As I'm using a GPL set of routines for the fixed maths functions, I've decided to release the whole code to my maths plug-in (you lukcy people you...).
generous) - its just for looking at.
+ Code Snippet#include "stdafx.h"
#include "stdio.h"
#include <math.h>
#include "Math.h"
#include "stdlib.h"
#include "time.h"
#include "vector"
#include "..Headersglobstruct.h"
GlobStruct* g_pGlob = NULL;
#define NEGATIVE (int) -1
#define ZERO (int) 0
#define POSITIVE (int) 1
char hexs[]={"0123456789ABCDEF"};
#define _BYTE(x) ((x) & 0xFF)
#define int2sll(X) (((sll) (X)) << 32)
#define sll2int(X) ((long) ((X) >> 32))
#define sllint(X) ((X) & (ull) 0xffffffff00000000)
#define sllfrac(X) ((X) & (ull) 0x00000000ffffffff)
#define sllneg(X) (-(X))
#define _slladd(X,Y) ((X) + (Y))
#define _sllsub(X,Y) ((X) - (Y))
/* Constants (converted from double) */
#define CONST_0 (sll) 0x0000000000000000
#define CONST_1 (sll) 0x0000000100000000
#define CONST_2 (sll) 0x0000000200000000
#define CONST_3 (sll) 0x0000000300000000
#define CONST_4 (sll) 0x0000000400000000
#define CONST_10 (sll) 0x0000000a00000000
#define CONST_1_2 (sll) 0x0000000080000000
#define CONST_1_3 (sll) 0x0000000055555555
#define CONST_1_4 (sll) 0x0000000040000000
#define CONST_1_5 (sll) 0x0000000033333333
#define CONST_1_6 (sll) 0x000000002aaaaaaa
#define CONST_1_7 (sll) 0x0000000024924924
#define CONST_1_8 (sll) 0x0000000020000000
#define CONST_1_9 (sll) 0x000000001c71c71c
#define CONST_1_10 (sll) 0x0000000019999999
#define CONST_1_11 (sll) 0x000000001745d174
#define CONST_1_12 (sll) 0x0000000015555555
#define CONST_1_20 (sll) 0x000000000ccccccc
#define CONST_1_30 (sll) 0x0000000008888888
#define CONST_1_42 (sll) 0x0000000006186186
#define CONST_1_56 (sll) 0x0000000004924924
#define CONST_1_72 (sll) 0x00000000038e38e3
#define CONST_1_90 (sll) 0x0000000002d82d82
#define CONST_1_110 (sll) 0x000000000253c825
#define CONST_1_132 (sll) 0x0000000001f07c1f
#define CONST_1_156 (sll) 0x0000000001a41a41
#define CONST_E (sll) 0x00000002b7e15162
#define CONST_1_E (sll) 0x000000005e2d58d8
#define CONST_SQRTE (sll) 0x00000001a61298e1
#define CONST_1_SQRTE (sll) 0x000000009b4597e3
#define CONST_LOG2_E (sll) 0x0000000171547652
#define CONST_LOG10_E (sll) 0x000000006f2dec54
#define CONST_LN2 (sll) 0x00000000b17217f7
#define CONST_LN10 (sll) 0x000000024d763776
#define CONST_PI (sll) 0x00000003243f6a88
#define CONST_PI_2 (sll) 0x00000001921fb544
#define CONST_PI_4 (sll) 0x00000000c90fdaa2
#define CONST_1_PI (sll) 0x00000000517cc1b7
#define CONST_2_PI (sll) 0x00000000a2f9836e
#define CONST_2_SQRTPI (sll) 0x0000000120dd7504
#define CONST_SQRT2 (sll) 0x000000016a09e667
#define CONST_1_SQRT2 (sll) 0x00000000b504f333
unsigned int seed;
BOOL APIENTRY DllMain( HANDLE hModule,
DWORD ul_reason_for_call,
LPVOID lpReserved
)
{
srand((unsigned) time(NULL));
seed=time(NULL);
switch (ul_reason_for_call)
{
case DLL_PROCESS_ATTACH:
case DLL_THREAD_ATTACH:
case DLL_THREAD_DETACH:
case DLL_PROCESS_DETACH:
break;
}
return TRUE;
}
void Constructor ( void )
{
// Create memory here
