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+// polynomial for approximating log10(1+x)
+//
+// Copyright (c) 2019-2023, Arm Limited.
+// SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
+
+deg = 6; // poly degree
+// |log10(1+x)| > 0x1p-5 outside the interval
+a = -0x1.p-5;
+b = 0x1.p-5;
+
+ln10 = evaluate(log(10),0);
+invln10hi = double(1/ln10 + 0x1p21) - 0x1p21; // round away last 21 bits
+invln10lo = double(1/ln10 - invln10hi);
+
+// find log10(1+x)/x polynomial with minimal relative error
+// (minimal relative error polynomial for log10(1+x) is the same * x)
+deg = deg-1; // because of /x
+
+// f = log(1+x)/x; using taylor series
+f = 0;
+for i from 0 to 60 do { f = f + (-x)^i/(i+1); };
+f = f/ln10;
+
+// return p that minimizes |f(x) - poly(x) - x^d*p(x)|/|f(x)|
+approx = proc(poly,d) {
+  return remez(1 - poly(x)/f(x), deg-d, [a;b], x^d/f(x), 1e-10);
+};
+
+// first coeff is fixed, iteratively find optimal double prec coeffs
+poly = invln10hi + invln10lo;
+for i from 1 to deg do {
+  p = roundcoefficients(approx(poly,i), [|D ...|]);
+  poly = poly + x^i*coeff(p,0);
+};
+display = hexadecimal;
+print("invln10hi:", invln10hi);
+print("invln10lo:", invln10lo);
+print("rel error:", accurateinfnorm(1-poly(x)/f(x), [a;b], 30));
+print("in [",a,b,"]");
+print("coeffs:");
+for i from 0 to deg do coeff(poly,i);
+
+display = decimal;
+print("in [",a,b,"]");