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Update comments in mpa.c
Fixed comment style and clearer wording in some cases.
This commit is contained in:
Siddhesh Poyarekar
parent
3a235abb5a
commit
950c99ca90
45
ChangeLog
45
ChangeLog
@ -1,3 +1,48 @@
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2013-01-09 Siddhesh Poyarekar <siddhesh@redhat.com>
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* sysdeps/ieee754/dbl-64/mpa.c (mcr): Reword comment.
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(__acr): Likewise.
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(__cpy): Likewise.
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(norm): Likewise.
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(denorm): Likewise.
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(__mp_dbl): Likewise.
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(__dbl_mp): Likewise.
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(add_magnitudes): Likewise.
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(sub_magnitudes): Likewise.
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(__add): Likewise.
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(__sub): Likewise.
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(__mul): Likewise.
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(__inv): Likewise.
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(__dvd): Likewise.
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* sysdeps/powerpc/powerpc32/power4/fpu/mpa.c (mcr): Likewise.
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(__acr): Likewise.
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(__cpy): Likewise.
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(norm): Likewise.
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(denorm): Likewise.
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(__mp_dbl): Likewise.
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(__dbl_mp): Likewise.
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(add_magnitudes): Likewise.
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(sub_magnitudes): Likewise.
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(__add): Likewise.
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(__sub): Likewise.
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(__mul): Likewise.
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(__inv): Likewise.
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(__dvd): Likewise.
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* sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (mcr): Likewise.
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(__acr): Likewise.
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(__cpy): Likewise.
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(norm): Likewise.
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(denorm): Likewise.
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(__mp_dbl): Likewise.
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(__dbl_mp): Likewise.
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(add_magnitudes): Likewise.
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(sub_magnitudes): Likewise.
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(__add): Likewise.
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(__sub): Likewise.
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(__mul): Likewise.
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(__inv): Likewise.
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(__dvd): Likewise.
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2013-01-08 Joseph Myers <joseph@codesourcery.com>
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* io/sys/stat.h [__GNUC__ && __GNUC__ >= 2 &&
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@ -45,7 +45,7 @@
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#include "endian.h"
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#include "mpa.h"
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#include "mpa2.h"
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#include <sys/param.h> /* For MIN() */
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#include <sys/param.h>
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#ifndef SECTION
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# define SECTION
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@ -57,10 +57,8 @@ const mp_no mptwo = {1, {1.0, 2.0}};
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#endif
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#ifndef NO___ACR
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/* mcr() compares the sizes of the mantissas of two multiple precision */
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/* numbers. Mantissas are compared regardless of the signs of the */
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/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
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/* disregarded. */
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/* Compare mantissa of two multiple precision numbers regardless of the sign
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and exponent of the numbers. */
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static int
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mcr(const mp_no *x, const mp_no *y, int p) {
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int i;
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@ -71,8 +69,7 @@ mcr(const mp_no *x, const mp_no *y, int p) {
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return 0;
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}
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/* acr() compares the absolute values of two multiple precision numbers */
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/* Compare the absolute values of two multiple precision numbers. */
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int
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__acr(const mp_no *x, const mp_no *y, int p) {
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int i;
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@ -92,19 +89,18 @@ __acr(const mp_no *x, const mp_no *y, int p) {
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}
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#endif
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#ifndef NO___CPY
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/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
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/* Copy multiple precision number X into Y. They could be the same
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number. */
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void __cpy(const mp_no *x, mp_no *y, int p) {
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EY = EX;
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for (int i=0; i <= p; i++) Y[i] = X[i];
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}
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#endif
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#ifndef NO___MP_DBL
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, normalized case (|x| >= 2**(-1022))) */
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/* Convert a multiple precision number *X into a double precision
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number *Y, normalized case (|x| >= 2**(-1022))). */