}
void Destructor ( void )
{
// Free memory here
}
void ReceiveCoreDataPtr ( LPVOID pCore )
{
// Get Core Data Pointer here
g_pGlob = (GlobStruct*)pCore;
}
// This is an example of an exported variable
__int64 hextointLI(LPSTR hex)
{
register int pos;
__int64 base,total;
total=0;
if ((hex) && strlen(hex)>0)
{
base=1;
for (pos=0; pos<(int) strlen(hex); pos++)
{
register char one;
register int loop;
one=toupper(*(hex+(strlen(hex)-1-pos)));
for (loop=0; loop<(int) strlen(hexs); loop++)
{
if (one==hexs[loop])
{
// A valid number found
total+=(loop*base);
break;
}
}
base<<=4;
}
}
return (total);
}
int hextoint(LPSTR hex)
{
register int pos,base,total;
total=0;
if ((hex) && strlen(hex)>0)
{
base=1;
for (pos=0; pos<(int) strlen(hex); pos++)
{
register char one;
register int loop;
one=toupper(*(hex+(strlen(hex)-1-pos)));
for (loop=0; loop<(int) strlen(hexs); loop++)
{
if (one==hexs[loop])
{
// A valid number found
total+=(loop*base);
break;
}
}
base<<=4;
}
}
return (total);
}
double PI(void)
{
return ((double) 3.14159265358979);
}
double PHI(void)
{
return ((double) 1.6180339887);
}
double PHI2(void)
{
return ((double) 0.6180339);
}
unsigned __int64 factorial(unsigned __int64 f)
{
register unsigned __int64 total;
total=(f==0 || f==1 ? 1 : f);
while (f>1)
{
total*=(f-1);
f--;
}
return (total);
}
DWORD valF(LPSTR string)
{
float value;
value=(float) atof(string);
return (*(DWORD *) &value);
}
DWORD valF(LPSTR string,DWORD dp)
{
float value;
value=(float) valD(string,dp);
return (*(DWORD *) &value);
}
double valD(LPSTR string)
{
return (atof(string));
}
double valD(LPSTR string,DWORD dp)
{
char *buffer;
int decimal,sign;
char *buffer2;
double value;
value=0.0;
buffer = _fcvt(atof(string), dp, &decimal, &sign );
ZeroMemory(&buffer2,sizeof(buffer2));
if ((buffer2=(char *) calloc(1,1024))!=NULL)
{
if (sign!=0)
{
strcat(buffer2,"-");
}
if (decimal>0)
{
strncat(buffer2,buffer,decimal);
if (dp)
{
strcat(buffer2,".");
}
}
else
{
if (dp)
{
strcat(buffer2,".");
}
decimal=0;
}
strcat(buffer2,(char *) (buffer+decimal));
value=atof(buffer2);
}
free(buffer2);
return (value);
}
int sgn(int value)
{
return (value<0 ? NEGATIVE :
value>0 ? POSITIVE : ZERO);
}
int sgn(LONGLONG value)
{
return (value<0 ? NEGATIVE :
value>0 ? POSITIVE : ZERO);
}
int sgn(float value)
{
return (value<0.0 ? NEGATIVE :
value>0.0 ? POSITIVE : ZERO);
}
int sgn(double value)
{
return (value<0.0 ? NEGATIVE :
value>0.0 ? POSITIVE : ZERO);
}
double besselFO0(double value)
{
return (_j0(value));
}
double besselFO1(double value)
{
return (_j1(value));
}
double besselFON(int value1,double value2)
{
return (_jn(value1,value2));
}
double besselSO0(double value)
{
return (_y0(value));
}
double besselSO1(double value)
{
return (_y1(value));
}
double besselSON(int value1,double value2)
{
return (_yn(value1,value2));
}
double _log(double value)
{
return (log(value));
}
double _log10(double value)
{
return (log10(value));
}
DWORD rrand(DWORD min,DWORD max)
{
register DWORD range;
srand(seed*(unsigned int) time(NULL));
range=max-min+1;
