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All rights reserved.\n// Use of this source code is governed by a BSD-style license that can be\n// found in the LICENSE file.\n\n// Lifted from Lighthouse: https://github.com/GoogleChrome/lighthouse/blob/36cac182a6c637b1671c57326d7c0241633d0076/shared/statistics.js\n\n/**\n * @license\n * Copyright 2017 Google LLC\n * SPDX-License-Identifier: Apache-2.0\n */\n\n// The exact double values for the max and min scores possible in each range.\nconst MIN_PASSING_SCORE = 0.90000000000000002220446049250313080847263336181640625;\nconst MAX_AVERAGE_SCORE = 0.899999999999999911182158029987476766109466552734375;\nconst MIN_AVERAGE_SCORE = 0.5;\nconst MAX_FAILING_SCORE = 0.499999999999999944488848768742172978818416595458984375;\n\n/**\n * Approximates the Gauss error function, the probability that a random variable\n * from the standard normal distribution lies within [-x, x]. Moved from\n * traceviewer.b.math.erf, based on Abramowitz and Stegun, formula 7.1.26.\n */\nfunction erf(x: number): number {\n  // erf(-x) = -erf(x);\n  const sign = Math.sign(x);\n  x = Math.abs(x);\n\n  const a1 = 0.254829592;\n  const a2 = -0.284496736;\n  const a3 = 1.421413741;\n  const a4 = -1.453152027;\n  const a5 = 1.061405429;\n  const p = 0.3275911;\n  const t = 1 / (1 + p * x);\n  const y = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))));\n  return sign * (1 - y * Math.exp(-x * x));\n}\n\n/**\n * Returns the score (1 - percentile) of `value` in a log-normal distribution\n * specified by the `median` value, at which the score will be 0.5, and a 10th\n * percentile value, at which the score will be 0.9. The score represents the\n * amount of the distribution greater than `value`. All values should be in the\n * same units (e.g. milliseconds). See\n *   https://www.desmos.com/calculator/o98tbeyt1t\n * for an interactive view of the relationship between these parameters and the\n * typical parameterization (location and shape) of the log-normal distribution.\n */\nexport function getLogNormalScore({median, p10}: {median: number, p10: number}, value: number): number {\n  // Required for the log-normal distribution.\n  if (median <= 0) {\n    throw new Error('median must be greater than zero');\n  }\n  if (p10 <= 0) {\n    throw new Error('p10 must be greater than zero');\n  }\n  // Not strictly required, but if p10 > median, it flips around and becomes the p90 point.\n  if (p10 >= median) {\n    throw new Error('p10 must be less than the median');\n  }\n\n  // Non-positive values aren't in the distribution, so always 1.\n  if (value <= 0) {\n    return 1;\n  }\n\n  // Closest double to `erfc-1(1/5)`.\n  const INVERSE_ERFC_ONE_FIFTH = 0.9061938024368232;\n\n  // Shape (σ) is `|log(p10/median) / (sqrt(2)*erfc^-1(1/5))|` and\n  // standardizedX is `1/2 erfc(log(value/median) / (sqrt(2)*σ))`, so simplify a bit.\n  const xRatio = Math.max(Number.MIN_VALUE, value / median);  // value and median are > 0, so is ratio.\n  const xLogRatio = Math.log(xRatio);\n  const p10Ratio = Math.max(Number.MIN_VALUE, p10 / median);  // p10 and median are > 0, so is ratio.\n  const p10LogRatio = -Math.log(p10Ratio);                    // negate to keep σ positive.\n  const standardizedX = xLogRatio * INVERSE_ERFC_ONE_FIFTH / p10LogRatio;\n  const complementaryPercentile = (1 - erf(standardizedX)) / 2;\n\n  // Clamp to avoid floating-point out-of-bounds issues and keep score in expected range.\n  let score;\n  if (value <= p10) {\n    // Passing. Clamp to [0.9, 1].\n    score = Math.max(MIN_PASSING_SCORE, Math.min(1, complementaryPercentile));\n  } else if (value <= median) {\n    // Average. Clamp to [0.5, 0.9).\n    score = Math.max(MIN_AVERAGE_SCORE, Math.min(MAX_AVERAGE_SCORE, complementaryPercentile));\n  } else {\n    // Failing. Clamp to [0, 0.5).\n    score = Math.max(0, Math.min(MAX_FAILING_SCORE, complementaryPercentile));\n  }\n  return score;\n}\n\n/**\n * Interpolates the y value at a point x on the line defined by (x0, y0) and (x1, y1)\n */\nexport function linearInterpolation(x0: number, y0: number, x1: number, y1: number, x: number): number {\n  const slope = (y1 - y0) / (x1 - x0);\n  return y0 + (x - x0) * slope;\n}\n"]}