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static void norm(const mp_no *x, double *y, int p)
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{
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#define R RADIXI
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@ -154,8 +150,8 @@ static void norm(const mp_no *x, double *y, int p)
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, denormalized case (|x| < 2**(-1022))) */
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/* Convert a multiple precision number *X into a double precision
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number *Y, Denormal case (|x| < 2**(-1022))). */
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static void denorm(const mp_no *x, double *y, int p)
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{
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int i,k;
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@ -198,9 +194,8 @@ static void denorm(const mp_no *x, double *y, int p)
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision number *y. */
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/* The result is correctly rounded to the nearest/even. *x is left unchanged */
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/* Convert multiple precision number *X into double precision number *Y. The
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result is correctly rounded to the nearest/even. */
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void __mp_dbl(const mp_no *x, double *y, int p) {
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if (X[0] == ZERO) {*y = ZERO; return; }
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@ -212,11 +207,8 @@ void __mp_dbl(const mp_no *x, double *y, int p) {
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}
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#endif
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/* dbl_mp() converts a double precision number x into a multiple precision */
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/* number *y. If the precision p is too small the result is truncated. x is */
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/* left unchanged. */
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/* Get the multiple precision equivalent of X into *Y. If the precision is too
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small, the result is truncated. */
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void
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SECTION
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__dbl_mp(double x, mp_no *y, int p) {
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@ -224,16 +216,16 @@ __dbl_mp(double x, mp_no *y, int p) {
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int i,n;
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double u;
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/* Sign */
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/* Sign. */
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if (x == ZERO) {Y[0] = ZERO; return; }
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else if (x > ZERO) Y[0] = ONE;
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else {Y[0] = MONE; x=-x; }
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/* Exponent */
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/* Exponent. */
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for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
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for ( ; x < ONE; EY -= ONE) x *= RADIX;
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/* Digits */
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/* Digits. */
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n=MIN(p,4);
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for (i=1; i<=n; i++) {
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u = (x + TWO52) - TWO52;
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@ -242,13 +234,10 @@ __dbl_mp(double x, mp_no *y, int p) {
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for ( ; i<=p; i++) Y[i] = ZERO;
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}
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/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
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/* abs(*x) >= abs(*y) > 0. */
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/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
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/* No guard digit is used. The result equals the exact sum, truncated. */
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/* *x & *y are left unchanged. */
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/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
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sign of the sum *Z is not changed. X and Y may overlap but not X and Z or
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Y and Z. No guard digit is used. The result equals the exact sum,
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truncated. */
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static void
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SECTION
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add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -286,13 +275,10 @@ add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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else EZ += ONE;
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}
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/* sub_magnitudes() subtracts the magnitudes of *x & *y assuming that */
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/* abs(*x) > abs(*y) > 0. */
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/* The sign of the difference *z is undefined. x&y may overlap but not x&z */
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/* or y&z. One guard digit is used. The error is less than one ulp. */
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/* *x & *y are left unchanged. */
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/* Subtract the magnitudes of *X and *Y assuming that abs (*x) > abs (*y) > 0.
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The sign of the difference *Z is not changed. X and Y may overlap but not X
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and Z or Y and Z. One guard digit is used. The error is less than one
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ULP. */
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static void
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SECTION
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sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -344,11 +330,9 @@ sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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Z[k++] = ZERO;
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}
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/* Add two multiple precision numbers. Set *z = *x + *y. x&y may overlap */
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/* but not x&z or y&z. One guard digit is used. The error is less than */
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/* one ulp. *x & *y are left unchanged. */
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/* Add *X and *Y and store the result in *Z. X and Y may overlap, but not X
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and Z or Y and Z. One guard digit is used. The error is less than one
