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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
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4
ChangeLog
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@ -1,5 +1,9 @@
2013-01-14 Siddhesh Poyarekar <siddhesh@redhat.com> 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 * sysdeps/powerpc/powerpc32/power4/fpu/mpa.c (__inv): Remove
local variable MPTWO. local variable MPTWO.
* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (__inv): * sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (__inv):

509
sysdeps/ieee754/dbl-64/mpa.c
View File

@ -60,29 +60,44 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign /* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */ and exponent of the numbers. */
static int 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; int i;
for (i=1; i<=p; i++) { for (i = 1; i <= p; i++)
if (X[i] == Y[i]) continue; {
else if (X[i] > Y[i]) return 1; if (X[i] == Y[i])
else return -1; } continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0; return 0;
} }
/* Compare the absolute values of two multiple precision numbers. */ /* Compare the absolute values of two multiple precision numbers. */
int 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; int i;
if (X[0] == ZERO) { if (X[0] == ZERO)
if (Y[0] == ZERO) i= 0; {
else i=-1; if (Y[0] == ZERO)
i = 0;
else
i = -1;
} }
else if (Y[0] == ZERO) i= 1; else if (Y[0] == ZERO)
else { i = 1;
if (EX > EY) i= 1; else
else if (EX < EY) i=-1; {
else i= mcr(x,y,p); if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
} }
return i; return i;
@ -92,50 +107,75 @@ __acr(const mp_no *x, const mp_no *y, int p) {
#ifndef NO___CPY #ifndef NO___CPY
/* Copy multiple precision number X into Y. They could be the same /* Copy multiple precision number X into Y. They could be the same
number. */ 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; 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 #endif
#ifndef NO___MP_DBL #ifndef NO___MP_DBL
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */ 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; int i;
double a, c, u, v, z[5]; double a, c, u, v, z[5];
if (p<5) { if (p < 5)
if (p==1) c = X[1]; {
else if (p==2) c = X[1] + R* X[2]; if (p == 1)
else if (p==3) c = X[1] + R*(X[2] + R* X[3]); c = X[1];
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]); 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 { else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;) for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{a *= TWO; z[1] *= TWO; } {
a *= TWO;
z[1] *= TWO;
}
for (i=2; i<5; i++) { for (i = 2; i < 5; i++)
{
z[i] = X[i] * a; z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER; u = (z[i] + CUTTER) - CUTTER;
if (u > z[i]) u -= RADIX; if (u > z[i])
u -= RADIX;
z[i] -= u; z[i] -= u;
z[i - 1] += u * RADIXI; z[i - 1] += u * RADIXI;
} }
u = (z[3] + TWO71) - TWO71; u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19; if (u > z[3])
u -= TWO19;
v = z[3] - u; v = z[3] - u;
if (v == TWO18) { if (v == TWO18)
if (z[4] == ZERO) { {
for (i=5; i <= p; i++) { if (z[4] == ZERO)
if (X[i] == ZERO) continue; {
else {z[3] += ONE; break; } for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
} }
} }
else z[3] += ONE; }
else
z[3] += ONE;
} }
c = (z[1] + R * (z[2] + R * z[3])) / a; c = (z[1] + R * (z[2] + R * z[3])) / a;
@ -143,8 +183,10 @@ static void norm(const mp_no *x, double *y, int p)
c *= X[0]; c *= X[0];
for (i=1; i<EX; i++) c *= RADIX; for (i = 1; i < EX; i++)
for (i=1; i>EX; i--) c *= RADIXI; c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c; *y = c;
#undef R #undef R
@ -152,39 +194,105 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */ 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; int i, k;
double c, u, z[5]; double c, u, z[5];
#define R RADIXI #define R RADIXI
if (EX < -44 || (EX == -44 && X[1] < TWO5)) if (EX < -44 || (EX == -44 && X[1] < TWO5))
{ *y=ZERO; return; } {
*y = ZERO;
return;
}
if (p==1) { 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;} if (EX == -42)
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} {
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
} }
else if (p==2) { else if (EX == -43)
