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/*
THE COMPUTER CODE CONTAINED HEREIN IS THE SOLE PROPERTY OF PARALLAX
SOFTWARE CORPORATION ("PARALLAX"). PARALLAX, IN DISTRIBUTING THE CODE TO
END-USERS, AND SUBJECT TO ALL OF THE TERMS AND CONDITIONS HEREIN, GRANTS A
ROYALTY-FREE, PERPETUAL LICENSE TO SUCH END-USERS FOR USE BY SUCH END-USERS
IN USING, DISPLAYING, AND CREATING DERIVATIVE WORKS THEREOF, SO LONG AS
SUCH USE, DISPLAY OR CREATION IS FOR NON-COMMERCIAL, ROYALTY OR REVENUE
FREE PURPOSES. IN NO EVENT SHALL THE END-USER USE THE COMPUTER CODE
CONTAINED HEREIN FOR REVENUE-BEARING PURPOSES. THE END-USER UNDERSTANDS
AND AGREES TO THE TERMS HEREIN AND ACCEPTS THE SAME BY USE OF THIS FILE.
COPYRIGHT 1993-1998 PARALLAX SOFTWARE CORPORATION. ALL RIGHTS RESERVED.
*/
/*
*
* C version of fixed point library
*
*/
#include <stdlib.h>
#include <math.h>
#include "dxxerror.h"
#include "maths.h"
//negate a quad
void fixquadnegate(quadint *q)
{
q->low = 0 - q->low;
q->high = 0 - q->high - (q->low != 0);
}
//multiply two ints & add 64-bit result to 64-bit sum
void fixmulaccum(quadint *q,fix a,fix b)
{
u_int32_t aa,bb;
u_int32_t ah,al,bh,bl;
u_int32_t t,c=0,old;
int neg;
neg = ((a^b) < 0);
aa = labs(a); bb = labs(b);
ah = aa>>16; al = aa&0xffff;
bh = bb>>16; bl = bb&0xffff;
t = ah*bl + bh*al;
if (neg)
fixquadnegate(q);
old = q->low;
q->low += al*bl;
if (q->low < old) q->high++;
old = q->low;
q->low += (t<<16);
if (q->low < old) q->high++;
q->high += ah*bh + (t>>16) + c;
if (neg)
fixquadnegate(q);
}
//extract a fix from a quad product
fix fixquadadjust(quadint *q)
{
return (q->high<<16) + (q->low>>16);
}
#define EPSILON (F1_0/100)
fix fixmul(fix a, fix b)
{
return (fix)((((fix64) a) * b) / 65536);
}
fix64 fixmul64(fix a, fix b)
{
return (fix64)((((fix64) a) * b) / 65536);
}
fix fixdiv(fix a, fix b)
{
return b ? (fix)((((fix64)a) *65536)/b) : 1;
}
fix fixmuldiv(fix a, fix b, fix c)
{
return c ? (fix)((((fix64)a)*b)/c) : 1;
}
//given cos & sin of an angle, return that angle.
//parms need not be normalized, that is, the ratio of the parms cos/sin must
//equal the ratio of the actual cos & sin for the result angle, but the parms
//need not be the actual cos & sin.
//NOTE: this is different from the standard C atan2, since it is left-handed.
fixang fix_atan2(fix cos,fix sin)
{
double d, dsin, dcos;
fixang t;
//Assert(!(cos==0 && sin==0));
//find smaller of two
dsin = (double)sin;
dcos = (double)cos;
d = sqrt((dsin * dsin) + (dcos * dcos));
if (d==0.0)
return 0;
if (labs(sin) < labs(cos)) { //sin is smaller, use arcsin
t = fix_asin((fix)((dsin / d) * 65536.0));
if (cos<0)
t = 0x8000 - t;
return t;
}
else {
t = fix_acos((fix)((dcos / d) * 65536.0));
if (sin<0)
t = -t;
return t;
}
}
int32_t fixdivquadlong(u_int32_t nl,u_int32_t nh,u_int32_t d)
{
int64_t n = (int64_t)nl | (((int64_t)nh) << 32 );
return (signed int) (n / ((int64_t)d));
}
unsigned int fixdivquadlongu(uint nl, uint nh, uint d)
{
u_int64_t n = (u_int64_t)nl | (((u_int64_t)nh) << 32 );
return (unsigned int) (n / ((u_int64_t)d));
}
u_int32_t quad_sqrt(u_int32_t low,int32_t high)
{
int i, cnt;
u_int32_t r,old_r,t;
quadint tq;
if (high<0)
return 0;
if (high==0 && (int32_t)low>=0)
return long_sqrt((int32_t)low);
if (high & 0xff000000) {
cnt=12+16; i = high >> 24;
} else if (high & 0xff0000) {
cnt=8+16; i = high >> 16;
} else if (high & 0xff00) {
cnt=4+16; i = high >> 8;
} else {
cnt=0+16; i = high;
}
r = guess_table[i]<<cnt;
//quad loop usually executed 4 times
r = fixdivquadlongu(low,high,r)/2 + r/2;
r = fixdivquadlongu(low,high,r)/2 + r/2;
r = fixdivquadlongu(low,high,r)/2 + r/2;
do {
old_r = r;
t = fixdivquadlongu(low,high,r);
if (t==r) //got it!
