Fix code formatting in mpa.c

This includes the overridden mpa.c in power4.
This commit is contained in:
Siddhesh Poyarekar 2013-01-14 21:31:25 +05:30
parent e34ab70550
commit 1066a53440
4 changed files with 1487 additions and 718 deletions

View File

@ -1,5 +1,9 @@
2013-01-14 Siddhesh Poyarekar <siddhesh@redhat.com>
* sysdeps/ieee754/dbl-64/mpa.c: Fix formatting.
* sysdeps/powerpc/powerpc32/power4/fpu/mpa.c: Likewise.
* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c: Likewise.
* sysdeps/powerpc/powerpc32/power4/fpu/mpa.c (__inv): Remove
local variable MPTWO.
* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (__inv):

View File

@ -60,30 +60,45 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */
static int
mcr(const mp_no *x, const mp_no *y, int p) {
mcr (const mp_no *x, const mp_no *y, int p)
{
int i;
for (i=1; i<=p; i++) {
if (X[i] == Y[i]) continue;
else if (X[i] > Y[i]) return 1;
else return -1; }
for (i = 1; i <= p; i++)
{
if (X[i] == Y[i])
continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0;
}
/* Compare the absolute values of two multiple precision numbers. */
int
__acr(const mp_no *x, const mp_no *y, int p) {
__acr (const mp_no *x, const mp_no *y, int p)
{
int i;
if (X[0] == ZERO) {
if (Y[0] == ZERO) i= 0;
else i=-1;
}
else if (Y[0] == ZERO) i= 1;
else {
if (EX > EY) i= 1;
else if (EX < EY) i=-1;
else i= mcr(x,y,p);
}
if (X[0] == ZERO)
{
if (Y[0] == ZERO)
i = 0;
else
i = -1;
}
else if (Y[0] == ZERO)
i = 1;
else
{
if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
}
return i;
}
@ -92,59 +107,86 @@ __acr(const mp_no *x, const mp_no *y, int p) {
#ifndef NO___CPY
/* Copy multiple precision number X into Y. They could be the same
number. */
void __cpy(const mp_no *x, mp_no *y, int p) {
void
__cpy (const mp_no *x, mp_no *y, int p)
{
EY = EX;
for (int i=0; i <= p; i++) Y[i] = X[i];
for (int i = 0; i <= p; i++)
Y[i] = X[i];
}
#endif
#ifndef NO___MP_DBL
/* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */
static void norm(const mp_no *x, double *y, int p)
static void
norm (const mp_no *x, double *y, int p)
{
#define R RADIXI
#define R RADIXI
int i;
double a,c,u,v,z[5];
if (p<5) {
if (p==1) c = X[1];
else if (p==2) c = X[1] + R* X[2];
else if (p==3) c = X[1] + R*(X[2] + R* X[3]);
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]);
}
else {
for (a=ONE, z[1]=X[1]; z[1] < TWO23; )
{a *= TWO; z[1] *= TWO; }
for (i=2; i<5; i++) {
z[i] = X[i]*a;
u = (z[i] + CUTTER)-CUTTER;
if (u > z[i]) u -= RADIX;
z[i] -= u;
z[i-1] += u*RADIXI;
double a, c, u, v, z[5];
if (p < 5)
{
if (p == 1)
c = X[1];
else if (p == 2)
c = X[1] + R * X[2];
else if (p == 3)
c = X[1] + R * (X[2] + R * X[3]);
else if (p == 4)
c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
}
u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19;
v = z[3]-u;
if (v == TWO18) {
if (z[4] == ZERO) {
for (i=5; i <= p; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{
a *= TWO;
z[1] *= TWO;
}
}
else z[3] += ONE;
}
c = (z[1] + R *(z[2] + R * z[3]))/a;
}
for (i = 2; i < 5; i++)
{
z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER;
if (u > z[i])
u -= RADIX;
z[i] -= u;
z[i - 1] += u * RADIXI;
}
u = (z[3] + TWO71) - TWO71;
if (u > z[3])
u -= TWO19;
v = z[3] - u;
if (v == TWO18)
{
if (z[4] == ZERO)
{
for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
else
z[3] += ONE;
}
c = (z[1] + R * (z[2] + R * z[3])) / a;
}
c *= X[0];
for (i=1; i<EX; i++) c *= RADIX;
for (i=1; i>EX; i--) c *= RADIXI;
for (i = 1; i < EX; i++)
c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c;
#undef R
@ -152,58 +194,129 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */
static void denorm(const mp_no *x, double *y, int p)
static void
denorm (const mp_no *x, double *y, int p)
{
int i,k;
double c,u,z[5];
int i, k;
double c, u, z[5];
#define R RADIXI
if (EX<-44 || (EX==-44 && X[1]<TWO5))
{ *y=ZERO; return; }
if (EX < -44 || (EX == -44 && X[1] < TWO5))
{
*y = ZERO;
return;
}
if (p==1) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=ZERO; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=ZERO; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else if (p==2) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=X[2]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; k=1;}
z[3] = X[k];
}
if (p == 1)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = ZERO;
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else if (p == 2)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = X[2];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
k = 1;
}
z[3] = X[k];
}
u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5;
