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soarMath.c
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soarMath.c
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#include <PalmOS.h>
#include "soaring.h"
#include "soarMath.h"
#include "soarMap.h"
#include "soarUtil.h"
#include "soarRSA.h"
#include "Mathlib.h"
// Get two 32 bit ints from a double.
#define EXTRACT_WORDS(ix0,ix1,d) { (ix0)=__HI32(d); (ix1)=__LO32(d); }
// Get the more significant 32 bit int from a double.
#define GET_HIGH_WORD(i,d) (i)=__HI32(d)
// Get the less significant 32 bit int from a double.
#define GET_LOW_WORD(i,d) (i)=__LO32(d)
// Set a double from two 32 bit ints.
#define INSERT_WORDS(d,ix0,ix1) { __HI32(d)=(ix0); __LO32(d)=(ix1); }
// Set the more significant 32 bits of a double from an int.
#define SET_HIGH_WORD(d,v) __HI32(d)=(v)
// Set the less significant 32 bits of a double from an int.
#define SET_LOW_WORD(d,v) __LO32(d)=(v)
static const double one = 1.0, tiny=1.0e-300;
#ifdef MATHLIB_FUNCS
double Sqrt(double x) {
return(sqrt(x));
}
#else
double Sqrt(double x) {
double z;
const int32_t sign = (Int16)0x80000000;
int32_t ix0,s0,q,m,t,i;
u_int32_t r,t1,s1,ix1,q1;
EXTRACT_WORDS(ix0,ix1,x);
/* take care of Inf and NaN */
if((ix0&0x7ff00000)==0x7ff00000) {
return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf
sqrt(-inf)=sNaN */
}
/* take care of zero */
if(ix0<=0) {
if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */
else if(ix0<0)
return (x-x)/(x-x); /* sqrt(-ve) = sNaN */
}
/* normalize x */
m = (ix0>>20);
if(m==0) { /* subnormal x */
while(ix0==0) {
m -= 21;
ix0 |= (ix1>>11); ix1 <<= 21;
}
for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1;
m -= i-1;
ix0 |= (ix1>>(32-i));
ix1 <<= i;
}
m -= 1023; /* unbias exponent */
ix0 = (ix0&0x000fffff)|0x00100000;
if(m&1){ /* odd m, double x to make it even */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
}
m >>= 1; /* m = [m/2] */
/* generate sqrt(x) bit by bit */
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */
r = 0x00200000; /* r = moving bit from right to left */
while(r!=0) {
t = s0+r;
if(t<=ix0) {
s0 = t+r;
ix0 -= t;
q += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
r = sign;
while(r!=0) {
t1 = s1+r;
t = s0;
if((t<ix0)||((t==ix0)&&(t1<=ix1))) {
s1 = t1+r;
if(((t1&sign)==sign)&&(s1&sign)==0) s0 += 1;
ix0 -= t;
if (ix1 < t1) ix0 -= 1;
ix1 -= t1;
q1 += r;
}
ix0 += ix0 + ((ix1&sign)>>31);
ix1 += ix1;
r>>=1;
}
/* use floating add to find out rounding direction */
if((ix0|ix1)!=0) {
z = one-tiny; /* trigger inexact flag */
if (z>=one) {
z = one+tiny;
if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;}
else if (z>one) {
if (q1==(u_int32_t)0xfffffffe) q+=1;
q1+=2;
} else
q1 += (q1&1);
}
}
ix0 = (q>>1)+0x3fe00000;
ix1 = q1>>1;
if ((q&1)==1) ix1 |= sign;
ix0 += (m <<20);
INSERT_WORDS(z,ix0,ix1);
return z;
}
#endif
#ifdef MATHLIB_FUNCS
double Sin(double x) {
return(sin(x));
}
double Cos(double x) {
return(cos(x));
}
#endif
#ifdef TABLE_FUNCS
static const float sin_tab[] = {
0.000000, 0.012272, 0.024541, 0.036807,
0.049068, 0.061321, 0.073565, 0.085797,
0.098017, 0.110222, 0.122411, 0.134581,
0.146730, 0.158858, 0.170962, 0.183040,
0.195090, 0.207111, 0.219101, 0.231058,
0.242980, 0.254866, 0.266713, 0.278520,
