > p = primes;
< a name = "l101" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < sqrt_primes; i++)
< a name = "l102" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l103" > < / a > num_powprimes += < / span > < span class = cF5 > Floor< / span > < span class = cF0 > (< / span > < span class = cF5 > Ln< / span > < span class = cF7 > (< / span > < span class = cF0 > N< / span > < span class = cF7 > )< / span > < span class = cF0 > / < / span > < span class = cF5 > Ln< / span > < span class = cF7 > (< / span > < span class = cF0 > p-> prime< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l104" > < / a > p++;
< a name = "l105" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l106" > < / a >
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< a name = "l107" > < / a > p = primes;
< a name = "l108" > < / a > pp = powprimes = < / span > < span class = cF5 > MAlloc< / span > < span class = cF0 > (num_powprimes * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF0 > PowPrime< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l109" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < sqrt_primes; i++)
< a name = "l110" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l111" > < / a > p-> pp = pp;
< a name = "l112" > < / a > j = p-> prime;
< a name = "l113" > < / a > k = < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l114" > < / a > sf = < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l115" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (j < N)
< a name = "l116" > < / a > {
< a name = "l117" > < / a > sf += j;
< a name = "l118" > < / a > pp-> n = j;
< a name = "l119" > < / a > pp-> sumfact = sf;
< a name = "l120" > < / a > j *= p-> prime;
< a name = "l121" > < / a > pp++;
< a name = "l122" > < / a > p-> pow_count++;
< a name = "l123" > < / a > }
< a name = "l124" > < / a > p++;
< a name = "l125" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l126" > < / a > *_num_powprimes = num_powprimes;
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< a name = "l127" > < / a >
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< a name = "l128" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > powprimes;
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< a name = "l129" > < / a > }
< a name = "l130" > < / a >
< a name = "l131" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > SumFact(< / span > < span class = cF9 > I64< / span > < span class = cF0 > n, < / span > < span class = cF9 > I64< / span > < span class = cF0 > sqrt_primes, Prime *p)
< a name = "l132" > < / a > {
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< a name = "l133" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, k, sf = < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l134" > < / a > PowPrime *pp;
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< a name = "l135" > < / a >
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< a name = "l136" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n < < / span > < span class = cFE > 2< / span > < span class = cF0 > )
< a name = "l137" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l138" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < sqrt_primes; i++)
< a name = "l139" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l140" > < / a > k = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l141" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (!< / span > < span class = cF7 > (< / span > < span class = cF0 > n % p-> prime< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l142" > < / a > {
< a name = "l143" > < / a > n /= p-> prime;
< a name = "l144" > < / a > k++;
< a name = "l145" > < / a > }
< a name = "l146" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k)
< a name = "l147" > < / a > {
< a name = "l148" > < / a > pp = p-> pp + (k - < / span > < span class = cFE > 1< / span > < span class = cF0 > );
< a name = "l149" > < / a > sf *= pp-> sumfact;
< a name = "l150" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n == < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l151" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > sf;
< a name = "l152" > < / a > }
< a name = "l153" > < / a > p++;
< a name = "l154" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l155" > < / a >
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< a name = "l156" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > sf * (< / span > < span class = cFE > 1< / span > < span class = cF0 > + n); < / span > < span class = cF2 > //Prime< / span > < span class = cF0 >
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< a name = "l157" > < / a > }
< a name = "l158" > < / a >
< a name = "l159" > < / a > < / span > < span class = cF1 > Bool< / span > < span class = cF0 > TestSumFact(< / span > < span class = cF9 > I64< / span > < span class = cF0 > n, < / span > < span class = cF9 > I64< / span > < span class = cF0 > target_sf, < / span > < span class = cF9 > I64< / span > < span class = cF0 > sqrt_primes, < / span > < span class = cF9 > I64< / span > < span class = cF0 > cbrt_primes, Prime *p)
< a name = "l160" > < / a > {
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< a name = "l161" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i = < / span > < span class = cFE > 0< / span > < span class = cF0 > , k, b, x1, x2;