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ULP. */
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void
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SECTION
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__add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -369,11 +353,9 @@ __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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}
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}
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/* Subtract two multiple precision numbers. *z is set to *x - *y. x&y may */
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/* overlap but not x&z or y&z. One guard digit is used. The error is */
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/* less than one ulp. *x & *y are left unchanged. */
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/* Subtract *Y from *X and return the result in *Z. X and Y may overlap but
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not X and Z or Y and Z. One guard digit is used. The error is less than
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one ULP. */
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void
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SECTION
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__sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -394,12 +376,9 @@ __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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}
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}
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/* Multiply two multiple precision numbers. *z is set to *x * *y. x&y */
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/* may overlap but not x&z or y&z. In case p=1,2,3 the exact result is */
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/* truncated to p digits. In case p>3 the error is bounded by 1.001 ulp. */
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/* *x & *y are left unchanged. */
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/* Multiply *X and *Y and store result in *Z. X and Y may overlap but not X
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and Z or Y and Z. For P in [1, 2, 3], the exact result is truncated to P
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digits. In case P > 3 the error is bounded by 1.001 ULP. */
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void
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SECTION
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__mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -414,7 +393,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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return;
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}
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/* Multiply, add and carry */
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/* Multiply, add and carry. */
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k2 = (__glibc_unlikely (p < 3)) ? p + p : p + 3;
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Z[k2] = ZERO;
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@ -443,7 +422,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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}
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EZ = EX + EY;
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/* Is there a carry beyond the most significant digit? */
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/* Is there a carry beyond the most significant digit? */
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if (__glibc_unlikely (Z[1] == ZERO))
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{
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for (i = 1; i <= p; i++)
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@ -454,12 +433,12 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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Z[0] = X[0] * Y[0];
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}
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/* Invert *X and store in *Y. Relative error bound:
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- For P = 2: 1.001 * R ^ (1 - P)
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- For P = 3: 1.063 * R ^ (1 - P)
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- For P > 3: 2.001 * R ^ (1 - P)
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/* Invert a multiple precision number. Set *y = 1 / *x. */
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/* Relative error bound = 1.001*r**(1-p) for p=2, 1.063*r**(1-p) for p=3, */
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/* 2.001*r**(1-p) for p>3. */
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/* *x=0 is not permissible. *x is left unchanged. */
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*X = 0 is not permissible. */
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static
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SECTION
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void __inv(const mp_no *x, mp_no *y, int p) {
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@ -480,12 +459,13 @@ void __inv(const mp_no *x, mp_no *y, int p) {
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}
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}
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/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
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or Y and Z. Relative error bound:
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- For P = 2: 2.001 * R ^ (1 - P)
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- For P = 3: 2.063 * R ^ (1 - P)
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- For P > 3: 3.001 * R ^ (1 - P)
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/* Divide one multiple precision number by another.Set *z = *x / *y. *x & *y */
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/* are left unchanged. x&y may overlap but not x&z or y&z. */
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/* Relative error bound = 2.001*r**(1-p) for p=2, 2.063*r**(1-p) for p=3 */
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/* and 3.001*r**(1-p) for p>3. *y=0 is not permissible. */
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*X = 0 is not permissible. */
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void
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SECTION
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__dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
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@ -44,15 +44,13 @@
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#include "endian.h"
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#include "mpa.h"
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#include "mpa2.h"
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#include <sys/param.h> /* For MIN() */
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#include <sys/param.h>
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const mp_no mpone = {1, {1.0, 1.0}};
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const mp_no mptwo = {1, {1.0, 2.0}};
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/* mcr() compares the sizes of the mantissas of two multiple precision */
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/* numbers. Mantissas are compared regardless of the signs of the */