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;} z[1] = TWO10;
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} 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;
} }
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]; z[3] = X[k];
} }
u = (z[3] + TWO57) - TWO57; u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5; if (u > z[3])
u -= TWO5;
if (u==z[3]) { if (u == z[3])
for (i=k+1; i <= p; i++) { {
if (X[i] == ZERO) continue; for (i = k + 1; i <= p; i++)
else {z[3] += ONE; break; } {
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
} }
} }
@ -196,9 +304,14 @@ static void denorm(const mp_no *x, double *y, int p)
/* Convert multiple precision number *X into double precision number *Y. The /* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */ 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 (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10))) if (__glibc_likely (EX > -42 || (EX == -42 && X[1] >= TWO10)))
norm (x, y, p); norm (x, y, p);
@ -211,27 +324,44 @@ void __mp_dbl(const mp_no *x, double *y, int p) {
small, the result is truncated. */ small, the result is truncated. */
void void
SECTION SECTION
__dbl_mp(double x, mp_no *y, int p) { __dbl_mp (double x, mp_no *y, int p)
{
int i, n; int i, n;
double u; double u;
/* Sign. */ /* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; } if (x == ZERO)
else if (x > ZERO) Y[0] = ONE; {
else {Y[0] = MONE; x=-x; } Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */ /* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI; for (EY = ONE; x >= RADIX; EY += ONE)
for ( ; x < ONE; EY -= ONE) x *= RADIX; x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */ /* Digits. */
n = MIN (p, 4); n = MIN (p, 4);
for (i=1; i<=n; i++) { for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52; u = (x + TWO52) - TWO52;
if (u>x) u -= ONE; if (u > x)
Y[i] = u; x -= u; x *= RADIX; } u -= ONE;
for ( ; i<=p; i++) Y[i] = ZERO; 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 /* 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. */ truncated. */
static void static void
SECTION SECTION
add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k; int i, j, k;
EZ = EX; EZ = EX;
i=p; j=p+ EY - EX; k=p+1; i = p;
j = p + EY - EX;
k = p + 1;
if (j < 1) if (j < 1)
{__cpy(x,z,p); return; } {
else Z[k] = ZERO; __cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j]; Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
if (Z[1] == ZERO) { if (Z[1] == ZERO)
for (i=1; i<=p; i++) Z[i] = Z[i+1]; } {
else EZ += ONE; 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. /* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
@ -281,43 +427,64 @@ add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
ULP. */ ULP. */
static void static void
SECTION SECTION
sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
int i, j, k; int i, j, k;
EZ = EX; EZ = EX;
if (EX == EY) { if (EX == EY)
{
i = j = k = p; i = j = k = p;
Z[k] = Z[k+1] = ZERO; } Z[k] = Z[k + 1] = ZERO;
else { }
else
{
j = EX - EY; j = EX - EY;
if (j > p) {__cpy(x,z,p); return; } if (j > p)
else { {
i=p; j=p+1-j; k=p; __cpy (x, z, p);
if (Y[j] > ZERO) { return;
}
else
{
i = p;
j = p + 1 - j;
k = p;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--]; Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE; } Z[k] = MONE;
else { }
else
{
Z[k + 1] = ZERO; Z[k + 1] = ZERO;
Z[k] = ZERO; j--;} Z[k] = ZERO;
j--;
}
} }
} }
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]); Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
@ -335,21 +502,48 @@ sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
ULP. */ ULP. */
void void
SECTION 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] == Y[0]) { return;
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 { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
} }
@ -358,21 +552,49 @@ __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
one ULP. */ one ULP. */
void void
SECTION 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] != Y[0]) { Z[0] = -Z[0];
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; } return;
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
} }
else { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
} }
