"""Exact finite geometry and interval-integration validation.
Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
"""
from pathlib import Path
import sys,json,copy
from fractions import Fraction
sys.path.insert(0,str(Path(__file__).resolve().parents[1]/'code'))
from eve3d_v6.certificates import *
root=Path(__file__).resolve().parents[1];count=0
for angle,expected in [(0,1),(Fraction(1,6),Fraction(1,2)),(Fraction(1,4),0),(Fraction(1,3),Fraction(-1,2)),(Fraction(1,2),-1)]:
    lo,hi=cos_interval(angle);assert lo<=expected<=hi;count+=1
pl,ph=pi_interval();assert Fraction(3141592653589793238,10**18)<pl<ph<Fraction(3141592653589793239,10**18);count+=1
for theta in ['0','1/7','1/3','1/2']:
    geo=orbit_boxes(theta,6);assert verify_orbit_boxes(geo)['verified'];count+=1
cert=json.loads((root/'examples/approximation_certificate.json').read_text());ext=extract_template(cert)
new={'schema':'eve3d-v6-binary-construction-1','request':cert['request'],'coefficients':ext['coefficients'],
     'geometry':orbit_boxes(ext['rounding_fraction'],6),'threshold':cert['threshold']}
result=verify_binary_construction(new);assert result['verified'];count+=1
(root/'examples/binary_construction_certificate.json').write_text(json.dumps(new,indent=2)+'\n')
(root/'verification/binary_construction.json').write_text(json.dumps(result,indent=2)+'\n')
wrong=copy.deepcopy(new);wrong['geometry']['theta']='1/3'
try:verify_binary_construction(wrong);raise AssertionError('Tampered geometry accepted')
except ValueError:count+=1
print(json.dumps({'status':'passed','checks':count,'scope':'Exact orbit volumes, symmetry, rational cosine enclosures, and a finite binary response-approximation certificate.'},indent=2))