if (u > z[3])
u -= TWO5;
if (u==z[3]) {
for (i=k+1; i <= p; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
if (u == z[3])
{
for (i = k + 1; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
}
c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10);
c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
*y = c*TWOM1032;
*y = c * TWOM1032;
#undef R
}
/* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */
void __mp_dbl(const mp_no *x, double *y, int p) {
if (X[0] == ZERO) {*y = ZERO; return; }
void
__mp_dbl (const mp_no *x, double *y, int p)
{
if (X[0] == ZERO)
{
*y = ZERO;
return;
}
if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10)))
norm(x,y,p);
norm (x, y, p);
else
denorm(x,y,p);
denorm (x, y, p);
}
#endif
@ -211,27 +324,44 @@ void __mp_dbl(const mp_no *x, double *y, int p) {
small, the result is truncated. */
void
SECTION
__dbl_mp(double x, mp_no *y, int p) {
int i,n;
__dbl_mp (double x, mp_no *y, int p)
{
int i, n;
double u;
/* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; }
else if (x > ZERO) Y[0] = ONE;
else {Y[0] = MONE; x=-x; }
if (x == ZERO)
{
Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
for ( ; x < ONE; EY -= ONE) x *= RADIX;
for (EY = ONE; x >= RADIX; EY += ONE)
x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */
n=MIN(p,4);
for (i=1; i<=n; i++) {
u = (x + TWO52) - TWO52;
if (u>x) u -= ONE;
Y[i] = u; x -= u; x *= RADIX; }
for ( ; i<=p; i++) Y[i] = ZERO;
n = MIN (p, 4);
for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52;
if (u > x)
u -= ONE;
Y[i] = u;
x -= u;
x *= RADIX;
}
for (; i <= p; i++)
Y[i] = ZERO;
}
/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
@ -240,39 +370,55 @@ __dbl_mp(double x, mp_no *y, int p) {
truncated. */
static void
SECTION
add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
int i,j,k;
add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k;
EZ = EX;
i=p; j=p+ EY - EX; k=p+1;
i = p;
j = p + EY - EX;
k = p + 1;
if (j<1)
{__cpy(x,z,p); return; }
else Z[k] = ZERO;
if (j < 1)
{
__cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) {
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
if (Z[1] == ZERO) {
for (i=1; i<=p; i++) Z[i] = Z[i+1]; }
else EZ += ONE;
if (Z[1] == ZERO)
{
for (i = 1; i <= p; i++)
Z[i] = Z[i + 1];
}
else
EZ += ONE;
}
/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
@ -281,52 +427,73 @@ add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
ULP. */
static void
SECTION
sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
int i,j,k;
sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k;
EZ = EX;
if (EX == EY) {
i=j=k=p;
Z[k] = Z[k+1] = ZERO; }
else {
j= EX - EY;
if (j > p) {__cpy(x,z,p); return; }
else {
i=p; j=p+1-j; k=p;
if (Y[j] > ZERO) {
Z[k+1] = RADIX - Y[j--];
Z[k] = MONE; }
else {
Z[k+1] = ZERO;
Z[k] = ZERO; j--;}
if (EX == EY)
{
i = j = k = p;
Z[k] = Z[k + 1] = ZERO;
}
else
{
j = EX - EY;
if (j > p)
{
__cpy (x, z, p);
return;
}
else
{
i = p;
j = p + 1 - j;
k = p;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE;
}
else
{
Z[k + 1] = ZERO;
Z[k] = ZERO;
j--;
}
}
}
}
for (; j>0; i--,j--) {
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (i=1; Z[i] == ZERO; i++) ;
for (i = 1; Z[i] == ZERO; i++);
EZ = EZ - i + 1;
for (k=1; i <= p+1; )
for (k = 1; i <= p + 1;)
Z[k++] = Z[i++];
for (; k <= p; )
for (; k <= p;)
Z[k++] = ZERO;
}
@ -335,22 +502,49 @@ sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
ULP. */
void
SECTION
__add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] == Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = Y[0]; }
else Z[0] = ZERO;
}
if (X[0] == Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
else
Z[0] = ZERO;
}
}
/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
@ -358,22 +552,50 @@ __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
one ULP. */
void
SECTION
__sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
Z[0] = -Z[0];
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] != Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
else Z[0] = ZERO;
}
if (X[0] != Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
else
Z[0] = ZERO;
}
}
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
@ -381,15 +603,15 @@ __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
digits. In case P > 3 the error is bounded by 1.001 ULP. */
void
SECTION
__mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k, k2;
double u;
/* Is z=0? */
if (__glibc_unlikely (X[0] * Y[0] == ZERO))
{
Z[0]=ZERO;
Z[0] = ZERO;
return;
}
@ -397,7 +619,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
