riscv
/
musl
mirror of https://git.musl-libc.org/git/musl
1
0
Fork 0
Code Issues Projects Releases Wiki Activity
Browse Source

math: fix remaining old long double code (erfl, fmal, lgammal, scalbnl) 

in lgammal don't handle 1 and 2 specially, in fma use the new ldshape
union instead of ld80 one.
rs-1.0
Szabolcs Nagy 13 years ago
parent
535104ab6a
commit
34660d73bd
5 changed files with 65 additions and 93 deletions
Whitespace
Show all changes Ignore whitespace when comparing lines Ignore changes in amount of whitespace Ignore changes in whitespace at EOL
Split View
Diff Options
Show Stats Download Patch File Download Diff File
  1. 37
      src/math/erfl.c
  2. 38
      src/math/fma.c
  3. 30
      src/math/fmal.c
  4. 45
      src/math/lgammal.c
  5. 8
      src/math/scalbnl.c

37
src/math/erfl.c
View File

@ -253,8 +253,8 @@ static long double erfc1(long double x)
static long double erfc2(uint32_t ix, long double x)
{
union ldshape u;
long double s,z,R,S;
uint32_t i0,i1;
if (ix < 0x3fffa000) /* 0.84375 <= |x| < 1.25 */
return erfc1(x);
@ -288,28 +288,22 @@ static long double erfc2(uint32_t ix, long double x)
S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] +
s * (sc[4] + s))));
}
z = x;
GET_LDOUBLE_WORDS(ix, i0, i1, z);
i1 = 0;
i0 &= 0xffffff00;
SET_LDOUBLE_WORDS(z, ix, i0, i1);
u.f = x;
u.i.m &= -1ULL << 40;
z = u.f;
return expl(-z*z - 0.5625) * expl((z - x) * (z + x) + R / S) / x;
}
long double erfl(long double x)
{
long double r, s, z, y;
uint32_t i0, i1, ix;
int sign;
union ldshape u = {x};
uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
int sign = u.i.se >> 15;
GET_LDOUBLE_WORDS(ix, i0, i1, x);
sign = ix >> 15;
ix &= 0x7fff;
if (ix == 0x7fff) {
if (ix >= 0x7fff0000)
/* erf(nan)=nan, erf(+-inf)=+-1 */
return 1 - 2*sign + 1/x;
}
ix = (ix << 16) | (i0 >> 16);
if (ix < 0x3ffed800) { /* |x| < 0.84375 */
if (ix < 0x3fde8000) { /* |x| < 2**-33 */
return 0.125 * (8 * x + efx8 * x); /* avoid underflow */
@ -332,17 +326,13 @@ long double erfl(long double x)
long double erfcl(long double x)
{
long double r, s, z, y;
uint32_t i0, i1, ix;
int sign;
union ldshape u = {x};
uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
int sign = u.i.se >> 15;
GET_LDOUBLE_WORDS(ix, i0, i1, x);
sign = ix>>15;
ix &= 0x7fff;
if (ix == 0x7fff)
if (ix >= 0x7fff0000)
/* erfc(nan) = nan, erfc(+-inf) = 0,2 */
return 2*sign + 1/x;
ix = (ix << 16) | (i0 >> 16);
if (ix < 0x3ffed800) { /* |x| < 0.84375 */
if (ix < 0x3fbe0000) /* |x| < 2**-65 */
return 1.0 - x;
@ -358,6 +348,7 @@ long double erfcl(long double x)
}
if (ix < 0x4005d600) /* |x| < 107 */
return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
return sign ? 2 - 0x1p-16382L : 0x1p-16382L*0x1p-16382L;
y = 0x1p-16382L;
return sign ? 2 - y : y*y;
}
#endif

38
src/math/fma.c
View File

@ -2,16 +2,6 @@
#include "libm.h"
#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
union ld80 {
long double x;
struct {
uint64_t m;
uint16_t e : 15;
uint16_t s : 1;
uint16_t pad;
} bits;
};
/* exact add, assumes exponent_x >= exponent_y */
static void add(long double *hi, long double *lo, long double x, long double y)
{
@ -45,25 +35,25 @@ return an adjusted hi so that rounding it to double (or less) precision is corre
*/
static long double adjust(long double hi, long double lo)
{
union ld80 uhi, ulo;
union ldshape uhi, ulo;
if (lo == 0)
return hi;
uhi.x = hi;
if (uhi.bits.m & 0x3ff)
uhi.f = hi;
if (uhi.i.m & 0x3ff)
return hi;
ulo.x = lo;
if (uhi.bits.s == ulo.bits.s)
uhi.bits.m++;
ulo.f = lo;
if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
uhi.i.m++;
else {
uhi.bits.m--;
/* handle underflow and take care of ld80 implicit msb */
if (uhi.bits.m == (uint64_t)-1/2) {
uhi.bits.m *= 2;
uhi.bits.e--;
if (uhi.i.m << 1 == 0) {
uhi.i.m = 0;
uhi.i.se--;
}
uhi.i.m--;
}
return uhi.x;
return uhi.f;
}
/* adjusted add so the result is correct when rounded to double (or less) precision */
@ -82,9 +72,9 @@ static long double dmul(long double x, long double y)
static int getexp(long double x)
{
union ld80 u;
u.x = x;
return u.bits.e;
union ldshape u;
u.f = x;
return u.i.se & 0x7fff;
}
double fma(double x, double y, double z)