@ -381,8 +603,8 @@ __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. */ digits. In case P > 3 the error is bounded by 1.001 ULP. */
void void
SECTION 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; int i, j, k, k2;
double u; double u;
@ -439,19 +661,27 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P) - For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */ *X = 0 is not permissible. */
static static void
SECTION SECTION
void __inv(const mp_no *x, mp_no *y, int p) { __inv (const mp_no *x, mp_no *y, int p)
{
int i; int i;
double t; double t;
mp_no z, w; 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, static const int np1[] =
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}; { 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); __cpy (x, &z, p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX; 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++) { for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p); __cpy (y, &w, p);
__mul (x, &w, y, p); __mul (x, &w, y, p);
__sub (&mptwo, y, &z, p); __sub (&mptwo, y, &z, p);
@ -468,10 +698,15 @@ void __inv(const mp_no *x, mp_no *y, int p) {
*X = 0 is not permissible. */ *X = 0 is not permissible. */
void void
SECTION 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; mp_no w;
if (X[0] == ZERO) Z[0] = ZERO; if (X[0] == ZERO)
else {__inv(y,&w,p); __mul(x,&w,z,p);} Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
} }

561
sysdeps/powerpc/powerpc32/power4/fpu/mpa.c
View File

@ -51,29 +51,46 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign /* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */ 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 i;
long p2 = p; long p2 = p;
for (i=1; i<=p2; i++) { for (i = 1; i <= p2; i++)
if (X[i] == Y[i]) continue; {
else if (X[i] > Y[i]) return 1; if (X[i] == Y[i])
else return -1; } continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0; return 0;
} }
/* Compare the absolute values of two multiple precision numbers. */ /* 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; long i;
if (X[0] == ZERO) { if (X[0] == ZERO)
if (Y[0] == ZERO) i= 0; {
else i=-1; if (Y[0] == ZERO)
i = 0;
else
i = -1;
} }
else if (Y[0] == ZERO) i= 1; else if (Y[0] == ZERO)
else { i = 1;
if (EX > EY) i= 1; else
else if (EX < EY) i=-1; {
else i= mcr(x,y,p); if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
} }
return i; return i;
@ -81,52 +98,77 @@ int __acr(const mp_no *x, const mp_no *y, int p) {
/* Copy multiple precision number X into Y. They could be the same /* Copy multiple precision number X into Y. They could be the same
number. */ 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; long i;
EY = EX; EY = EX;
for (i=0; i <= p; i++) Y[i] = X[i]; for (i = 0; i <= p; i++)
Y[i] = X[i];
return; return;
} }
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */ 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; long i;
double a, c, u, v, z[5]; double a, c, u, v, z[5];
if (p<5) { if (p < 5)
if (p==1) c = X[1]; {
else if (p==2) c = X[1] + R* X[2]; if (p == 1)
else if (p==3) c = X[1] + R*(X[2] + R* X[3]); c = X[1];
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]); 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 { else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;) for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{a *= TWO; z[1] *= TWO; } {
a *= TWO;
z[1] *= TWO;
}
for (i=2; i<5; i++) { for (i = 2; i < 5; i++)
{
z[i] = X[i] * a; z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER; u = (z[i] + CUTTER) - CUTTER;
if (u > z[i]) u -= RADIX; if (u > z[i])
u -= RADIX;
z[i] -= u; z[i] -= u;
z[i - 1] += u * RADIXI; z[i - 1] += u * RADIXI;
} }
u = (z[3] + TWO71) - TWO71; u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19; if (u > z[3])
u -= TWO19;
v = z[3] - u; v = z[3] - u;
if (v == TWO18) { if (v == TWO18)
if (z[4] == ZERO) { {
for (i=5; i <= p; i++) { if (z[4] == ZERO)
if (X[i] == ZERO) continue; {
else {z[3] += ONE; break; } for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
} }
} }
else z[3] += ONE; }
else
z[3] += ONE;
} }
c = (z[1] + R * (z[2] + R * z[3])) / a; c = (z[1] + R * (z[2] + R * z[3])) / a;
@ -134,8 +176,10 @@ static void norm(const mp_no *x, double *y, int p)
c *= X[0]; c *= X[0];