0.290285, 0.302006, 0.313682, 0.325310,
0.336890, 0.348419, 0.359895, 0.371317,
0.382683, 0.393992, 0.405241, 0.416430,
0.427555, 0.438616, 0.449611, 0.460539,
0.471397, 0.482184, 0.492898, 0.503538,
0.514103, 0.524590, 0.534998, 0.545325,
0.555570, 0.565732, 0.575808, 0.585798,
0.595699, 0.605511, 0.615232, 0.624860,
0.634393, 0.643832, 0.653173, 0.662416,
0.671559, 0.680601, 0.689541, 0.698376,
0.707107, 0.715731, 0.724247, 0.732654,
0.740951, 0.749136, 0.757209, 0.765167,
0.773010, 0.780737, 0.788346, 0.795837,
0.803208, 0.810457, 0.817585, 0.824589,
0.831470, 0.838225, 0.844854, 0.851355,
0.857729, 0.863973, 0.870087, 0.876070,
0.881921, 0.887640, 0.893224, 0.898674,
0.903989, 0.909168, 0.914210, 0.919114,
0.923880, 0.928506, 0.932993, 0.937339,
0.941544, 0.945607, 0.949528, 0.953306,
0.956940, 0.960431, 0.963776, 0.966976,
0.970031, 0.972940, 0.975702, 0.978317,
0.980785, 0.983105, 0.985278, 0.987301,
0.989177, 0.990903, 0.992480, 0.993907,
0.995185, 0.996313, 0.997290, 0.998118,
0.998795, 0.999322, 0.999699, 0.999925,
1.000000
};
double Sin(double x) {
const double percent = x/TWOPI;
const Int32 idx_untrimmed = (percent+200)*512;
const Int16 idx = idx_untrimmed % 512;
double retval = 0;
if (idx < 128)
retval = sin_tab[idx];
else if (idx < 256)
retval = sin_tab[256 - idx];
else if (idx < 384)
retval = -sin_tab[idx - 256];
else
retval = -sin_tab[512 - idx];
return(retval);
}
double Cos(double x) {
const double percent = x/TWOPI;
const Int32 idx_untrimmed = (percent+200)*512;
const Int16 idx = idx_untrimmed % 512;
double retval = 0;
if (idx < 128)
retval = sin_tab[128 - idx];
else if (idx < 256)
retval = -sin_tab[idx - 128];
else if (idx < 384)
retval = -sin_tab[384 - idx];
else
retval = sin_tab[idx - 384];
return(retval);
}
#endif
#ifdef FUNCS_121
// *********************************************************
// ***
// *** Routines to compute sine and cosine to 12.1 digits
// *** of accuracy.
// ***
// *********************************************************
//
// cos_121s computes cosine (x)
//
// Accurate to about 12.1 decimal digits over the range [0, pi/2].
// The input argument is in radians.
//
// Algorithm:
// cos(x)= c1 + c2*x**2 + c3*x**4 + c4*x**6 + c5*x**8 + c6*x**10 + c7*x**12
// which is the same as:
// cos(x)= c1 + x**2(c2 + c3*x**2 + c4*x**4 + c5*x**6 + c6*x**8 + c7*x**10)
// cos(x)= c1 + x**2(c2 + x**2(c3 + c4*x**2 + c5*x**4 + c6*x**6 + c7*x**8 ))
// cos(x)= c1 + x**2(c2 + x**2(c3 + x**2(c4 + c5*x**2 + c6*x**4 + c7*x**6 )))
// cos(x)= c1 + x**2(c2 + x**2(c3 + x**2(c4 + x**2(c5 + c6*x**2 + c7*x**4 ))))
// cos(x)= c1 + x**2(c2 + x**2(c3 + x**2(c4 + x**2(c5 + x**2(c6 + c7*x**2 )))))
//
double cos_121s(double x)
{
const double c1= 0.99999999999925182;
const double c2=-0.49999999997024012;
const double c3= 0.041666666473384543;
const double c4=-0.001388888418000423;
const double c5= 0.0000248010406484558;
const double c6=-0.0000002752469638432;
const double c7= 0.0000000019907856854;
double x2; // The input argument squared
x2=x * x;
return (c1 + x2*(c2 + x2*(c3 + x2*(c4 + x2*(c5 + x2*(c6 + c7*x2))))));
}
//
// This is the main cosine approximation "driver"
// It reduces the input argument's range to [0, pi/2],
// and then calls the approximator.
// See the notes for an explanation of the range reduction.
