From 248e0e62bc765905091cfffde6bc23d51c1d3d7e Mon Sep 17 00:00:00 2001
From: Mark Meserve <mark.meserve@ni.com>
Date: Fri, 3 May 2019 16:46:22 -0500
Subject: uhdlib: add rational approximation to math utilities

---
 host/lib/include/uhdlib/utils/math.hpp | 75 ++++++++++++++++++++++++++++++++++
 1 file changed, 75 insertions(+)

diff --git a/host/lib/include/uhdlib/utils/math.hpp b/host/lib/include/uhdlib/utils/math.hpp
index b7f06ea24..24db23c50 100644
--- a/host/lib/include/uhdlib/utils/math.hpp
+++ b/host/lib/include/uhdlib/utils/math.hpp
@@ -9,7 +9,9 @@
 #ifndef INCLUDED_UHDLIB_UTILS_MATH_HPP
 #define INCLUDED_UHDLIB_UTILS_MATH_HPP
 
+#include <uhdlib/utils/narrow.hpp>
 #include <cmath>
+#include <vector>
 
 namespace uhd { namespace math {
 
@@ -20,6 +22,79 @@ T ceil_log2(T num){
     return std::ceil(std::log(num)/std::log(T(2)));
 }
 
+/**
+ * Function which attempts to find integer values a and b such that
+ * a / b approximates the decimal represented by f within max_error and
+ * b is not greater than maximum_denominator.
+ *
+ * If the approximation cannot achieve the desired error without exceeding
+ * the maximum denominator, b is set to the maximum value and a is set to
+ * the closest value.
+ *
+ * @param f is a positive decimal to be converted, must be between 0 and 1
+ * @param maximum_denominator maximum value allowed for b
+ * @param max_error how close to f the expression a / b should be
+ */
+template <typename IntegerType>
+std::pair<IntegerType, IntegerType> rational_approximation(
+    const double f, const IntegerType maximum_denominator, const double max_error)
+{
+    static constexpr IntegerType MIN_DENOM     = 1;
+    static constexpr size_t MAX_APPROXIMATIONS = 64;
+
+    UHD_ASSERT_THROW(maximum_denominator <= std::numeric_limits<IntegerType>::max());
+    UHD_ASSERT_THROW(f < 1 and f >= 0);
+
+    // This function uses a successive approximations formula to attempt to
+    // find a "best" rational to use to represent a decimal. This algorithm
+    // finds a continued fraction of up to 64 terms, or such that the last
+    // term is less than max_error
+
+    if (f < max_error) {
+        return {0, MIN_DENOM};
+    }
+
+    double c                         = f;
+    std::vector<double> saved_denoms = {c};
+
+    // Create the continued fraction by taking the reciprocal of the
+    // fractional part, expressing the denominator as a mixed number,
+    // then repeating the algorithm on the fractional part of that mixed
+    // number until a maximum number of terms or the fractional part is
+    // nearly zero.
+    for (int i = 0; i < MAX_APPROXIMATIONS; ++i) {
+        double x = std::floor(1.0 / c);
+        c        = (1.0 / c) - x;
+
+        saved_denoms.push_back(x);
+
+        if (std::abs(c) < max_error)
+            break;
+    }
+
+    double num   = 1.0;
+    double denom = saved_denoms.back();
+
+    // Calculate a single rational which will be equivalent to the
+    // continued fraction created earlier.  Because the continued fraction
+    // is composed of only integers, the final rational will be as well.
+    for (auto it = saved_denoms.rbegin() + 1; it != saved_denoms.rend() - 1; ++it) {
+        double new_denom = denom * (*it) + num;
+        if (new_denom > maximum_denominator) {
+            // We can't do any better than using the maximum denominator
+            num   = std::round(f * maximum_denominator);
+            denom = maximum_denominator;
+            break;
+        }
+
+        num   = denom;
+        denom = new_denom;
+    }
+
+    return {uhd::narrow<IntegerType>(num), uhd::narrow<IntegerType>(denom)};
+}
+
+
 }} /* namespace uhd::math */
 
 #endif /* INCLUDED_UHDLIB_UTILS_MATH_HPP */
-- 
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