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Commit b1951d7f authored by POLLIEN Baptiste's avatar POLLIEN Baptiste
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Adding lemma for rotation matrix

parent 756f5bc0
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sw/airborne/.frama-c/wp/script/lemma_float_rmat_of_eulers_321_2.json
View file @ b1951d7f
[ { "prover": "Z3:4.8.6:noBV", "verdict": "timeout", "time": 10. },
{ "prover": "Z3:4.8.6:counterexamples", "verdict": "timeout", "time": 10. },
{ "prover": "Z3:4.8.6", "verdict": "timeout", "time": 10. },
{ "prover": "Coq:8.12.2", "verdict": "unknown" },
[ { "prover": "Z3:4.8.6:noBV", "verdict": "timeout", "time": 15. },
{ "prover": "Z3:4.8.6:counterexamples", "verdict": "timeout", "time": 15. },
{ "prover": "Z3:4.8.6", "verdict": "timeout", "time": 15. },
{ "prover": "Coq:8.12.2", "verdict": "valid", "time": 0.52 },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout", "time": 10. },
{ "prover": "Alt-Ergo:2.3.3", "verdict": "timeout", "time": 10. } ]
"verdict": "timeout", "time": 15. },
{ "prover": "Alt-Ergo:2.3.3", "verdict": "timeout", "time": 16.9815,
"steps": 46 } ]
sw/airborne/.frama-c/wp/script/lemma_rotatio_matrix_to_eq.json 0 → 100644
View file @ b1951d7f
[ { "prover": "Z3:4.8.6:noBV", "verdict": "timeout", "time": 15. },
{ "prover": "Z3:4.8.6:counterexamples", "verdict": "timeout", "time": 15. },
{ "prover": "Z3:4.8.6", "verdict": "timeout", "time": 15. },
{ "prover": "Coq:8.12.2", "verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout", "time": 15. },
{ "prover": "Alt-Ergo:2.3.3", "verdict": "timeout", "time": 15. },
{ "header": "Definition", "tactic": "Wp.unfold", "params": {},
"select": { "select": "inside-goal", "occur": 0,
"target": "(L_l_RMat_of_FloatRMat Mf32_0 rm_0)",
"pattern": "L_l_RMat_of_FloatRMat$Mf32$rm" },
"children": { "Unfold 'L_l_RMat_of_FloatRMat'": [ { "prover": "Z3:4.8.6:noBV",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6",
"verdict": "timeout",
"time": 15. },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. },
{ "header": "Definition",
"tactic": "Wp.unfold",
"params": {},
"select": { "select": "inside-goal",
"occur": 0,
"target": "let a_0 = (shiftfield_F9_FloatRMat_m rm_0) in\n(P_rotation_matrix\n {\n F12_RealRMat_s_a00 = Mf32_0[(shift_float32 a_0 0)] ;\n F12_RealRMat_s_a01 = Mf32_0[(shift_float32 a_0 1)] ;\n F12_RealRMat_s_a02 = Mf32_0[(shift_float32 a_0 2)] ;\n F12_RealRMat_s_a10 = Mf32_0[(shift_float32 a_0 3)] ;\n F12_RealRMat_s_a11 = Mf32_0[(shift_float32 a_0 4)] ;\n F12_RealRMat_s_a12 = Mf32_0[(shift_float32 a_0 5)] ;\n F12_RealRMat_s_a20 = Mf32_0[(shift_float32 a_0 6)] ;\n F12_RealRMat_s_a21 = Mf32_0[(shift_float32 a_0 7)] ;\n F12_RealRMat_s_a22 = Mf32_0[(shift_float32 a_0 8)]\n })",
"pattern": "P_rotation_matrix{RealRMat_s}[][]" },
"children": { "Unfold 'P_rotation_matrix'":
[ { "prover": "Z3:4.8.6:noBV",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6",
"verdict": "timeout",
"time": 15. },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. },