< a name = "l162" > < / a > PowPrime *pp;
< a name = "l163" > < / a > < / span > < span class = cF1 > F64< / span > < span class = cF0 > disc;
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< a name = "l164" > < / a >
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< a name = "l165" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n < < / span > < span class = cFE > 2< / span > < span class = cF0 > )
< a name = "l166" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l167" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (i++ < cbrt_primes)
< a name = "l168" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l169" > < / a > k = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l170" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (!< / span > < span class = cF7 > (< / span > < span class = cF0 > n % p-> prime< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l171" > < / a > {
< a name = "l172" > < / a > n /= p-> prime;
< a name = "l173" > < / a > k++;
< a name = "l174" > < / a > }
< a name = "l175" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k)
< a name = "l176" > < / a > {
< a name = "l177" > < / a > pp = p-> pp + (k - < / span > < span class = cFE > 1< / span > < span class = cF0 > );
< a name = "l178" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (< / span > < span class = cF5 > ModU64< / span > < span class = cF7 > (< / span > < span class = cF0 > & target_sf, pp-> sumfact< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l179" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l180" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n == < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l181" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l182" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (target_sf == < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l183" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > TRUE< / span > < span class = cF0 > ;
< a name = "l184" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l185" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l186" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l187" > < / a > }
< a name = "l188" > < / a > p++;
< a name = "l189" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l190" > < / a > < / span > < span class = cF2 > /*< / span > < span class = cF0 > < / span > < span class = cF2 > At this point we have three possible cases to test< / span > < span class = cF0 >
< a name = "l191" > < / a > < / span > < span class = cF2 > 1)n==p1 < / span > < span class = cF0 > < / span > < span class = cF2 > -> sf==(1+p1)< / span > < span class = cF0 > < / span > < span class = cF2 > ?< / span > < span class = cF0 >
< a name = "l192" > < / a > < / span > < span class = cF2 > 2)n==p1*p1< / span > < span class = cF0 > < / span > < span class = cF2 > -> sf==(1+p1+p1^2) < / span > < span class = cF0 > < / span > < span class = cF2 > ?< / span > < span class = cF0 >
< a name = "l193" > < / a > < / span > < span class = cF2 > 3)n==p1*p2< / span > < span class = cF0 > < / span > < span class = cF2 > -> sf==(p1+1)*(p2+1) ?< / span > < span class = cF0 >
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< a name = "l194" > < / a >
< a name = "l195" > < / a > < / span > < span class = cF2 > */< / span > < span class = cF0 >
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< a name = "l196" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (< / span > < span class = cFE > 1< / span > < span class = cF0 > + n == target_sf)
< a name = "l197" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l198" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (i++ < sqrt_primes)
< a name = "l199" > < / a > {
< a name = "l200" > < / a > k = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l201" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (!< / span > < span class = cF7 > (< / span > < span class = cF0 > n % p-> prime< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l202" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l203" > < / a > n /= p-> prime;
< a name = "l204" > < / a > k++;
< a name = "l205" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l206" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k)
< a name = "l207" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l208" > < / a > pp = p-> pp + (k - < / span > < span class = cFE > 1< / span > < span class = cF0 > );
< a name = "l209" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (< / span > < span class = cF5 > ModU64< / span > < span class = cF7 > (< / span > < span class = cF0 > & target_sf, pp-> sumfact< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l210" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l211" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n == < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l212" > < / a > {
< a name = "l213" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (target_sf == < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l214" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > TRUE< / span > < span class = cF0 > ;
