}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double
-half = 0.5L,
-one = 1.0L,
pi = 3.14159265358979323846264L,
-two63 = 9.223372036854775808e18L,
/* lgam(1+x) = 0.5 x + x a(x)/b(x)
-0.268402099609375 <= x <= 0
w6 = -1.880801938119376907179E-3L,
w7 = 4.885026142432270781165E-3L;
-static const long double zero = 0.0L;
-
+/* sin(pi*x) assuming x > 2^-1000, if sin(pi*x)==0 the sign is arbitrary */
static long double sin_pi(long double x)
{
- 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 */
+ /* spurious inexact if odd int */
+ x *= 0.5;
+ x = 2.0*(x - floorl(x)); /* x mod 2.0 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorl(y);
- if (z != y) { /* inexact anyway */
- y *= 0.5;
- y = 2.0*(y - floorl(y));/* y = |x| mod 2.0 */
- n = (int) (y*4.0);
- } else {
- if (ix >= 0x403f8000) { /* 2^64 */
- y = zero; /* y must be even */
- n = 0;
- } else {
- if (ix < 0x403e8000) /* 2^63 */
- z = y + two63; /* exact */
- GET_LDOUBLE_WORDS(se, i0, i1, z);
- n = i1 & 1;
- y = n;
- n <<= 2;
- }
- }
+ n = (int)(x*4.0);
+ n = (n+1)/2;
+ x -= n*0.5f;
+ x *= pi;
switch (n) {
- case 0:
- y = sinl(pi * y);
- break;
- case 1:
- case 2:
- y = cosl(pi * (half - y));
- break;
- case 3:
- case 4:
- y = sinl(pi * (one - y));
- break;
- case 5:
- case 6:
- y = -cosl(pi * (y - 1.5));
- break;
- default:
- y = sinl(pi * (y - 2.0));
- break;
+ default: /* case 4: */
+ case 0: return __sinl(x, 0.0, 0);
+ case 1: return __cosl(x, 0.0);
+ case 2: return __sinl(-x, 0.0, 0);
+ case 3: return -__cosl(x, 0.0);
}
- return -y;
}
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 one / fabsl(x);
- }
-
- ix = (ix << 16) | (i0 >> 16);
- /* purge off +-inf, NaN, +-0, and negative arguments */
+ /* purge off +-inf, NaN, +-0, tiny and negative arguments */
if (ix >= 0x7fff0000)
return x * x;
-
if (ix < 0x3fc08000) { /* |x|<2**-63, return -log(|x|) */
- if (se & 0x8000) {
+ if (sign) {
*sg = -1;
- return -logl(-x);
+ x = -x;
}
return -logl(x);
}
- if (se & 0x8000) {
- t = sin_pi (x);
- if (t == zero)
- return one / fabsl(t); /* -integer */
- nadj = logl(pi / fabsl(t * x));
- if (t < zero)
- *sg = -1;
+ if (sign) {
x = -x;
+ t = sin_pi(x);
+ if (t == 0.0)
+ return 1.0 / (x-x); /* -integer */
+ if (t > 0.0)
+ *sg = -1;
+ else
+ t = -t;
+ nadj = logl(pi / (t * x));
}
- /* purge off 1 and 2 */
- if ((((ix - 0x3fff8000) | i0 | i1) == 0) ||
- (((ix - 0x40008000) | i0 | i1) == 0))
+ /* purge off 1 and 2 (so the sign is ok with downward rounding) */
+ if ((ix == 0x3fff8000 || ix == 0x40008000) && u.i.m == 0) {
r = 0;
- else if (ix < 0x40008000) { /* x < 2.0 */
+ } else if (ix < 0x40008000) { /* x < 2.0 */
if (ix <= 0x3ffee666) { /* 8.99993896484375e-1 */
/* lgamma(x) = lgamma(x+1) - log(x) */
- r = -logl (x);
+ r = -logl(x);
if (ix >= 0x3ffebb4a) { /* 7.31597900390625e-1 */
- y = x - one;
+ y = x - 1.0;
i = 0;
} else if (ix >= 0x3ffced33) { /* 2.31639862060546875e-1 */
- y = x - (tc - one);
+ y = x - (tc - 1.0);
i = 1;
} else { /* x < 0.23 */
y = x;
i = 2;
}
} else {
- r = zero;
+ r = 0.0;
if (ix >= 0x3fffdda6) { /* 1.73162841796875 */
/* [1.7316,2] */
y = x - 2.0;
i = 1;
} else {
/* [0.9, 1.23] */
- y = x - one;
+ y = x - 1.0;
i = 2;
}
}
case 0:
p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5))));
p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y))));
- r += half * y + y * p1/p2;
+ r += 0.5 * y + y * p1/p2;
break;
case 1:
p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6)))));
case 2:
p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6))))));
p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y)))));
- r += (-half * y + p1 / p2);
+ r += (-0.5 * y + p1 / p2);
}
} else if (ix < 0x40028000) { /* 8.0 */
/* x < 8.0 */
i = (int)x;
- t = zero;
y = x - (double)i;
p = y * (s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6))))));
q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y))))));
- r = half * y + p / q;
- z = one;/* lgamma(1+s) = log(s) + lgamma(s) */
+ r = 0.5 * y + p / q;
+ z = 1.0;
+ /* lgamma(1+s) = log(s) + lgamma(s) */
switch (i) {
case 7:
z *= (y + 6.0); /* FALLTHRU */
z *= (y + 3.0); /* FALLTHRU */
case 3:
z *= (y + 2.0); /* FALLTHRU */
- r += logl (z);
+ r += logl(z);
break;
}
} else if (ix < 0x40418000) { /* 2^66 */
/* 8.0 <= x < 2**66 */
- t = logl (x);
- z = one / x;
+ t = logl(x);
+ z = 1.0 / x;
y = z * z;
w = w0 + z * (w1 + y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7))))));
- r = (x - half) * (t - one) + w;
+ r = (x - 0.5) * (t - 1.0) + w;
} else /* 2**66 <= x <= inf */
- r = x * (logl (x) - one);
- if (se & 0x8000)
+ r = x * (logl(x) - 1.0);
+ if (sign)
r = nadj - r;
return r;
}
+#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
+// TODO: broken implementation to make things compile
+long double __lgammal_r(long double x, int *sg)
+{
+ return __lgamma_r(x, sg);
+}
#endif
-extern int __signgam;
-
long double lgammal(long double x)
{
return __lgammal_r(x, &__signgam);
projects / musl / blobdiff