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/*
* Copyright (C) 2000, Imperial College
*
* This file is part of the Imperial College Exact Real Arithmetic Library.
* See the copyright notice included in the distribution for conditions
* of use.
*/
#include <stdio.h>
#include "real.h"
#include "real-impl.h"
#include <math.h>
/*
* This is the toplevel function called by the user to force information
* from a real stream.
*/
void
force_R_Digs(Real x, int digitsNeeded)
{
DigsX *digsX;
void runStack();
void force_To_Alt_Entry();
if (x->gen.tag.type == ALT) {
if (x->alt.redirect == NULL) {
PUSH_2(force_To_Alt_Entry, x);
runStack();
}
force_R_Digs(x->alt.redirect, digitsNeeded);
return;
}
if (x->gen.tag.type == CLOSURE) {
if (x->cls.redirect == NULL) {
PUSH_2(x->cls.force, x);
runStack();
}
force_R_Digs(x->cls.redirect, digitsNeeded);
return;
}
x = makeStream(x);
/*
* So now we know that x is a real stream. If x is signed and
* the sign has not been determined, we force it.
*/
if (x->gen.tag.type == SIGNX) {
if (x->signX.tag.value == SIGN_UNKN) {
PUSH_2(x->signX.force, x);
runStack();
}
digsX = (DigsX *) x->signX.x;
}
else
digsX = (DigsX *) x;
if (digsX->tag.type != DIGSX)
Error(FATAL, E_INT, "force_R_Digs", "badly formed real");
/*
* Now, if there is not enough information available, we force
* the number of digits needed.
*/
if (digsX->count < (unsigned int)digitsNeeded) {
PUSH_3(digsX->force, digsX, digitsNeeded - digsX->count);
runStack();
}
}
/* force_R_Dec
* July 2000, Marko Krznaric
*
* force_R_Digs(x,digitsNeeded) is a function which forces an
* emission of digitsNeeded digit matrices from x (of the
* type Real).
*
* On the other hand, force_R_Dec(x,decimalPrecision) guarantees
* that enough digit matrices, say digitsNeeded, will be emitted
* from a real number x in order to have required absolute
* decimal precision, i.e. it guarantees that the result will be
* accurate within 10^(-decimalPrecision).
*
* NOTES:
* - initGuess = an initial guess (minimum number) of digit
* matrices which has to be emitted from a real number x.
* - digitsNeeded = number of digit matrices required.
* - e = number of 'bad' digits.
* - using function retrieveInfo, we can extract the sign (=sign),
* the number of digits emitted so far (=count) and the
* compressed digits (=digits) for a Real x.
* - 3.322 = an upper bound for log2(10).
*
*
* PROBLEMS:
* - should decimalPrecision & digitsNeeded be of type long int?
*
*/
void
force_R_Dec(Real x, int decimalPrecision)
{
int initGuess = ceil(3.322 * decimalPrecision) + 2;
int digitsNeeded;
int e = 0;
mpz_t digits;
Sign sign;
int count;
mpz_init(digits);
digitsNeeded = initGuess;
force_R_Digs(x, digitsNeeded);
retrieveInfo(x, &sign, &count, digits);
switch (sign) {
case SZERO:
/*
* SZERO: every digit matrix will half the interval
* (starting with [-1,1]). Easy to determine digitsNeeded.
*/
digitsNeeded = initGuess - 1;
break;
case SPOS:
case SNEG:
/*
* SPOS, SNEG: e, the number of 'bad' digits is actually
* the number of leading 1s in the binary representation
* of digits (the value of compressed digits).
*/
while (digitsNeeded < forceDecUpperBound) {
force_R_Digs(x, digitsNeeded);
retrieveInfo(x, &sign, &count, digits);
if (sign == SNEG)
mpz_neg(digits, digits);
e = leadingOnes (digits);
digitsNeeded = 2 * e + 2 + initGuess;
if (count > e)
/* not all of the extracted digit matrices are 'bad',
* i.e. the interval is bounded. Therefore, we can
* leave the loop.
*/
break;
}
if (digitsNeeded >= forceDecUpperBound)
Error(FATAL, E_INT, "force_R_Dec",
"forceDecUpperBound reached (1)");
break;
case SINF:
/* SINF: we are still dealing with the unbounded interval,
* i.e. the interval contains infinity, as far as digits
* (the value of compressed digits matrices) is either
* -1, 0 or 1. As soon as we get something greater (in
* absolute value) than 1, the interval doesn't contain
* the infinity, and we can calculate digitsNeeded.
*/
while (digitsNeeded < forceDecUpperBound) {
force_R_Digs(x, digitsNeeded);
retrieveInfo(x, &sign, &count, digits);
if (mpz_cmpabs_ui(digits, 1) > 0) {
e = count - mpz_sizeinbase(digits, 2);
digitsNeeded = 2 * e + 2 + initGuess;
break;
}
else {
e = count;
digitsNeeded = 2 * e + 2+ initGuess;
}
}
if (digitsNeeded >= forceDecUpperBound)
Error(FATAL, E_INT, "force_R_Dec",
"forceDecUpperBound reached (2)");
break;
case SIGN_UNKN:
Error(FATAL, E_INT, "force_R_Dec", "argument is signed");
break;
default:
Error(FATAL, E_INT, "force_R_Dec", "bad sign");
break;
}
force_R_Digs(x, digitsNeeded);
mpz_clear(digits);
}
/* leadingOnes
* July 2000, Marko Krznaric
*
* For input variable c (of type mpz_t) check how many 1s
* are leading the binary representation of c.
*
* We use this function as an auxiliary function to
* force_R_Dec. We have to check how many D+ (D-) digit
* matrices follow S+ (S-). This seems to be the fastest
* way to do it.
*
* If c is zero or negative - result = 0.
* If there are no zeros at all - result = binary size of c.
* Otherwise, we scan from left-most digit and count until
* we reach 0.
*
* NOTES:
* - The index of the right-most digit is 0, while the index
* of the left-most digit is (size-1).
*/
int
leadingOnes(mpz_t c)
{
int size = mpz_sizeinbase(c,2);
int i;
int count = 0;
if (mpz_sgn(c) <= 0)
return 0;
if (mpz_scan0(c, 0) == (long unsigned int)size)
return size;
for (i = size - 1; i >= 0; i--) {
if (mpz_scan1(c, i) == (long unsigned int)i)
count++;
else
return count;
}
return 0;
}
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