/* * Licensed to the Apache Software Foundation (ASF) under one * or more contributor license agreements. See the NOTICE file * distributed with this work for additional information * regarding copyright ownership. The ASF licenses this file * to you under the Apache License, Version 2.0 (the * "License"); you may not use this file except in compliance * with the License. You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, * software distributed under the License is distributed on an * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY * KIND, either express or implied. See the License for the * specific language governing permissions and limitations * under the License. */ #ifndef _CUBICINTERPOLATION_INTERNAL_HPP_ #define _CUBICINTERPOLATION_INTERNAL_HPP_ #include "CubicInterpolation.hpp" #include #include namespace datasketches { template static double interpolateUsingXAndYTables(const double xArr[], const double yArr[], const int offset, const double x); template static double cubicInterpolate(const double x0, const double y0, const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x); template static int findStraddle(const double xArr[], const int len, const double x); template static int recursiveFindStraddle(const double xArr[], const int l, const int r, const double x); template static double interpolateUsingXArrAndYStride(const double xArr[], const double yStride, const int offset, const double x); const int numEntries = 40; //Computed for Coupon lgK = 26 ONLY. Designed for the cubic interpolator function. const double xArrComputed[numEntries] = { 0.0, 1.0, 20.0, 400.0, 8000.0, 160000.0, 300000.0, 600000.0, 900000.0, 1200000.0, 1500000.0, 1800000.0, 2100000.0, 2400000.0, 2700000.0, 3000000.0, 3300000.0, 3600000.0, 3900000.0, 4200000.0, 4500000.0, 4800000.0, 5100000.0, 5400000.0, 5700000.0, 6000000.0, 6300000.0, 6600000.0, 6900000.0, 7200000.0, 7500000.0, 7800000.0, 8100000.0, 8400000.0, 8700000.0, 9000000.0, 9300000.0, 9600000.0, 9900000.0, 10200000.0 }; //Computed for Coupon lgK = 26 ONLY. Designed for the cubic interpolator function. const double yArrComputed[numEntries] = { 0.0000000000000000, 1.0000000000000000, 20.0000009437402611, 400.0003963713384110, 8000.1589294602090376, 160063.6067763759638183, 300223.7071597663452849, 600895.5933856170158833, 902016.8065120954997838, 1203588.4983199508860707, 1505611.8245524743106216, 1808087.9449319066479802, 2111018.0231759352609515, 2414403.2270142501220107, 2718244.7282051891088486, 3022543.7025524540804327, 3327301.3299219091422856, 3632518.7942584538832307, 3938197.2836029687896371, 4244337.9901093561202288, 4550942.1100616492331028, 4858010.8438911894336343, 5165545.3961938973516226, 5473546.9757476449012756, 5782016.7955296505242586, 6090956.0727340159937739, 6400366.0287892958149314, 6710247.8893762007355690, 7020602.8844453142955899, 7331432.2482349723577499, 7642737.2192891482263803, 7954519.0404754765331745, 8266778.9590033423155546, 8579518.2264420464634895, 8892738.0987390466034412, 9206439.8362383283674717, 9520624.7036988288164139, 9835293.9703129194676876, 10150448.9097250290215015, 10466090.8000503256917000 }; template double CubicInterpolation::usingXAndYTables(const double x) { return usingXAndYTables(xArrComputed, yArrComputed, numEntries, x); } template double CubicInterpolation::usingXAndYTables(const double xArr[], const double yArr[], const int len, const double x) { int offset; if (x < xArr[0] || x > xArr[len-1]) { throw std::invalid_argument("x value out of range: " + std::to_string(x)); } if (x == xArr[len-1]) { // corner case return (yArr[len-1]); } offset = findStraddle(xArr, len, x); if (offset < 0 && offset > len-2) { throw std::logic_error("offset must be >= 0 and <= " + std::to_string(len) + "-2"); } if (offset == 0) { // corner case return (interpolateUsingXAndYTables(xArr, yArr, (offset-0), x)); } else if (offset == numEntries-2) { // corner case return (interpolateUsingXAndYTables(xArr, yArr, (offset-2), x)); } // main case return (interpolateUsingXAndYTables(xArr, yArr, (offset-1), x)); } // In C: again-two-registers cubic_interpolate_aux L1368 template static double interpolateUsingXAndYTables(const double xArr[], const double yArr[], const int offset, const double x) { return (cubicInterpolate(xArr[offset+0], yArr[offset+0], xArr[offset+1], yArr[offset+1], xArr[offset+2], yArr[offset+2], xArr[offset+3], yArr[offset+3], x) ); } template static inline double cubicInterpolate(const double x0, const double y0, const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x) { double l0_numer = (x - x1) * (x - x2) * (x - x3); double l1_numer = (x - x0) * (x - x2) * (x - x3); double l2_numer = (x - x0) * (x - x1) * (x - x3); double l3_numer = (x - x0) * (x - x1) * (x - x2); double l0_denom = (x0 - x1) * (x0 - x2) * (x0 - x3); double l1_denom = (x1 - x0) * (x1 - x2) * (x1 - x3); double l2_denom = (x2 - x0) * (x2 - x1) * (x2 - x3); double l3_denom = (x3 - x0) * (x3 - x1) * (x3 - x2); double term0 = y0 * l0_numer / l0_denom; double term1 = y1 * l1_numer / l1_denom; double term2 = y2 * l2_numer / l2_denom; double term3 = y3 * l3_numer / l3_denom; return (term0 + term1 + term2 + term3); } /* returns j such that xArr[j] <= x and x < xArr[j+1] */ template static int findStraddle(const double xArr[], const int len, const double x) { if ((len < 2) || (x < xArr[0]) || (x > xArr[len-1])) { throw std::logic_error("invariant violated during interpolation"); } return(recursiveFindStraddle(xArr, 0, len-1, x)); } /* the invariant here is that xArr[l] <= x && x < xArr[r] */ template static int recursiveFindStraddle(const double xArr[], const int l, const int r, const double x) { int m; if (l >= r) { throw std::logic_error("lower bound not less than upper bound in search"); } if ((xArr[l] > x) || (x >= xArr[r])) { // the invariant throw std::logic_error("target value invariant violated in search"); } if (l+1 == r) return (l); m = l + ((r-l)/2); if (xArr[m] <= x) return (recursiveFindStraddle(xArr, m, r, x)); else return (recursiveFindStraddle(xArr, l, m, x)); } //Interpolate using X table and Y stride /** * Cubic interpolation using interpolation X table and Y stride. * * @param xArr The x array * @param yStride The y stride * @param xArrLen the length of xArr * @param x The value x * @return cubic interpolation */ //In C: again-two-registers cubic_interpolate_with_x_arr_and_y_stride L1411 // Used by HllEstimators template double CubicInterpolation::usingXArrAndYStride(const double xArr[], const int xArrLen, const double yStride, const double x) { const int xArrLenM1 = xArrLen - 1; if ((xArrLen < 4) || (x < xArr[0]) || (x > xArr[xArrLenM1])) { throw std::logic_error("impossible values during interpolaiton"); } if (x == xArr[xArrLenM1]) { /* corner case */ return (yStride * (xArrLenM1)); } const int offset = findStraddle(xArr, xArrLen, x); //uses recursion const int xArrLenM2 = xArrLen - 2; if ((offset < 0) || (offset > xArrLenM2)) { throw std::logic_error("invalid offset during interpolation"); } if (offset == 0) { /* corner case */ return (interpolateUsingXArrAndYStride(xArr, yStride, (offset - 0), x)); } else if (offset == xArrLenM2) { /* corner case */ return (interpolateUsingXArrAndYStride(xArr, yStride, (offset - 2), x)); } /* main case */ return (interpolateUsingXArrAndYStride(xArr, yStride, (offset - 1), x)); } //In C: again-two-registers cubic_interpolate_with_x_arr_and_y_stride_aux L1402 template static double interpolateUsingXArrAndYStride(const double xArr[], const double yStride, const int offset, const double x) { return cubicInterpolate( xArr[offset + 0], yStride * (offset + 0), xArr[offset + 1], yStride * (offset + 1), xArr[offset + 2], yStride * (offset + 2), xArr[offset + 3], yStride * (offset + 3), x); } } #endif // _CUBICINTERPOLATION_INTERNAL_HPP_