k2 = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
Z[k2] = ZERO;
for (k = k2; k > p; )
for (k = k2; k > p;)
{
for (i = k - p, j = p; i < p + 1; i++, j--)
Z[k] += X[i] * Y[j];
@ -411,7 +633,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
while (k > 1)
{
for (i = 1,j = k - 1; i < k; i++, j--)
for (i = 1, j = k - 1; i < k; i++, j--)
Z[k] += X[i] * Y[j];
u = (Z[k] + CUTTER) - CUTTER;
@ -426,7 +648,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
if (__glibc_unlikely (Z[1] == ZERO))
{
for (i = 1; i <= p; i++)
Z[i] = Z[i+1];
Z[i] = Z[i + 1];
EZ--;
}
@ -439,24 +661,32 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */
static
static void
SECTION
void __inv(const mp_no *x, mp_no *y, int p) {
__inv (const mp_no *x, mp_no *y, int p)
{
int i;
double t;
mp_no z,w;
static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
mp_no z, w;
static const int np1[] =
{ 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
};
__cpy(x,&z,p); z.e=0; __mp_dbl(&z,&t,p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX;
__cpy (x, &z, p);
z.e = 0;
__mp_dbl (&z, &t, p);
t = ONE / t;
__dbl_mp (t, y, p);
EY -= EX;
for (i=0; i<np1[p]; i++) {
__cpy(y,&w,p);
__mul(x,&w,y,p);
__sub(&mptwo,y,&z,p);
__mul(&w,&z,y,p);
}
for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p);
__mul (x, &w, y, p);
__sub (&mptwo, y, &z, p);
__mul (&w, &z, y, p);
}
}
/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
@ -468,10 +698,15 @@ void __inv(const mp_no *x, mp_no *y, int p) {
*X = 0 is not permissible. */
void
SECTION
__dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
mp_no w;
if (X[0] == ZERO) Z[0] = ZERO;
else {__inv(y,&w,p); __mul(x,&w,z,p);}
if (X[0] == ZERO)
Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
}

View File

@ -51,91 +51,135 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */
static int mcr(const mp_no *x, const mp_no *y, int p) {
static int
mcr (const mp_no *x, const mp_no *y, int p)
{
long i;
long p2 = p;
for (i=1; i<=p2; i++) {
if (X[i] == Y[i]) continue;
else if (X[i] > Y[i]) return 1;
else return -1; }
for (i = 1; i <= p2; i++)
{
if (X[i] == Y[i])
continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0;
}
/* Compare the absolute values of two multiple precision numbers. */
int __acr(const mp_no *x, const mp_no *y, int p) {
int
__acr (const mp_no *x, const mp_no *y, int p)
{
long i;
if (X[0] == ZERO) {
if (Y[0] == ZERO) i= 0;
else i=-1;
}
else if (Y[0] == ZERO) i= 1;
else {
if (EX > EY) i= 1;
else if (EX < EY) i=-1;
else i= mcr(x,y,p);
}
if (X[0] == ZERO)
{
if (Y[0] == ZERO)
i = 0;
else
i = -1;
}
else if (Y[0] == ZERO)
i = 1;
else
{
if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
}
return i;
}
/* Copy multiple precision number X into Y. They could be the same
number. */
void __cpy(const mp_no *x, mp_no *y, int p) {
void
__cpy (const mp_no *x, mp_no *y, int p)
{
long i;
EY = EX;
for (i=0; i <= p; i++) Y[i] = X[i];
for (i = 0; i <= p; i++)
Y[i] = X[i];
return;
}
/* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */
static void norm(const mp_no *x, double *y, int p)
static void
norm (const mp_no *x, double *y, int p)
{
#define R RADIXI
#define R RADIXI
long i;
double a,c,u,v,z[5];
if (p<5) {
if (p==1) c = X[1];
else if (p==2) c = X[1] + R* X[2];
else if (p==3) c = X[1] + R*(X[2] + R* X[3]);
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]);
}
else {
for (a=ONE, z[1]=X[1]; z[1] < TWO23; )
{a *= TWO; z[1] *= TWO; }
for (i=2; i<5; i++) {
z[i] = X[i]*a;
u = (z[i] + CUTTER)-CUTTER;
if (u > z[i]) u -= RADIX;
z[i] -= u;
z[i-1] += u*RADIXI;
double a, c, u, v, z[5];
if (p < 5)
{
if (p == 1)
c = X[1];
else if (p == 2)
c = X[1] + R * X[2];
else if (p == 3)
c = X[1] + R * (X[2] + R * X[3]);
else if (p == 4)
c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
}
else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{
a *= TWO;
z[1] *= TWO;
}
u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19;
v = z[3]-u;
for (i = 2; i < 5; i++)
{
z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER;
if (u > z[i])
u -= RADIX;
z[i] -= u;
z[i - 1] += u * RADIXI;
}
if (v == TWO18) {
if (z[4] == ZERO) {
for (i=5; i <= p; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
}
}
else z[3] += ONE;
u = (z[3] + TWO71) - TWO71;
if (u > z[3])
u -= TWO19;
v = z[3] - u;
if (v == TWO18)
{
if (z[4] == ZERO)
{
for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
else
z[3] += ONE;
}
c = (z[1] + R * (z[2] + R * z[3])) / a;
}
c = (z[1] + R *(z[2] + R * z[3]))/a;
}
c *= X[0];
for (i=1; i<EX; i++) c *= RADIX;
for (i=1; i>EX; i--) c *= RADIXI;
for (i = 1; i < EX; i++)
c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c;