< a name = "l215" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l216" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l217" > < / a > }
< a name = "l218" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l219" > < / a > p++;
< a name = "l220" > < / a > }
< a name = "l221" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (< / span > < span class = cFE > 1< / span > < span class = cF0 > + n == target_sf)
< a name = "l222" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > TRUE< / span > < span class = cF0 > ;
< a name = "l223" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l224" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l225" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l226" > < / a >
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< a name = "l227" > < / a > k =< / span > < span class = cF5 > Sqrt< / span > < span class = cF0 > (n);
< a name = "l228" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k * k == n)
< a name = "l229" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l230" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (< / span > < span class = cFE > 1< / span > < span class = cF0 > + k + n == target_sf)
< a name = "l231" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > TRUE< / span > < span class = cF0 > ;
< a name = "l232" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l233" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l234" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l235" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l236" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l237" > < / a > < / span > < span class = cF2 > // n==p1*p2 -> sf==(p1+1)*(p2+1) ?< / span > < span class = cF0 > < / span > < span class = cF2 > where p1 != 1 & & p2 != 1< / span > < span class = cF0 >
< a name = "l238" > < / a > < / span > < span class = cF2 > // if p1==1 || p2==1, it is FALSE because we checked a single prime above.< / span > < span class = cF0 >
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< a name = "l239" > < / a >
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< a name = "l240" > < / a > < / span > < span class = cF2 > // sf==(p1+1)*(n/p1+1)< / span > < span class = cF0 >
< a name = "l241" > < / a > < / span > < span class = cF2 > // sf==n+p1+n/p1+1< / span > < span class = cF0 >
< a name = "l242" > < / a > < / span > < span class = cF2 > // sf*p1==n*p1+p1^2+n+p1< / span > < span class = cF0 >
< a name = "l243" > < / a > < / span > < span class = cF2 > // p1^2+(n+1-sf)*p1+n=0< / span > < span class = cF0 >
< a name = "l244" > < / a > < / span > < span class = cF2 > // x=(-b+/-sqrt(b^2-4ac))/2a< / span > < span class = cF0 >
< a name = "l245" > < / a > < / span > < span class = cF2 > // a=1< / span > < span class = cF0 >
< a name = "l246" > < / a > < / span > < span class = cF2 > // x=(-b+/-sqrt(b^2-4c))/2< / span > < span class = cF0 >
< a name = "l247" > < / a > < / span > < span class = cF2 > // b=n+1-sf;c=n< / span > < span class = cF0 >
< a name = "l248" > < / a > b = n + < / span > < span class = cFE > 1< / span > < span class = cF0 > - target_sf;
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< a name = "l249" > < / a > < / span > < span class = cF2 > // x=(-b+/-sqrt(b^2-4n))/2< / span > < span class = cF0 >
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< a name = "l250" > < / a > disc = b * b - < / span > < span class = cFE > 4< / span > < span class = cF0 > * n;
< a name = "l251" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (disc < < / span > < span class = cFE > 0< / span > < span class = cF0 > )
< a name = "l252" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l253" > < / a > x1 = (-b - < / span > < span class = cF5 > Sqrt< / span > < span class = cF7 > (< / span > < span class = cF0 > disc< / span > < span class = cF7 > )< / span > < span class = cF0 > ) / < / span > < span class = cFE > 2< / span > < span class = cF0 > ;
< a name = "l254" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (x1 < = < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l255" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l256" > < / a > x2 = n / x1;
< a name = "l257" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (x2 > < / span > < span class = cFE > 1< / span > < span class = cF0 > & & x1 * x2 == n)
< a name = "l258" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > TRUE< / span > < span class = cF0 > ;
< a name = "l259" > < / a > < / span > < span class = cF1 > else< / span > < span class = cF0 >
< a name = "l260" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > < / span > < span class = cF3 > FALSE< / span > < span class = cF0 > ;
< a name = "l261" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l262" > < / a > }
< a name = "l263" > < / a >
< a name = "l264" > < / a > < / span > < span class = cF1 > U0< / span > < span class = cF0 > PutFactors(< / span > < span class = cF9 > I64< / span > < span class = cF0 > n) < / span > < span class = cF2 > //For debugging< / span > < span class = cF0 >
< a name = "l265" > < / a > {
