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| #define  | INTERSECT_CMP(amin,  amax,  bmin,  bmax)   ((amin > bmax) || (bmin > amax)) | 
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| #define  | CONTAIN_CMP(amin,  amax,  bmin,  bmax)   ((bmin > amin) || (bmax < amax)) | 
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| #define  | WITHIN_CMP(amin,  amax,  bmin,  bmax)   ((amin > bmin) || (amax < bmax)) | 
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| #define  | DISJOINT_CMP(amin,  amax,  bmin,  bmax)   ((amin <= bmax) && (bmin <= amax)) | 
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| #define  | EQUAL_CMP(amin,  amax,  bmin,  bmax)   ((amin != bmin) || (amax != bmax)) | 
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| #define  | FCMP(A,  B)   ((int)(A) - (int)(B)) | 
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| #define  | RT_CMP(nextflag) | 
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| #define  | RT_CMP_KORR(type,  korr_func,  len,  nextflag) | 
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| #define  | RT_CMP_GET(type,  get_func,  len,  nextflag) | 
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| #define  | RT_VOL_KORR(type,  korr_func,  len,  cast) | 
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| #define  | RT_VOL_GET(type,  get_func,  len,  cast) | 
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| #define  | RT_D_MBR_KORR(type,  korr_func,  len,  cast) | 
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| #define  | RT_D_MBR_GET(type,  get_func,  len,  cast) | 
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| #define  | RT_COMB_KORR(type,  korr_func,  store_func,  len) | 
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| #define  | RT_COMB_GET(type,  get_func,  store_func,  len) | 
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| #define  | RT_OVL_AREA_KORR(type,  korr_func,  len) | 
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| #define  | RT_OVL_AREA_GET(type,  get_func,  len) | 
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| #define  | RT_AREA_INC_KORR(type,  korr_func,  len) | 
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| #define  | RT_AREA_INC_GET(type,  get_func,  len) | 
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| #define  | RT_PERIM_INC_KORR(type,  korr_func,  len) | 
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| #define  | RT_PERIM_INC_GET(type,  get_func,  len) | 
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| #define  | RT_PAGE_MBR_KORR(type,  korr_func,  store_func,  len) | 
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| #define  | RT_PAGE_MBR_GET(type,  get_func,  store_func,  len) | 
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 | 
| int  | rtree_key_cmp (HA_KEYSEG *keyseg, uchar *b, uchar *a, uint key_length, uint nextflag) | 
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| double  | rtree_rect_volume (HA_KEYSEG *keyseg, uchar *a, uint key_length) | 
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| int  | rtree_d_mbr (HA_KEYSEG *keyseg, uchar *a, uint key_length, double *res) | 
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| int  | rtree_combine_rect (HA_KEYSEG *keyseg, uchar *a, uchar *b, uchar *c, uint key_length) | 
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| double  | rtree_overlapping_area (HA_KEYSEG *keyseg, uchar *a, uchar *b, uint key_length) | 
|   | 
| double  | rtree_area_increase (HA_KEYSEG *keyseg, uchar *a, uchar *b, uint key_length, double *ab_area) | 
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| double  | rtree_perimeter_increase (HA_KEYSEG *keyseg, uchar *a, uchar *b, uint key_length, double *ab_perim) | 
|   | 
| int  | rtree_page_mbr (MI_INFO *info, HA_KEYSEG *keyseg, uchar *page_buf, uchar *c, uint key_length) | 
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