| {"_row_type": "meta", "benchmark_metrics": {"comparison_vs_ieee_fp32": {"gf32_phi_distance": 0.01354, "ieee_exp_bits": 8, "ieee_mant_bits": 23, "ieee_phi_distance": 0.27, "phi_advantage": "19.9x closer to sacred ratio"}, "decode_latency_target_ns": 250, "encode_latency_target_ns": 300, "exp_latency_target_ns": 500, "floor_latency_target_ns": 50, "ln_latency_target_ns": 300, "memory_savings_vs_fp32": 0.0, "pow_integer_latency_target_ns": 500, "use_cases": ["near_ieee754_precision", "wider_dynamic_range", "phi_optimized_layout", "scientific_computing", "financial_calculations"]}, "created_at": "2026-04-06T15:54:08Z", "description": "GoldenFloat32 Conformance Vectors -- NUMERIC-STANDARD-001", "format_bits": 32, "format_family": "GF32", "format_name": "GF32", "format_spec": {"bits": 32, "exp_bias": 2047, "exp_bits": 12, "exp_mant_ratio": 0.6315789473684211, "mant_bits": 19, "memory_ratio_vs_fp32": 1.0, "sign_bits": 1}, "generated_at": "2026-04-04T19:00:00Z", "invariants": [{"assertion": "BITS == 32", "name": "gf32_bits_constant"}, {"assertion": "SIGN_BITS == 1", "name": "gf32_sign_bits_is_one"}, {"assertion": "EXP_BITS == 12", "name": "gf32_exp_bits_is_twelve"}, {"assertion": "MANT_BITS == 19", "name": "gf32_mant_bits_is_nineteen"}, {"assertion": "max_value() >= min_positive()", "name": "gf32_max_ge_min_positive"}, {"assertion": "PHI_DISTANCE < 0.015", "name": "gf32_phi_distance_near_optimal"}, {"assertion": "EXP_BIAS > 0", "name": "gf32_exp_bias_positive"}, {"assertion": "EXP_BITS > 8", "name": "gf32_exp_wider_than_ieee"}, {"assertion": "MANT_BITS < 23", "name": "gf32_mant_narrower_than_ieee"}, {"assertion": "pow(x, 0.0) == 1.0 for all positive x", "name": "gf32_pow_zero_exponent_identity"}, {"assertion": "pow(x, 1.0) == x for all valid x", "name": "gf32_pow_one_exponent_identity"}, {"assertion": "abs(exp_approx(ln_approx(x)) - x) < 0.01 for x=2.0", "name": "gf32_ln_exp_inversion"}, {"assertion": "floor(x) is integer for all f32 x", "name": "gf32_floor_returns_integer"}, {"assertion": "floor(2.5) <= floor(3.5)", "name": "gf32_floor_monotonic"}], "is_primary": false, "module": "GF32", "phi_distance": 0.01354495894042812, "ring": 27, "sacred_ok": true, "schema_version": 2, "seal": "sha256:82fbc99214151dd05105b81789e7fa5856da74c80fa24aa1ee0ef18b5084d738", "spec_path": "specs/numeric/gf32.t27", "updated_at": "2026-04-06T15:54:08Z", "validated_at": "2026-04-06T15:54:08Z", "vector_name": "gf32 Vectors", "verdict": "CLEAN", "version": "1.0"} | |
| {"_row_type": "vector", "expected": {"decoded": 0.0, "tolerance_abs": 0.0}, "inputs": {"raw": 0}, "test_name": "gf32_decode_zero", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"decoded": 0.0, "raw": 0, "tolerance_abs": 0.0}, "inputs": {"value": 0.0}, "test_name": "gf32_encode_zero_roundtrip", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"total": 32}, "inputs": {"exp_bits": 12, "mant_bits": 19, "sign_bits": 1}, "test_name": "gf32_bits_sum_correct", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"max_value_positive": true}, "inputs": {}, "test_name": "gf32_max_value_positive", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"min_positive_gt_zero": true}, "inputs": {}, "test_name": "gf32_min_positive_greater_than_zero", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"epsilon": 1.9073486328125e-06, "positive": true}, "inputs": {}, "test_name": "gf32_epsilon_positive", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"less_than": 0.015}, "inputs": {"phi_distance": 0.01354495894042812}, "test_name": "gf32_phi_distance_near_optimal", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"target": 1.0, "tolerance_abs": 0.0}, "inputs": {"ratio": 1.0}, "test_name": "gf32_memory_ratio_equals_one", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"valid": true}, "inputs": {}, "test_name": "gf32_validate_format_success", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"decoded": 1.0, "exp_biased": 2047, "mant": 0, "tolerance_abs": 1.9073486328125e-06}, "inputs": {"value": 1.0}, "test_name": "gf32_one_point_zero", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"decoded": 1.618034, "sacred_ok": true, "tolerance_abs": 1e-05}, "inputs": {"value": 1.61803398875}, "test_name": "gf32_phi_golden_ratio", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"advantage_factor": 19.9, "gf32_exp_wider": true, "gf32_phi_closer": true}, "inputs": {"ieee_exp_bits": 8, "ieee_mant_bits": 23, "ieee_phi_distance": 