diff --git a/include/eve/module/contfrac/impl/lentz.hpp b/include/eve/module/contfrac/impl/lentz.hpp
index e623e589ce..6e242aeb7d 100644
--- a/include/eve/module/contfrac/impl/lentz.hpp
+++ b/include/eve/module/contfrac/impl/lentz.hpp
@@ -92,7 +92,7 @@ namespace eve::detail
     using r_t = std::decay_t<tmp_t>;
     using u_t =   underlying_type_t<r_t>;
     u_t tiny = 16*smallestposval(as<u_t>()) ;
-    u_t terminator(eps <= 0 ? 16*eve::eps(as<u_t>()) : u_t(eps));
+    u_t terminator(eps <= 0 ? eve::abs(eps)*eve::eps(as<u_t>()) : u_t(eps));
     size_t counter(max_terms);
 
     r_t f{};
@@ -150,7 +150,7 @@ namespace eve::detail
     using r_t = std::decay_t<tmp_t>;
     using u_t =   underlying_type_t<r_t>;
     u_t tiny = 16*smallestposval(as<u_t>()) ;
-    u_t terminator(eps <= 0 ? 16*eve::eps(as<u_t>()) : u_t(eps));
+    u_t terminator(eps <= 0 ? eve::abs(eps)*eve::eps(as<u_t>()) : u_t(eps));
     size_t counter(max_terms);
 
     r_t f{};
diff --git a/include/eve/module/contfrac/lentz_a.hpp b/include/eve/module/contfrac/lentz_a.hpp
index a2966aef4d..601e9e5c4a 100644
--- a/include/eve/module/contfrac/lentz_a.hpp
+++ b/include/eve/module/contfrac/lentz_a.hpp
@@ -28,35 +28,32 @@ namespace eve
 //!   @code
 //!   namespace eve
 //!   {
-//!     template< typename Gen, eve::floating_value T>
-//!     T lentz_a(Gen g, const T& eps, size_t & max_terms) noexcept;
+//!     template< typename Gen, eve::scalar_ordered_value T> auto lentz_a(Gen g, const T& tol, size_t & max_terms) noexcept;
 //!   }
 //!   @endcode
 //!
 //!   **Parameters**
 //!
 //!     * `g`   : generator function.
-//!     * `eps` : tolerance value.
+//!     * `tol` : tolerance value. If negative the effective tolerance will be abs(tol)*eve::eps(as(< u_t>)
+//!               where u_t is the underlying floating type  associated to the return type of the invocable g.
 //!     * `max_terms` : no more than max_terms calls to the generator will be made,
 //!
-//!   The generator type should be a function object which supports the following operations:
-//!   *  Gen::result_type : The type that is the result of invoking operator().
-//!     This can be either an arithmetic or complex type,
-//!      or a std::tuple of two floating values
-//!   *  The call to g()  returns an object of type Gen::result_type.
-//!      Each time this operator is called then the next pair of a and b values is returned.
-//!      Or, if result_type is not a pair type, then the next b value
-//!      is returned and all the a values are assumed to be 1.
+//!   The generator type should be an invocable which supports the following operations:
+//!   *  The call to g()  returns a floating value or a pair (kumi::tuple) of such.
+//!      Each time this operator is called then the next pair of a and b values has to be returned, 
+//!      or, if result_type is not a pair type, then the next b value
+//!      has to be returned and all the a values are assumed to be equal to one.
 //!
-//!   * In all the continued fraction evaluation functions the tolerance parameter
-//!     is the precision desired in the result,
-//!     evaluation of the fraction will continue until the last term evaluated leaves
-//!     the relative error in the result less than tolerance.
+//!   *  In all the continued fraction evaluation functions the effective tol parameter
+//!      is the relative precision desired in the result,
+//!      The evaluation of the fraction will continue until the last term evaluated leaves
+//!      the relative error in the result less than tolerance or the max_terms iteration is reached.
 //!
 //!   **Return value**
 //!
 //!     The value of the continued fraction is returned.
-//!     \f$\displaystyle \frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\cdots\vphantom{\frac{1}{1}} }}}\f$
+//!     \f$\displaystyle \frac{a_0}{b_0+\frac{a_1}{b_1+\frac{a_2}{b_2+\cdots\vphantom{\frac{1}{1}} }}}\f$
 //!
 //!   @groupheader{Example}
 //!
diff --git a/include/eve/module/contfrac/lentz_b.hpp b/include/eve/module/contfrac/lentz_b.hpp
index aeda38e556..80865ca676 100644
--- a/include/eve/module/contfrac/lentz_b.hpp
+++ b/include/eve/module/contfrac/lentz_b.hpp
@@ -28,36 +28,38 @@ namespace eve
 //!   @code
 //!   namespace eve
 //!   {
-//!     template< typename Gen, eve::floating_value T>
-//!     T lentz_b(Gen g, const T& eps, size_t & max_terms) noexcept;
+//!     template< typename Gen, eve::floating_value T> auto lentz_b(Gen g, const T& tol, size_t & max_terms) noexcept;
 //!   }
 //!   @endcode
 //!
 //!   **Parameters**
 //!
 //!     * `g`   : generator function.
-//!     * `eps` : tolerance value.
-//!     * `max_terms` : no more than max_terms calls to the generator will be made,
+//!     * `tol` : tolerance value. If negative the effective tolerance will be abs(tol)*eve::eps(as(< u_t>)
+//!               where u_t is the underlying floating type associated to the return type of the invocable g.
+//!     * `max_terms` : no more than max_terms calls to the generator will be made.
 //!
-//!   The generator type should be a function object which supports the following operations:
-//!   *  Gen::result_type : The type that is the result of invoking operator().
-//!     This can be either an arithmetic or complex type,
-//!      or a std::tuple of two floating values
-//!   *  The call to g()  returns an object of type Gen::result_type.
-//!      Each time this operator is called then the next pair of a and b values is returned.
-//!      Or, if result_type is not a pair type, then the next b value
-//!      is returned and all the a values are assumed to be 1.
+//!   The generator type should be an invocable  which supports the following operations:
+//!   *  The call to g()  returns a floating  value or a pair (kumi::tuple) of such.
+//!      Each time this operator is called then the next pair of a and b values  has to be returned,
+//!      or, if result_type is not a pair type, then the next b value
+//!       has to be returned and all the a values are assumed to be equal to one.
 //!
-//!   * In all the continued fraction evaluation functions the tolerance parameter
-//!     is the precision desired in the result,
-//!     evaluation of the fraction will continue until the last term evaluated leaves
-//!     the relative error in the result less than tolerance.
+//!   * In all the continued fraction evaluation functions the  effective tol parameter
+//!     is the relative precision desired in the result,
+//!     The evaluation of the fraction will continue until the last term evaluated leaves
+//!     the relative error in the result less than tolerance or the max_terms iteration is reached.
 //!
 //!   **Return value**
 //!
 //!     The value of the continued fraction is returned.
 //!     \f$\displaystyle b_0+\frac{a_1}{b_1+\frac{a_2}{b_2+\frac{a_3}{b_3+\cdots\vphantom{\frac{1}{1}} }}}\f$
 //!
+//!     Note that the the first a value (a0) generated is not used here.
+//!
+//!   @note the implementation is largely inspired by the boost/math/fraction one, with less requirements on the invocable.
+//!         Peculiarly lambda functions can be used.
+//!
 //!   @groupheader{Example}
 //!
 //!   @godbolt{doc/polynomial/regular/lentz_b.cpp}