"""Cost function which assigns a cost to a font enrichment latency."""

import math

NO_COST_THRESHOLD_S = 0.4

TIMEOUT_THRESHOLD_S = 3.5

MAX_COST = 1000

SIGMOID_WIDTH = 11.5

def cost(time_ms):

"""Assigns a cost to a measure of request latency.

The general approach is this:

- For request times less than some threshold cost is nearly 0 (while the

page is still loading other resources).

- For requests above the threshold cost rises non-linearly.

- However, there is a certain point beyond which cost maxes out. Typically

browsers at some point will give up on a font load and proceed without it.

So any wait beyond that point will not have any further negative effects.

To model this behaviour we use a sigmoid function, specifically the logistic function.

It is specifically shaped such that cost beings to rise after NO_COST_THRESHOLD and

hit's it's maximum value shortly after the TIMEOUT_THRESHOLD.

See the design doc

(https://docs.google.com/document/d/1kx62tpy5hGIbHh6tHMAryon9Sgye--W_IsHTeCMlmEo/edit)

for a more detailed discussion.

"""

time_s = time_ms / 1000

width = TIMEOUT_THRESHOLD_S - NO_COST_THRESHOLD_S

scale = SIGMOID_WIDTH / width

value = scale * (time_s - 0.5 * width - NO_COST_THRESHOLD_S)

return MAX_COST * (1 / (1 + math.exp(-value)))