0.27}, "test_name": "gf32_ieee_comparison", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 1.0, "tolerance_abs": 1e-06}, "inputs": {"base": 2.0, "exponent": 0.0}, "test_name": "gf32_pow_zero_exponent_returns_one", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 32.0, "tolerance_abs": 1e-05}, "inputs": {"base": 2.0, "exponent": 5.0}, "test_name": "gf32_pow_positive_integer_exponent", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 0.125, "tolerance_abs": 1e-05}, "inputs": {"base": 2.0, "exponent": -3.0}, "test_name": "gf32_pow_negative_integer_exponent", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 2.0, "tolerance_abs": 0.0001}, "inputs": {"base": 4.0, "exponent": 0.5}, "test_name": "gf32_pow_fractional_exponent", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 0.0, "tolerance_abs": 1e-06}, "inputs": {"x": 1.0}, "test_name": "gf32_ln_approx_of_one", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 1.0, "tolerance_abs": 0.01}, "inputs": {"x": 2.718281828459045}, "test_name": "gf32_ln_approx_of_e", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 1.0, "tolerance_abs": 1e-06}, "inputs": {"x": 0.0}, "test_name": "gf32_exp_approx_zero", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 2.718281828459045, "tolerance_abs": 0.01}, "inputs": {"x": 1.0}, "test_name": "gf32_exp_approx_one", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": 3.0, "tolerance_abs": 1e-06}, "inputs": {"x": 3.7}, "test_name": "gf32_floor_positive", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "expected": {"result": -4.0, "tolerance_abs": 1e-06}, "inputs": {"x": -3.2}, "test_name": "gf32_floor_negative", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: BITS == 32", "expected": {"value": true}, "input": {"assertion": "BITS == 32"}, "name": "inv_gf32_bits_constant", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: SIGN_BITS == 1", "expected": {"value": true}, "input": {"assertion": "SIGN_BITS == 1"}, "name": "inv_gf32_sign_bits_is_one", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: EXP_BITS == 12", "expected": {"value": true}, "input": {"assertion": "EXP_BITS == 12"}, "name": "inv_gf32_exp_bits_is_twelve", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: MANT_BITS == 19", "expected": {"value": true}, "input": {"assertion": "MANT_BITS == 19"}, "name": "inv_gf32_mant_bits_is_nineteen", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: max_value() >= min_positive()", "expected": {"value": true}, "input": {"assertion": "max_value() >= min_positive()"}, "name": "inv_gf32_max_ge_min_positive", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: PHI_DISTANCE < 0.015", "expected": {"value": true}, "input": {"assertion": "PHI_DISTANCE < 0.015"}, "name": "inv_gf32_phi_distance_near_optimal", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: EXP_BIAS > 0", "expected": {"value": true}, "input": {"assertion": "EXP_BIAS > 0"}, "name": "inv_gf32_exp_bias_positive", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: EXP_BITS > 8", "expected": {"value": true}, "input": {"assertion": "EXP_BITS > 8"}, "name": "inv_gf32_exp_wider_than_ieee", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: MANT_BITS < 23", "expected": {"value": true}, "input": {"assertion": "MANT_BITS < 23"}, "name": "inv_gf32_mant_narrower_than_ieee", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: pow(x, 0.0) == 1.0 for all positive x", "expected": {"value": true}, "input": {"assertion": "pow(x, 0.0) == 1.0 for all positive x"}, "name": "inv_gf32_pow_zero_exponent_identity", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: pow(x, 1.0) == x for all valid x", "expected": {"value": true}, "input": {"assertion": "pow(x, 1.0) == x for all valid x"}, "name": "inv_gf32_pow_one_exponent_identity", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: abs(exp_approx(ln_approx(x)) - x) < 0.01 for x=2.0", "expected": {"value": true}, "input": {"assertion": "abs(exp_approx(ln_approx(x)) - x) < 0.01 for x=2.0"}, "name": "inv_gf32_ln_exp_inversion", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: floor(x) is integer for all f32 x", "expected": {"value": true}, "input": {"assertion": "floor(x) is integer for all f32 x"}, "name": "inv_gf32_floor_returns_integer", "verdict": "CLEAN"} | |
| {"_row_type": "vector", "description": "Invariant: floor(2.5) <= floor(3.5)", "expected": {"value": true}, "input": {"assertion": "floor(2.5) <= floor(3.5)"}, "name": "inv_gf32_floor_monotonic", "verdict": "CLEAN"} | |