#include <series_carry_naive.hpp>

Static Public Member Functions

template<typename S , typename I > static S binpow_no_tangent (const S &me, const I &r)
static generic name ()
template<typename S > static S op (const S &x, nat r)
static syntactic op (const syntactic &x, const syntactic &r)
template<typename R , typename S > static void set_op (R &x, const S &y, nat r)
template<typename S , typename I > static S op_init (const S &x, nat r, const I &i)
static nat nr_init ()
template<typename S > static S def (const S &me, const S &a, nat r)

Detailed Description

Definition at line 390 of file series_carry_naive.hpp.

Member Function Documentation

static S binpow_no_tangent	(	const S &	me,
		const I &	r
	)		`[inline, static]`

Definition at line 394 of file series_carry_naive.hpp.

References mmx::coefficients(), default_p_expansion, I, mmx::lshiftz(), M, mmx::rshiftz(), and mmx::square().

Referenced by ser_carry_separable_root_op::def().

                                              {
    typedef Scalar_type(S) M;
    // me^r - r * (me - me[0]) * me[0]^(r-1) - me[0]^r
    //M me0= me[0]; S me1= lshiftz (me,1);
    if (r <= 1) return S (0);
    if (r == 2) return lshiftz (square (rshiftz (me, 1)), 2);

    I h= r >> 1;
    S s_h (coefficients (as<default_p_expansion(M)> (integer (h))));
    M x= me[0];
    S x_h_1= binpow (S(x), h-1);
    S y= me - me[0];
    S z= rshiftz (binpow_no_tangent (me, h), 1);
    S t0= s_h * y;
    S t1= square (rshiftz (t0 * x_h_1, 1));
    S t2= x_h_1 * z * (t0 + x);
    S w= lshiftz (square (z) + t1, 2) + lshiftz (t2 + t2, 1);
    if ((r & 1) == 1) {
      I h2= h << 1;
      S s_h2 (coefficients (as<default_p_expansion(M)> (integer (h2))));
      w= lshiftz (me * rshiftz (w, 1), 1)
        + lshiftz (s_h2 * square (rshiftz (y * x_h_1, 1)) * x, 2);
    }
    return w; }

static S def	(	const S &	me,
		const S &	a,
		nat	r
	)		`[inline, static]`

Definition at line 438 of file series_carry_naive.hpp.

References ser_carry_separable_root_op::binpow_no_tangent(), mmx::coefficients(), default_p_expansion, and M.

                                       {
    typedef Scalar_type(S) M;
    if (r == 2) {
      return ((a - S (me[0]) * me[0] - binpow_no_tangent (me, r))
              / M (r)) / me[0];
    }
    S ser_r (coefficients (as<default_p_expansion(M)> (integer (r))));
    S me_0_r_1= binpow (S (me[0]), r - 1);
    S me_0_r= me[0] * me_0_r_1;
    return (a - me_0_r - binpow_no_tangent (me, r))
      / (ser_r * me_0_r_1); }

static generic name ( ) [inline, static]

Definition at line 419 of file series_carry_naive.hpp.

{ return "separable_root"; }

static nat nr_init ( ) [inline, static]

Definition at line 435 of file series_carry_naive.hpp.

{ return 1; }

static S op	(	const S &	x,
		nat	r
	)		`[inline, static]`

Definition at line 422 of file series_carry_naive.hpp.

References mmx::separable_root().

{ return separable_root (x, r); }

static syntactic op	(	const syntactic &	x,
		const syntactic &	r
	)		`[inline, static]`

Definition at line 425 of file series_carry_naive.hpp.

                                              {
    return apply ("separable_root", x, r); }

static S op_init	(	const S &	x,
		nat	r,
		const I &	i
	)		`[inline, static]`

Definition at line 432 of file series_carry_naive.hpp.

References mmx::separable_root_init().

                                          {
    return separable_root_init (x, r, i); }

static void set_op	(	R &	x,
		const S &	y,
		nat	r
	)		`[inline, static]`

Definition at line 429 of file series_carry_naive.hpp.

References mmx::separable_root().

{ x= separable_root (y, r); }

The documentation for this struct was generated from the following file:

/Users/mourrain/Devel/mmx/algebramix/include/algebramix/series_carry_naive.hpp