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< a name = "l266" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, k, sqrt = < / span > < span class = cF5 > Ceil< / span > < span class = cF0 > (< / span > < span class = cF5 > Sqrt< / span > < span class = cF7 > (< / span > < span class = cF0 > n< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l267" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 2< / span > < span class = cF0 > ; i < = sqrt; i++)
< a name = "l268" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l269" > < / a > k = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l270" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (!< / span > < span class = cF7 > (< / span > < span class = cF0 > n % i< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l271" > < / a > {
< a name = "l272" > < / a > k++;
< a name = "l273" > < / a > n /= i;
< a name = "l274" > < / a > }
< a name = "l275" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k)
< a name = "l276" > < / a > {
< a name = "l277" > < / a > < / span > < span class = cF6 > " %d" < / span > < span class = cF0 > , i;
< a name = "l278" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k > < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l279" > < / a > < / span > < span class = cF6 > " ^%d" < / span > < span class = cF0 > , k;
< a name = "l280" > < / a > < / span > < span class = cF6 > ''< / span > < span class = cF0 > < / span > < span class = cF3 > CH_SPACE< / span > < span class = cF0 > ;
< a name = "l281" > < / a > }
< a name = "l282" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l283" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n != < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l284" > < / a > < / span > < span class = cF6 > " %d " < / span > < span class = cF0 > , n;
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< a name = "l285" > < / a > }
< a name = "l286" > < / a >
< a name = "l287" > < / a > < / span > < span class = cF1 > class< / span > < span class = cF0 > RangeJob
< a name = "l288" > < / a > {
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< a name = "l289" > < / a > < / span > < span class = cF9 > CDoc< / span > < span class = cF0 > *doc;
< a name = "l290" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > num, lo, hi, N, sqrt_primes, cbrt_primes;
< a name = "l291" > < / a > Prime *primes;
< a name = "l292" > < / a > < / span > < span class = cF9 > CJob< / span > < span class = cF0 > *cmd;
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< a name = "l293" > < / a >
< a name = "l294" > < / a > } rj[< / span > < span class = cFB > mp_count< / span > < span class = cF0 > ];
< a name = "l295" > < / a >
< a name = "l296" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > TestCoreSubRange(RangeJob *r)
< a name = "l297" > < / a > {
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< a name = "l298" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, j, m, n, n2, sf, res = < / span > < span class = cFE > 0< / span > < span class = cF0 > , range = r-> hi - r-> lo,
< a name = "l299" > < / a > *sumfacts = < / span > < span class = cF5 > MAlloc< / span > < span class = cF0 > (range * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF9 > I64< / span > < span class = cF7 > )< / span > < span class = cF0 > ),
< a name = "l300" > < / a > *residue = < / span > < span class = cF5 > MAlloc< / span > < span class = cF0 > (range * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF9 > I64< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l301" > < / a > < / span > < span class = cF9 > U16< / span > < span class = cF0 > *pow_count = < / span > < span class = cF5 > MAlloc< / span > < span class = cF0 > (range * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF9 > U16< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l302" > < / a > Prime *p = r-> primes;
< a name = "l303" > < / a > PowPrime *pp;
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< a name = "l304" > < / a >
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< a name = "l305" > < / a > < / span > < span class = cF5 > MemSetI64< / span > < span class = cF0 > (sumfacts, < / span > < span class = cFE > 1< / span > < span class = cF0 > , range);
< a name = "l306" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (n = r-> lo; n < r-> hi; n++)
< a name = "l307" > < / a > residue[n - r-> lo] = n;
< a name = "l308" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (j = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; j < r-> sqrt_primes; j++)
< a name = "l309" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l310" > < / a > < / span > < span class = cF5 > MemSet< / span > < span class = cF0 > (pow_count, < / span > < span class = cFE > 0< / span > < span class = cF0 > , range * < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF9 > U16< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l311" > < / a > m = < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l312" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < p-> pow_count; i++)
< a name = "l313" > < / a > {
< a name = "l314" > < / a > m *= p-> prime;
< a name = "l315" > < / a > n = m - r-> lo % m;
< a name = "l316" > < / a > < / span > < span class = cF1 > while< / span > < span class = cF0 > (n < range)
< a name = "l317" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l318" > < / a > pow_count[n]++;
< a name = "l319" > < / a > n += m;