return;
@ -144,46 +188,112 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */
static void denorm(const mp_no *x, double *y, int p)
static void
denorm (const mp_no *x, double *y, int p)
{
long i,k;
long i, k;
long p2 = p;
double c,u,z[5];
double c, u, z[5];
#define R RADIXI
if (EX<-44 || (EX==-44 && X[1]<TWO5))
{ *y=ZERO; return; }
if (EX < -44 || (EX == -44 && X[1] < TWO5))
{
*y = ZERO;
return;
}
if (p2==1) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=ZERO; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=ZERO; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else if (p2==2) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=X[2]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; k=1;}
z[3] = X[k];
}
if (p2 == 1)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = ZERO;
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else if (p2 == 2)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = X[2];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
k = 1;
}
z[3] = X[k];
}
u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5;
if (u > z[3])
u -= TWO5;
if (u==z[3]) {
for (i=k+1; i <= p2; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
if (u == z[3])
{
for (i = k + 1; i <= p2; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
}
c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10);
c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
*y = c*TWOM1032;
*y = c * TWOM1032;
return;
#undef R
@ -191,39 +301,65 @@ static void denorm(const mp_no *x, double *y, int p)
/* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */
void __mp_dbl(const mp_no *x, double *y, int p) {
void
__mp_dbl (const mp_no *x, double *y, int p)
{
if (X[0] == ZERO)
{
*y = ZERO;
return;
}
if (X[0] == ZERO) {*y = ZERO; return; }
if (EX> -42) norm(x,y,p);
else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
else denorm(x,y,p);
if (EX > -42)
norm (x, y, p);
else if (EX == -42 && X[1] >= TWO10)
norm (x, y, p);
else
denorm (x, y, p);
}
/* Get the multiple precision equivalent of X into *Y. If the precision is too
small, the result is truncated. */
void __dbl_mp(double x, mp_no *y, int p) {
long i,n;
void
__dbl_mp (double x, mp_no *y, int p)
{
long i, n;
long p2 = p;
double u;
/* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; }
else if (x > ZERO) Y[0] = ONE;
else {Y[0] = MONE; x=-x; }
if (x == ZERO)
{
Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
for ( ; x < ONE; EY -= ONE) x *= RADIX;
for (EY = ONE; x >= RADIX; EY += ONE)
x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */
n=MIN(p2,4);
for (i=1; i<=n; i++) {
u = (x + TWO52) - TWO52;
if (u>x) u -= ONE;
Y[i] = u; x -= u; x *= RADIX; }
for ( ; i<=p2; i++) Y[i] = ZERO;
n = MIN (p2, 4);
for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52;
if (u > x)
u -= ONE;
Y[i] = u;
x -= u;
x *= RADIX;
}
for (; i <= p2; i++)
Y[i] = ZERO;
return;
}
@ -231,93 +367,132 @@ void __dbl_mp(double x, mp_no *y, int p) {
sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
Y and Z. No guard digit is used. The result equals the exact sum,
truncated. */
static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
long i,j,k;
static void
add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k;
long p2 = p;
EZ = EX;
i=p2; j=p2+ EY - EX; k=p2+1;
i = p2;
j = p2 + EY - EX;
k = p2 + 1;
if (j<1)
{__cpy(x,z,p); return; }
else Z[k] = ZERO;
if (j < 1)
{
__cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) {
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
if (Z[1] == ZERO) {
for (i=1; i<=p2; i++) Z[i] = Z[i+1]; }
else EZ += ONE;
if (Z[1] == ZERO)
{
for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
}
else
EZ += ONE;
}
/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
The sign of the difference *Z is not changed. X and Y may overlap but not X
and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */
static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
long i,j,k;
static void
sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k;
long p2 = p;
EZ = EX;
if (EX == EY) {
i=j=k=p2;
Z[k] = Z[k+1] = ZERO; }
else {
j= EX - EY;
if (j > p2) {__cpy(x,z,p); return; }
else {
i=p2; j=p2+1-j; k=p2;
if (Y[j] > ZERO) {
Z[k+1] = RADIX - Y[j--];
Z[k] = MONE; }
else {
Z[k+1] = ZERO;
Z[k] = ZERO; j--;}
if (EX == EY)
{
i = j = k = p2;
Z[k] = Z[k + 1] = ZERO;
}
else
{
j = EX - EY;
if (j > p2)
{
__cpy (x, z, p);
return;
}
else
{
i = p2;
j = p2 + 1 - j;
k = p2;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE;
}
else
{
Z[k + 1] = ZERO;
Z[k] = ZERO;
j--;
}
}
}
}
for (; j>0; i--,j--) {
