"""Independent JS 4.2 endpoint/envelope arithmetic, using published formulas.
See CHECK.md for the analytic half-line bounds and the fixed-N interpretation.
"""
import sys
sys.dont_write_bytecode=True
from pathlib import Path
sys.path.insert(0,str(Path(__file__).resolve().parent))
from independent_check import A,GAMMA,ULOW,save

L=A('2736.86'); w=L-5*L.log(); v=w-5*w.log()
C=A('3.98'); delta=A('1.3'); b=2*A('2.0452')*7
nu_page=1/(b*w.log())
nu_small=100/(w**(delta/2)*(delta*w.log())**2)
beta=1-nu_page
Epage=nu_page*w
Esmall=nu_small*w
# Ecal(exp(w))/exp(w), with alpha1=7.
ecal=4*w**(A(9)/2)/v**7+4/w**(A(5)/2)+18*w*(-w/12).exp()+A('2.5')*w**(A(11)/2)*(-w/6).exp()
pp=w*w*(1/(2*A(2).log()*w**5)*(-w/2).exp()+A('0.4')*w**3*(-w).exp())
mult=1+1/(L**2*w**3)+1/((1-4/w)*L)
deletion=A('0.9')*(w/2-L).exp()*L**4/(w**7*L.log())
p2= A('1.1')*7*w.log()*(C+w*w*(-Epage).exp()/beta)+27*w*w*ecal+pp
p1=p2+(A('0.67')+2*(-w/6).exp())/w**5
c4=(p1*mult+A('2.2')/L**2)+deletion
j=A('1.3841')*7*w.log()/(7*w.log()).log()

# Uniform bound for c4(N)/log N: replace w/L by 1 in every positive term.
# This also allows the beta(N) denominator to be frozen at beta(w0).
norm_page=A('1.1')*7*w.log()*(C/w+w*(-Epage).exp()/beta)
norm_small=A('1.1')*7*w.log()*(C/w+w*(-Esmall).exp()/beta)
assert norm_small < norm_page
norm=norm_page+27*w*ecal+pp/w+(A('0.67')+2*(-w/6).exp())/w**6
norm=norm*mult+A('2.2')/L**3+deletion/L
# Products with j(N) are decreasing as explained in CHECK.md.
norm_j=norm*j

# c1,c2: each nonconstant term decreases in w >= w0.
c1=C+w*w*((-Epage).exp()/beta+w**7*(A('1.02')*(-w/2).exp()+3*(-2*w/3).exp())+A('9.4')*w**A('1.515')*(-A('0.8274')*w.sqrt()).exp())
c2=c1*mult+1/L**2+A('1.3841')*L**4*(-L).exp()/L.log()
ll=L.log().log(); logq=(7*w.log()).log(); logdelta=(delta*w.log()).log()
c3=(A('1.5')/L+(L+7*L.log())/(L-7*L.log()))*(L/w)**delta*(GAMMA.exp()*(1+delta.log()/ll)+A('2.5')/(logdelta*ll))+A('1e-1000')
a1=c2*A('1.3841')*7*L.log()/(L**(2-delta)*ll*logq)+c3
afactor=ll/(L**(1+delta)*A('0.6601618158'))*(GAMMA.exp()*(A(7).log()+ll)+A('2.5')/logq)
aval=a1*afactor
eps=A('0.0005543'); eps1=A(1)/11; xi=A(801); cc=40*(A('0.25')-14*L.log()/L)
hc=3/cc*(-cc).exp(); h10=A('0.3')*(-A(10)).exp()
fmin=1-A('0.000105'); mmax=A('0.000105')
case_a=40*(1-xi/L**2)*(fmin-eps*114*A(2).exp()*h10)-norm/ULOW
brace=fmin-eps1*(1-fmin)-(1+eps1)*eps*114*A(2).exp()*hc-(3*eps1+aval)*(mmax+eps*114*A(2).exp()*hc)-aval-2*xi/L**2
case_b=40*brace-norm_j/ULOW
gates={
    'threshold_slack':w-A('7.9').exp(),
    'logH_minus_7logL':w/2-7*w.log()-7*L.log(),
    '7logL_minus_log1e9':7*L.log()-A(10**9).log(),
    'V_factor':1-xi/L**2,
    'support_log_slack':L/4-7*w.log()-A('2.5')*L.log()-400*(1+A('9e-7')/A(400).log()),
    'D_over_z2_log_slack':A('0.2')*L-14*L.log(),
    'Kdelta_minus_3022':w**delta-3022,
    'eps_slack':1/A(74)-eps,
    'prime_13_primorial_slack':w**delta-15015,
    'prime_17_primorial_slack':255255-w**delta,
}
assert all(x>0 for x in gates.values())
assert cc>7
assert case_a>38 and case_b>5
out={'L':L,'w':w,'v':v,'c':cc,'c4_at_start':c4,'j_at_start':j,'c4_over_L_uniform':norm,'c4_j_over_L_uniform':norm_j,
     'c1':c1,'c2':c2,'c3_upper':c3,'a1_upper':a1,'a_upper':aval,'h_c':hc,
     'case_a_uniform_coefficient':case_a,'case_b_uniform_coefficient':case_b,'gates':gates,
     'derivative_small_exponent':Esmall*(1-delta/2-2/w.log()),
     'derivative_page_exponent':Epage*(1-1/w.log())}
save('js_uniform.json',out)
print(Path('js_uniform.json').read_text())