//
//double cos_121(double x){
double Cos(double x){
Int16 quad; // what quadrant are we in?
x=Fmod(x, TWOPI); // Get rid of values > 2* pi
if(x<0)x=-x; // cos(-x) = cos(x)
quad=(Int16)(x * TWOOVERPI); // Get quadrant # (0 to 3) we're in
switch (quad){
case 0: return cos_121s(x);
case 1: return -cos_121s(PI-x);
case 2: return -cos_121s(x-PI);
case 3: return cos_121s(TWOPI-x);
default: return cos_121s(x);
}
}
//
// The sine is just cosine shifted a half-pi, so
// we'll adjust the argument and call the cosine approximation.
//
//double sin_121(double x){
double Sin(double x){
return(Cos(HALFPI-x));
}
#endif
#ifdef FUNCS_32
// *********************************************************
// ***
// *** Routines to compute sine and cosine to 3.2 digits
// *** of accuracy.
// ***
// *********************************************************
//
// cos_32s computes cosine (x)
//
// Accurate to about 3.2 decimal digits over the range [0, pi/2].
// The input argument is in radians.
//
// Algorithm:
// cos(x)= c1 + c2*x**2 + c3*x**4
// which is the same as:
// cos(x)= c1 + x**2(c2 + c3*x**2)
//
float cos_32s(float x)
{
const float c1= 0.99940307;
const float c2=-0.49558072;
const float c3= 0.03679168;
float x2; // The input argument squared
x2=x * x;
return(c1 + x2*(c2 + c3 * x2));
}
//
// This is the main cosine approximation "driver"
// It reduces the input argument's range to [0, pi/2],
// and then calls the approximator.
// See the notes for an explanation of the range reduction.
//
double Cos(double inputx)
{
Int32 quad; // what quadrant are we in?
float x;
x=(float)(Fmod(inputx, TWOPI)); // Get rid of values > 2* pi
if(x<0)x=-x; // cos(-x) = cos(x)
quad=(Int32)(x * TWOOVERPI); // Get quadrant # (0 to 3) we're in
switch (quad){
case 0: return((double)cos_32s(x));
case 1: return((double)-cos_32s(PI-x));
case 2: return((double)-cos_32s(x-PI));
case 3: return((double)cos_32s(TWOPI-x));
default: return((double)cos_32s(x));
}
}
//
// The sine is just cosine shifted a half-pi, so
// we'll adjust the argument and call the cosine approximation.
//
//float sin_32(float x){
double Sin(double x){
return(Cos(HALFPI-x));
}
#endif
#ifdef MATHLIB_FUNCS
double Fabs(double x) {
return(fabs(x));
}
#else
double Fabs(double x) {
u_int32_t high;
GET_HIGH_WORD(high,x);
SET_HIGH_WORD(x,high&0x7fffffff);
return x;
}
#endif
double Fnabs (double value) {
if (Fabs (value) > 1.0) return (( value < 0.0) ? -1.0 : 1.0);
return(value);
}
#ifdef MATHLIB_FUNCS
double Fmod(double x, double y) {
return(fmod(x, y));
}
#else
double Fmod(double x, double y) {
return(x - y * Floor(x/y));
}
#endif
static const double
two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */
twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */
huge = 1.0e+300;
#ifdef MATHLIB_FUNCS
double Floor(double x) {
return(floor(x));
}
#else
double Floor(double x) {
int32_t i0,i1,j0;
u_int32_t i,j;
EXTRACT_WORDS(i0,i1,x);
j0 = ((i0>>20)&0x7ff)-0x3ff;
if(j0<20) {
if(j0<0) { /* raise inexact if x != 0 */
if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */
if(i0>=0) {
i0=i1=0;
} else if(((i0&0x7fffffff)|i1)!=0) {
i0=0xbff00000;i1=0;
}
}
} else {
i = (0x000fffff)>>j0;
if(((i0&i)|i1)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) i0 += (0x00100000)>>j0;
i0 &= (~i); i1=0;
}
}
} else if (j0>51) {
if(j0==0x400) return x+x; /* inf or NaN */
else return x; /* x is integral */
} else {
i = ((u_int32_t)(0xffffffff))>>(j0-20);