for (i=1; i<EX; i++) c *= RADIX; for (i = 1; i < EX; i++)
for (i=1; i>EX; i--) c *= RADIXI; c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c; *y = c;
return; return;
@ -144,7 +188,8 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */ 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; long p2 = p;
@ -152,32 +197,97 @@ static void denorm(const mp_no *x, double *y, int p)
#define R RADIXI #define R RADIXI
if (EX < -44 || (EX == -44 && X[1] < TWO5)) if (EX < -44 || (EX == -44 && X[1] < TWO5))
{ *y=ZERO; return; } {
*y = ZERO;
return;
}
if (p2==1) { 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;} if (EX == -42)
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} {
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
} }
else if (p2==2) { else if (EX == -43)
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;} z[1] = TWO10;
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} 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;
} }
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]; z[3] = X[k];
} }
u = (z[3] + TWO57) - TWO57; u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5; if (u > z[3])
u -= TWO5;
if (u==z[3]) { if (u == z[3])
for (i=k+1; i <= p2; i++) { {
if (X[i] == ZERO) continue; for (i = k + 1; i <= p2; i++)
else {z[3] += ONE; break; } {
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
} }
} }
@ -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 /* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */ 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);
if (EX> -42) norm(x,y,p); else if (EX == -42 && X[1] >= TWO10)
else if (EX==-42 && X[1]>=TWO10) norm(x,y,p); norm (x, y, p);
else denorm(x,y,p); else
denorm (x, y, p);
} }
/* Get the multiple precision equivalent of X into *Y. If the precision is too /* Get the multiple precision equivalent of X into *Y. If the precision is too
small, the result is truncated. */ small, the result is truncated. */
void __dbl_mp(double x, mp_no *y, int p) { void
__dbl_mp (double x, mp_no *y, int p)
{
long i, n; long i, n;
long p2 = p; long p2 = p;
double u; double u;
/* Sign. */ /* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; } if (x == ZERO)
else if (x > ZERO) Y[0] = ONE; {
else {Y[0] = MONE; x=-x; } Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */ /* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI; for (EY = ONE; x >= RADIX; EY += ONE)
for ( ; x < ONE; EY -= ONE) x *= RADIX; x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */ /* Digits. */
n = MIN (p2, 4); n = MIN (p2, 4);
for (i=1; i<=n; i++) { for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52; u = (x + TWO52) - TWO52;
if (u>x) u -= ONE; if (u > x)
Y[i] = u; x -= u; x *= RADIX; } u -= ONE;
for ( ; i<=p2; i++) Y[i] = ZERO; Y[i] = u;
x -= u;
x *= RADIX;
}
for (; i <= p2; i++)
Y[i] = ZERO;
return; return;
} }
@ -231,84 +367,123 @@ 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 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, Y and Z. No guard digit is used. The result equals the exact sum,
truncated. */ truncated. */
static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { static void
add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k; long i, j, k;
long p2 = p; long p2 = p;
EZ = EX; EZ = EX;
i=p2; j=p2+ EY - EX; k=p2+1; i = p2;
j = p2 + EY - EX;
k = p2 + 1;
if (j < 1) if (j < 1)
{__cpy(x,z,p); return; } {
else Z[k] = ZERO; __cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j]; Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
if (Z[1] == ZERO) { if (Z[1] == ZERO)
for (i=1; i<=p2; i++) Z[i] = Z[i+1]; } {
else EZ += ONE; 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. /* 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 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 and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */ ULP. */
static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { static void
sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k; long i, j, k;
long p2 = p; long p2 = p;
EZ = EX; EZ = EX;
if (EX == EY) { if (EX == EY)
{
i = j = k = p2; i = j = k = p2;
Z[k] = Z[k+1] = ZERO; } Z[k] = Z[k + 1] = ZERO;
else { }
else
{
j = EX - EY; j = EX - EY;
if (j > p2) {__cpy(x,z,p); return; } if (j > p2)
else { {
i=p2; j=p2+1-j; k=p2; __cpy (x, z, p);