{ "header": "Definition",
"tactic": "Wp.unfold",
"params": {},
"select":
{ "select": "inside-goal",
"occur": 0,
"target": "L_id_rmat",
"pattern": "L_id_rmat" },
"children":
{ "Unfold 'L_id_rmat'":
[ { "prover": "Z3:4.8.6:noBV",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6",
"verdict": "timeout",
"time": 15. },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. },
{ "header": "Definition",
"tactic": "Wp.unfold",
"params": {},
"select":
{ "select": "inside-goal",
"occur": 0,
"target": "let a_0 = (shiftfield_F9_FloatRMat_m rm_0) in\n(L_transpose\n {\n F12_RealRMat_s_a00 = Mf32_0[(shift_float32 a_0 0)] ;\n F12_RealRMat_s_a01 = Mf32_0[(shift_float32 a_0 1)] ;\n F12_RealRMat_s_a02 = Mf32_0[(shift_float32 a_0 2)] ;\n F12_RealRMat_s_a10 = Mf32_0[(shift_float32 a_0 3)] ;\n F12_RealRMat_s_a11 = Mf32_0[(shift_float32 a_0 4)] ;\n F12_RealRMat_s_a12 = Mf32_0[(shift_float32 a_0 5)] ;\n F12_RealRMat_s_a20 = Mf32_0[(shift_float32 a_0 6)] ;\n F12_RealRMat_s_a21 = Mf32_0[(shift_float32 a_0 7)] ;\n F12_RealRMat_s_a22 = Mf32_0[(shift_float32 a_0 8)]\n })",
"pattern": "L_transpose{RealRMat_s}[][][][][]" },
"children":
{ "Unfold 'L_transpose'":
[ { "prover": "Z3:4.8.6:noBV",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6",
"verdict": "timeout",
"time": 15. },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. },
{ "header": "Definition",
"tactic": "Wp.unfold",
"params": {},
"select":
{ "select": "inside-goal",
"occur": 0,
"target": "let a_0 = (shiftfield_F9_FloatRMat_m rm_0) in\nlet r_0 = Mf32_0[(shift_float32 a_0 0)] in\nlet r_1 = Mf32_0[(shift_float32 a_0 1)] in\nlet r_2 = Mf32_0[(shift_float32 a_0 2)] in\nlet r_3 = Mf32_0[(shift_float32 a_0 3)] in\nlet r_4 = Mf32_0[(shift_float32 a_0 4)] in\nlet r_5 = Mf32_0[(shift_float32 a_0 5)] in\nlet r_6 = Mf32_0[(shift_float32 a_0 6)] in\nlet r_7 = Mf32_0[(shift_float32 a_0 7)] in\nlet r_8 = Mf32_0[(shift_float32 a_0 8)] in\n(L_mult_RealRMat\n {\n F12_RealRMat_s_a00 = r_0 ;\n F12_RealRMat_s_a01 = r_1 ;\n F12_RealRMat_s_a02 = r_2 ;\n F12_RealRMat_s_a10 = r_3 ;\n F12_RealRMat_s_a11 = r_4 ;\n F12_RealRMat_s_a12 = r_5 ;\n F12_RealRMat_s_a20 = r_6 ;\n F12_RealRMat_s_a21 = r_7 ;\n F12_RealRMat_s_a22 = r_8\n }\n {\n F12_RealRMat_s_a00 = r_0 ;\n F12_RealRMat_s_a01 = r_3 ;\n F12_RealRMat_s_a02 = r_6 ;\n F12_RealRMat_s_a10 = r_1 ;\n F12_RealRMat_s_a11 = r_4 ;\n F12_RealRMat_s_a12 = r_7 ;\n F12_RealRMat_s_a20 = r_2 ;\n F12_RealRMat_s_a21 = r_5 ;\n F12_RealRMat_s_a22 = r_8\n })",
"pattern": "L_mult_RealRMat{RealRMat_s}{RealRMat_s}" },
"children":
{ "Unfold 'L_mult_RealRMat'":
[ { "prover": "Z3:4.8.6:noBV",
"verdict": "timeout",
"time": 15. },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6",
"verdict": "timeout",
"time": 15. },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "timeout",
"time": 15. },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. },
{ "header": "Definition",
"tactic": "Wp.unfold",
"params": {},
"select":
{ "select": "inside-goal",
"occur": 0,
