Square Root Function: That Scales The Kernel

The sqrt function below uses the sqrt_kernel and findExponent functions from previous posts. Note that my actual implementation is placed in a namespace so the system sqrt will not be picked up or conflict.

#include <boost/assert.hpp>  
   
 typedef double type_t;  
 const type_t epsilon = 1e-15;  
 const type_t ten   = 10;  
   
 type_t  
 pow10(type_t value){  
   return pow( ten, value );  
 }  
   
 type_t  
 sqrt(type_t n, type_t eps = epsilon) {  
   BOOST_ASSERT(n >= 0);  
   if(n == 0) return 0.0;  
   
   type_t ScalingExponent = findExponent(n);  
   n *= pow10(-ScalingExponent);  
   
   type_t result = sqrt_kernel(n,eps);  
   
   type_t Exponent = findExponent(result);  
   return result * pow10( -Exponent + (ScalingExponent/2) );  
 }