if (Y[j] > ZERO) { return;
}
else
{
i = p2;
j = p2 + 1 - j;
k = p2;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--]; Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE; } Z[k] = MONE;
else { }
else
{
Z[k + 1] = ZERO; Z[k + 1] = ZERO;
Z[k] = ZERO; j--;} Z[k] = ZERO;
j--;
}
} }
} }
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]); Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
@ -326,21 +501,49 @@ 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 /* 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 and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */ 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] == Y[0]) { return;
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 { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
return; return;
} }
@ -348,21 +551,50 @@ void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but /* 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 not X and Z or Y and Z. One guard digit is used. The error is less than
one ULP. */ 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] != Y[0]) { Z[0] = -Z[0];
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; } return;
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
} }
else { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
return; return;
} }
@ -370,22 +602,35 @@ void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X /* 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 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. */ 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 i, i1, i2, j, k, k2;
long p2 = p; long p2 = p;
double u, zk, zk2; double u, zk, zk2;
/* Is z=0? */ /* Is z=0? */
if (X[0] * Y[0] == ZERO) if (X[0] * Y[0] == ZERO)
{ Z[0]=ZERO; return; } {
Z[0] = ZERO;
return;
}
/* Multiply, add and carry */ /* Multiply, add and carry */
k2 = (p2 < 3) ? p2 + p2 : p2 + 3; k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
zk = Z[k2] = ZERO; zk = Z[k2] = ZERO;
for (k=k2; k>1; ) { for (k = k2; k > 1;)
if (k > p2) {i1=k-p2; i2=p2+1; } {
else {i1=1; i2=k; } if (k > p2)
{
i1 = k - p2;
i2 = p2 + 1;
}
else
{
i1 = 1;
i2 = k;
}
#if 1 #if 1
/* Rearrange this inner loop to allow the fmadd instructions to be /* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have independent and execute in parallel on processors that have
@ -416,11 +661,13 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
} }
#else #else
/* The original code. */ /* The original code. */
for (i=i1,j=i2-1; i<i2; i++,j--) zk += X[i]*Y[j]; for (i = i1, j = i2 - 1; i < i2; i++, j--)
zk += X[i] * Y[j];
#endif #endif
u = (zk + CUTTER) - CUTTER; u = (zk + CUTTER) - CUTTER;
if (u > zk) u -= RADIX; if (u > zk)
u -= RADIX;
Z[k] = zk - u; Z[k] = zk - u;
zk = u * RADIXI; zk = u * RADIXI;
--k; --k;
@ -428,9 +675,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
Z[k] = zk; Z[k] = zk;
/* Is there a carry beyond the most significant digit? */ /* Is there a carry beyond the most significant digit? */
if (Z[1] == ZERO) { if (Z[1] == ZERO)
for (i=1; i<=p2; i++) Z[i]=Z[i+1]; {
EZ = EX + EY - 1; } for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
EZ = EX + EY - 1;
}
else else
EZ = EX + EY; EZ = EX + EY;
@ -444,17 +694,26 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P) - For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */ *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; long i;
double t; double t;
mp_no z, w; 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, static const int np1[] =
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}; { 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); __cpy (x, &z, p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX; 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++) { for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p); __cpy (y, &w, p);
__mul (x, &w, y, p); __mul (x, &w, y, p);
__sub (&mptwo, y, &z, p); __sub (&mptwo, y, &z, p);
@ -470,11 +729,17 @@ void __inv(const mp_no *x, mp_no *y, int p) {
- For P > 3: 3.001 * R ^ (1 - P) - For P > 3: 3.001 * R ^ (1 - P)
*X = 0 is not permissible. */ *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; mp_no w;
if (X[0] == ZERO) Z[0] = ZERO; if (X[0] == ZERO)
