// UDS_to_digits().
// General includes.
#include "cl_sysdep.h"
// Specification.
#include "cl_I.h"
// Implementation.
#include "cl_DS.h"
#include "cl_I_cached_power.h"
namespace cln {
// Timing für Dezimal-Umwandlung einer Zahl mit N Digits = (N*32) Bits,
// auf einem i486 33 MHz unter Linux:
// N standard dnq(div) dnq(mul) combined
// 10 0.00031 0.00043 0.00059 0.00031
// 25 0.00103 0.00125 0.00178 0.00103
// 50 0.0030 0.0034 0.0051 0.0030
// 100 0.0100 0.0108 0.0155 0.0100
// 250 0.054 0.055 0.064 0.054
// 500 0.207 0.209 0.229 0.207
// 750 0.47 0.48 0.47 0.47
// 1000 0.81 0.81 0.86 0.81
// 1250 1.25 1.12 1.20 1.12
// 1500 1.81 1.60 1.64 1.61
// 1750 2.45 2.24 2.15 2.25
// 1940 3.01 3.03 3.12 2.80
// 2000 3.20 3.11 3.30 2.89
// 2500 5.00 4.11 4.38 3.91
// 3000 7.3 5.8 5.7 5.5
// 4000 13.0 12.4 12.9 9.7
// 5000 20.3 15.3 15.1 12.4
// 10000 81.4 57.8 56.4 32.5
// 25000 112
// 50000 265
// dnq(div) means divide-and-conquer using division by B at the topmost call,
// threshold = 1015.
// dnq(mul) means divide-and-conquer using multiplication by 1/B at the topmost
// call, threshold = 2050.
// combined means divide-and-conquer as long as length >= threshold.
const unsigned int cl_digits_div_threshold = 1015;
const int cl_digits_algo = 1;
// like I_to_digits, except that the result has exactly erg_len characters.
static inline void I_to_digits_noshrink (const cl_I& X, uintD base, uintL erg_len, cl_digits* erg)
{
I_to_digits(X,base,erg);
if (erg->len > erg_len) cl_abort();
var uintL count = erg_len - erg->len;
if (count > 0)
{ var uintB* ptr = erg->MSBptr;
do { *--ptr = '0'; } while (--count > 0);
erg->MSBptr = ptr; erg->len = erg->len;
}
}
void I_to_digits (const cl_I& X, uintD base, cl_digits* erg)
{
// Methode:
// Umwandlung ins Stellensystem der Basis b geht durch Umwandlung ins Stellen-
// system der Basis b^k (k>=1, b^k<2^intDsize, k maximal) vor sich.
// Aufsuchen von k und b^k aus einer Tabelle.
// Reduktion der UDS zu einer NUDS X.
// Falls X=0: die eine Ziffer 0.
// Falls X>0:
// Dividiere X durch das Wort b^k,
// (Single-Precision-Division, vgl. UDS_DIVIDE mit n=1:
// r:=0, j:=m=Länge(X),
// while j>0 do
// j:=j-1, r:=r*beta+X[j], X[j]:=floor(r/b^k), r:=r-b^k*q[j].
// r=Rest.)
// zerlege den Rest (mit k-1 Divisionen durch b) in k Ziffern, wandle diese
// Ziffern einzeln in Ascii um und lege sie an die DIGITS an.
// Teste auf Speicherüberlauf.
// X := Quotient.
// Mache aus X wieder eine NUDS (maximal 1 Nulldigit streichen).
// Dies solange bis X=0.
// Streiche die führenden Nullen.
