mirror of git://git.musl-libc.org/musl
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.
This commit is contained in:
Szabolcs Nagy
parent
535104ab6a
commit
34660d73bd
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@ -253,8 +253,8 @@ static long double erfc1(long double x)
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static long double erfc2(uint32_t ix, long double x)
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{
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union ldshape u;
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long double s,z,R,S;
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uint32_t i0,i1;
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if (ix < 0x3fffa000) /* 0.84375 <= |x| < 1.25 */
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return erfc1(x);
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@ -288,28 +288,22 @@ static long double erfc2(uint32_t ix, long double x)
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S = sc[0] + s * (sc[1] + s * (sc[2] + s * (sc[3] +
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s * (sc[4] + s))));
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}
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z = x;
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GET_LDOUBLE_WORDS(ix, i0, i1, z);
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i1 = 0;
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i0 &= 0xffffff00;
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SET_LDOUBLE_WORDS(z, ix, i0, i1);
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u.f = x;
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u.i.m &= -1ULL << 40;
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z = u.f;
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return expl(-z*z - 0.5625) * expl((z - x) * (z + x) + R / S) / x;
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}
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long double erfl(long double x)
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{
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long double r, s, z, y;
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uint32_t i0, i1, ix;
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int sign;
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union ldshape u = {x};
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uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
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int sign = u.i.se >> 15;
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GET_LDOUBLE_WORDS(ix, i0, i1, x);
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sign = ix >> 15;
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ix &= 0x7fff;
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if (ix == 0x7fff) {
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if (ix >= 0x7fff0000)
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/* erf(nan)=nan, erf(+-inf)=+-1 */
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return 1 - 2*sign + 1/x;
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}
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ix = (ix << 16) | (i0 >> 16);
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if (ix < 0x3ffed800) { /* |x| < 0.84375 */
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if (ix < 0x3fde8000) { /* |x| < 2**-33 */
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return 0.125 * (8 * x + efx8 * x); /* avoid underflow */
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@ -332,17 +326,13 @@ long double erfl(long double x)
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long double erfcl(long double x)
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{
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long double r, s, z, y;
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uint32_t i0, i1, ix;
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int sign;
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union ldshape u = {x};
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uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
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int sign = u.i.se >> 15;
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GET_LDOUBLE_WORDS(ix, i0, i1, x);
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sign = ix>>15;
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ix &= 0x7fff;
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if (ix == 0x7fff)
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if (ix >= 0x7fff0000)
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/* erfc(nan) = nan, erfc(+-inf) = 0,2 */
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return 2*sign + 1/x;
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ix = (ix << 16) | (i0 >> 16);
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if (ix < 0x3ffed800) { /* |x| < 0.84375 */
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if (ix < 0x3fbe0000) /* |x| < 2**-65 */
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return 1.0 - x;
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@ -358,6 +348,7 @@ long double erfcl(long double x)
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}
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if (ix < 0x4005d600) /* |x| < 107 */
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return sign ? 2 - erfc2(ix,x) : erfc2(ix,x);
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return sign ? 2 - 0x1p-16382L : 0x1p-16382L*0x1p-16382L;
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y = 0x1p-16382L;
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return sign ? 2 - y : y*y;
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}
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#endif
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@ -2,16 +2,6 @@
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#include "libm.h"
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#if LDBL_MANT_DIG==64 && LDBL_MAX_EXP==16384
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union ld80 {
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long double x;
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struct {
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uint64_t m;
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uint16_t e : 15;
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uint16_t s : 1;
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uint16_t pad;
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} bits;
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};
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/* exact add, assumes exponent_x >= exponent_y */
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static void add(long double *hi, long double *lo, long double x, long double y)
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{
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@ -45,25 +35,25 @@ return an adjusted hi so that rounding it to double (or less) precision is corre
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*/
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static long double adjust(long double hi, long double lo)
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{
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union ld80 uhi, ulo;
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union ldshape uhi, ulo;
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if (lo == 0)
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return hi;
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uhi.x = hi;
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if (uhi.bits.m & 0x3ff)
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uhi.f = hi;
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if (uhi.i.m & 0x3ff)
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return hi;
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ulo.x = lo;
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if (uhi.bits.s == ulo.bits.s)
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uhi.bits.m++;
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ulo.f = lo;
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if ((uhi.i.se & 0x8000) == (ulo.i.se & 0x8000))
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uhi.i.m++;
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else {
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uhi.bits.m--;
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/* handle underflow and take care of ld80 implicit msb */
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if (uhi.bits.m == (uint64_t)-1/2) {
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uhi.bits.m *= 2;
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uhi.bits.e--;
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if (uhi.i.m << 1 == 0) {
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uhi.i.m = 0;
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uhi.i.se--;
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}
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uhi.i.m--;
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}
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return uhi.x;
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return uhi.f;
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}
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/* adjusted add so the result is correct when rounded to double (or less) precision */
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@ -82,9 +72,9 @@ static long double dmul(long double x, long double y)
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static int getexp(long double x)
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{
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union ld80 u;
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u.x = x;
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return u.bits.e;
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union ldshape u;
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u.f = x;
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return u.i.se & 0x7fff;
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}
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double fma(double x, double y, double z)
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@ -34,6 +34,13 @@ long double fmal(long double x, long double y, long double z)
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}
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#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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#include <fenv.h>
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#if LDBL_MANT_DIG == 64
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#define LASTBIT(u) (u.i.m & 1)
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#define SPLIT (0x1p32L + 1)
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#elif LDBL_MANT_DIG == 113
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#define LASTBIT(u) (u.i.lo & 1)
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#define SPLIT (0x1p57L + 1)
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#endif
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/*
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* A struct dd represents a floating-point number with twice the precision
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@ -75,12 +82,12 @@ static inline struct dd dd_add(long double a, long double b)
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static inline long double add_adjusted(long double a, long double b)
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{
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struct dd sum;
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union IEEEl2bits u;
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union ldshape u;
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sum = dd_add(a, b);
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if (sum.lo != 0) {
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u.e = sum.hi;
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if ((u.bits.manl & 1) == 0)
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u.f = sum.hi;
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if (!LASTBIT(u))
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sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
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}
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return (sum.hi);
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@ -95,7 +102,7 @@ static inline long double add_and_denormalize(long double a, long double b, int
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{
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struct dd sum;
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int bits_lost;
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union IEEEl2bits u;
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union ldshape u;
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sum = dd_add(a, b);
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@ -110,9 +117,9 @@ static inline long double add_and_denormalize(long double a, long double b, int
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* break the ties manually.
