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// communication functions
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int pack_reverse_comm(int, int, double *);
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void unpack_reverse_comm(int, int *, double *);
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int pack_comm(int , int *, double *, int, int *);
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int pack_forward_comm(int , int *, double *, int, int *);
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// vector functions, inline for efficiency
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inline double vec3_dot(double *x, double *y) {