7 #include "cl_numtheory.h"
13 #include "cl_xmacros.h"
16 inline int jacobi_aux (uint32 a, uint32 b)
20 // (a/b) * v is invariant.
22 // b=1 implies (a/b) = 1.
25 // b>1 and a=0 imply (a/b) = 0.
28 // a > b/2, so (a/b) = (-1/b) * ((b-a)/b),
29 // and (-1/b) = -1 if b==3 mod 4.
33 case 3: v = -v; break;
39 // b>1 and a=2a', so (a/b) = (2/b) * (a'/b),
40 // and (2/b) = -1 if b==3,5 mod 8.
43 case 1: case 7: break;
44 case 3: case 5: v = -v; break;
49 // a and b odd, 0 < a < b/2 < b, so apply quadratic reciprocity
50 // law (a/b) = (-1)^((a-1)/2)((b-1)/2) * (b/a).
54 // Now a > 2*b, set a := a mod b.
58 { a = a-b; do { a = a-b; } while (a >= b); }
62 int jacobi (sint32 a, sint32 b)
64 // Check b > 0, b odd.
71 a = (uint32)a % (uint32)b;
73 a = b-1-((uint32)(~a) % (uint32)b);
74 return jacobi_aux(a,b);