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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-lib.h"
void log2Cont();
void logInside();
void logLow();
void logHigh();
/*
* This diverges when the argument is zero.
*/
Real
log_R(Real x)
{
Bool xGtEq0, xLtEq2, xGtEqOneHalf, xLtEq2_and_GtEqOneHalf;
Bool xLtEqOverOneHalf_and_GtEq0;
Real in, low, high, ltZero;
static int doneInit = 0;
if (!doneInit) {
registerForceFunc(logInside, "logInside", 2);
registerForceFunc(logLow, "logLow", 2);
registerForceFunc(logHigh, "logHigh", 2);
registerForceFunc(log2Cont, "log2Cont", 3);
doneInit++;
}
xGtEq0 = gtEq_R_0(x);
xLtEq2 = ltEq_R_QInt(x, 2, 1);
xGtEqOneHalf = gtEq_R_QInt(x, 1, 2);
xLtEq2_and_GtEqOneHalf = and_B_B(xLtEq2, xGtEqOneHalf);
xLtEqOverOneHalf_and_GtEq0 = and_B_B(ltEq_R_QInt(x, 1001, 2000), xGtEq0);
in = (Real) allocCls(logInside, (void *) x);
in->cls.tag.isSigned = TRUE;
low = (Real) allocCls(logLow, (void *) x);
low->cls.tag.isSigned = TRUE;
high = (Real) allocCls(logHigh, (void *) x);
high->cls.tag.isSigned = TRUE;
ltZero = realError("(log_R x) and x < 0");
return realIf(4,
xLtEq2_and_GtEqOneHalf, in,
gtEq_R_QInt(x, 1999, 1000), high,
xLtEqOverOneHalf_and_GtEq0, low,
not_B(xGtEq0), ltZero);
}
static TenXY *nextTensor(Real, Real, int);
void
logInside()
{
Cls *cls, *newCls;
ClsData *data;
Real x;
void stdTensorCont();
cls = (Cls *) POP;
x = (Real) cls->userData;
if ((data = (ClsData *) malloc(sizeof(ClsData))) == NULL)
Error(FATAL, E_INT, "logInside", "malloc failed");
data->n = 1;
data->x = x;
data->nextTensor = nextTensor;
newCls = allocCls(stdTensorCont, (void *) data);
newCls->tag.isSigned = FALSE;
cls->redirect = tensor_Int(x, (Real) newCls, 1, 0, 1, 1, -1, 1, -1, 0);
#ifdef DAVINCI
beginGraphUpdate();
newEdgeToOnlyChild(newCls, x);
drawEqEdge(cls, cls->redirect);
endGraphUpdate();
#endif
}
void
logHigh()
{
Cls *cls, *newCls;
Real w, x;
cls = (Cls *) POP;
x = (Real) cls->userData;
w = div_R_Int(x, 2);
w = log_R(w);
newCls = allocCls(log2Cont, (void *) 0);
newCls->tag.isSigned = FALSE;
w = add_R_R(w, (Real) newCls);
w->tenXY.forceY = log2Cont; /* see the note below */
/* now guard tensor to prevent it being copied */
cls->redirect = (Real) allocSignX(w, SIGN_UNKN);
}
void
logLow()
{
Cls *cls, *newCls;
Real w, x;
cls = (Cls *) POP;
x = (Real) cls->userData;
w = mul_R_Int(x, 2);
w = log_R(w);
newCls = allocCls(log2Cont, (void *) 0);
newCls->tag.isSigned = FALSE;
w = sub_R_R(w, (Real) newCls);
w->tenXY.forceY = log2Cont; /* see the note below */
/* now guard tensor to prevent it being copied */
cls->redirect = (Real) allocSignX(w, SIGN_UNKN);
}
/*
* This closure works a little different from most. Most simply create
* an lft and set the redirect field of the closure to point to the new
* heap object. In this case, we can do a bit better. This continuation
* represents (log 2). One option would be to follow the usual strategy
* and to arrange for (log 2) to be shared whenever possible. However,
* we know that this is used internally to log_R only and only in
* those circumstances when the argument falls outside the working range
* of the log tensor chain. Moreover, we know that the consumer of this
* real is either an addition or substraction tensor. Whatever it is,
* it is certain to be a tensor. The other argument of the tensor will
* reduce at most to a matrix and hence the tensor itself will never
* reduce.
*
* This property allows us to adopt a different strategy. Rather than create
* the next matrix in the (log 2) chain, we put the matrix directly into
* the consuming tensor. This avoids creating garbage in the stack and
* avoids a separate reduction step.
*
* There is a slighlt better scheme than this. Rather than plunk in
* each successive
* matrix into the tensor (each providing 4 digits), it would be better
* to accumulate a sequence of matrices (up to the capacity of a small matrix)
* and then plunk it into the tensor. This would avoid using bignum stuff until
* it becomes necessary. Perhaps I'll do this later.
*
* For this it is useful to bear in mind that when a sequence of matrices
* starts from n = 0, then the largest entry is always d. When the sequence
* starts with n > 0, then the largest entry is c. To decide if there
* is going to be an overflow, it suffices to check if c (for example)
* will overflow.
*/
static void nextMatrix(Tensor, int);
void
log2Cont()
{
TenXY *tenXY;
Cls *cls;
int digitsNeeded;
int n;
tenXY = (TenXY *) POP;
digitsNeeded = POP;
cls = (Cls *) tenXY->y;
n = (int) cls->userData;
while (digitsNeeded > 0) {
nextMatrix(tenXY->ten, n);
if (n == 0)
digitsNeeded -= 2;
else
digitsNeeded -= 4;
n += 1;
}
cls->userData = (void *) n;
}
/*
* We set a rather arbitrary (but large) limit on the value of n
* for log 2. On a 32 bit machine it is 536,870,911.
* Larger than this and the matrix entries are no longer small.
*/
static void
nextMatrix(Tensor ten, int n)
{
SmallMatrix smallMat;
if (n == 0) {
smallMat[0][0] = 1;
smallMat[0][1] = 1;
smallMat[1][0] = 1;
smallMat[1][1] = 2;
}
else {
if (n <= (MAXINT - 2) / 4) {
smallMat[0][0] = 3 * n + 1;
smallMat[0][1] = 2 * n + 1;
smallMat[1][0] = 4 * n + 2;
smallMat[1][1] = 3 * n + 2;
}
else
Error(FATAL, E_INT, "nextMatrix (log2)",
"n > %d", (MAXINT - 2) / 4);
}
multVectorPairTimesSmallMatrix(ten[0], ten[1], smallMat);
multVectorPairTimesSmallMatrix(ten[2], ten[3], smallMat);
normalizeTensor(ten);
}
static TenXY *
nextTensor(Real x, Real y, int n)
{
return (TenXY *) tensor_Int(x, y, n, 0, 2*n+1, n+1, n+1, 2*n+1, 0, n);
}
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