if((i1&i)==0) return x; /* x is integral */
if(huge+x>0.0) { /* raise inexact flag */
if(i0<0) {
if(j0==20) i0+=1;
else {
j = i1+(1<<(52-j0));
if(j<i1) i0 +=1 ; /* got a carry */
i1=j;
}
}
i1 &= (~i);
}
}
INSERT_WORDS(x,i0,i1);
return x;
}
#endif
#ifdef MATHLIB_FUNCS
double Ceil(double x) {
return(ceil(x));
}
#else
double Ceil(double x) {
if (Floor(x) < x) {
return(Floor(x)+1.0);
} else {
return(x);
}
}
#endif
#ifdef MATHLIB_FUNCS
double Atan(double x) {
return(atan(x));
}
#else
double Atan(double x) {
const double M_PI = 3.141592654;
const double A0 = 0.9999992083;
const double A1 = 0.3332870775;
const double B1 = 0.5985998078;
const double A2 = 0.0635500089;
const double B2 = 0.3953544718;
const double A0X = 0.2388229612;
const double A1X = 2.445205396;
const double B1X = 3.943529789;
const double A2X = 1.314747223;
const double B2X = 1.798249626;
// correct to 3e-7. 4 multiplies/divides
double x2;
double v;
x2 = x*x;
if (x > 1.0) v = M_PI/2 - (A0 - A1/(x2 + B1 - A2/(x2 + B2)))/x;
else if (x >= 0.0) v = x*(A0X + A1X/(x2 + B1X - A2X/(x2 + B2X)));
else v = -Atan(-x);
return v;
}
#endif
#ifdef MATHLIB_FUNCS
double Atan2(double y, double x) {
return(atan2(y, x));
}
#else
double Atan2(double y, double x) {
if (x > 0.0) {
return(Atan(y/x));
} else if (x < 0.0 && y >= 0.0) {
return(Atan(y/x) + PI);
} else if (x == 0.0 && y > 0.0) {
return(HALFPI);
} else if (x < 0.0 && y < 0.0) {
return(Atan(y/x) - PI);
} else if (x == 0.0 && y < 0.0) {
return(HALFPI * -1.0);
} else if (x == 0.0 && y == 0.0) {
return(0);
} else {
return(0);
}
}
#endif
#ifdef MATHLIB_FUNCS
double Asin(double x) {
return(asin(x));
}
#else
double Asin(double x) {
return(2.0*Atan(x/(1.0+Sqrt(1.0-x*x))));
}
#endif
#ifdef MATHLIB_FUNCS
double Acos(double x) {
return(acos(x));
}
#else
double Acos(double x) {
if (x >= 0.0) {
return(2.0*Atan(Sqrt((1.0-x)/(1.0+x))));
} else {
return(PI - 2.0*Atan(Sqrt((1.0+x)/(1.0-x))));
}
// return(PI/2.0 - Asin(x));
}
#endif
double acos(double x) {
return(PI/2.0 - asin(x));
}
Boolean LoadUnloadMathLib(Boolean load)
{
Err error;
UInt16 usecount;
if (load) {
/* Load the MathLib System Library */
error = SysLibFind(MathLibName, &MathLibRef);
if (error)
error = SysLibLoad(LibType, MathLibCreator, &MathLibRef);
ErrFatalDisplayIf(error, "Can't find MathLib"); // Just an example; handle it gracefully
error = MathLibOpen(MathLibRef, MathLibVersion);
ErrFatalDisplayIf(error, "Can't open MathLib");
} else {
error = MathLibClose(MathLibRef, &usecount);
ErrFatalDisplayIf(error, "Can't close MathLib");
if (usecount == 0)
SysLibRemove(MathLibRef);
}
return(true);
}
/*
NN.C - natural numbers routines
*/
//#include <PalmOS.h>
//#include "soarRSA.h"
//#include "soarNN.h"
#ifndef USEASM
/* Decodes character string b into a, where character string is ordered
from most to least significant.
Lengths: a[digits], b[len].
Assumes b[i] = 0 for i < len - digits * NN_DIGIT_LEN. (Otherwise most
significant bytes are truncated.)
*/
void NN_Decode (a, digits, b, len)
NN_DIGIT *a;
unsigned char *b;
unsigned int digits, len;
{
NN_DIGIT t;
unsigned int i, u;
int j;
/* @##$ unsigned/signed bug fix added JSAK - Fri 31/05/96 18:09:11 */
for (i = 0, j = len - 1; i < digits && j >= 0; i++) {
t = 0;
for (u = 0; j >= 0 && u < NN_DIGIT_BITS; j--, u += 8)
t |= ((NN_DIGIT)b[j]) << u;
a[i] = t;
}
for (; i < digits; i++)
a[i] = 0;
}
/* Encodes b into character string a, where character string is ordered
from most to least significant.
