#!/usr/bin/env python3
"""
try to understand which transfer characteristics can be used to create stable logic.
"""

def fwd(offset: float, amp: float):
    return lambda x: min(1.0, offset + amp*x)

def inv(offset: float, amp: float):
    return lambda x: max(0.0, 1.0 - offset - amp*x)

def test_stability(fwd, inv):
    low = 0.0
    high = 1.0
    mid = 0.5
    for i in range(32):
        low, high, mid = fwd(inv(high)), fwd(inv(low)), fwd(inv(mid))
        print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")

print("stability: 0.2 + 2.0*x")
test_stability(fwd(0.2, 2.0), inv(0.2, 2.0))

print("stability: 0.2 + 1.5*x")
test_stability(fwd(0.2, 1.5), inv(0.2, 1.5))

print("stability: 0.2 + 1.1*x")
test_stability(fwd(0.2, 1.1), inv(0.2, 1.1))

print("stability: 0.4 + 1.1*x")
test_stability(fwd(0.4, 1.1), inv(0.4, 1.1))

print("stability: 0.5 + 2.0*x")
test_stability(fwd(0.5, 2.0), inv(0.5, 2.0))

print("stability: 0.9*x")
test_stability(fwd(0.0, 0.9), inv(0.0, 0.9))

print("stability: 0.2 + 1.5*x; 0.9 - 0.7*x")
test_stability(fwd(0.2, 1.5), inv(0.1, 0.7))
print("stability: 0.1 + 1.3*x; 0.9 - 0.7*x")
test_stability(fwd(0.1, 1.3), inv(0.1, 0.7))

print("""\
    offset isn't a deal-breaker until it approaches 50%.
    for any offset < 0.5, amplification > 1.0, there is *some* stable pair of levels.
    as offset increases, the stable pairs become closer together
""")

def test_stability_inv(inv, mid=0.5):
    low = 0.0
    high = 1.0
    for i in range(32):
        low, high, mid = inv(high), inv(low), inv(mid)
        print(f"low {low:.2f} high {high:.2f} bistable {mid:.2f}")

print("stability_inv: 0.2 + 2.0*x")
test_stability_inv(inv(0.2, 2.0))

print("stability_inv: 0.2 + 1.1*x")
test_stability_inv(inv(0.2, 1.1))

print("stability_inv: 0.5 + 1.1*x")
test_stability_inv(inv(0.5, 1.1), 0.2)

print("stability_inv: 0.7 + 1.1*x")
test_stability_inv(inv(0.7, 1.1), 0.1)

print("""\
    inverter-only circuits can be stable, even if they ordinarily bias to just one direction...
    the same amp > 1.0 condition holds.
    importantly, offset > 0.5 becomes *fine*
""")