seed=rand();
return ((seed % range + min));
}
double rndf(double min,double max)
{
register double value;
srand(seed*(unsigned int) time(NULL));
seed=rand();
value=(double) ((double) seed/(double) RAND_MAX);
return ((double) (value*(max-min)+min));
}
DWORD strf(DWORD pOldString,double value)
{
LPSTR buffer=NULL;
const int size=256;
if(pOldString) g_pGlob->CreateDeleteString ( (DWORD*)&pOldString, 0 );
g_pGlob->CreateDeleteString ( (DWORD*)&buffer, size);
ZeroMemory(buffer,size);
sprintf(buffer,"%.15lf",value);
return ((DWORD) buffer);
}
DWORD bytes16ToBottomDWORD(DWORD part2,DWORD part1)
{
return ((_BYTE(part2)<<8) | (_BYTE(part1)));
}
DWORD bytes16ToTopDWORD(DWORD part2,DWORD part1)
{
return ((_BYTE(part2)<<24) | (_BYTE(part1)<<16));
}
DWORD bytes32ToDWORD(DWORD part4,DWORD part3,DWORD part2,DWORD part1)
{
return ((_BYTE(part4)<<24) | (_BYTE(part3)<<16) | (_BYTE(part2)<<8) | (_BYTE(part1)));
}
DWORD DWORDToByte(DWORD value,DWORD bank)
{
DWORD val;
val=(bank==0 ? value :
bank==1 ? value>>8 :
bank==2 ? value>>16 : value>>24);
return (_BYTE(val));
}
DWORD fcmp(float value1,float value2,float epsilon)
{
return (fabs(value1-value2)<=fabs(value1)*epsilon ? (DWORD) true : (DWORD) false);
}
DWORD dfcmp(double value1,double value2,double epsilon)
{
return (fabs(value1-value2)<=fabs(value1)*epsilon ? (DWORD) true : (DWORD) false);
}
sll slladd(sll x, sll y)
{
return (x + y);
}
sll sllsub(sll x, sll y)
{
return (x - y);
}
/*
* Let a = A * 2^32 + a_hi * 2^0 + a_lo * 2^(-32)
* Let b = B * 2^32 + b_hi * 2^0 + b_lo * 2^(-32)
*
* Where:
* *_hi is the integer part
* *_lo the fractional part
* A and B are the sign (0 for positive, -1 for negative).
*
* a * b = (A * 2^32 + a_hi * 2^0 + a_lo * 2^-32)
* * (B * 2^32 + b_hi * 2^0 + b_lo * 2^-32)
*
* Expanding the terms, we get:
*
* = A * B * 2^64 + A * b_h * 2^32 + A * b_l * 2^0
* + a_h * B * 2^32 + a_h * b_h * 2^0 + a_h * b_l * 2^-32
* + a_l * B * 2^0 + a_l * b_h * 2^-32 + a_l * b_l * 2^-64
*
* Grouping by powers of 2, we get:
*
* = A * B * 2^64
* Meaningless overflow from sign extension - ignore
*
* + (A * b_h + a_h * B) * 2^32
* Overflow which we can't handle - ignore
*
* + (A * b_l + a_h * b_h + a_l * B) * 2^0
* We only need the low 32 bits of this term, as the rest is overflow
*
* + (a_h * b_l + a_l * b_h) * 2^-32
* We need all 64 bits of this term
*
* + a_l * b_l * 2^-64
* We only need the high 32 bits of this term, as the rest is underflow
*
* Note that:
* a > 0 && b > 0: A = 0, B = 0 and the third term is a_h * b_h
* a < 0 && b > 0: A = -1, B = 0 and the third term is a_h * b_h - b_l
* a > 0 && b < 0: A = 0, B = -1 and the third term is a_h * b_h - a_l
* a < 0 && b < 0: A = -1, B = -1 and the third term is a_h * b_h - a_l - b_l
*/
/*
sll sllmul(sll left, sll right)
{
register sll retval;
__asm__(
"# sllmulnt"
" movl %1, %%eaxnt"
" mull %3nt"
" movl %%edx, %%ebxnt"
"nt"
" movl %2, %%eaxnt"
" mull %4nt"
" movl %%eax, %%ecxnt"
"nt"
" movl %1, %%eaxnt"
" mull %4nt"
" addl %%eax, %%ebxnt"
" adcl %%edx, %%ecxnt"
"nt"
" movl %2, %%eaxnt"
" mull %3nt"
