#include "libm.h"
static const float
-two23= 8.3886080000e+06, /* 0x4b000000 */
-half= 5.0000000000e-01, /* 0x3f000000 */
-one = 1.0000000000e+00, /* 0x3f800000 */
pi = 3.1415927410e+00, /* 0x40490fdb */
a0 = 7.7215664089e-02, /* 0x3d9e233f */
a1 = 3.2246702909e-01, /* 0x3ea51a66 */
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
-static const float zero = 0.0000000000e+00;
-
-static float sin_pif(float x)
+/* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
+static float sin_pi(float x)
{
- float y,z;
- int n,ix;
-
- GET_FLOAT_WORD(ix, x);
- ix &= 0x7fffffff;
-
- if(ix < 0x3e800000)
- return __sindf(pi*x);
+ double_t y;
+ int n;
- y = -x; /* negative x is assumed */
+ /* spurious inexact if odd int */
+ x = 2*(x*0.5f - floorf(x*0.5f)); /* x mod 2.0 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorf(y);
- if (z != y) { /* inexact anyway */
- y *= (float)0.5;
- y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
- n = (int) (y*(float)4.0);
- } else {
- if (ix >= 0x4b800000) {
- y = zero; /* y must be even */
- n = 0;
- } else {
- if (ix < 0x4b000000)
- z = y + two23; /* exact */
- GET_FLOAT_WORD(n, z);
- n &= 1;
- y = n;
- n <<= 2;
- }
- }
+ n = (int)(x*4);
+ n = (n+1)/2;
+ y = x - n*0.5f;
+ y *= 3.14159265358979323846;
switch (n) {
- case 0: y = __sindf(pi*y); break;
- case 1:
- case 2: y = __cosdf(pi*((float)0.5-y)); break;
- case 3:
- case 4: y = __sindf(pi*(one-y)); break;
- case 5:
- case 6: y = -__cosdf(pi*(y-(float)1.5)); break;
- default: y = __sindf(pi*(y-(float)2.0)); break;
+ default: /* case 4: */
+ case 0: return __sindf(y);
+ case 1: return __cosdf(y);
+ case 2: return __sindf(-y);
+ case 3: return -__cosdf(y);
}
- return -y;
}
-
-float lgammaf_r(float x, int *signgamp)
+float __lgammaf_r(float x, int *signgamp)
{
+ union {float f; uint32_t i;} u = {x};
float t,y,z,nadj,p,p1,p2,p3,q,r,w;
- int32_t hx;
- int i,ix;
-
- GET_FLOAT_WORD(hx, x);
+ uint32_t ix;
+ int i,sign;
/* purge off +-inf, NaN, +-0, tiny and negative arguments */
*signgamp = 1;
- ix = hx & 0x7fffffff;
+ sign = u.i>>31;
+ ix = u.i & 0x7fffffff;
if (ix >= 0x7f800000)
return x*x;
- if (ix == 0)
- return one/zero;
if (ix < 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
- if (hx < 0) {
+ if (sign) {
*signgamp = -1;
- return -logf(-x);
+ x = -x;
}
return -logf(x);
}
- if (hx < 0) {
- if (ix >= 0x4b000000) /* |x| >= 2**23, must be -integer */
- return one/zero;
- t = sin_pif(x);
- if (t == zero) /* -integer */
- return one/zero;
- nadj = logf(pi/fabsf(t*x));
- if (t < zero)
- *signgamp = -1;
+ if (sign) {
x = -x;
+ t = sin_pi(x);
+ if (t == 0.0f) /* -integer */
+ return 1.0f/(x-x);
+ if (t > 0.0f)
+ *signgamp = -1;
+ else
+ t = -t;
+ nadj = logf(pi/(t*x));
}
/* purge off 1 and 2 */
if (ix <= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
r = -logf(x);
if (ix >= 0x3f3b4a20) {
- y = one - x;
+ y = 1.0f - x;
i = 0;
} else if (ix >= 0x3e6d3308) {
- y = x - (tc-one);
+ y = x - (tc-1.0f);
i = 1;
} else {
y = x;
i = 2;
}
} else {
- r = zero;
+ r = 0.0f;
if (ix >= 0x3fdda618) { /* [1.7316,2] */
- y = (float)2.0 - x;
+ y = 2.0f - x;
i = 0;
} else if (ix >= 0x3F9da620) { /* [1.23,1.73] */
y = x - tc;
i = 1;
} else {
- y = x - one;
+ y = x - 1.0f;
i = 2;
}
}
p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
p = y*p1+p2;
- r += (p-(float)0.5*y);
+ r += p - 0.5f*y;
break;
case 1:
z = y*y;
break;
case 2:
p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
- p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
- r += (-(float)0.5*y + p1/p2);
+ p2 = 1.0f+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
+ r += -0.5f*y + p1/p2;
}
} else if (ix < 0x41000000) { /* x < 8.0 */
i = (int)x;
- y = x-(float)i;
+ y = x - (float)i;
p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
- q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
- r = half*y+p/q;
- z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
+ q = 1.0f+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
+ r = 0.5f*y+p/q;
+ z = 1.0f; /* lgamma(1+s) = log(s) + lgamma(s) */
switch (i) {
- case 7: z *= y + (float)6.0; /* FALLTHRU */
- case 6: z *= y + (float)5.0; /* FALLTHRU */
- case 5: z *= y + (float)4.0; /* FALLTHRU */
- case 4: z *= y + (float)3.0; /* FALLTHRU */
- case 3: z *= y + (float)2.0; /* FALLTHRU */
+ case 7: z *= y + 6.0f; /* FALLTHRU */
+ case 6: z *= y + 5.0f; /* FALLTHRU */
+ case 5: z *= y + 4.0f; /* FALLTHRU */
+ case 4: z *= y + 3.0f; /* FALLTHRU */
+ case 3: z *= y + 2.0f; /* FALLTHRU */
r += logf(z);
break;
}
} else if (ix < 0x5c800000) { /* 8.0 <= x < 2**58 */
t = logf(x);
- z = one/x;
+ z = 1.0f/x;
y = z*z;
w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
- r = (x-half)*(t-one)+w;
+ r = (x-0.5f)*(t-1.0f)+w;
} else /* 2**58 <= x <= inf */
- r = x*(logf(x)-one);
- if (hx < 0)
+ r = x*(logf(x)-1.0f);
+ if (sign)
r = nadj - r;
return r;
}
+
+weak_alias(__lgammaf_r, lgammaf_r);
projects / musl / blobdiff