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (i=1; Z[i] == ZERO; i++) ;
for (i = 1; Z[i] == ZERO; i++);
EZ = EZ - i + 1;
for (k=1; i <= p2+1; )
for (k = 1; i <= p2 + 1;)
Z[k++] = Z[i++];
for (; k <= p2; )
for (; k <= p2;)
Z[k++] = ZERO;
return;
@ -326,111 +501,186 @@ static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */
void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] == Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = Y[0]; }
else Z[0] = ZERO;
}
if (X[0] == Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
else
Z[0] = ZERO;
}
return;
}
/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
not X and Z or Y and Z. One guard digit is used. The error is less than
one ULP. */
void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
Z[0] = -Z[0];
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] != Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
else Z[0] = ZERO;
}
if (X[0] != Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
else
Z[0] = ZERO;
}
return;
}
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
digits. In case P > 3 the error is bounded by 1.001 ULP. */
void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, i1, i2, j, k, k2;
long p2 = p;
double u, zk, zk2;
/* Is z=0? */
if (X[0]*Y[0]==ZERO)
{ Z[0]=ZERO; return; }
/* Is z=0? */
if (X[0] * Y[0] == ZERO)
{
Z[0] = ZERO;
return;
}
/* Multiply, add and carry */
k2 = (p2<3) ? p2+p2 : p2+3;
zk = Z[k2]=ZERO;
for (k=k2; k>1; ) {
if (k > p2) {i1=k-p2; i2=p2+1; }
else {i1=1; i2=k; }
/* Multiply, add and carry */
k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
zk = Z[k2] = ZERO;
for (k = k2; k > 1;)
{
if (k > p2)
{
i1 = k - p2;
i2 = p2 + 1;
}
else
{
i1 = 1;
i2 = k;
}
#if 1
/* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have
dual symmetrical FP pipelines. */
if (i1 < (i2-1))
{
/* Make sure we have at least 2 iterations. */
if (((i2 - i1) & 1L) == 1L)
/* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have
dual symmetrical FP pipelines. */
if (i1 < (i2 - 1))
{
/* Handle the odd iterations case. */
zk2 = x->d[i2-1]*y->d[i1];
/* Make sure we have at least 2 iterations. */
if (((i2 - i1) & 1L) == 1L)
{
/* Handle the odd iterations case. */
zk2 = x->d[i2 - 1] * y->d[i1];
}
else
zk2 = 0.0;
/* Do two multiply/adds per loop iteration, using independent
accumulators; zk and zk2. */
for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
{
zk += x->d[i] * y->d[j];
zk2 += x->d[i + 1] * y->d[j - 1];
}
zk += zk2; /* Final sum. */
}
else
zk2 = 0.0;
/* Do two multiply/adds per loop iteration, using independent
accumulators; zk and zk2. */
for (i=i1,j=i2-1; i<i2-1; i+=2,j-=2)
else
{
zk += x->d[i]*y->d[j];
zk2 += x->d[i+1]*y->d[j-1];
/* Special case when iterations is 1. */
zk += x->d[i1] * y->d[i1];
}
zk += zk2; /* Final sum. */
}
else
{
/* Special case when iterations is 1. */
zk += x->d[i1]*y->d[i1];
}
#else
/* The original code. */
for (i=i1,j=i2-1; i<i2; i++,j--) zk += X[i]*Y[j];
/* The original code. */
for (i = i1, j = i2 - 1; i < i2; i++, j--)
zk += X[i] * Y[j];
#endif
u = (zk + CUTTER)-CUTTER;
if (u > zk) u -= RADIX;
Z[k] = zk - u;
zk = u*RADIXI;
--k;
}
u = (zk + CUTTER) - CUTTER;
if (u > zk)
u -= RADIX;
Z[k] = zk - u;
zk = u * RADIXI;
--k;
}
Z[k] = zk;
/* Is there a carry beyond the most significant digit? */
if (Z[1] == ZERO) {
for (i=1; i<=p2; i++) Z[i]=Z[i+1];
EZ = EX + EY - 1; }
if (Z[1] == ZERO)
{
for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
EZ = EX + EY - 1;
}
else
EZ = EX + EY;
@ -444,22 +694,31 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */
void __inv(const mp_no *x, mp_no *y, int p) {
void
__inv (const mp_no *x, mp_no *y, int p)
{
long i;
double t;
mp_no z,w;
static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
mp_no z, w;
static const int np1[] =
{ 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
};
__cpy(x,&z,p); z.e=0; __mp_dbl(&z,&t,p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX;
__cpy (x, &z, p);
z.e = 0;
__mp_dbl (&z, &t, p);
t = ONE / t;
__dbl_mp (t, y, p);
EY -= EX;
for (i=0; i<np1[p]; i++) {
__cpy(y,&w,p);
__mul(x,&w,y,p);
__sub(&mptwo,y,&z,p);
__mul(&w,&z,y,p);
}
for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p);
__mul (x, &w, y, p);
__sub (&mptwo, y, &z, p);
__mul (&w, &z, y, p);
}
return;
}
@ -470,11 +729,17 @@ void __inv(const mp_no *x, mp_no *y, int p) {
- For P > 3: 3.001 * R ^ (1 - P)
*X = 0 is not permissible. */
void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
mp_no w;
if (X[0] == ZERO) Z[0] = ZERO;
else {__inv(y,&w,p); __mul(x,&w,z,p);}
if (X[0] == ZERO)
Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
return;
}

View File