"target": "let a_0 = (shiftfield_F9_FloatRMat_m rm_0) in\nlet r_0 = Mf32_0[(shift_float32 a_0 0)] in\nlet r_1 = Mf32_0[(shift_float32 a_0 1)] in\nlet r_2 = Mf32_0[(shift_float32 a_0 2)] in\nlet r_3 = Mf32_0[(shift_float32 a_0 3)] in\nlet r_4 = Mf32_0[(shift_float32 a_0 4)] in\nlet r_5 = Mf32_0[(shift_float32 a_0 5)] in\nlet r_6 = ((r_0*r_3)+(r_1*r_4)+(r_2*r_5)) in\nlet r_7 = Mf32_0[(shift_float32 a_0 6)] in\nlet r_8 = Mf32_0[(shift_float32 a_0 7)] in\nlet r_9 = Mf32_0[(shift_float32 a_0 8)] in\nlet r_10 = ((r_0*r_7)+(r_1*r_8)+(r_2*r_9)) in\nlet r_11 = ((r_3*r_7)+(r_4*r_8)+(r_5*r_9)) in\n(EqS12_RealRMat_s\n {\n F12_RealRMat_s_a00 = (r_0*r_0)+(r_1*r_1)+(r_2*r_2) ;\n F12_RealRMat_s_a01 = r_6 ;\n F12_RealRMat_s_a02 = r_10 ;\n F12_RealRMat_s_a10 = r_6 ;\n F12_RealRMat_s_a11 = (r_3*r_3)+(r_4*r_4)+(r_5*r_5) ;\n F12_RealRMat_s_a12 = r_11 ;\n F12_RealRMat_s_a20 = r_10 ;\n F12_RealRMat_s_a21 = r_11 ;\n F12_RealRMat_s_a22 = (r_7*r_7)+(r_8*r_8)+(r_9*r_9)\n }\n {\n F12_RealRMat_s_a00 = 1 ;\n F12_RealRMat_s_a01 = 0 ;\n F12_RealRMat_s_a02 = 0 ;\n F12_RealRMat_s_a10 = 0 ;\n F12_RealRMat_s_a11 = 1 ;\n F12_RealRMat_s_a12 = 0 ;\n F12_RealRMat_s_a20 = 0 ;\n F12_RealRMat_s_a21 = 0 ;\n F12_RealRMat_s_a22 = 1\n })",
"pattern": "EqS12_RealRMat_s{RealRMat_s}{RealRMat_s}" },
"children":
{ "Unfold 'EqS12_RealRMat_s'":
[ { "prover": "Z3:4.8.6:noBV",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6:counterexamples",
"verdict": "unknown" },
{ "prover": "Z3:4.8.6",
"verdict": "unknown" },
{ "prover": "Coq:8.12.2",
"verdict": "unknown" },
{ "prover": "CVC4:1.9-prerelease:strings+counterexamples",
"verdict": "unknown" },
{ "prover": "Alt-Ergo:2.3.3",
"verdict": "timeout",
"time": 15. } ] } } ] } } ] } } ] } } ] } } ] } } ]
sw/airborne/.frama-c/wp/script/lemma_rotation_matrix_to_eq.json 0 → 100644
View file @ b1951d7f
[ { "header": "Definition", "tactic": "Wp.unfold", "params": {},
"select": { "select": "inside-goal", "occur": 0,
"target": "(P_rotation_matrix (L_l_RMat_of_FloatRMat Mf32_0 rm_0))",
"pattern": "P_rotation_matrixL_l_RMat_of_FloatRMat" },
"children": { "Unfold 'P_rotation_matrix'": [ { "prover": "Z3:4.8.6:counterexamples",
"verdict": "valid",
"time": 13.61,
"steps": 27265631 } ] } } ]
sw/airborne/math/pprz_algebra_float_convert_rmat_frama_c.h
View file @ b1951d7f
......@@ -126,6 +126,21 @@ logic RealRMat l_RMat_of_FloatRMat(struct FloatRMat *rmat) =
mult_RealRMat(rmat, transpose(rmat)) == id_rmat;
*/
/*@
lemma rotation_matrix_to_eq:
\forall struct FloatRMat *rm;
\valid(rm)
==>
(rotation_matrix(l_RMat_of_FloatRMat(rm)) <==>
(SQR(rm->m[0]) + SQR(rm->m[1]) + SQR(rm->m[2]) == 1.0
&& SQR(rm->m[3]) + SQR(rm->m[4]) + SQR(rm->m[5]) == 1.0
&& SQR(rm->m[6]) + SQR(rm->m[7]) + SQR(rm->m[8]) == 1.0
&& rm->m[0] * rm->m[3] + rm->m[1] * rm->m[4] + rm->m[2] * rm->m[5] == 0
&& rm->m[0] * rm->m[6] + rm->m[1] * rm->m[7] + rm->m[2] * rm->m[8] == 0
&& rm->m[3] * rm->m[6] + rm->m[4] * rm->m[7] + rm->m[5] * rm->m[8] == 0
));
*/
/*******************************
* CONVERT QUAT TO RMAT
* *****************************/
......
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