return r;
r = t/2 + r/2;
} while (!(r==t || r==old_r));
t = fixdivquadlongu(low,high,r);
//edited 05/17/99 Matt Mueller - tq.high is undefined here.. so set them to = 0
tq.low=tq.high=0;
//end edit -MM
fixmulaccum(&tq,r,t);
if (tq.low!=low || tq.high!=high)
r++;
return r;
}
//computes the square root of a long, returning a short
ushort long_sqrt(int32_t a)
{
int cnt,r,old_r,t;
if (a<=0)
return 0;
if (a & 0xff000000)
cnt=12;
else if (a & 0xff0000)
cnt=8;
else if (a & 0xff00)
cnt=4;
else
cnt=0;
r = guess_table[(a>>cnt)&0xff]<<cnt;
//the loop nearly always executes 3 times, so we'll unroll it 2 times and
//not do any checking until after the third time. By my calcutations, the
//loop is executed 2 times in 99.97% of cases, 3 times in 93.65% of cases,
//four times in 16.18% of cases, and five times in 0.44% of cases. It never
//executes more than five times. By timing, I determined that is is faster
//to always execute three times and not check for termination the first two
//times through. This means that in 93.65% of cases, we save 6 cmp/jcc pairs,
//and in 6.35% of cases we do an extra divide. In real life, these numbers
//might not be the same.
r = ((a/r)+r)/2;
r = ((a/r)+r)/2;
do {
old_r = r;
t = a/r;
if (t==r) //got it!
return r;
r = (t+r)/2;
} while (!(r==t || r==old_r));
if (a % r)
r++;
return r;
}
//computes the square root of a fix, returning a fix
fix fix_sqrt(fix a)
{
return ((fix) long_sqrt(a)) << 8;
}
//compute sine and cosine of an angle, filling in the variables
//either of the pointers can be NULL
//with interpolation
void fix_sincos(fix a,fix *s,fix *c)
{
int i,f;
fix ss,cc;
i = (a>>8)&0xff;
f = a&0xff;
ss = sincos_table[i];
if (s) *s = (ss + (((sincos_table[i+1] - ss) * f)>>8))<<2;
cc = sincos_table[i+64];
if (c) *c = (cc + (((sincos_table[i+64+1] - cc) * f)>>8))<<2;
}
//compute sine and cosine of an angle, filling in the variables
//either of the pointers can be NULL
//no interpolation
void fix_fastsincos(fix a,fix *s,fix *c)
{
int i;
i = (a>>8)&0xff;
if (s) *s = sincos_table[i] << 2;
if (c) *c = sincos_table[i+64] << 2;
}
//compute inverse sine
fixang fix_asin(fix v)
{
fix vv;
int i,f,aa;
vv = labs(v);
if (vv >= f1_0) //check for out of range
return 0x4000;
i = (vv>>8)&0xff;
f = vv&0xff;
aa = asin_table[i];
aa = aa + (((asin_table[i+1] - aa) * f)>>8);
if (v < 0)
aa = -aa;
return aa;
}
//compute inverse cosine
fixang fix_acos(fix v)
{
fix vv;
int i,f,aa;
vv = labs(v);
if (vv >= f1_0) //check for out of range
return 0;
i = (vv>>8)&0xff;
f = vv&0xff;
aa = acos_table[i];
aa = aa + (((acos_table[i+1] - aa) * f)>>8);
if (v < 0)
aa = 0x8000 - aa;
return aa;
}
#define TABLE_SIZE 1024
//for passed value a, returns 1/sqrt(a)
fix fix_isqrt( fix a )
{
int i, b = a;
int cnt = 0;
int r;
if ( a == 0 ) return 0;
while( b >= TABLE_SIZE ) {
b >>= 1;
cnt++;
}
r = isqrt_guess_table[b] >> ((cnt+1)/2);
for (i=0; i<3; i++ ) {
int old_r = r;
r = fixmul( ( (3*65536) - fixmul(fixmul(r,r),a) ), r) / 2;
if ( old_r >= r ) return (r+old_r)/2;
}
return r;
}
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