diff options
Diffstat (limited to 'libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c')
-rw-r--r-- | libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c | 182 |
1 files changed, 59 insertions, 123 deletions
diff --git a/libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c b/libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c index d15680e77..9fcaa763c 100644 --- a/libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c +++ b/libc/sysdeps/powerpc/powerpc64/power4/fpu/mpa.c @@ -2,7 +2,7 @@ /* * IBM Accurate Mathematical Library * written by International Business Machines Corp. - * Copyright (C) 2001, 2006 Free Software Foundation + * Copyright (C) 2001-2013 Free Software Foundation, Inc. * * 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 @@ -23,9 +23,7 @@ /* FUNCTIONS: */ /* mcr */ /* acr */ -/* cr */ /* cpy */ -/* cpymn */ /* norm */ /* denorm */ /* mp_dbl */ @@ -46,11 +44,13 @@ #include "endian.h" #include "mpa.h" #include "mpa2.h" -#include <sys/param.h> /* For MIN() */ -/* 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. */ +#include <sys/param.h> + +const mp_no mpone = {1, {1.0, 1.0}}; +const mp_no mptwo = {1, {1.0, 2.0}}; + +/* Compare mantissa of two multiple precision numbers regardless of the sign + and exponent of the numbers. */ static int mcr(const mp_no *x, const mp_no *y, int p) { long i; long p2 = p; @@ -61,9 +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; @@ -81,21 +79,8 @@ int __acr(const mp_no *x, const mp_no *y, int 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. */ +/* 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; @@ -105,35 +90,12 @@ void __cpy(const mp_no *x, mp_no *y, int p) { 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) { - - long i,k; - long n2 = n; - long m2 = m; - - EY = EX; k=MIN(m2,n2); - for (i=0; i <= k; i++) Y[i] = X[i]; - for ( ; i <= n2; i++) Y[i] = ZERO; - - 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.d + #define R RADIXI long i; -#if 0 - int k; -#endif double a,c,u,v,z[5]; if (p<5) { if (p==1) c = X[1]; @@ -180,18 +142,15 @@ 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; long p2 = p; double c,u,z[5]; -#if 0 - double a,v; -#endif -#define R radixi.d +#define R RADIXI if (EX<-44 || (EX==-44 && X[1]<TWO5)) { *y=ZERO; return; } @@ -230,14 +189,9 @@ 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 0 - int i,k; - double a,c,u,v,z[5]; -#endif if (X[0] == ZERO) {*y = ZERO; return; } @@ -246,27 +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; @@ -276,13 +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; @@ -319,13 +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; @@ -378,11 +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; @@ -402,11 +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; @@ -426,12 +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; @@ -449,19 +387,19 @@ 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 - /* rearange 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 symetrical FP pipelines. */ + 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. */ zk2 = x->d[i2-1]*y->d[i1]; } else - zk2 = zero.d; + zk2 = 0.0; /* Do two multiply/adds per loop iteration, using independent accumulators; zk and zk2. */ for (i=i1,j=i2-1; i<i2-1; i+=2,j-=2) @@ -469,7 +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 { @@ -477,7 +415,7 @@ void __mul(const mp_no *x, const mp_no *y, mp_no *z, int p) { zk += x->d[i1]*y->d[i1]; } #else - /* The orginal code. */ + /* The original code. */ for (i=i1,j=i2-1; i<i2; i++,j--) zk += X[i]*Y[j]; #endif @@ -489,7 +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; } @@ -500,17 +438,14 @@ 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; -#if 0 - int l; -#endif 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, @@ -532,12 +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; |