// Aufsuchen von k-1 und b^k aus der Tabelle:
var const power_table_entry* tableptr = &power_table[base-2];
var uintC k = tableptr->k;
var uintD b_hoch_k = tableptr->b_to_the_k; // b^k
var uintB* erg_ptr = erg->LSBptr;
#define next_digit(d) { *--erg_ptr = (d<10 ? '0'+d : 'A'-10+d); }
// Spezialfälle:
if (zerop(X))
{ next_digit(0); goto fertig; } // 0 -> eine Ziffer '0'
else if ((base & (base-1)) == 0)
{ // Schneller Algorithmus für Zweierpotenzen
var const uintD* MSDptr;
var uintC len;
var const uintD* LSDptr;
I_to_NDS_nocopy(X, MSDptr=,len=,LSDptr=,cl_false,);
var int b = (base==2 ? 1 : base==4 ? 2 : base==8 ? 3 : base==16 ? 4 : /*base==32*/ 5);
var uintD carry = 0;
var int carrybits = 0;
loop
{ if (fixnump(X) && erg->LSBptr-erg_ptr>=cl_value_len)
break;
if (carrybits >= b)
{ var uintD d = carry & (base-1);
next_digit(d);
carry = carry >> b; carrybits -= b;
}
else
{ var uintD d = carry;
if (LSDptr != MSDptr)
{ carry = lsprefnext(LSDptr);
d |= (carry << carrybits) & (base-1);
next_digit(d);
carry = carry >> (b-carrybits); carrybits = intDsize - (b-carrybits);
}
else
{ next_digit(d); break; }
}
}
}
else if (fixnump(X) || TheBignum(X)->length < cl_digits_div_threshold
|| !cl_digits_algo)
{ // Standard-Algorithmus
CL_ALLOCA_STACK;
var uintD* MSDptr;
var uintC len;
var uintD* LSDptr;
I_to_NDS(X, MSDptr=,len=,LSDptr=);
// normalisiere zu einer NUDS:
if (mspref(MSDptr,0)==0) { msshrink(MSDptr); len--; }
loop
{ // Noch die NUDS MSDptr/len/.. mit len>0 abzuarbeiten.
// Single-Precision-Division durch b^k:
var uintD rest = divu_loop_msp(b_hoch_k,MSDptr,len);
// Zerlegen des Restes in seine k Ziffern:
var uintC count = k-1;
if (fixnump(X) && count>cl_value_len-1)
count = cl_value_len-1;
if ((intDsize>=11) || (count>0))
// (Bei intDsize>=11 ist wegen b<=36 zwangsläufig
// k = ceiling(intDsize*log(2)/log(b))-1 >= 2, also count = k-1 > 0.)
do { var uintD d;
#if HAVE_DD
divuD((uintDD)rest,base,rest=,d=);
#else
divuD(0,rest,base,rest=,d=);
#endif
next_digit(d);
} until (--count == 0);
next_digit(rest); // letzte der k Ziffern ablegen
// Quotienten normalisieren (max. 1 Digit streichen):
if (mspref(MSDptr,0)==0) { msshrink(MSDptr); len--; if (len==0) break; }
} }
else
{ // Divide-and-conquer:
// Find largest i such that B = base^(k*2^i) satisfies B <= X.
// Divide by B: X = X1*B + X0. Convert X0 to string, fill up
// for k*2^i characters, convert X1 to string. (Have to convert
// X0 first because the conversion may temporarily prepend some
// zero characters.)
var uintL ilen_X = integer_length(X);
var const cached_power_table_entry * p;
var uintL ilen_B;
var uintL i;
for (i = 0; ; i++)
{ p = cached_power(base,i);
ilen_B = integer_length(p->base_pow);
if (2*ilen_B >= ilen_X) break;
// 2*ilen_B < ilen_X, so certainly B^2 < X, let's continue with i+1.
}
// 2*ilen_B >= ilen_X, implies X < 2*B^2.
// Of course also X >= B, implies ilen_X >= ilen_B.
#ifdef MUL_REPLACES_DIV
// Divide by B by computing
// q := floor((X * floor(2^ilen_X/B)) / 2^ilen_X).
// We have q <= floor(X/B) <= q+1, so we may have to increment q.
// Note also that
// floor(2^ilen_X/B) = floor(floor(2^(2*ilen_B)/B)/2^(2*ilen_B-ilen_X))
var cl_I q = (X * (p->inv_base_pow >> (2*ilen_B-ilen_X))) >> ilen_X;
var cl_I r = X - q * p->base_pow;
if (r < 0) cl_abort();
if (r >= p->base_pow)
{ q = q+1; r = r - p->base_pow;
if (r >= p->base_pow) cl_abort();
}
#else
var cl_I_div_t q_r = floor2(X,p->base_pow);
var const cl_I& q = q_r.quotient;
var const cl_I& r = q_r.remainder;
#endif
var const cl_I& X1 = q;
var const cl_I& X0 = r;
var uintL B_baselen = (uintL)(k)<<i;
I_to_digits_noshrink(X0,base,B_baselen,erg);
erg->LSBptr -= B_baselen;
I_to_digits(X1,base,erg);
erg->LSBptr += B_baselen;
erg_ptr = erg->MSBptr;
}
#undef next_digit
// Streiche führende Nullen:
while (*erg_ptr == '0') { erg_ptr++; }
fertig:
erg->MSBptr = erg_ptr;
erg->len = erg->LSBptr - erg_ptr;
}
// Bit complexity (N := length(X)): O(log(N)*M(N)).
} // namespace cln
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