" addl %%ebx, %%eaxnt"
" adcl %%ecx, %%edxnt"
"nt"
" btl $31, %2nt"
" jnc 1fnt"
" subl %3, %%edxnt"
"1: btl $31, %4nt"
" jnc 1fnt"
" subl %1, %%edxnt"
"1:nt"
: "=&A" (retval)
: "m" (left), "m" (((unsigned *) &left)[1]),
"m" (right), "m" (((unsigned *) &right)[1])
: "ebx", "ecx", "cc"
);
return retval;
}
*/
/* Plain C version: not optimal but portable. */
sll sllmul(sll a, sll b)
{
sll a_lo, b_lo;
sll a_hi, b_hi;
sll x;
a_lo = a;
a_hi = (ull) a >> 32;
b_lo = b;
b_hi = (ull) b >> 32;
x = ((ull) (a_hi * b_hi) << 32)
+ (((ull) a_lo * b_lo) >> 32)
+ (sll) a_lo * b_hi
+ (sll) b_lo * a_hi;
return x;
}
sll sllinv(sll v)
{
int sgn = 0;
sll u;
ull s = -1;
/* Use positive numbers, or the approximation won't work */
if (v < CONST_0) {
v = sllneg(v);
sgn = 1;
}
/* An approximation - must be larger than the actual value */
for (u = v; u; u >>= 1)
s >>= 1;
/* Newton's Method */
u = sllmul(s, _sllsub(CONST_2, sllmul(v, s)));
u = sllmul(u, _sllsub(CONST_2, sllmul(v, u)));
u = sllmul(u, _sllsub(CONST_2, sllmul(v, u)));
u = sllmul(u, _sllsub(CONST_2, sllmul(v, u)));
u = sllmul(u, _sllsub(CONST_2, sllmul(v, u)));
u = sllmul(u, _sllsub(CONST_2, sllmul(v, u)));
return ((sgn) ? sllneg(u): u);
}
sll slldiv(sll left, sll right)
{
return sllmul(left, sllinv(right));
}
sll sllmul2(sll x)
{
return x << 1;
}
sll sllmul4(sll x)
{
return x << 2;
}
sll sllmul2n(sll x, int n)
{
sll y;
y = x << n;
return y;
}
sll slldiv2(sll x)
{
return x >> 1;
}
sll slldiv4(sll x)
{
return x >> 2;
}
sll slldiv2n(sll x, int n)
{
sll y;
y = x >> n;
return y;
}
/*
* Unpack the IEEE floating point double format and put it in fixed point
* sll format.
*/
sll dbl2sll(double dbl)
{
union {
double d;
unsigned u[2];
ull ull;
sll sll;
} in, retval;
register unsigned exp;
/* Move into memory as args might be passed in regs */
in.d = dbl;
/* Leading 1 is assumed by IEEE */
retval.u[1] = 0x40000000;
/* Unpack the mantissa into the unsigned long */
retval.u[1] |= (in.u[1] << 10) & 0x3ffffc00;
retval.u[1] |= (in.u[0] >> 22) & 0x000003ff;
retval.u[0] = in.u[0] << 10;
/* Extract the exponent and align the decimals */
exp = (in.u[1] >> 20) & 0x7ff;
if (exp)
retval.ull >>= 1053 - exp;
else
return 0L;
/* Negate if negative flag set */
if (in.u[1] & 0x80000000)
retval.sll = -retval.sll;
return retval.sll;
}
double sll2dbl(sll s)
{
union {
double d;
unsigned u[2];
ull ull;
sll sll;
} in, retval;
register unsigned int exp;
register unsigned int flag;
if (s == 0)
return 0.0;
/* Move into memory as args might be passed in regs */
in.sll = s;
/* Handle the negative flag */
if (in.sll < 1) {
flag = 0x80000000;
in.ull = sllneg(in.sll);
} else
flag = 0x00000000;
/* Normalize */
for (exp = 1053; in.ull && (in.u[1] & 0x80000000) == 0; exp--) {
in.ull <<= 1;
}
in.ull <<= 1;
exp++;
in.ull >>= 12;
retval.ull = in.ull;
retval.u[1] |= flag | (exp << 20);
return retval.d;
}
/*
* Calculate cos x where -pi/4 <= x <= pi/4
*
* Description:
* cos x = 1 - x^2 / 2! + x^4 / 4! - ... + x^(2N) / (2N)!
* Note that (pi/4)^12 / 12! < 2^-32 which is the smallest possible number.