< a name = "l320" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l321" > < / a > }
< a name = "l322" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (n = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; n < range; n++)
< a name = "l323" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (i = pow_count[n])
< a name = "l324" > < / a > {
< a name = "l325" > < / a > pp = & p-> pp[i - < / span > < span class = cFE > 1< / span > < span class = cF0 > ];
< a name = "l326" > < / a > sumfacts[n] *= pp-> sumfact;
< a name = "l327" > < / a > residue [n] /= pp-> n;
< a name = "l328" > < / a > }
< a name = "l329" > < / a > p++;
< a name = "l330" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l331" > < / a >
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< a name = "l332" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (n = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; n < range; n++)
< a name = "l333" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (residue[n] != < / span > < span class = cFE > 1< / span > < span class = cF0 > )
< a name = "l334" > < / a > sumfacts[n] *= < / span > < span class = cFE > 1< / span > < span class = cF0 > + residue[n];
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< a name = "l335" > < / a >
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< a name = "l336" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (n = r-> lo; n < r-> hi; n++)
< a name = "l337" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l338" > < / a > sf = sumfacts[n - r-> lo];
< a name = "l339" > < / a > n2 = sf - n - < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l340" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (n < n2 < r-> N)
< a name = "l341" > < / a > {
< a name = "l342" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (r-> lo < = n2< r-> hi & & sumfacts[n2 - r-> lo] - n2 - < / span > < span class = cFE > 1< / span > < span class = cF0 > == n ||
< a name = "l343" > < / a > TestSumFact< / span > < span class = cF7 > (< / span > < span class = cF0 > n2, sf, r-> sqrt_primes, r-> cbrt_primes, r-> primes< / span > < span class = cF7 > )< / span > < span class = cF0 > )
< a name = "l344" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l345" > < / a > < / span > < span class = cF5 > DocPrint< / span > < span class = cF0 > (r-> doc, < / span > < span class = cF6 > " %u:%u\n" < / span > < span class = cF0 > , n, sf - n - < / span > < span class = cFE > 1< / span > < span class = cF0 > );
< a name = "l346" > < / a > res++;
< a name = "l347" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l348" > < / a > }
< a name = "l349" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l350" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (pow_count);
< a name = "l351" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (residue);
< a name = "l352" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (sumfacts);
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< a name = "l353" > < / a >
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< a name = "l354" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > res;
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< a name = "l355" > < / a > }
< a name = "l356" > < / a >
< a name = "l357" > < / a > #< / span > < span class = cF1 > define< / span > < span class = cF0 > CORE_SUB_RANGE < / span > < span class = cFE > 0x1000< / span > < span class = cF0 >
< a name = "l358" > < / a >
< a name = "l359" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > TestCoreRange(RangeJob *r)
< a name = "l360" > < / a > {
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< a name = "l361" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > i, n, res = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l362" > < / a > RangeJob rj;
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< a name = "l363" > < / a >
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< a name = "l364" > < / a > < / span > < span class = cF5 > MemCopy< / span > < span class = cF0 > (& rj, r, < / span > < span class = cF1 > sizeof< / span > < span class = cF7 > (< / span > < span class = cF0 > RangeJob< / span > < span class = cF7 > )< / span > < span class = cF0 > );
< a name = "l365" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = r-> lo; i < r-> hi; i += CORE_SUB_RANGE)
< a name = "l366" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l367" > < / a > rj.lo = i;
< a name = "l368" > < / a > rj.hi = i + CORE_SUB_RANGE;
< a name = "l369" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (rj.hi > r-> hi)
< a name = "l370" > < / a > rj.hi = r-> hi;
< a name = "l371" > < / a > res += TestCoreSubRange(& rj);
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< a name = "l372" > < / a >
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< a name = "l373" > < / a > n = rj.hi - rj.lo;
< a name = "l374" > < / a > < / span > < span class = cF1 > lock< / span > < span class = cF0 > {< / span > < span class = cFB > progress1< / span > < span class = cF0 > += n;}
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< a name = "l375" > < / a >
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< a name = "l376" > < / a > < / span > < span class = cF5 > Yield< / span > < span class = cF0 > ;
