rotmg.hpp

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//
// Copyright (c) 2017-2021, University of Tennessee. All rights reserved.
// Copyright (c) 2025, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_BLAS_ROTMG_HH
#define TLAPACK_BLAS_ROTMG_HH
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
 
template <TLAPACK_REAL T,
          enable_if_t<is_real<T>, int> = 0,
          disable_if_allow_optblas_t<T> = 0>
int rotmg(T& d1, T& d2, T& a, const T& b, T h[4])
{
    // check arguments
    tlapack_check_false(d1 <= 0);
 
    // Constants
    const T zero(0);
    const T one(1);
    const T gam(4096);
    const T gamsq = gam * gam;
    const T rgamsq = one / gamsq;
 
    int flag;
    h[0] = zero;
    h[1] = zero;
    h[2] = zero;
    h[3] = zero;
 
    if (d1 < zero) {
        flag = -1;
        d1 = zero;
        d2 = zero;
        a = zero;
    }
    else {
        const T p2 = d2 * b;
        if (p2 == zero) {
            flag = -2;
        }
        else {
            const T p1 = d1 * a;
            const T q2 = p2 * b;
            const T q1 = p1 * a;
 
            if (abs(q1) > abs(q2)) {
                flag = zero;
                h[1] = -b / a;
                h[2] = p2 / p1;
                const T u = one - h[2] * h[1];
                if (u > zero) {
                    d1 /= u;
                    d2 /= u;
                    a *= u;
                }
            }
            else if (q2 < zero) {
                flag = -1;
                d1 = zero;
                d2 = zero;
                a = zero;
            }
            else {
                flag = 1;
                h[0] = p1 / p2;
                h[3] = a / b;
                const T u = one + h[0] * h[3];
                const T stemp = d2 / u;
                d2 = d1 / u;
                d1 = stemp;
                a = b * u;
            }
 
            if (d1 != zero) {
                while ((d1 <= rgamsq) || (d1 >= gamsq)) {
                    if (flag == 0) {
                        h[0] = one;
                        h[3] = one;
                        flag = -1;
                    }
                    else {
                        h[1] = -one;
                        h[2] = one;
                        flag = -1;
                    }
                    if (d1 <= rgamsq) {
                        d1 *= gam * gam;
                        a /= gam;
                        h[0] /= gam;
                        h[2] /= gam;
                    }
                    else {
                        d1 /= gam * gam;
                        a *= gam;
                        h[0] *= gam;
                        h[2] *= gam;
                    }
                }
            }
 
            if (d2 != zero) {
                while ((abs(d2) <= rgamsq) || (abs(d2) >= gamsq)) {
                    if (flag == 0) {
                        h[0] = one;
                        h[3] = one;
                        flag = -1;
                    }
                    else {
                        h[1] = -one;
                        h[2] = one;
                        flag = -1;
                    }
                    if (abs(d2) <= rgamsq) {
                        d2 *= gam * gam;
                        h[1] /= gam;
                        h[3] /= gam;
                    }
                    else {
                        d2 /= gam * gam;
                        h[1] *= gam;
                        h[3] *= gam;
                    }
                }
            }
        }
    }
 
    return flag;
}
 
#ifdef TLAPACK_USE_LAPACKPP
 
template <TLAPACK_REAL T,
          enable_if_t<is_real<T>, int> = 0,
          enable_if_allow_optblas_t<T> = 0>
int rotmg(T& d1, T& d2, T& a, const T b, T h[4])
{
    T param[5];
    ::blas::rotmg(&d1, &d2, &a, b, param);
 
    // Collect the output
    h[0] = param[1];
    h[1] = param[2];
    h[2] = param[3];
    h[3] = param[4];
 
    return param[0];
}
 
#endif
 
}  // namespace tlapack
 
#endif  //  #ifndef TLAPACK_BLAS_ROTMG_HH