*/
sll _sllcos(sll x)
{
sll retval, x2;
x2 = sllmul(x, x);
/*
* cos x = t0 + t1 + t2 + t3 + t4 + t5 + t6
*
* f0 = 0! = 1
* f1 = 2! = 2 * 1 * f0 = 2 * f0
* f2 = 4! = 4 * 3 * f1 = 12 x f1
* f3 = 6! = 6 * 5 * f2 = 30 * f2
* f4 = 8! = 8 * 7 * f3 = 56 * f3
* f5 = 10! = 10 * 9 * f4 = 90 * f4
* f6 = 12! = 12 * 11 * f5 = 132 * f5
*
* t0 = 1
* t1 = -t0 * x2 / 2 = -t0 * x2 * CONST_1_2
* t2 = -t1 * x2 / 12 = -t1 * x2 * CONST_1_12
* t3 = -t2 * x2 / 30 = -t2 * x2 * CONST_1_30
* t4 = -t3 * x2 / 56 = -t3 * x2 * CONST_1_56
* t5 = -t4 * x2 / 90 = -t4 * x2 * CONST_1_90
* t6 = -t5 * x2 / 132 = -t5 * x2 * CONST_1_132
*/
retval = _sllsub(CONST_1, sllmul(x2, CONST_1_132));
retval = _sllsub(CONST_1, sllmul(sllmul(x2, retval), CONST_1_90));
retval = _sllsub(CONST_1, sllmul(sllmul(x2, retval), CONST_1_56));
retval = _sllsub(CONST_1, sllmul(sllmul(x2, retval), CONST_1_30));
retval = _sllsub(CONST_1, sllmul(sllmul(x2, retval), CONST_1_12));
retval = _sllsub(CONST_1, slldiv2(sllmul(x2, retval)));
return retval;
}
/*
* Calculate sin x where -pi/4 <= x <= pi/4
*
* Description:
* sin x = x - x^3 / 3! + x^5 / 5! - ... + x^(2N+1) / (2N+1)!
* Note that (pi/4)^13 / 13! < 2^-32 which is the smallest possible number.
*/
sll _sllsin(sll x)
{
sll retval, x2;
x2 = sllmul(x, x);
/*
* sin x = t0 + t1 + t2 + t3 + t4 + t5 + t6
*
* f0 = 0! = 1
* f1 = 3! = 3 * 2 * f0 = 6 * f0
* f2 = 5! = 5 * 4 * f1 = 20 x f1
* f3 = 7! = 7 * 6 * f2 = 42 * f2
* f4 = 9! = 9 * 8 * f3 = 72 * f3
* f5 = 11! = 11 * 10 * f4 = 110 * f4
* f6 = 13! = 13 * 12 * f5 = 156 * f5
*
* t0 = 1
* t1 = -t0 * x2 / 6 = -t0 * x2 * CONST_1_6
* t2 = -t1 * x2 / 20 = -t1 * x2 * CONST_1_20
* t3 = -t2 * x2 / 42 = -t2 * x2 * CONST_1_42
* t4 = -t3 * x2 / 72 = -t3 * x2 * CONST_1_72
* t5 = -t4 * x2 / 110 = -t4 * x2 * CONST_1_110
* t6 = -t5 * x2 / 156 = -t5 * x2 * CONST_1_156
*/
retval = _sllsub(x, sllmul(x2, CONST_1_156));
retval = _sllsub(x, sllmul(sllmul(x2, retval), CONST_1_110));
retval = _sllsub(x, sllmul(sllmul(x2, retval), CONST_1_72));
retval = _sllsub(x, sllmul(sllmul(x2, retval), CONST_1_42));
retval = _sllsub(x, sllmul(sllmul(x2, retval), CONST_1_20));
retval = _sllsub(x, sllmul(sllmul(x2, retval), CONST_1_6));
return retval;
}
sll sllcos(sll x)
{
int i;
sll retval;
/* Calculate cos (x - i * pi/2), where -pi/4 <= x - i * pi/2 <= pi/4 */
i = sll2int(_slladd(sllmul(x, CONST_2_PI), CONST_1_2));
x = _sllsub(x, sllmul(int2sll(i), CONST_PI_2));
switch (i & 3) {
default:
case 0:
retval = _sllcos(x);
break;
case 1:
retval = sllneg(_sllsin(x));
break;
case 2:
retval = sllneg(_sllcos(x));
break;
case 3:
retval = _sllsin(x);
break;
}
return retval;
}
sll sllsin(sll x)
{
int i;
sll retval;
/* Calculate sin (x - n * pi/2), where -pi/4 <= x - i * pi/2 <= pi/4 */
i = sll2int(_slladd(sllmul(x, CONST_2_PI), CONST_1_2));
x = _sllsub(x, sllmul(int2sll(i), CONST_PI_2));
switch (i & 3) {
default:
case 0:
retval = _sllsin(x);
break;
case 1:
retval = _sllcos(x);
break;
case 2:
retval = sllneg(_sllsin(x));
break;
case 3:
retval = sllneg(_sllcos(x));
break;
}
return retval;
}
sll slltan(sll x)
{
int i;
sll retval;
i = sll2int(_slladd(sllmul(x, CONST_2_PI), CONST_1_2));
x = _sllsub(x, sllmul(int2sll(i), CONST_PI_2));
switch (i & 3) {
default:
case 0:
case 2:
retval = slldiv(_sllsin(x), _sllcos(x));
break;
case 1:
case 3:
retval = sllneg(slldiv(_sllcos(x), _sllsin(x)));
break;
}
return retval;
}
/*
* atan x = SUM[n=0,) (-1)^n * x^(2n + 1)/(2n + 1), |x| < 1
*
* Two term approximation
* a = x - x^3/3
* Gives us
* atan x = a + ??