else {__inv(y,&w,p); __mul(x,&w,z,p);} Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
return; return;
} }

561
sysdeps/powerpc/powerpc64/power4/fpu/mpa.c
View File

@ -51,29 +51,46 @@ const mp_no mptwo = {1, {1.0, 2.0}};
/* Compare mantissa of two multiple precision numbers regardless of the sign /* Compare mantissa of two multiple precision numbers regardless of the sign
and exponent of the numbers. */ 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 i;
long p2 = p; long p2 = p;
for (i=1; i<=p2; i++) { for (i = 1; i <= p2; i++)
if (X[i] == Y[i]) continue; {
else if (X[i] > Y[i]) return 1; if (X[i] == Y[i])
else return -1; } continue;
else if (X[i] > Y[i])
return 1;
else
return -1;
}
return 0; return 0;
} }
/* Compare the absolute values of two multiple precision numbers. */ /* 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; long i;
if (X[0] == ZERO) { if (X[0] == ZERO)
if (Y[0] == ZERO) i= 0; {
else i=-1; if (Y[0] == ZERO)
i = 0;
else
i = -1;
} }
else if (Y[0] == ZERO) i= 1; else if (Y[0] == ZERO)
else { i = 1;
if (EX > EY) i= 1; else
else if (EX < EY) i=-1; {
else i= mcr(x,y,p); if (EX > EY)
i = 1;
else if (EX < EY)
i = -1;
else
i = mcr (x, y, p);
} }
return i; return i;
@ -81,52 +98,77 @@ int __acr(const mp_no *x, const mp_no *y, int p) {
/* Copy multiple precision number X into Y. They could be the same /* Copy multiple precision number X into Y. They could be the same
number. */ 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; long i;
EY = EX; EY = EX;
for (i=0; i <= p; i++) Y[i] = X[i]; for (i = 0; i <= p; i++)
Y[i] = X[i];
return; return;
} }
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, normalized case (|x| >= 2**(-1022))). */ 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; long i;
double a, c, u, v, z[5]; double a, c, u, v, z[5];
if (p<5) { if (p < 5)
if (p==1) c = X[1]; {
else if (p==2) c = X[1] + R* X[2]; if (p == 1)
else if (p==3) c = X[1] + R*(X[2] + R* X[3]); c = X[1];
else if (p==4) c =(X[1] + R* X[2]) + R*R*(X[3] + R*X[4]); 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 { else
{
for (a = ONE, z[1] = X[1]; z[1] < TWO23;) for (a = ONE, z[1] = X[1]; z[1] < TWO23;)
{a *= TWO; z[1] *= TWO; } {
a *= TWO;
z[1] *= TWO;
}
for (i=2; i<5; i++) { for (i = 2; i < 5; i++)
{
z[i] = X[i] * a; z[i] = X[i] * a;
u = (z[i] + CUTTER) - CUTTER; u = (z[i] + CUTTER) - CUTTER;
if (u > z[i]) u -= RADIX; if (u > z[i])
u -= RADIX;
z[i] -= u; z[i] -= u;
z[i - 1] += u * RADIXI; z[i - 1] += u * RADIXI;
} }
u = (z[3] + TWO71) - TWO71; u = (z[3] + TWO71) - TWO71;
if (u > z[3]) u -= TWO19; if (u > z[3])
u -= TWO19;
v = z[3] - u; v = z[3] - u;
if (v == TWO18) { if (v == TWO18)
if (z[4] == ZERO) { {
for (i=5; i <= p; i++) { if (z[4] == ZERO)
if (X[i] == ZERO) continue; {
else {z[3] += ONE; break; } for (i = 5; i <= p; i++)
{
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
} }
} }
else z[3] += ONE; }
else
z[3] += ONE;
} }
c = (z[1] + R * (z[2] + R * z[3])) / a; c = (z[1] + R * (z[2] + R * z[3])) / a;
@ -134,8 +176,10 @@ static void norm(const mp_no *x, double *y, int p)
c *= X[0]; c *= X[0];
for (i=1; i<EX; i++) c *= RADIX; for (i = 1; i < EX; i++)
for (i=1; i>EX; i--) c *= RADIXI; c *= RADIX;
for (i = 1; i > EX; i--)
c *= RADIXI;
*y = c; *y = c;
return; return;
@ -144,7 +188,8 @@ static void norm(const mp_no *x, double *y, int p)
/* Convert a multiple precision number *X into a double precision /* Convert a multiple precision number *X into a double precision
number *Y, Denormal case (|x| < 2**(-1022))). */ 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; long p2 = p;
@ -152,32 +197,97 @@ static void denorm(const mp_no *x, double *y, int p)
#define R RADIXI #define R RADIXI
if (EX < -44 || (EX == -44 && X[1] < TWO5)) if (EX < -44 || (EX == -44 && X[1] < TWO5))
{ *y=ZERO; return; } {
*y = ZERO;
return;
}
if (p2==1) { 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;} if (EX == -42)
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} {
z[1] = X[1] + TWO10;
z[2] = ZERO;
z[3] = ZERO;
k = 3;
} }
else if (p2==2) { else if (EX == -43)
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;} z[1] = TWO10;
else {z[1]= TWO10; z[2]=ZERO; z[3]=X[1]; k=1;} 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;
} }
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]; z[3] = X[k];