Lengths: a[len], b[digits].
Assumes NN_Bits (b, digits) <= 8 * len. (Otherwise most significant
digits are truncated.)
*/
void NN_Encode (a, len, b, digits)
NN_DIGIT *b;
unsigned char *a;
unsigned int digits, len;
{
NN_DIGIT t;
unsigned int i, u;
int j;
/* @##$ unsigned/signed bug fix added JSAK - Fri 31/05/96 18:09:11 */
for (i = 0, j = len - 1; i < digits && j >= 0; i++) {
t = b[i];
for (u = 0; j >= 0 && u < NN_DIGIT_BITS; j--, u += 8)
a[j] = (unsigned char)(t >> u);
}
for (; j >= 0; j--)
a[j] = 0;
}
/* Assigns a = 0. */
void NN_AssignZero (a, digits)
NN_DIGIT *a;
unsigned int digits;
{
if(digits) {
do {
*a++ = 0;
}while(--digits);
}
}
#endif
/* Assigns a = 2^b.
Lengths: a[digits].
Requires b < digits * NN_DIGIT_BITS.
*/
void NN_Assign2Exp (a, b, digits)
NN_DIGIT *a;
unsigned int b, digits;
{
NN_AssignZero (a, digits);
if (b >= digits * NN_DIGIT_BITS)
return;
a[b / NN_DIGIT_BITS] = (NN_DIGIT)1 << (b % NN_DIGIT_BITS);
}
/* Computes a = b - c. Returns borrow.
Lengths: a[digits], b[digits], c[digits].
*/
NN_DIGIT NN_Sub (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
NN_DIGIT temp, borrow = 0;
if(digits)
do {
/* Bug fix 16/10/95 - JSK, code below removed, caused bug with
Sun Compiler SC4.
if((temp = (*b++) - borrow) == MAX_NN_DIGIT)
temp = MAX_NN_DIGIT - *c++;
*/
temp = *b - borrow;
b++;
if(temp == MAX_NN_DIGIT) {
temp = MAX_NN_DIGIT - *c;
c++;
}else { /* Patch to prevent bug for Sun CC */
if((temp -= *c) > (MAX_NN_DIGIT - *c))
borrow = 1;
else
borrow = 0;
c++;
}
*a++ = temp;
}while(--digits);
return(borrow);
}
/* Computes a = b * c.
Lengths: a[2*digits], b[digits], c[digits].
Assumes digits < MAX_NN_DIGITS.
*/
void NN_Mult (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
NN_DIGIT t[2*MAX_NN_DIGITS];
NN_DIGIT dhigh, dlow, carry;
unsigned int bDigits, cDigits, i, j;
NN_AssignZero (t, 2 * digits);
bDigits = NN_Digits (b, digits);
cDigits = NN_Digits (c, digits);
for (i = 0; i < bDigits; i++) {
carry = 0;
if(*(b+i) != 0) {
for(j = 0; j < cDigits; j++) {
dmult(*(b+i), *(c+j), &dhigh, &dlow);
if((*(t+(i+j)) = *(t+(i+j)) + carry) < carry)
carry = 1;
else
carry = 0;
if((*(t+(i+j)) += dlow) < dlow)
carry++;
carry += dhigh;
}
}
*(t+(i+cDigits)) += carry;
}
NN_Assign(a, t, 2 * digits);
}
/* Computes a = b * 2^c (i.e., shifts left c bits), returning carry.
Requires c < NN_DIGIT_BITS. */
NN_DIGIT NN_LShift (a, b, c, digits)
NN_DIGIT *a, *b;
unsigned int c, digits;
{
NN_DIGIT temp, carry = 0;
unsigned int t;
if(c < NN_DIGIT_BITS)
if(digits) {
t = NN_DIGIT_BITS - c;
do {
temp = *b++;
*a++ = (temp << c) | carry;
carry = c ? (temp >> t) : 0;
}while(--digits);
}
return (carry);
}
/* Computes a = c div 2^c (i.e., shifts right c bits), returning carry.
