ser_carry_separable_root_op Struct Reference

#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 391 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 395 of file series_carry_naive.hpp.

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

00396 00397 00398 00399 00400 00401 00402 00403 00404 00405 00406 00407 00408 00409 00410 00411 00412 00413 00414 00415 00416 00417     } 00418

class="fragment">00395 { 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 439 of file series_carry_naive.hpp.

References binpow(), mmx::coefficients(), default_p_expansion, and M.

00439                                        {
00440     typedef Scalar_type(S) M;
00441     if (r == 2) {
00442       return ((a - S (me[0]) * me[0] - binpow_no_tangent (me, r))
00443               / M (r)) / me[0];
00444     }
00445     S ser_r (coefficients (as<default_p_expansion (M)> (integer (r))));
00446     S me_0_r_1= binpow (S (me[0]), r - 1);
00447     S me_0_r= me[0] * me_0_r_1;
00448     return (a - me_0_r - binpow_no_tangent (me, r))
00449       / (ser_r * me_0_r_1); }

static generic name ( ) [inline, static]

Definition at line 420 of file series_carry_naive.hpp.

00420 { return "separable_root"; }

static nat nr_init ( ) [inline, static]

Definition at line 436 of file series_carry_naive.hpp.

00436 { return 1; }

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

Definition at line 426 of file series_carry_naive.hpp.

00426                                               {
00427     return apply ("separable_root", x, r); }

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

Definition at line 423 of file series_carry_naive.hpp.

References mmx::separable_root().

00423 { return separable_root (x, r); }

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

Definition at line 433 of file series_carry_naive.hpp.

References mmx::separable_root_init().

00433                                           {
00434     return separable_root_init (x, r, i); }

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

Definition at line 430 of file series_carry_naive.hpp.

References mmx::separable_root().

00430 { x= separable_root (y, r); }

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

include/algebramix/series_carry_naive.hpp