diff options
| -rw-r--r-- | ChangeLog | 45 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/mpa.c | 114 | ||||
| -rw-r--r-- | sysdeps/powerpc/powerpc32/power4/fpu/mpa.c | 119 | ||||
| -rw-r--r-- | sysdeps/powerpc/powerpc64/power4/fpu/mpa.c | 119 |
4 files changed, 190 insertions, 207 deletions
@@ -1,3 +1,48 @@ +2013-01-09 Siddhesh Poyarekar <siddhesh@redhat.com> + + * sysdeps/ieee754/dbl-64/mpa.c (mcr): Reword comment. + (__acr): Likewise. + (__cpy): Likewise. + (norm): Likewise. + (denorm): Likewise. + (__mp_dbl): Likewise. + (__dbl_mp): Likewise. + (add_magnitudes): Likewise. + (sub_magnitudes): Likewise. + (__add): Likewise. + (__sub): Likewise. + (__mul): Likewise. + (__inv): Likewise. + (__dvd): Likewise. + * sysdeps/powerpc/powerpc32/power4/fpu/mpa.c (mcr): Likewise. + (__acr): Likewise. + (__cpy): Likewise. + (norm): Likewise. + (denorm): Likewise. + (__mp_dbl): Likewise. + (__dbl_mp): Likewise. + (add_magnitudes): Likewise. + (sub_magnitudes): Likewise. + (__add): Likewise. + (__sub): Likewise. + (__mul): Likewise. + (__inv): Likewise. + (__dvd): Likewise. + * sysdeps/powerpc/powerpc64/power4/fpu/mpa.c (mcr): Likewise. + (__acr): Likewise. + (__cpy): Likewise. + (norm): Likewise. + (denorm): Likewise. + (__mp_dbl): Likewise. + (__dbl_mp): Likewise. + (add_magnitudes): Likewise. + (sub_magnitudes): Likewise. + (__add): Likewise. + (__sub): Likewise. + (__mul): Likewise. + (__inv): Likewise. + (__dvd): Likewise. + 2013-01-08 Joseph Myers <joseph@codesourcery.com> * io/sys/stat.h [__GNUC__ && __GNUC__ >= 2 && diff --git a/sysdeps/ieee754/dbl-64/mpa.c b/sysdeps/ieee754/dbl-64/mpa.c index b0571f9..7abad67 100644 --- a/sysdeps/ieee754/dbl-64/mpa.c +++ b/sysdeps/ieee754/dbl-64/mpa.c @@ -45,7 +45,7 @@ #include "endian.h" #include "mpa.h" #include "mpa2.h" -#include <sys/param.h> /* For MIN() */ +#include <sys/param.h> #ifndef SECTION # define SECTION @@ -57,10 +57,8 @@ const mp_no mptwo = {1, {1.0, 2.0}}; #endif #ifndef NO___ACR -/* 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) { int i; @@ -71,8 +69,7 @@ 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) { int i; @@ -92,19 +89,18 @@ __acr(const mp_no *x, const mp_no *y, int p) { } #endif - #ifndef NO___CPY -/* 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) { EY = EX; for (int i=0; i <= p; i++) Y[i] = X[i]; } #endif - #ifndef NO___MP_DBL -/* Convert a multiple precision number *x into a double precision */ -/* number *y, normalized case (|x| >= 2**(-1022))) */ +/* 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 @@ -154,8 +150,8 @@ 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) { int i,k; @@ -198,9 +194,8 @@ 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; } @@ -212,11 +207,8 @@ void __mp_dbl(const mp_no *x, double *y, int p) { } #endif - -/* 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 SECTION __dbl_mp(double x, mp_no *y, int p) { @@ -224,16 +216,16 @@ __dbl_mp(double x, mp_no *y, int p) { int i,n; 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(p,4); for (i=1; i<=n; i++) { u = (x + TWO52) - TWO52; @@ -242,13 +234,10 @@ __dbl_mp(double x, mp_no *y, int p) { for ( ; i<=p; i++) Y[i] = ZERO; } - -/* 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 SECTION add_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { @@ -286,13 +275,10 @@ 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 SECTION sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { @@ -344,11 +330,9 @@ sub_magnitudes(const mp_no *x, const mp_no *y, mp_no *z, int p) { Z[k++] = ZERO; } - -/* 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 SECTION __add(const mp_no *x, const mp_no *y, mp_no *z, int p) { @@ -369,11 +353,9 @@ __add(const mp_no *x, const mp_no *y, mp_no *z, int p) { } } - -/* 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 SECTION __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) { @@ -394,12 +376,9 @@ __sub(const mp_no *x, const mp_no *y, mp_no *z, int p) { } } - -/* 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 SECTION __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { @@ -414,7 +393,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { return; } - /* Multiply, add and carry */ + /* Multiply, add and carry. */ k2 = (__glibc_unlikely (p < 3)) ? p + p : p + 3; Z[k2] = ZERO; @@ -443,7 +422,7 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { } EZ = EX + EY; - /* Is there a carry beyond the most significant digit? */ + /* Is there a carry beyond the most significant digit? */ if (__glibc_unlikely (Z[1] == ZERO)) { for (i = 1; i <= p; i++) @@ -454,12 +433,12 @@ __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { Z[0] = X[0] * Y[0]; } +/* 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. */ static SECTION void __inv(const mp_no *x, mp_no *y, int p) { @@ -480,12 +459,13 @@ void __inv(const mp_no *x, mp_no *y, int p) { } } +/* 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 SECTION __dvd(const mp_no *x, const mp_no *y, mp_no *z, int p) { diff --git a/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c b/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c index b6f8341..9fcaa76 100644 --- a/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c +++ b/sysdeps/powerpc/powerpc32/power4/fpu/mpa.c @@ -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; diff --git a/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c b/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c index b6f8341..9fcaa76 100644 --- a/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c +++ b/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c @@ -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; |