} }
u = (z[3] + TWO57) - TWO57; u = (z[3] + TWO57) - TWO57;
if (u > z[3]) u -= TWO5; if (u > z[3])
u -= TWO5;
if (u==z[3]) { if (u == z[3])
for (i=k+1; i <= p2; i++) { {
if (X[i] == ZERO) continue; for (i = k + 1; i <= p2; i++)
else {z[3] += ONE; break; } {
if (X[i] == ZERO)
continue;
else
{
z[3] += ONE;
break;
}
} }
} }
@ -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 /* Convert multiple precision number *X into double precision number *Y. The
result is correctly rounded to the nearest/even. */ 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);
if (EX> -42) norm(x,y,p); else if (EX == -42 && X[1] >= TWO10)
else if (EX==-42 && X[1]>=TWO10) norm(x,y,p); norm (x, y, p);
else denorm(x,y,p); else
denorm (x, y, p);
} }
/* Get the multiple precision equivalent of X into *Y. If the precision is too /* Get the multiple precision equivalent of X into *Y. If the precision is too
small, the result is truncated. */ small, the result is truncated. */
void __dbl_mp(double x, mp_no *y, int p) { void
__dbl_mp (double x, mp_no *y, int p)
{
long i, n; long i, n;
long p2 = p; long p2 = p;
double u; double u;
/* Sign. */ /* Sign. */
if (x == ZERO) {Y[0] = ZERO; return; } if (x == ZERO)
else if (x > ZERO) Y[0] = ONE; {
else {Y[0] = MONE; x=-x; } Y[0] = ZERO;
return;
}
else if (x > ZERO)
Y[0] = ONE;
else
{
Y[0] = MONE;
x = -x;
}
/* Exponent. */ /* Exponent. */
for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI; for (EY = ONE; x >= RADIX; EY += ONE)
for ( ; x < ONE; EY -= ONE) x *= RADIX; x *= RADIXI;
for (; x < ONE; EY -= ONE)
x *= RADIX;
/* Digits. */ /* Digits. */
n = MIN (p2, 4); n = MIN (p2, 4);
for (i=1; i<=n; i++) { for (i = 1; i <= n; i++)
{
u = (x + TWO52) - TWO52; u = (x + TWO52) - TWO52;
if (u>x) u -= ONE; if (u > x)
Y[i] = u; x -= u; x *= RADIX; } u -= ONE;
for ( ; i<=p2; i++) Y[i] = ZERO; Y[i] = u;
x -= u;
x *= RADIX;
}
for (; i <= p2; i++)
Y[i] = ZERO;
return; return;
} }
@ -231,84 +367,123 @@ 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 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, Y and Z. No guard digit is used. The result equals the exact sum,
truncated. */ truncated. */
static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { static void
add_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k; long i, j, k;
long p2 = p; long p2 = p;
EZ = EX; EZ = EX;
i=p2; j=p2+ EY - EX; k=p2+1; i = p2;
j = p2 + EY - EX;
k = p2 + 1;
if (j < 1) if (j < 1)
{__cpy(x,z,p); return; } {
else Z[k] = ZERO; __cpy (x, z, p);
return;
}
else
Z[k] = ZERO;
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += X[i] + Y[j]; Z[k] += X[i] + Y[j];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] >= RADIX) { if (Z[k] >= RADIX)
{
Z[k] -= RADIX; Z[k] -= RADIX;
Z[--k] = ONE; } Z[--k] = ONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
if (Z[1] == ZERO) { if (Z[1] == ZERO)
for (i=1; i<=p2; i++) Z[i] = Z[i+1]; } {
else EZ += ONE; 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. /* 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 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 and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */ ULP. */
static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { static void
sub_magnitudes (const mp_no *x, const mp_no *y, mp_no *z, int p)
{
long i, j, k; long i, j, k;
long p2 = p; long p2 = p;
EZ = EX; EZ = EX;
if (EX == EY) { if (EX == EY)
{
i = j = k = p2; i = j = k = p2;
Z[k] = Z[k+1] = ZERO; } Z[k] = Z[k + 1] = ZERO;
else { }
else
{
j = EX - EY; j = EX - EY;
if (j > p2) {__cpy(x,z,p); return; } if (j > p2)
else { {
i=p2; j=p2+1-j; k=p2; __cpy (x, z, p);
if (Y[j] > ZERO) { return;
}
else
{
i = p2;
j = p2 + 1 - j;
k = p2;
if (Y[j] > ZERO)
{
Z[k + 1] = RADIX - Y[j--]; Z[k + 1] = RADIX - Y[j--];
Z[k] = MONE; } Z[k] = MONE;
else { }
else
{
Z[k + 1] = ZERO; Z[k + 1] = ZERO;
Z[k] = ZERO; j--;} Z[k] = ZERO;
j--;
}
} }
} }
for (; j>0; i--,j--) { for (; j > 0; i--, j--)
{
Z[k] += (X[i] - Y[j]); Z[k] += (X[i] - Y[j]);
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
for (; i>0; i--) { for (; i > 0; i--)
{
Z[k] += X[i]; Z[k] += X[i];
if (Z[k] < ZERO) { if (Z[k] < ZERO)
{
Z[k] += RADIX; Z[k] += RADIX;
Z[--k] = MONE; } Z[--k] = MONE;
}
else else
