These work

frontend/src/lib/format.ts

@@ -65,6 +65,81 @@ export function formatRelativeTime(isoDate: string): string {
   return new Date(isoDate).toLocaleDateString();
 }
 
+// Percentile-based scale: maps between percentile space (0–100) and absolute values
+// using the histogram's CDF. Each percentile step = 1% of data.
+export interface PercentileScale {
+  toValue: (percentile: number) => number;
+  toPercentile: (value: number) => number;
+}
+
+export function buildPercentileScale(hist: {
+  min: number;
+  max: number;
+  p1: number;
+  p99: number;
+  counts: number[];
+}): PercentileScale {
+  const n = hist.counts.length;
+  const total = hist.counts.reduce((a, b) => a + b, 0);
+
+  if (n === 0 || total === 0) {
+    const range = hist.max - hist.min || 1;
+    return {
+      toValue: (p) => hist.min + (p / 100) * range,
+      toPercentile: (v) => ((v - hist.min) / range) * 100,
+    };
+  }
+
+  // Bin boundaries: [min, p1, ..middle edges.., p99, max]
+  const boundaries: number[] = [];
+  if (n === 1) {
+    boundaries.push(hist.min, hist.max);
+  } else {
+    boundaries.push(hist.min, hist.p1);
+    if (n > 2) {
+      const middleWidth = (hist.p99 - hist.p1) / (n - 2);
+      for (let i = 1; i < n - 1; i++) {
+        boundaries.push(hist.p1 + i * middleWidth);
+      }
+    }
+    boundaries.push(hist.max);
+  }
+
+  // Cumulative fraction: cumFrac[0]=0, cumFrac[n]=1
+  const cumFrac: number[] = [0];
+  for (let i = 0; i < n; i++) {
+    cumFrac.push(cumFrac[i] + hist.counts[i] / total);
+  }
+  cumFrac[n] = 1; // ensure exact 1.0
+
+  return {
+    toValue(percentile: number): number {
+      const target = Math.max(0, Math.min(1, percentile / 100));
+      if (target <= 0) return boundaries[0];
+      if (target >= 1) return boundaries[n];
+      let i = 0;
+      for (; i < n - 1; i++) {
+        if (cumFrac[i + 1] > target) break;
+      }
+      const binFrac = cumFrac[i + 1] - cumFrac[i];
+      const t = binFrac > 0 ? (target - cumFrac[i]) / binFrac : 0;
+      return boundaries[i] + t * (boundaries[i + 1] - boundaries[i]);
+    },
+
+    toPercentile(value: number): number {
+      if (value <= boundaries[0]) return 0;
+      if (value >= boundaries[n]) return 100;
+      let i = 0;
+      for (; i < n - 1; i++) {
+        if (boundaries[i + 1] > value) break;
+      }
+      const binWidth = boundaries[i + 1] - boundaries[i];
+      const t = binWidth > 0 ? (value - boundaries[i]) / binWidth : 0;
+      return (cumFrac[i] + t * (cumFrac[i + 1] - cumFrac[i])) * 100;
+    },
+  };
+}
+
 // Calculate weighted mean from histogram with outlier bins.
 // Bin 0 = [min, p1), bins 1..n-2 = [p1, p99) evenly, bin n-1 = [p99, max].
 export function calculateHistogramMean(histogram: {