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/* numbers, even if x->d[0] or y->d[0] are zero. Exponents are also */
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/* disregarded. */
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/* Compare mantissa of two multiple precision numbers regardless of the sign
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and exponent of the numbers. */
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static int mcr(const mp_no *x, const mp_no *y, int p) {
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long i;
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long p2 = p;
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@ -63,9 +61,7 @@ static int mcr(const mp_no *x, const mp_no *y, int p) {
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return 0;
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}
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/* acr() compares the absolute values of two multiple precision numbers */
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/* Compare the absolute values of two multiple precision numbers. */
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int __acr(const mp_no *x, const mp_no *y, int p) {
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long i;
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@ -83,8 +79,8 @@ int __acr(const mp_no *x, const mp_no *y, int p) {
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return i;
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}
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/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
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/* Copy multiple precision number X into Y. They could be the same
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number. */
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void __cpy(const mp_no *x, mp_no *y, int p) {
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long i;
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@ -94,9 +90,8 @@ void __cpy(const mp_no *x, mp_no *y, int p) {
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return;
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}
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, normalized case (|x| >= 2**(-1022))) */
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/* Convert a multiple precision number *X into a double precision
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number *Y, normalized case (|x| >= 2**(-1022))). */
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static void norm(const mp_no *x, double *y, int p)
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{
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#define R RADIXI
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@ -147,8 +142,8 @@ static void norm(const mp_no *x, double *y, int p)
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision */
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/* number *y, denormalized case (|x| < 2**(-1022))) */
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/* Convert a multiple precision number *X into a double precision
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number *Y, Denormal case (|x| < 2**(-1022))). */
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static void denorm(const mp_no *x, double *y, int p)
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{
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long i,k;
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@ -194,9 +189,8 @@ static void denorm(const mp_no *x, double *y, int p)
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#undef R
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}
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/* Convert a multiple precision number *x into a double precision number *y. */
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/* The result is correctly rounded to the nearest/even. *x is left unchanged */
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/* Convert multiple precision number *X into double precision number *Y. The
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result is correctly rounded to the nearest/even. */
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void __mp_dbl(const mp_no *x, double *y, int p) {
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if (X[0] == ZERO) {*y = ZERO; return; }
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@ -206,27 +200,24 @@ void __mp_dbl(const mp_no *x, double *y, int p) {
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else denorm(x,y,p);
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}
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/* dbl_mp() converts a double precision number x into a multiple precision */
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/* number *y. If the precision p is too small the result is truncated. x is */
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/* left unchanged. */
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/* Get the multiple precision equivalent of X into *Y. If the precision is too
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small, the result is truncated. */
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void __dbl_mp(double x, mp_no *y, int p) {
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long i,n;
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long p2 = p;
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double u;
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/* Sign */
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/* Sign. */
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if (x == ZERO) {Y[0] = ZERO; return; }
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else if (x > ZERO) Y[0] = ONE;
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else {Y[0] = MONE; x=-x; }
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/* Exponent */
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/* Exponent. */
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for (EY=ONE; x >= RADIX; EY += ONE) x *= RADIXI;
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for ( ; x < ONE; EY -= ONE) x *= RADIX;
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/* Digits */
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/* Digits. */
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n=MIN(p2,4);
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for (i=1; i<=n; i++) {
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u = (x + TWO52) - TWO52;
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@ -236,13 +227,10 @@ void __dbl_mp(double x, mp_no *y, int p) {
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return;
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}
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/* add_magnitudes() adds the magnitudes of *x & *y assuming that */
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/* abs(*x) >= abs(*y) > 0. */
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/* The sign of the sum *z is undefined. x&y may overlap but not x&z or y&z. */
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/* No guard digit is used. The result equals the exact sum, truncated. */
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/* *x & *y are left unchanged. */
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|
||||
/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
|
||||