Z[--k] = ZERO; Z[--k] = ZERO;
} }
@ -326,21 +501,49 @@ 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 /* 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 and Z or Y and Z. One guard digit is used. The error is less than one
ULP. */ 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] == Y[0]) { return;
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 { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
return; return;
} }
@ -348,21 +551,50 @@ void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but /* 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 not X and Z or Y and Z. One guard digit is used. The error is less than
one ULP. */ 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; int n;
if (X[0] == ZERO) {__cpy(y,z,p); Z[0] = -Z[0]; return; } if (X[0] == ZERO)
else if (Y[0] == ZERO) {__cpy(x,z,p); return; } {
__cpy (y, z, p);
if (X[0] != Y[0]) { Z[0] = -Z[0];
if (__acr(x,y,p) > 0) {add_magnitudes(x,y,z,p); Z[0] = X[0]; } return;
else {add_magnitudes(y,x,z,p); Z[0] = -Y[0]; }
} }
else { else if (Y[0] == ZERO)
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]; } __cpy (x, z, p);
else Z[0] = ZERO; 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;
} }
return; return;
} }
@ -370,22 +602,35 @@ void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X /* 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 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. */ 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 i, i1, i2, j, k, k2;
long p2 = p; long p2 = p;
double u, zk, zk2; double u, zk, zk2;
/* Is z=0? */ /* Is z=0? */
if (X[0] * Y[0] == ZERO) if (X[0] * Y[0] == ZERO)
{ Z[0]=ZERO; return; } {
Z[0] = ZERO;
return;
}
/* Multiply, add and carry */ /* Multiply, add and carry */
k2 = (p2 < 3) ? p2 + p2 : p2 + 3; k2 = (p2 < 3) ? p2 + p2 : p2 + 3;
zk = Z[k2] = ZERO; zk = Z[k2] = ZERO;
for (k=k2; k>1; ) { for (k = k2; k > 1;)
if (k > p2) {i1=k-p2; i2=p2+1; } {
else {i1=1; i2=k; } if (k > p2)
{
i1 = k - p2;
i2 = p2 + 1;
}
else
{
i1 = 1;
i2 = k;
}
#if 1 #if 1
/* Rearrange this inner loop to allow the fmadd instructions to be /* Rearrange this inner loop to allow the fmadd instructions to be
independent and execute in parallel on processors that have independent and execute in parallel on processors that have
@ -416,11 +661,13 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
} }
#else #else
/* The original code. */ /* The original code. */
for (i=i1,j=i2-1; i<i2; i++,j--) zk += X[i]*Y[j]; for (i = i1, j = i2 - 1; i < i2; i++, j--)
zk += X[i] * Y[j];
#endif #endif
u = (zk + CUTTER) - CUTTER; u = (zk + CUTTER) - CUTTER;
if (u > zk) u -= RADIX; if (u > zk)
u -= RADIX;
Z[k] = zk - u; Z[k] = zk - u;
zk = u * RADIXI; zk = u * RADIXI;
--k; --k;
@ -428,9 +675,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
Z[k] = zk; Z[k] = zk;
/* Is there a carry beyond the most significant digit? */ /* Is there a carry beyond the most significant digit? */
if (Z[1] == ZERO) { if (Z[1] == ZERO)
for (i=1; i<=p2; i++) Z[i]=Z[i+1]; {
EZ = EX + EY - 1; } for (i = 1; i <= p2; i++)
Z[i] = Z[i + 1];
EZ = EX + EY - 1;
}
else else
EZ = EX + EY; EZ = EX + EY;
@ -444,17 +694,26 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
- For P > 3: 2.001 * R ^ (1 - P) - For P > 3: 2.001 * R ^ (1 - P)
*X = 0 is not permissible. */ *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; long i;
double t; double t;
mp_no z, w; 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, static const int np1[] =
4,4,4,4,4,4,4,4,4,4,4,4,4,4,4}; { 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); __cpy (x, &z, p);
t=ONE/t; __dbl_mp(t,y,p); EY -= EX; 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++) { for (i = 0; i < np1[p]; i++)
{
__cpy (y, &w, p); __cpy (y, &w, p);
__mul (x, &w, y, p); __mul (x, &w, y, p);
__sub (&mptwo, y, &z, p); __sub (&mptwo, y, &z, p);
@ -470,11 +729,17 @@ void __inv(const mp_no *x, mp_no *y, int p) {
- For P > 3: 3.001 * R ^ (1 - P) - For P > 3: 3.001 * R ^ (1 - P)
*X = 0 is not permissible. */ *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; mp_no w;
if (X[0] == ZERO) Z[0] = ZERO; if (X[0] == ZERO)
else {__inv(y,&w,p); __mul(x,&w,z,p);} Z[0] = ZERO;
else
{
__inv (y, &w, p);
__mul (x, &w, z, p);
}
return; return;
} }