Requires: c < NN_DIGIT_BITS. */
NN_DIGIT NN_RShift (a, b, c, digits)
NN_DIGIT *a, *b;
unsigned int c, digits;
{
NN_DIGIT temp, carry = 0;
unsigned int t;
if(c < NN_DIGIT_BITS)
if(digits) {
t = NN_DIGIT_BITS - c;
do {
digits--;
temp = *(b+digits);
*(a+digits) = (temp >> c) | carry;
carry = c ? (temp << t) : 0;
}while(digits);
}
return (carry);
}
/* Computes a = c div d and b = c mod d.
Lengths: a[cDigits], b[dDigits], c[cDigits], d[dDigits].
Assumes d > 0, cDigits < 2 * MAX_NN_DIGITS,
dDigits < MAX_NN_DIGITS.
*/
void NN_Div (a, b, c, cDigits, d, dDigits)
NN_DIGIT *a, *b, *c, *d;
unsigned int cDigits, dDigits;
{
NN_DIGIT ai, cc[2*MAX_NN_DIGITS+1], dd[MAX_NN_DIGITS], s;
NN_DIGIT t[2], u, v, *ccptr;
NN_HALF_DIGIT aHigh, aLow, cHigh, cLow;
int i;
unsigned int ddDigits, shift;
ddDigits = NN_Digits (d, dDigits);
if(ddDigits == 0)
return;
shift = NN_DIGIT_BITS - NN_DigitBits (d[ddDigits-1]);
NN_AssignZero (cc, ddDigits);
cc[cDigits] = NN_LShift (cc, c, shift, cDigits);
NN_LShift (dd, d, shift, ddDigits);
s = dd[ddDigits-1];
NN_AssignZero (a, cDigits);
for (i = cDigits-ddDigits; i >= 0; i--) {
if (s == MAX_NN_DIGIT)
ai = cc[i+ddDigits];
else {
ccptr = &cc[i+ddDigits-1];
s++;
cHigh = (NN_HALF_DIGIT)HIGH_HALF (s);
cLow = (NN_HALF_DIGIT)LOW_HALF (s);
*t = *ccptr;
*(t+1) = *(ccptr+1);
if (cHigh == MAX_NN_HALF_DIGIT)
aHigh = (NN_HALF_DIGIT)HIGH_HALF (*(t+1));
else
aHigh = (NN_HALF_DIGIT)(*(t+1) / (cHigh + 1));
u = (NN_DIGIT)aHigh * (NN_DIGIT)cLow;
v = (NN_DIGIT)aHigh * (NN_DIGIT)cHigh;
if ((*t -= TO_HIGH_HALF (u)) > (MAX_NN_DIGIT - TO_HIGH_HALF (u)))
t[1]--;
*(t+1) -= HIGH_HALF (u);
*(t+1) -= v;
while ((*(t+1) > cHigh) ||
((*(t+1) == cHigh) && (*t >= TO_HIGH_HALF (cLow)))) {
if ((*t -= TO_HIGH_HALF (cLow)) > MAX_NN_DIGIT - TO_HIGH_HALF (cLow))
t[1]--;
*(t+1) -= cHigh;
aHigh++;
}
if (cHigh == MAX_NN_HALF_DIGIT)
aLow = (NN_HALF_DIGIT)LOW_HALF (*(t+1));
else
aLow =
(NN_HALF_DIGIT)((TO_HIGH_HALF (*(t+1)) + HIGH_HALF (*t)) / (cHigh + 1));
u = (NN_DIGIT)aLow * (NN_DIGIT)cLow;
v = (NN_DIGIT)aLow * (NN_DIGIT)cHigh;
if ((*t -= u) > (MAX_NN_DIGIT - u))
t[1]--;
if ((*t -= TO_HIGH_HALF (v)) > (MAX_NN_DIGIT - TO_HIGH_HALF (v)))
t[1]--;
*(t+1) -= HIGH_HALF (v);
while ((*(t+1) > 0) || ((*(t+1) == 0) && *t >= s)) {
if ((*t -= s) > (MAX_NN_DIGIT - s))
t[1]--;
aLow++;
}
ai = TO_HIGH_HALF (aHigh) + aLow;
s--;
}
cc[i+ddDigits] -= subdigitmult(&cc[i], &cc[i], ai, dd, ddDigits);
while (cc[i+ddDigits] || (NN_Cmp (&cc[i], dd, ddDigits) >= 0)) {
ai++;
cc[i+ddDigits] -= NN_Sub (&cc[i], &cc[i], dd, ddDigits);
}
a[i] = ai;
}
NN_AssignZero (b, dDigits);
NN_RShift (b, cc, shift, ddDigits);
}
/* Computes a = b mod c.