* Let ?? = arctan ?
* atan x = a + arctan ?
* Rearrange
* atan x - a = arctan ?
* Apply tan to both sides
* tan (atan x - a) = tan arctan ?
* tan (atan x - a) = ?
* Applying the standard formula
* tan (u - v) = (tan u - tan v) / (1 + tan u * tan v)
* Gives us
* tan (atan x - a) = (tan atan x - tan a) / (1 + tan arctan x * tan a)
* Let t = tan a
* tan (atan x - a) = (x - t) / (1 + x * t)
* So finally
* arctan x = a + arctan ((tan x - t) / (1 + x * t))
* And the typical worst case is x = 1.0 which converges in 3 iterations.
*/
sll _sllatan(sll x)
{
sll a, t, retval;
/* First iteration */
a = sllmul(x, _sllsub(CONST_1, sllmul(x, sllmul(x, CONST_1_3))));
retval = a;
/* Second iteration */
t = slldiv(_sllsin(a), _sllcos(a));
x = slldiv(_sllsub(x, t), _slladd(CONST_1, sllmul(t, x)));
a = sllmul(x, _sllsub(CONST_1, sllmul(x, sllmul(x, CONST_1_3))));
retval = _slladd(retval, a);
/* Third iteration */
t = slldiv(_sllsin(a), _sllcos(a));
x = slldiv(_sllsub(x, t), _slladd(CONST_1, sllmul(t, x)));
a = sllmul(x, _sllsub(CONST_1, sllmul(x, sllmul(x, CONST_1_3))));
return _slladd(retval, a);
}
sll sllatan(sll x)
{
sll retval;
if (x < -sllneg(CONST_1))
retval = sllneg(CONST_PI_2);
else if (x > CONST_1)
retval = CONST_PI_2;
else
return _sllatan(x);
return _sllsub(retval, _sllatan(sllinv(x)));
}
/*
* Calculate e^x where -0.5 <= x <= 0.5
*
* Description:
* e^x = x^0 / 0! + x^1 / 1! + ... + x^N / N!
* Note that 0.5^11 / 11! < 2^-32 which is the smallest possible number.