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*/
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if (sum.lo != 0) {
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u.e = sum.hi;
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bits_lost = -u.bits.exp - scale + 1;
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if (bits_lost != 1 ^ (int)(u.bits.manl & 1))
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u.f = sum.hi;
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bits_lost = -u.i.se - scale + 1;
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if ((bits_lost != 1) ^ LASTBIT(u))
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sum.hi = nextafterl(sum.hi, INFINITY * sum.lo);
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}
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return scalbnl(sum.hi, scale);
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@ -125,20 +132,15 @@ static inline long double add_and_denormalize(long double a, long double b, int
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*/
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static inline struct dd dd_mul(long double a, long double b)
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{
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#if LDBL_MANT_DIG == 64
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static const long double split = 0x1p32L + 1.0;
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#elif LDBL_MANT_DIG == 113
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static const long double split = 0x1p57L + 1.0;
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#endif
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struct dd ret;
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long double ha, hb, la, lb, p, q;
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p = a * split;
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p = a * SPLIT;
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ha = a - p;
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ha += p;
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la = a - ha;
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p = b * split;
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p = b * SPLIT;
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hb = b - p;
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hb += p;
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lb = b - hb;
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@ -202,13 +202,11 @@ w7 = 4.885026142432270781165E-3L;
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static long double sin_pi(long double x)
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{
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union ldshape u = {x};
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uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
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long double y, z;
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int n, ix;
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uint32_t se, i0, i1;
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int n;
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GET_LDOUBLE_WORDS(se, i0, i1, x);
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ix = se & 0x7fff;
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ix = (ix << 16) | (i0 >> 16);
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if (ix < 0x3ffd8000) /* 0.25 */
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return sinl(pi * x);
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y = -x; /* x is assume negative */
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@ -229,8 +227,8 @@ static long double sin_pi(long double x)
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} else {
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if (ix < 0x403e8000) /* 2^63 */
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z = y + two63; /* exact */
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GET_LDOUBLE_WORDS(se, i0, i1, z);
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n = i1 & 1;
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u.f = z;
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n = u.i.m & 1;
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y = n;
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n <<= 2;
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}
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@ -261,33 +259,28 @@ static long double sin_pi(long double x)
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long double __lgammal_r(long double x, int *sg) {
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long double t, y, z, nadj, p, p1, p2, q, r, w;
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int i, ix;
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uint32_t se, i0, i1;
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union ldshape u = {x};
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uint32_t ix = (u.i.se & 0x7fffU)<<16 | u.i.m>>48;
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int sign = u.i.se >> 15;
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int i;
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*sg = 1;
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GET_LDOUBLE_WORDS(se, i0, i1, x);
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ix = se & 0x7fff;
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if ((ix | i0 | i1) == 0) {
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if (se & 0x8000)
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*sg = -1;
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return 1.0 / fabsl(x);
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}
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ix = (ix << 16) | (i0 >> 16);
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/* purge off +-inf, NaN, +-0, and negative arguments */
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if (ix >= 0x7fff0000)
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return x * x;
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if (x == 0) {
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*sg -= 2*sign;
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return 1.0 / fabsl(x);
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}
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if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */
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if (se & 0x8000) {
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if (sign) {
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*sg = -1;
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return -logl(-x);
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}
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return -logl(x);
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}
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if (se & 0x8000) {
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if (sign) {
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t = sin_pi (x);
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if (t == 0.0)
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return 1.0 / fabsl(t); /* -integer */
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@ -297,11 +290,7 @@ long double __lgammal_r(long double x, int *sg) {
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x = -x;
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}
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/* purge off 1 and 2 */
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if ((((ix - 0x3fff8000) | i0 | i1) == 0) ||
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(((ix - 0x40008000) | i0 | i1) == 0))
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r = 0;
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else if (ix < 0x40008000) { /* x < 2.0 */
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if (ix < 0x40008000) { /* x < 2.0 */
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if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */
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/* lgamma(x) = lgamma(x+1) - log(x) */
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r = -logl(x);
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@ -380,7 +369,7 @@ long double __lgammal_r(long double x, int *sg) {
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r = (x - 0.5) * (t - 1.0) + w;
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} else /* 2**66 <= x <= inf */
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r = x * (logl(x) - 1.0);
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if (se & 0x8000)
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if (sign)
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r = nadj - r;
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return r;
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}
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@ -8,7 +8,7 @@ long double scalbnl(long double x, int n)
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#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
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long double scalbnl(long double x, int n)
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{
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union IEEEl2bits scale;
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union ldshape u;
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if (n > 16383) {
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x *= 0x1p16383L;
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@ -29,8 +29,8 @@ long double scalbnl(long double x, int n)
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n = -16382;
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}
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}
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scale.e = 1.0;
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scale.bits.exp = 0x3fff + n;
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return x * scale.e;
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u.f = 1.0;
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u.i.se = 0x3fff + n;
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return x * u.f;
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}
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#endif
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