diff options
Diffstat (limited to 'sysdeps/ieee754/dbl-64/mpa.c')
| -rw-r--r-- | sysdeps/ieee754/dbl-64/mpa.c | 497 |
1 files changed, 497 insertions, 0 deletions
diff --git a/sysdeps/ieee754/dbl-64/mpa.c b/sysdeps/ieee754/dbl-64/mpa.c new file mode 100644 index 0000000000..cdd15a1602 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/mpa.c @@ -0,0 +1,497 @@ + +/* + * IBM Accurate Mathematical Library + * Copyright (c) International Business Machines Corp., 2001 + * + * This program is free software; you can redistribute it and/or modify + * it under the terms of the GNU Lesser General Public License as published by + * the Free Software Foundation; either version 2 of the License, or + * (at your option) any later version. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU Lesser General Public License + * along with this program; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ +/************************************************************************/ +/* MODULE_NAME: mpa.c */ +/* */ +/* FUNCTIONS: */ +/* mcr */ +/* acr */ +/* cr */ +/* cpy */ +/* cpymn */ +/* norm */ +/* denorm */ +/* mp_dbl */ +/* dbl_mp */ +/* add_magnitudes */ +/* sub_magnitudes */ +/* add */ +/* sub */ +/* mul */ +/* inv */ +/* dvd */ +/* */ +/* Arithmetic functions for multiple precision numbers. */ +/* Relative errors are bounded */ +/************************************************************************/ + + +#include "endian.h" +#include "mpa.h" +#include "mpa2.h" +/* mcr() compares the sizes of the mantissas of two multiple precision */ +/* numbers. Mantissas are compared regardless of the signs of the */ +/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */ +/* disregarded. */ +static int 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; } + return 0; +} + + + +/* acr() compares the absolute values of two multiple precision numbers */ +int 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); + } + + return i; +} + + +/* cr90 compares the values of two multiple precision numbers */ +int cr(const mp_no *x, const mp_no *y, int p) { + int i; + + if (X[0] > Y[0]) i= 1; + else if (X[0] < Y[0]) i=-1; + else if (X[0] < ZERO ) i= acr(y,x,p); + else i= acr(x,y,p); + + return i; +} + + +/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */ +void cpy(const mp_no *x, mp_no *y, int p) { + int i; + + EY = EX; + for (i=0; i <= p; i++) Y[i] = X[i]; + + return; +} + + +/* Copy a multiple precision number x of precision m into a */ +/* multiple precision number y of precision n. In case n>m, */ +/* the digits of y beyond the m'th are set to zero. In case */ +/* n<m, the digits of x beyond the n'th are ignored. */ +/* x=y is permissible. */ + +void cpymn(const mp_no *x, int m, mp_no *y, int n) { + + int i,k; + + EY = EX; k=MIN(m,n); + for (i=0; i <= k; i++) Y[i] = X[i]; + for ( ; i <= n; i++) Y[i] = ZERO; + + 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) +{ + #define R radixi.d + int i,k; + 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; + } + + 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; + + *y = c; + return; +#undef R +} + +/* Convert a multiple precision number *x into a double precision */ +/* number *y, denormalized case (|x| < 2**(-1022))) */ +static void denorm(const mp_no *x, double *y, int p) +{ + int i,k; + double a,c,u,v,z[5]; + +#define R radixi.d + 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]; + } + + u = (z[3] + TWO57) - TWO57; + 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; } + } + } + + c = X[0]*((z[1] + R*(z[2] + R*z[3])) - TWO10); + + *y = c*TWOM1032; + return; + +#undef R +} + +/* Convert a multiple precision number *x into a double precision number *y. */ +/* The result is correctly rounded to the nearest/even. *x is left unchanged */ + +void mp_dbl(const mp_no *x, double *y, int p) { + + int i,k; + double a,c,u,v,z[5]; + + 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); +} + + +/* dbl_mp() converts a double precision number x into a multiple precision */ +/* number *y. If the precision p is too small the result is truncated. x is */ +/* left unchanged. */ + +void 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; } + + /* Exponent */ + 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; + return; +} + + +/* add_magnitudes() adds the magnitudes of *x & *y assuming that */ +/* abs(*x) >= abs(*y) > 0. */ +/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */ +/* No guard digit is used. The result equals the exact sum, truncated. */ +/* *x & *y are left unchanged. */ + +static void 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; + + 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 (; 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; +} + + +/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */ +/* abs(*x) > abs(*y) > 0. */ +/* The sign of the difference *z is undefined. x&y may overlap but not x&z */ +/* or y&z. One guard digit is used. The error is less than one ulp. */ +/* *x & *y are left unchanged. */ + +static void 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--;} + } + } + + 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=1; Z[i] == ZERO; i++) ; + EZ = EZ - i + 1; + for (k=1; i <= p+1; ) + Z[k++] = Z[i++]; + for (; k <= p; ) + Z[k++] = ZERO; + + return; +} + + +/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */ +/* but not x&z or y&z. One guard digit is used. The error is less than */ +/* one ulp. *x & *y are left unchanged. */ + +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] == 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 two multiple precision numbers. *z is set to *x - *y. x&y may */ +/* overlap but not x&z or y&z. One guard digit is used. The error is */ +/* less than one ulp. *x & *y are left unchanged. */ + +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] != 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 two multiple precision numbers. *z is set to *x * *y. x&y */ +/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */ +/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */ +/* *x & *y are left unchanged. */ + +void mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { + + int i, i1, i2, j, k, k2; + double u; + + /* Is z=0? */ + if (X[0]*Y[0]==ZERO) + { Z[0]=ZERO; return; } + + /* Multiply, add and carry */ + k2 = (p<3) ? p+p : p+3; + Z[k2]=ZERO; + for (k=k2; k>1; ) { + if (k > p) {i1=k-p; i2=p+1; } + else {i1=1; i2=k; } + for (i=i1,j=i2-1; i<i2; i++,j--) Z[k] += X[i]*Y[j]; + + u = (Z[k] + CUTTER)-CUTTER; + if (u > Z[k]) u -= RADIX; + Z[k] -= u; + Z[--k] = u*RADIXI; + } + + /* Is there a carry beyond the most significant digit? */ + if (Z[1] == ZERO) { + for (i=1; i<=p; i++) Z[i]=Z[i+1]; + EZ = EX + EY - 1; } + else + EZ = EX + EY; + + Z[0] = X[0] * Y[0]; + return; +} + + +/* Invert a multiple precision number. Set *y = 1 / *x. */ +/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */ +/* 2.001*r**(1-p) for p>3. */ +/* *x=0 is not permissible. *x is left unchanged. */ + +void inv(const mp_no *x, mp_no *y, int p) { + int i,l; + 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}; + const mp_no mptwo = {1,1.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, + 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, + 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0, + 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,}; + + 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); + } + return; +} + + +/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */ +/* are left unchanged. x&y may overlap but not x&z or y&z. */ +/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */ +/* and 3.001*r**(1-p) for p>3. *y=0 is not permissible. */ + +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);} + return; +} + |