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;
|
||||
@ -279,13 +267,10 @@ static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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;
|
||||
@ -338,11 +323,9 @@ static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
int n;
|
||||
@ -362,11 +345,9 @@ void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
int n;
|
||||
@ -386,12 +367,9 @@ void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
long i, i1, i2, j, k, k2;
|
||||
@ -409,12 +387,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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
|
||||
/* 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 */
|
||||
/* Make sure we have at least 2 iterations. */
|
||||
if (((i2 - i1) & 1L) == 1L)
|
||||
{
|
||||
/* Handle the odd iterations case. */
|
||||
@ -429,7 +407,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
zk += x->d[i]*y->d[j];
|
||||
zk2 += x->d[i+1]*y->d[j-1];
|
||||
}
|
||||
zk += zk2; /* final sum. */
|
||||
zk += zk2; /* Final sum. */
|
||||
}
|
||||
else
|
||||
{
|
||||
@ -449,7 +427,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
}
|
||||
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) {
|
||||
for (i=1; i<=p2; i++) Z[i]=Z[i+1];
|
||||
EZ = EX + EY - 1; }
|
||||
@ -460,12 +438,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
return;
|
||||
}
|
||||
|
||||
/* Invert *X and store in *Y. Relative error bound:
|
||||
- For P = 2: 1.001 * R ^ (1 - P)
|
||||
- For P = 3: 1.063 * R ^ (1 - P)
|
||||
- For P > 3: 2.001 * R ^ (1 - P)
|
||||
|
||||
/* 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. */
|
||||
|
||||
*X = 0 is not permissible. */
|
||||
void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
long i;
|
||||
double t;
|
||||
@ -489,12 +467,13 @@ void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
return;
|
||||
}
|
||||
|
||||
/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
|
||||
or Y and Z. Relative error bound:
|
||||
- For P = 2: 2.001 * R ^ (1 - P)
|
||||
- For P = 3: 2.063 * R ^ (1 - P)
|
||||
- For P > 3: 3.001 * R ^ (1 - P)
|
||||
|
||||
/* 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. */
|
||||
|
||||
*X = 0 is not permissible. */
|
||||
void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
|
||||
mp_no w;
|
||||
|
||||
@ -44,15 +44,13 @@
|
||||
#include "endian.h"
|
||||
#include "mpa.h"
|
||||
#include "mpa2.h"
|
||||
#include <sys/param.h> /* For MIN() */
|
||||
#include <sys/param.h>
|
||||
|
||||
const mp_no mpone = {1, {1.0, 1.0}};
|
||||
const mp_no mptwo = {1, {1.0, 2.0}};
|
||||
|
||||
/* 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. */
|
||||
/* 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) {
|
||||
long i;
|
||||
long p2 = p;
|
||||
@ -63,9 +61,7 @@ static int mcr(const mp_no *x, const mp_no *y, int p) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
|
||||
|
||||
/* acr() compares 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) {
|
||||
long i;
|
||||
|
||||
@ -83,8 +79,8 @@ int __acr(const mp_no *x, const mp_no *y, int p) {
|
||||
return i;
|
||||
}
|
||||
|
||||
|
||||
/* Copy a multiple precision number. Set *y=*x. x=y is permissible. */
|
||||
/* Copy multiple precision number X into Y. They could be the same
|
||||
number. */
|
||||
void __cpy(const mp_no *x, mp_no *y, int p) {
|
||||
long i;
|
||||
|
||||
@ -94,9 +90,8 @@ void __cpy(const mp_no *x, mp_no *y, int p) {
|
||||
return;
|
||||
}
|
||||
|
||||
|
||||
/* Convert a multiple precision number *x into a double precision */
|
||||
/* number *y, normalized case (|x| >= 2**(-1022))) */
|
||||
/* 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
|
||||
@ -147,8 +142,8 @@ static void norm(const mp_no *x, double *y, int p)
|
||||
#undef R
|
||||
}
|
||||
|
||||
/* Convert a multiple precision number *x into a double precision */
|
||||
/* number *y, denormalized case (|x| < 2**(-1022))) */
|
||||
/* 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)
|
||||
{
|
||||
long i,k;
|
||||
@ -194,9 +189,8 @@ static void denorm(const mp_no *x, double *y, int p)
|
||||
#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 */
|
||||
|
||||
/* 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; }
|
||||
@ -206,27 +200,24 @@ void __mp_dbl(const mp_no *x, double *y, int 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. */
|
||||
|
||||
/* 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;
|
||||
long p2 = p;
|
||||
double u;
|
||||
|
||||
/* Sign */
|
||||
/* Sign. */
|
||||
if (x == ZERO) {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 ( ; x < ONE; EY -= ONE) x *= RADIX;
|
||||
|
||||
/* Digits */
|
||||
/* Digits. */
|
||||
n=MIN(p2,4);
|
||||
for (i=1; i<=n; i++) {
|
||||
u = (x + TWO52) - TWO52;
|
||||
@ -236,13 +227,10 @@ void __dbl_mp(double x, mp_no *y, int p) {
|
||||
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. */
|
||||
|
||||
/* Add magnitudes of *X and *Y assuming that abs (*X) >= abs (*Y) > 0. The
|
||||
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;
|
||||
@ -279,13 +267,10 @@ static void add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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;
|
||||
@ -338,11 +323,9 @@ static void sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
int n;
|
||||
@ -362,11 +345,9 @@ void __add(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
int n;
|
||||
@ -386,12 +367,9 @@ void __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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. */
|
||||
|
||||
/* 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) {
|
||||
|
||||
long i, i1, i2, j, k, k2;
|
||||
@ -409,12 +387,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
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
|
||||
/* 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 */
|
||||
/* Make sure we have at least 2 iterations. */
|
||||
if (((i2 - i1) & 1L) == 1L)
|
||||
{
|
||||
/* Handle the odd iterations case. */
|
||||
@ -429,7 +407,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
zk += x->d[i]*y->d[j];
|
||||
zk2 += x->d[i+1]*y->d[j-1];
|
||||
}
|
||||
zk += zk2; /* final sum. */
|
||||
zk += zk2; /* Final sum. */
|
||||
}
|
||||
else
|
||||
{
|
||||
@ -449,7 +427,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
}
|
||||
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) {
|
||||
for (i=1; i<=p2; i++) Z[i]=Z[i+1];
|
||||
EZ = EX + EY - 1; }
|
||||
@ -460,12 +438,12 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
return;
|
||||
}
|
||||
|
||||
/* Invert *X and store in *Y. Relative error bound:
|
||||
- For P = 2: 1.001 * R ^ (1 - P)
|
||||
- For P = 3: 1.063 * R ^ (1 - P)
|
||||
- For P > 3: 2.001 * R ^ (1 - P)
|
||||
|
||||
/* 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. */
|
||||
|
||||
*X = 0 is not permissible. */
|
||||
void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
long i;
|
||||
double t;
|
||||
@ -489,12 +467,13 @@ void __inv(const mp_no *x, mp_no *y, int p) {
|
||||
return;
|
||||
}
|
||||
|
||||
/* Divide *X by *Y and store result in *Z. X and Y may overlap but not X and Z
|
||||
or Y and Z. Relative error bound:
|
||||
- For P = 2: 2.001 * R ^ (1 - P)
|
||||
- For P = 3: 2.063 * R ^ (1 - P)
|
||||
- For P > 3: 3.001 * R ^ (1 - P)
|
||||
|
||||
/* 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. */
|
||||
|
||||
*X = 0 is not permissible. */
|
||||
void __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) {
|
||||
|
||||
mp_no w;
|
||||
|
||||
Loading…
Reference in New Issue
Block a user