@ -51,91 +51,135 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */
static int mcr(const mp_no *x, const mp_no *y, int p) {
static int
mcr (const mp_no *x, const mp_no *y, int p)
{
long i;
long p2 = p;
for (i=1; i<=p2; i++) {
if (X[i] == Y[i]) continue;
else if (X[i] > Y[i]) return 1;
else return -1; }
for (i = 1; i <= p2; i++)
{
if (X[i] == Y[i])
continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0;
}
/* Compare the absolute values of two multiple precision numbers. */
int __acr(const mp_no *x, const mp_no *y, int p) {
int
__acr (const mp_no *x, const mp_no *y, int p)
{
long i;
if (X[0] == ZERO) {
if (Y[0] == ZERO) i= 0;
else i=-1;
}
else if (Y[0] == ZERO) i= 1;
else {
if (EX > EY) i= 1;
else if (EX < EY) i=-1;
else i= mcr(x,y,p);
}
if (X[0] == ZERO)
{
if (Y[0] == ZERO)
i = 0;
else
i = -1;
}
else if (Y[0] == ZERO)
i = 1;
else
{
if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
}
return i;
}
/* Copy multiple precision number X into Y. They could be the same
number. */
void __cpy(const mp_no *x, mp_no *y, int p) {
void
__cpy (const mp_no *x, mp_no *y, int p)
{
long i;
EY = EX;
for (i=0; i <= p; i++) Y[i] = X[i];
for (i = 0; i <= p; i++)
Y[i] = X[i];
return;
}
/* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */
static void norm(const mp_no *x, double *y, int p)
static void
norm (const mp_no *x, double *y, int p)
{
#define R RADIXI
#define R RADIXI
long i;
double a,c,u,v,z[5];
if (p<5) {
if (p==1) c = X[1];
else if (p==2) c = X[1] + R* X[2];
else if (p==3) c = X[1] + R*(X[2] + R* X[3]);
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]);
}
else {
for (a=ONE, z[1]=X[1]; z[1] < TWO23; )
{a *= TWO; z[1] *= TWO; }
for (i=2; i<5; i++) {
z[i] = X[i]*a;
u = (z[i] + CUTTER)-CUTTER;
if (u > z[i]) u -= RADIX;
z[i] -= u;
z[i-1] += u*RADIXI;
double a, c, u, v, z[5];
if (p < 5)
{
if (p == 1)
c = X[1];
else if (p == 2)
c = X[1] + R * X[2];
else if (p == 3)
c = X[1] + R * (X[2] + R * X[3]);
else if (p == 4)
c = (X[1] + R * X[2]) + R * R * (X[3] + R * X[4]);
}
else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{
a *= TWO;
z[1] *= TWO;
}
u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19;
v = z[3]-u;
for (i = 2; i < 5; i++)
{
z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER;
if (u > z[i])
u -= RADIX;
z[i] -= u;
z[i - 1] += u * RADIXI;
}
if (v == TWO18) {
if (z[4] == ZERO) {
for (i=5; i <= p; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
}
}
else z[3] += ONE;
u = (z[3] + TWO71) - TWO71;
if (u > z[3])
u -= TWO19;
v = z[3] - u;
if (v == TWO18)
{
if (z[4] == ZERO)
{
for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
else
z[3] += ONE;
}
c = (z[1] + R * (z[2] + R * z[3])) / a;
}
c = (z[1] + R *(z[2] + R * z[3]))/a;
}
c *= X[0];
for (i=1; i<EX; i++) c *= RADIX;
for (i=1; i>EX; i--) c *= RADIXI;
for (i = 1; i < EX; i++)
c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c;
return;
@ -144,46 +188,112 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */
static void denorm(const mp_no *x, double *y, int p)
static void
denorm (const mp_no *x, double *y, int p)
{
long i,k;
long i, k;
long p2 = p;
double c,u,z[5];
double c, u, z[5];
#define R RADIXI
if (EX<-44 || (EX==-44 && X[1]<TWO5))
{ *y=ZERO; return; }
if (EX < -44 || (EX == -44 && X[1] < TWO5))
{
*y = ZERO;
return;
}
if (p2==1) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=ZERO; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=ZERO; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else if (p2==2) {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; z[3]=ZERO; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; z[3]=X[2]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;}
}
else {
if (EX==-42) {z[1]=X[1]+TWO10; z[2]=X[2]; k=3;}
else if (EX==-43) {z[1]= TWO10; z[2]=X[1]; k=2;}
else {z[1]= TWO10; z[2]=ZERO; k=1;}
z[3] = X[k];
}
if (p2 == 1)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = ZERO;
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else if (p2 == 2)
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
z[3] = ZERO;
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
z[3] = X[2];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
z[3] = X[1];
k = 1;
}
}
else
{
if (EX == -42)
{
z[1] = X[1] + TWO10;
z[2] = X[2];
k = 3;
}
else if (EX == -43)
{
z[1] = TWO10;
z[2] = X[1];
k = 2;
}
else
{
z[1] = TWO10;
z[2] = ZERO;
k = 1;
}
z[3] = X[k];
}
u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5;
if (u > z[3])
u -= TWO5;
if (u==z[3]) {
for (i=k+1; i <= p2; i++) {
if (X[i] == ZERO) continue;
else {z[3] += ONE; break; }
if (u == z[3])
{
