[lmi-commits] [lmi] master b1b2ed4f 09/11: Revert "For immediate reversion: binary exponentiation"

[Greg Chicares]

branch: master
commit b1b2ed4fb027674e8d901ad93fb047e21d26b8ff
Author: Gregory W. Chicares <gchicares@sbcglobal.net>
Commit: Gregory W. Chicares <gchicares@sbcglobal.net>

    Revert "For immediate reversion: binary exponentiation"
    
    This reverts commit 284efedf7ad41b03c2e40221a6410caf3565b42b.
---
 sandbox_test.cpp | 94 --------------------------------------------------------
 1 file changed, 94 deletions(-)

diff --git a/sandbox_test.cpp b/sandbox_test.cpp
index 46dcacb2..6baaf4c8 100644
--- a/sandbox_test.cpp
+++ b/sandbox_test.cpp
@@ -23,101 +23,7 @@
 
 #include "test_tools.hpp"
 
-#include <cstdio>
-
-// Binary method for exponentiation.
-//
-// See Knuth, TAOCP volume 2, section 4.6.3 (p. 442 in 2nd ed.);
-// and SGI's power(), present elsewhere in the lmi sources.
-//
-// The printf statements that aren't commented out print a table
-// like Knuth's example. Enable the ones that are commented out
-// to see the details of each multiplication. Or :g/printf/d
-// to remove all that clutter.
-//
-// Knuth's algorithm takes one more multiplication for 'Y *= Z'
-// when Y has its initial value of unity. SGI refactors it to
-// avoid a goto, but the result is harder to understand.
-
-#pragma GCC diagnostic ignored "-Wunused-label"
-
-// TAOCP, volume 2, section 4.6.3, page 442
-double Algorithm_A(double x, int n)
-{
-    if(n <= 0) throw "n must be positive";
-    int mult_count {0};
-  A1:
-    int    N {n};
-    double Y {1.0};
-    double Z {x};
-    std::printf("               %3s  %7s  %7s\n"  , "N", "Y", "Z");
-    std::printf("After step A1  %3i  %7.f  %7.f\n",  N,   Y,   Z );
-  A2: // [Halve N.] (At this point, x^n = Y * Z^N .)
-    bool was_even = 0 == N % 2;
-    N /= 2; // integer division truncates
-    if(was_even) goto A5;
-  A3: // [Multiply Y by Z.]
-// std::printf("multiply #%i %7.f by %7.f yielding %7.f\n", mult_count, Y, Z, 
Y*Z);
-    Y *= Z;
-    ++mult_count;
-  A4: // [N == 0?]
-    std::printf("After step A4  %3i  %7.f  %7.f\n",  N,   Y,   Z );
-    if(0 == N)
-        {
-        std::printf("Algorithm A: %i multiplications\n", mult_count);
-        return Y;
-        }
-  A5: // [Square Z.]
-//std::printf("multiply #%i %7.f by %7.f yielding %7.f\n", mult_count, Z, Z, 
Z*Z);
-    Z *= Z;
-    ++mult_count;
-    goto A2;
-}
-
-// SGI extension to STL, somewhat refactored for clarity
-double power(double x, int n)
-{
-    if(n < 0)
-        {
-        throw std::logic_error("power() called with negative exponent.");
-        }
-
-    int mult_count {0};
-    while(0 == n % 2) // while ((n & 1) == 0)
-        {
-        n /= 2; // n >>= 1;
-// std::printf("multiply #%i %7.f by %7.f yielding %7.f\n", mult_count, x, x, 
x*x);
-        x *= x;
-        ++mult_count;
-std::printf("After step B1 %3i  %7.f\n", n, x);
-        }
-    double result = x;
-    n /= 2; // n >>= 1;
-    while (n != 0)
-        {
-// std::printf("multiply #%i %7.f by %7.f yielding %7.f\n", mult_count, x, x, 
x*x);
-        x *= x;
-        ++mult_count;
-std::printf("After step B2 %3i  %7.f\n", n, x);
-        if(0 != n % 2) // if((n & 1) != 0)
-            {
-// std::printf("multiply #%i %7.f by %7.f yielding %7.f\n", mult_count, 
result, x, result*x);
-            result *= x;
-            ++mult_count;
-            }
-        n /= 2; // n >>= 1;
-        }
-std::printf("power(): %i multiplications\n", mult_count);
-    return result;
-}
-
 int test_main(int, char*[])
 {
-    LMI_TEST(8388608 == Algorithm_A(2.0, 23));
-    LMI_TEST(8388608 == power      (2.0, 23));
-
-    LMI_TEST(2 * 8388608 == Algorithm_A(2.0, 24));
-    LMI_TEST(2 * 8388608 == power      (2.0, 24));
-
     return 0;
 }