Lengths: a[cDigits], b[bDigits], c[cDigits].
Assumes c > 0, bDigits < 2 * MAX_NN_DIGITS, cDigits < MAX_NN_DIGITS.
*/
void NN_Mod (a, b, bDigits, c, cDigits)
NN_DIGIT *a, *b, *c;
unsigned int bDigits, cDigits;
{
NN_DIGIT t[2 * MAX_NN_DIGITS];
NN_Div (t, a, b, bDigits, c, cDigits);
}
/* Computes a = b * c mod d.
Lengths: a[digits], b[digits], c[digits], d[digits].
Assumes d > 0, digits < MAX_NN_DIGITS.
*/
void NN_ModMult (a, b, c, d, digits)
NN_DIGIT *a, *b, *c, *d;
unsigned int digits;
{
NN_DIGIT t[2*MAX_NN_DIGITS];
NN_Mult (t, b, c, digits);
NN_Mod (a, t, 2 * digits, d, digits);
}
/* Computes a = b^c mod d.
Lengths: a[dDigits], b[dDigits], c[cDigits], d[dDigits].
Assumes d > 0, cDigits > 0, dDigits < MAX_NN_DIGITS.
*/
void NN_ModExp (a, b, c, cDigits, d, dDigits)
NN_DIGIT *a, *b, *c, *d;
unsigned int cDigits, dDigits;
{
NN_DIGIT bPower[3][MAX_NN_DIGITS], ci, t[MAX_NN_DIGITS];
int i;
unsigned int ciBits, j, s;
/* Store b, b^2 mod d, and b^3 mod d.
*/
NN_Assign (bPower[0], b, dDigits);
NN_ModMult (bPower[1], bPower[0], b, d, dDigits);
NN_ModMult (bPower[2], bPower[1], b, d, dDigits);
NN_ASSIGN_DIGIT (t, 1, dDigits);
cDigits = NN_Digits (c, cDigits);
for (i = cDigits - 1; i >= 0; i--) {
ci = c[i];
ciBits = NN_DIGIT_BITS;
/* Scan past leading zero bits of most significant digit.
*/
if (i == (int)(cDigits - 1)) {
while (! DIGIT_2MSB (ci)) {
ci <<= 2;
ciBits -= 2;
}
}
for (j = 0; j < ciBits; j += 2, ci <<= 2) {
/* Compute t = t^4 * b^s mod d, where s = two MSB's of ci. */
NN_ModMult (t, t, t, d, dDigits);
NN_ModMult (t, t, t, d, dDigits);
if ((s = DIGIT_2MSB (ci)) != 0)
NN_ModMult (t, t, bPower[s-1], d, dDigits);
}
}
NN_Assign (a, t, dDigits);
}
/* Compute a = 1/b mod c, assuming inverse exists.
Lengths: a[digits], b[digits], c[digits].
Assumes gcd (b, c) = 1, digits < MAX_NN_DIGITS.
*/
void NN_ModInv (a, b, c, digits)
NN_DIGIT *a, *b, *c;
unsigned int digits;
{
NN_DIGIT q[MAX_NN_DIGITS], t1[MAX_NN_DIGITS], t3[MAX_NN_DIGITS],
u1[MAX_NN_DIGITS], u3[MAX_NN_DIGITS], v1[MAX_NN_DIGITS],
v3[MAX_NN_DIGITS], w[2*MAX_NN_DIGITS];
int u1Sign;
/* Apply extended Euclidean algorithm, modified to avoid negative
numbers.
*/
NN_ASSIGN_DIGIT (u1, 1, digits);
NN_AssignZero (v1, digits);
NN_Assign (u3, b, digits);
NN_Assign (v3, c, digits);
u1Sign = 1;
while (! NN_Zero (v3, digits)) {
NN_Div (q, t3, u3, digits, v3, digits);
NN_Mult (w, q, v1, digits);
NN_Add (t1, u1, w, digits);
NN_Assign (u1, v1, digits);
NN_Assign (v1, t1, digits);
NN_Assign (u3, v3, digits);
NN_Assign (v3, t3, digits);
u1Sign = -u1Sign;
}
/* Negate result if sign is negative. */
if (u1Sign < 0)
NN_Sub (a, c, u1, digits);
else
NN_Assign (a, u1, digits);
}
/* Computes a = gcd(b, c).
Assumes b > c, digits < MAX_NN_DIGITS.