for (i = k + 1; i <= p2; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
}
}
}
c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10);
c = X[0] * ((z[1] + R * (z[2] + R * z[3])) - TWO10);
*y = c*TWOM1032;
*y = c * TWOM1032;
return;
#undef R
@ -191,39 +301,65 @@ static void denorm(const mp_no *x, double *y, int p)
/* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */
void __mp_dbl(const mp_no *x, double *y, int p) {
void
__mp_dbl (const mp_no *x, double *y, int p)
{
if (X[0] == ZERO)
{
*y = ZERO;
return;
}
if (X[0] == ZERO) {*y = ZERO; return; }
if (EX> -42) norm(x,y,p);
else if (EX==-42 && X[1]>=TWO10) norm(x,y,p);
else denorm(x,y,p);
if (EX > -42)
norm (x, y, p);
else if (EX == -42 && X[1] >= TWO10)
norm (x, y, p);
else
denorm (x, y, p);
}
/* Get the multiple precision equivalent of X into *Y. If the precision is too
small, the result is truncated. */
void __dbl_mp(double x, mp_no *y, int p) {
long i,n;
void
__dbl_mp (double x, mp_no *y, int p)
{
long i, n;
long p2 = p;
double u;
/* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; }
else if (x > ZERO) Y[0] = ONE;
else {Y[0] = MONE; x=-x; }
if (x == ZERO)
{
Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
for ( ; x < ONE; EY -= ONE) x *= RADIX;
for (EY = ONE; x >= RADIX; EY += ONE)
x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */
n=MIN(p2,4);
for (i=1; i<=n; i++) {
u = (x + TWO52) - TWO52;
if (u>x) u -= ONE;
Y[i] = u; x -= u; x *= RADIX; }
for ( ; i<=p2; i++) Y[i] = ZERO;
n = MIN (p2, 4);
for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52;
if (u > x)
u -= ONE;
Y[i] = u;
x -= u;
x *= RADIX;
}
for (; i <= p2; i++)
Y[i] = ZERO;
return;
}
@ -231,93 +367,132 @@ void __dbl_mp(double x, mp_no *y, int p) {
sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
Y and Z. No guard digit is used. The result equals the exact sum,
truncated. */
static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
long i,j,k;
static void
add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k;
long p2 = p;
EZ = EX;
i=p2; j=p2+ EY - EX; k=p2+1;
i = p2;
j = p2 + EY - EX;
k = p2 + 1;
if (j<1)
{__cpy(x,z,p); return; }
else Z[k] = ZERO;
if (j < 1)
{
__cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) {
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] >= RADIX) {
Z[k] -= RADIX;
Z[--k] = ONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] >= RADIX)
{
Z[k] -= RADIX;
Z[--k] = ONE;
}
else
Z[--k] = ZERO;
}
if (Z[1] == ZERO) {
for (i=1; i<=p2; i++) Z[i] = Z[i+1]; }
else EZ += ONE;
if (Z[1] == ZERO)
{
for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
}
else
EZ += ONE;
}
/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
The sign of the difference *Z is not changed. X and Y may overlap but not X
and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */
static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
long i,j,k;
static void
sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k;
long p2 = p;
EZ = EX;
if (EX == EY) {
i=j=k=p2;
Z[k] = Z[k+1] = ZERO; }
else {
j= EX - EY;
if (j > p2) {__cpy(x,z,p); return; }
else {
i=p2; j=p2+1-j; k=p2;
if (Y[j] > ZERO) {
Z[k+1] = RADIX - Y[j--];
Z[k] = MONE; }
else {
Z[k+1] = ZERO;
Z[k] = ZERO; j--;}
if (EX == EY)
{
i = j = k = p2;
Z[k] = Z[k + 1] = ZERO;
}
else
{
j = EX - EY;
if (j > p2)
{
__cpy (x, z, p);
return;
}
else
{
i = p2;
j = p2 + 1 - j;
k = p2;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE;
}
else
{
Z[k + 1] = ZERO;
Z[k] = ZERO;
j--;
}
}
}
}
for (; j>0; i--,j--) {
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (; i>0; i--) {
Z[k] += X[i];
if (Z[k] < ZERO) {
Z[k] += RADIX;
Z[--k] = MONE; }
else
Z[--k] = ZERO;
}
for (; i > 0; i--)
{
Z[k] += X[i];
if (Z[k] < ZERO)
{
Z[k] += RADIX;
Z[--k] = MONE;
}
else
Z[--k] = ZERO;
}
for (i=1; Z[i] == ZERO; i++) ;
for (i = 1; Z[i] == ZERO; i++);
EZ = EZ - i + 1;
for (k=1; i <= p2+1; )
for (k = 1; i <= p2 + 1;)
Z[k++] = Z[i++];
for (; k <= p2; )
for (; k <= p2;)
Z[k++] = ZERO;
return;
@ -326,111 +501,186 @@ static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */
void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__add (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] == Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = Y[0]; }
else Z[0] = ZERO;
}
if (X[0] == Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = Y[0];
}
else
Z[0] = ZERO;
}
return;
}
/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
not X and Z or Y and Z. One guard digit is used. The error is less than
one ULP. */
void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__sub (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; }