*/
sll _sllexp(sll x)
{
sll retval;
retval = _slladd(CONST_1, sllmul(0, sllmul(x, CONST_1_11)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_11)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_10)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_9)));
retval = _slladd(CONST_1, sllmul(retval, slldiv2n(x, 3)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_7)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_6)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_5)));
retval = _slladd(CONST_1, sllmul(retval, slldiv4(x)));
retval = _slladd(CONST_1, sllmul(retval, sllmul(x, CONST_1_3)));
retval = _slladd(CONST_1, sllmul(retval, slldiv2(x)));
return retval;
}
/*
* Calculate e^x where x is arbitrary
*/
sll sllexp(sll x)
{
int i;
sll e, retval;
e = CONST_E;
/* -0.5 <= x <= 0.5 */
i = sll2int(_slladd(x, CONST_1_2));
retval = _sllexp(_sllsub(x, int2sll(i)));
/* i >= 0 */
if (i < 0) {
i = -i;
e = CONST_1_E;
}
/* Scale the result */
for (;i; i >>= 1) {
if (i & 1)
retval = sllmul(retval, e);
e = sllmul(e, e);
}
return retval;
}
/*
* Calculate natural logarithm using Netwton-Raphson method
*/
sll slllog(sll x)
{
sll x1, ln = 0;
/* Scale: e^(-1/2) <= x <= e^(1/2) */
while (x < CONST_1_SQRTE) {
ln = _sllsub(ln, CONST_1);
x = sllmul(x, CONST_E);
}
while (x > CONST_SQRTE) {
ln = _slladd(ln, CONST_1);
x = sllmul(x, CONST_1_E);
}
/* First iteration */
x1 = sllmul(_sllsub(x, CONST_1), slldiv2(_sllsub(x, CONST_3)));
ln = _sllsub(ln, x1);
x = sllmul(x, _sllexp(x1));
/* Second iteration */
x1 = sllmul(_sllsub(x, CONST_1), slldiv2(_sllsub(x, CONST_3)));
ln = _sllsub(ln, x1);
x = sllmul(x, _sllexp(x1));
/* Third iteration */
x1 = sllmul(_sllsub(x, CONST_1), slldiv2(_sllsub(x, CONST_3)));
ln = _sllsub(ln, x1);
return ln;
}
/*
* ln x^y = y * log x
* e^(ln x^y) = e^(y * log x)
* x^y = e^(y * ln x)
*/
sll sllpow(sll x, sll y)
{
if (y == CONST_0)
return CONST_1;
return sllexp(sllmul(y, slllog(x)));
}
/*
* Consider a parabola centered on the y-axis
* y = a * x^2 + b
* Has zeros (y = 0) at
* a * x^2 + b = 0
* a * x^2 = -b
* x^2 = -b / a
* x = +- (-b / a)^(1 / 2)
* Letting a = 1 and b = -X
* y = x^2 - X
* x = +- X^(1 / 2)
* Which is convenient since we want to find the square root of X, and we can
* use Newton's Method to find the zeros of any f(x)
* xn = x - f(x) / f'(x)
* Applied Newton's Method to our parabola
* f(x) = x^2 - X
* xn = x - (x^2 - X) / (2 * x)
* xn = x - (x - X / x) / 2
* To make this converge quickly, we scale X so that
* X = 4^N * z
* Taking the roots of both sides
* X^(1 / 2) = (4^n * z)^(1 / 2)
* X^(1 / 2) = 2^n * z^(1 / 2)
* Let N = 2^n
* x^(1 / 2) = N * z^(1 / 2)
* We want this to converge to the positive root, so we must start at a point
* 0 < start <= x^(1 / 2)
* or
* x^(1/2) <= start <= infinity
* since
* (1/2)^(1/2) = 0.707
* 2^(1/2) = 1.414
* A good choice is 1 which lies in the middle, and takes 4 iterations to
* converge from either extreme.
*/
sll sllsqrt(sll x)
{
sll n, xn;
/* Start with a scaling factor of 1 */
n = CONST_1;
/* Quick solutions for the simple cases */
if (x <= CONST_0 || x == CONST_1)
return x;
/* Scale x so that 0.5 <= x < 2 */
while (x >= CONST_2) {
x = slldiv4(x);
n = sllmul2(n);
}
while (x < CONST_1_2) {
x = sllmul4(x);
n = slldiv2(n);
}
/* Simple solution if x = 4^n */
if (x == CONST_1)
return n;
/* The starting point */
xn = CONST_1;
/* Four iterations will be enough */
xn = _sllsub(xn, slldiv2(_sllsub(xn, slldiv(x, xn))));
xn = _sllsub(xn, slldiv2(_sllsub(xn, slldiv(x, xn))));
xn = _sllsub(xn, slldiv2(_sllsub(xn, slldiv(x, xn))));
xn = _sllsub(xn, slldiv2(_sllsub(xn, slldiv(x, xn))));
/* Scale the result */
return sllmul(n, xn);
}
DWORD fixtostring(DWORD pOldString,ull value)
{
LPSTR buffer=NULL;
char buffer2[256];
double _value;
if(pOldString) g_pGlob->CreateDeleteString ( (DWORD*)&pOldString, 0 );
g_pGlob->CreateDeleteString ( (DWORD*)&buffer, sizeof(buffer2));
ZeroMemory(buffer,sizeof(buffer2));
_value=sll2dbl(value);
sprintf(buffer2,"%.4lf",_value);
strcpy(buffer,buffer2);
return ((DWORD) buffer);
}