< a name = "l377" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
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< a name = "l378" > < / a >
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< a name = "l379" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > res;
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< a name = "l380" > < / a > }
< a name = "l381" > < / a >
< a name = "l382" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > MagicPairs(< / span > < span class = cF9 > I64< / span > < span class = cF0 > N)
< a name = "l383" > < / a > {
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< a name = "l384" > < / a > < / span > < span class = cF1 > F64< / span > < span class = cF0 > t0 = < / span > < span class = cF5 > tS< / span > < span class = cF0 > ;
< a name = "l385" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > res = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l386" > < / a > < / span > < span class = cF9 > I64< / span > < span class = cF0 > sqrt_primes, cbrt_primes, num_powprimes,
< a name = "l387" > < / a > i, k, n = (N - < / span > < span class = cFE > 1< / span > < span class = cF0 > ) / < / span > < span class = cFB > mp_count< / span > < span class = cF0 > + < / span > < span class = cFE > 1< / span > < span class = cF0 > ;
< a name = "l388" > < / a > Prime *primes = PrimesNew(N, & sqrt_primes, & cbrt_primes);
< a name = "l389" > < / a > PowPrime *powprimes = PowPrimesNew(N, sqrt_primes, primes, & num_powprimes);
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< a name = "l390" > < / a >
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< a name = "l391" > < / a > < / span > < span class = cF6 > " N:%u SqrtPrimes:%u CbrtPrimes:%u PowersOfPrimes:%u\n" < / span > < span class = cF0 > , N, sqrt_primes, cbrt_primes, num_powprimes;
< a name = "l392" > < / a > < / span > < span class = cFB > progress1< / span > < span class = cF0 > = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l393" > < / a > *< / span > < span class = cFB > progress1_desc< / span > < span class = cF0 > = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
< a name = "l394" > < / a > < / span > < span class = cFB > progress1_max< / span > < span class = cF0 > = N;
< a name = "l395" > < / a > k = < / span > < span class = cFE > 2< / span > < span class = cF0 > ;
< a name = "l396" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < < / span > < span class = cFB > mp_count< / span > < span class = cF0 > ; i++)
< a name = "l397" > < / a > < / span > < span class = cF7 > {< / span > < span class = cF0 >
< a name = "l398" > < / a > rj[i].doc = < / span > < span class = cF5 > DocPut< / span > < span class = cF0 > ;
< a name = "l399" > < / a > rj[i].num = i;
< a name = "l400" > < / a > rj[i].lo = k;
< a name = "l401" > < / a > k += n;
< a name = "l402" > < / a > < / span > < span class = cF1 > if< / span > < span class = cF0 > (k > N)
< a name = "l403" > < / a > k = N;
< a name = "l404" > < / a > rj[i].hi = k;
< a name = "l405" > < / a > rj[i].N = N;
< a name = "l406" > < / a > rj[i].sqrt_primes = sqrt_primes;
< a name = "l407" > < / a > rj[i].cbrt_primes = cbrt_primes;
< a name = "l408" > < / a > rj[i].primes = primes;
< a name = "l409" > < / a > rj[i].cmd = < / span > < span class = cF5 > JobQueue< / span > < span class = cF0 > (& TestCoreRange, & rj[i], < / span > < span class = cFB > mp_count< / span > < span class = cF0 > - < / span > < span class = cFE > 1< / span > < span class = cF0 > - i, < / span > < span class = cFE > 0< / span > < span class = cF0 > );
< a name = "l410" > < / a > < / span > < span class = cF7 > }< / span > < span class = cF0 >
< a name = "l411" > < / a > < / span > < span class = cF1 > for< / span > < span class = cF0 > (i = < / span > < span class = cFE > 0< / span > < span class = cF0 > ; i < < / span > < span class = cFB > mp_count< / span > < span class = cF0 > ; i++)
< a name = "l412" > < / a > res += < / span > < span class = cF5 > JobResGet< / span > < span class = cF0 > (rj[i].cmd);
< a name = "l413" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (powprimes);
< a name = "l414" > < / a > < / span > < span class = cF5 > Free< / span > < span class = cF0 > (primes);
< a name = "l415" > < / a > < / span > < span class = cF6 > " Found:%u Time:%9.4f\n" < / span > < span class = cF0 > , res, < / span > < span class = cF5 > tS< / span > < span class = cF0 > - t0;
< a name = "l416" > < / a > < / span > < span class = cFB > progress1< / span > < span class = cF0 > = < / span > < span class = cFB > progress1_max< / span > < span class = cF0 > = < / span > < span class = cFE > 0< / span > < span class = cF0 > ;
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< a name = "l417" > < / a >
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< a name = "l418" > < / a > < / span > < span class = cF1 > return< / span > < span class = cF0 > res;
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< a name = "l419" > < / a > }
< a name = "l420" > < / a >
< a name = "l421" > < / a > MagicPairs(< / span > < span class = cFE > 1000000< / span > < span class = cF0 > );
< / span > < / pre > < / body >
< / html >