30
src/math/fmal.c
View File

@ -34,6 +34,13 @@ long double fmal(long double x, long double y, long double z)
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include <fenv.h>
#if LDBL_MANT_DIG == 64
#define LASTBIT(u) (u.i.m & 1)
#define SPLIT (0x1p32L + 1)
#elif LDBL_MANT_DIG == 113
#define LASTBIT(u) (u.i.lo & 1)
#define SPLIT (0x1p57L + 1)
#endif
/*
* A struct dd represents a floating-point number with twice the precision
@ -75,12 +82,12 @@ static inline struct dd dd_add(long double a, long double b)
static inline long double add_adjusted(long double a, long double b)
{
struct dd sum;
union IEEEl2bits u;
union ldshape u;
sum = dd_add(a, b);
if (sum.lo != 0) {
u.e = sum.hi;
if ((u.bits.manl & 1) == 0)
u.f = sum.hi;
if (!LASTBIT(u))
sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
}
return (sum.hi);
@ -95,7 +102,7 @@ static inline long double add_and_denormalize(long double a, long double b, int
{
struct dd sum;
int bits_lost;
union IEEEl2bits u;
union ldshape u;
sum = dd_add(a, b);
@ -110,9 +117,9 @@ static inline long double add_and_denormalize(long double a, long double b, int
* break the ties manually.
*/
if (sum.lo != 0) {
u.e = sum.hi;
bits_lost = -u.bits.exp - scale + 1;
if (bits_lost != 1 ^ (int)(u.bits.manl & 1))
u.f = sum.hi;
bits_lost = -u.i.se - scale + 1;
if ((bits_lost != 1) ^ LASTBIT(u))
sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
}
return scalbnl(sum.hi, scale);
@ -125,20 +132,15 @@ static inline long double add_and_denormalize(long double a, long double b, int
*/
static inline struct dd dd_mul(long double a, long double b)
{
#if LDBL_MANT_DIG == 64
static const long double split = 0x1p32L + 1.0;
#elif LDBL_MANT_DIG == 113
static const long double split = 0x1p57L + 1.0;
#endif
struct dd ret;
long double ha, hb, la, lb, p, q;
p = a * split;
p = a * SPLIT;
ha = a - p;
ha += p;
la = a - ha;
p = b * split;
p = b * SPLIT;
hb = b - p;
hb += p;
lb = b - hb;

45
src/math/lgammal.c
View File

@ -202,13 +202,11 @@ w7 = 4.885026142432270781165E-3L;
static long double sin_pi(long double x)
{
union ldshape u = {x};
uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
long double y, z;
int n, ix;
uint32_t se, i0, i1;
int n;
GET_LDOUBLE_WORDS(se, i0, i1, x);
ix = se & 0x7fff;
ix = (ix << 16) | (i0 >> 16);
if (ix < 0x3ffd8000) /* 0.25 */
return sinl(pi * x);
y = -x; /* x is assume negative */
@ -229,8 +227,8 @@ static long double sin_pi(long double x)
} else {
if (ix < 0x403e8000) /* 2^63 */
z = y + two63; /* exact */
GET_LDOUBLE_WORDS(se, i0, i1, z);
n = i1 & 1;
u.f = z;
n = u.i.m & 1;
y = n;
n <<= 2;
}
@ -261,33 +259,28 @@ static long double sin_pi(long double x)
long double __lgammal_r(long double x, int *sg) {
long double t, y, z, nadj, p, p1, p2, q, r, w;
int i, ix;
uint32_t se, i0, i1;
union ldshape u = {x};
uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
int sign = u.i.se >> 15;
int i;
*sg = 1;
GET_LDOUBLE_WORDS(se, i0, i1, x);
ix = se & 0x7fff;
if ((ix | i0 | i1) == 0) {
if (se & 0x8000)
*sg = -1;
return 1.0 / fabsl(x);
}
ix = (ix << 16) | (i0 >> 16);
/* purge off +-inf, NaN, +-0, and negative arguments */
if (ix >= 0x7fff0000)
return x * x;
if (x == 0) {
*sg -= 2*sign;
return 1.0 / fabsl(x);
}
if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */
if (se & 0x8000) {
if (sign) {
*sg = -1;
return -logl(-x);
}
return -logl(x);
}
if (se & 0x8000) {
if (sign) {
t = sin_pi (x);
if (t == 0.0)
return 1.0 / fabsl(t); /* -integer */
@ -297,11 +290,7 @@ long double __lgammal_r(long double x, int *sg) {
x = -x;
}
/* purge off 1 and 2 */
if ((((ix - 0x3fff8000) | i0 | i1) == 0) ||
(((ix - 0x40008000) | i0 | i1) == 0))
r = 0;
else if (ix < 0x40008000) { /* x < 2.0 */
if (ix < 0x40008000) { /* x < 2.0 */
if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */
/* lgamma(x) = lgamma(x+1) - log(x) */
r = -logl(x);
@ -380,7 +369,7 @@ long double __lgammal_r(long double x, int *sg) {
r = (x - 0.5) * (t - 1.0) + w;
} else /* 2**66 <= x <= inf */
r = x * (logl(x) - 1.0);
if (se & 0x8000)
if (sign)
r = nadj - r;
return r;
}

8
src/math/scalbnl.c
View File

@ -8,7 +8,7 @@ long double scalbnl(long double x, int n)
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
long double scalbnl(long double x, int n)
{
union IEEEl2bits scale;
union ldshape u;
if (n > 16383) {
x *= 0x1p16383L;
@ -29,8 +29,8 @@ long double scalbnl(long double x, int n)
n = -16382;
}
}
scale.e = 1.0;
scale.bits.exp = 0x3fff + n;
return x * scale.e;
u.f = 1.0;
u.i.se = 0x3fff + n;
return x * u.f;
}
#endif

Write Preview
Loading…
Cancel
Save