else if (Y[0] == ZERO) {__cpy(x,z,p); return; }
if (X[0] == ZERO)
{
__cpy (y, z, p);
Z[0] = -Z[0];
return;
}
else if (Y[0] == ZERO)
{
__cpy (x, z, p);
return;
}
if (X[0] != Y[0]) {
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; }
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
}
else {
if ((n=__acr(x,y,p)) == 1) {sub_magnitudes(x,y,z,p); Z[0] = X[0]; }
else if (n == -1) {sub_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
else Z[0] = ZERO;
}
if (X[0] != Y[0])
{
if (__acr (x, y, p) > 0)
{
add_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else
{
add_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
}
else
{
if ((n = __acr (x, y, p)) == 1)
{
sub_magnitudes (x, y, z, p);
Z[0] = X[0];
}
else if (n == -1)
{
sub_magnitudes (y, x, z, p);
Z[0] = -Y[0];
}
else
Z[0] = ZERO;
}
return;
}
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
digits. In case P > 3 the error is bounded by 1.001 ULP. */
void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__mul (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, i1, i2, j, k, k2;
long p2 = p;
double u, zk, zk2;
/* Is z=0? */
if (X[0]*Y[0]==ZERO)
{ Z[0]=ZERO; return; }
/* Is z=0? */
if (X[0] * Y[0] == ZERO)
{
Z[0] = ZERO;
return;
}
/* Multiply, add and carry */
k2 = (p2<3) ? p2+p2 : p2+3;
zk = Z[k2]=ZERO;
for (k=k2; k>1; ) {
if (k > p2) {i1=k-p2; i2=p2+1; }
else {i1=1; i2=k; }
/* Multiply, add and carry */
k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
zk = Z[k2] = ZERO;
for (k = k2; k > 1;)
{
if (k > p2)
{
i1 = k - p2;
i2 = p2 + 1;
}
else
{
i1 = 1;
i2 = k;
}
#if 1
/* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have
dual symmetrical FP pipelines. */
if (i1 < (i2-1))
{
/* Make sure we have at least 2 iterations. */
if (((i2 - i1) & 1L) == 1L)
/* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have
dual symmetrical FP pipelines. */
if (i1 < (i2 - 1))
{
/* Handle the odd iterations case. */
zk2 = x->d[i2-1]*y->d[i1];
/* Make sure we have at least 2 iterations. */
if (((i2 - i1) & 1L) == 1L)
{
/* Handle the odd iterations case. */
zk2 = x->d[i2 - 1] * y->d[i1];
}
else
zk2 = 0.0;
/* Do two multiply/adds per loop iteration, using independent
accumulators; zk and zk2. */
for (i = i1, j = i2 - 1; i < i2 - 1; i += 2, j -= 2)
{
zk += x->d[i] * y->d[j];
zk2 += x->d[i + 1] * y->d[j - 1];
}
zk += zk2; /* Final sum. */
}
else
zk2 = 0.0;
/* Do two multiply/adds per loop iteration, using independent
accumulators; zk and zk2. */
for (i=i1,j=i2-1; i<i2-1; i+=2,j-=2)
else
{
zk += x->d[i]*y->d[j];
zk2 += x->d[i+1]*y->d[j-1];
/* Special case when iterations is 1. */
zk += x->d[i1] * y->d[i1];
}
zk += zk2; /* Final sum. */
}
else
{
/* Special case when iterations is 1. */
zk += x->d[i1]*y->d[i1];
}
#else
/* The original code. */
for (i=i1,j=i2-1; i<i2; i++,j--) zk += X[i]*Y[j];
/* The original code. */
for (i = i1, j = i2 - 1; i < i2; i++, j--)
zk += X[i] * Y[j];
#endif
u = (zk + CUTTER)-CUTTER;
if (u > zk) u -= RADIX;
Z[k] = zk - u;
zk = u*RADIXI;
--k;
}
u = (zk + CUTTER) - CUTTER;
if (u > zk)
u -= RADIX;
Z[k] = zk - u;
zk = u * RADIXI;
--k;
}
Z[k] = zk;
/* Is there a carry beyond the most significant digit? */
if (Z[1] == ZERO) {
for (i=1; i<=p2; i++) Z[i]=Z[i+1];
EZ = EX + EY - 1; }
if (Z[1] == ZERO)
{
for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
EZ = EX + EY - 1;
}
else
EZ = EX + EY;
@ -444,22 +694,31 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */
void __inv(const mp_no *x, mp_no *y, int p) {
void
__inv (const mp_no *x, mp_no *y, int p)
{
long i;
double t;
mp_no z,w;
static const int np1[] = {0,0,0,0,1,2,2,2,2,3,3,3,3,3,3,3,3,3,
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4};
mp_no z, w;
static const int np1[] =
{ 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
};
__cpy(x,&z,p); z.e=0; __mp_dbl(&z,&t,p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX;
__cpy (x, &z, p);
z.e = 0;
__mp_dbl (&z, &t, p);
t = ONE / t;
__dbl_mp (t, y, p);
EY -= EX;
for (i=0; i<np1[p]; i++) {
__cpy(y,&w,p);
__mul(x,&w,y,p);
__sub(&mptwo,y,&z,p);
__mul(&w,&z,y,p);
}
for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p);
__mul (x, &w, y, p);
__sub (&mptwo, y, &z, p);
__mul (&w, &z, y, p);
}
return;
}
@ -470,11 +729,17 @@ void __inv(const mp_no *x, mp_no *y, int p) {
- For P > 3: 3.001 * R ^ (1 - P)
*X = 0 is not permissible. */
void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
void
__dvd (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
mp_no w;
if (X[0] == ZERO) Z[0] = ZERO;
else {__inv(y,&w,p); __mul(x,&w,z,p);}
if (X[0] == ZERO)
Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
return;
}