[lmi-commits] [lmi] odd/brent a36f54b 2/8: Search for the square root of two

[Greg Chicares]

branch: odd/brent
commit a36f54ba8174eb839d766aa077b0fd1ea0659d21
Author: Gregory W. Chicares <gchicares@sbcglobal.net>
Commit: Gregory W. Chicares <gchicares@sbcglobal.net>

    Search for the square root of two
    
    Compare iterations against this published example:
      https://www.embeddedrelated.com/showarticle/855.php
    | Let’s give it a spin to find \( \sqrt{2} \):
    The trace for Chandrupatla's method matches closely, differing slightly
    only for the last two iterations, e.g.:
    | i= 9, x=1.414214, y=2.000000, err=-2.88658e-15
    compared to an error term of -2.22045e-15 in the lmi unit test. This
    example is therefore a witness supporting the hypothesis that the C++
    and python implementations are substantially the same.
    
    The 'brent' and 'genuine brent' traces are perfectly identical, and
    match the "embeddedrelated" values. Both require eight (postinitial)
    function evaluations, whereas 'chand' requires nine, so this example
    does not support a hypothesis that 'chand' is better.
---
 zero_test.cpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/zero_test.cpp b/zero_test.cpp
index 4b2d3c6..de22b9e 100644
--- a/zero_test.cpp
+++ b/zero_test.cpp
@@ -113,11 +113,11 @@ struct e_functor
 
 struct e_nineteenth
 {
-    double operator()(double z) {return std::pow(z, 19);}         // -1.0 , 4.0
+//  double operator()(double z) {return std::pow(z, 19);}         // -1.0 , 4.0
 //  double operator()(double z) {return std::cos(z) - 0.999;}     // -0.01, 0.8
 //  double operator()(double z) {return std::pow(z - 1.7, 17.0);} //  0.0 , 2.0
 //  double operator()(double z) {return std::pow((z - 1.0), 3);}  //  0.0 , 1.8
-//  double operator()(double z) {return std::pow(z, 2.0) - 2.0;}  //  0.0 , 2.0
+    double operator()(double z) {return std::pow(z, 2.0) - 2.0;}  //  0.0 , 2.0
 };
 
 /// A function that's unfriendly to the secant method.
@@ -275,8 +275,8 @@ int test_main(int, char*[])
     //   195 Brent's table 4.1 (IBM 360)
     //   171 x86_64 brent_zero (IEEE 754)
     //   169 x86_64 decimal_root (differs slightly due to rounding)
-    double lo =  -1.00;
-    double hi =   4.0 ;
+    double lo =   0.0 ;
+    double hi =   2.0 ;
 std::cout << "test genuine brent" << std::endl;
     double d = brent_zero(lo, hi, 1.0e-16, e_19);
 //  LMI_TEST(std::fabs(d) <= epsilon);