diff --git a/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c b/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c
index 9a7ab39dca4bde3be02b238a1d09bd1dba285373..9d23053b1f3b8db73f73861ff3d7487e60ba9af9 100644 (file)
/* e_lgammaf_r.c -- float version of e_lgamma_r.c.
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ * Conversion to float fixed By Steven G. Kargl.
*/
/*
static const volatile float vzero = 0;
static const float
-zero= 0.0000000000e+00,
-half= 5.0000000000e-01, /* 0x3f000000 */
-one = 1.0000000000e+00, /* 0x3f800000 */
+zero= 0,
+half= 0.5,
+one = 1,
pi = 3.1415927410e+00, /* 0x40490fdb */
-a0 = 7.7215664089e-02, /* 0x3d9e233f */
-a1 = 3.2246702909e-01, /* 0x3ea51a66 */
-a2 = 6.7352302372e-02, /* 0x3d89f001 */
-a3 = 2.0580807701e-02, /* 0x3ca89915 */
-a4 = 7.3855509982e-03, /* 0x3bf2027e */
-a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */
-a6 = 1.1927076848e-03, /* 0x3a9c54a1 */
-a7 = 5.1006977446e-04, /* 0x3a05b634 */
-a8 = 2.2086278477e-04, /* 0x39679767 */
-a9 = 1.0801156895e-04, /* 0x38e28445 */
-a10 = 2.5214456400e-05, /* 0x37d383a2 */
-a11 = 4.4864096708e-05, /* 0x383c2c75 */
-tc = 1.4616321325e+00, /* 0x3fbb16c3 */
-tf = -1.2148628384e-01, /* 0xbdf8cdcd */
-/* tt = -(tail of tf) */
-tt = 6.6971006518e-09, /* 0x31e61c52 */
-t0 = 4.8383611441e-01, /* 0x3ef7b95e */
-t1 = -1.4758771658e-01, /* 0xbe17213c */
-t2 = 6.4624942839e-02, /* 0x3d845a15 */
-t3 = -3.2788541168e-02, /* 0xbd064d47 */
-t4 = 1.7970675603e-02, /* 0x3c93373d */
-t5 = -1.0314224288e-02, /* 0xbc28fcfe */
-t6 = 6.1005386524e-03, /* 0x3bc7e707 */
-t7 = -3.6845202558e-03, /* 0xbb7177fe */
-t8 = 2.2596477065e-03, /* 0x3b141699 */
-t9 = -1.4034647029e-03, /* 0xbab7f476 */
-t10 = 8.8108185446e-04, /* 0x3a66f867 */
-t11 = -5.3859531181e-04, /* 0xba0d3085 */
-t12 = 3.1563205994e-04, /* 0x39a57b6b */
-t13 = -3.1275415677e-04, /* 0xb9a3f927 */
-t14 = 3.3552918467e-04, /* 0x39afe9f7 */
-u0 = -7.7215664089e-02, /* 0xbd9e233f */
-u1 = 6.3282704353e-01, /* 0x3f2200f4 */
-u2 = 1.4549225569e+00, /* 0x3fba3ae7 */
-u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */
-u4 = 2.2896373272e-01, /* 0x3e6a7578 */
-u5 = 1.3381091878e-02, /* 0x3c5b3c5e */
-v1 = 2.4559779167e+00, /* 0x401d2ebe */
-v2 = 2.1284897327e+00, /* 0x4008392d */
-v3 = 7.6928514242e-01, /* 0x3f44efdf */
-v4 = 1.0422264785e-01, /* 0x3dd572af */
-v5 = 3.2170924824e-03, /* 0x3b52d5db */
-s0 = -7.7215664089e-02, /* 0xbd9e233f */
-s1 = 2.1498242021e-01, /* 0x3e5c245a */
-s2 = 3.2577878237e-01, /* 0x3ea6cc7a */
-s3 = 1.4635047317e-01, /* 0x3e15dce6 */
-s4 = 2.6642270386e-02, /* 0x3cda40e4 */
-s5 = 1.8402845599e-03, /* 0x3af135b4 */
-s6 = 3.1947532989e-05, /* 0x3805ff67 */
-r1 = 1.3920053244e+00, /* 0x3fb22d3b */
-r2 = 7.2193557024e-01, /* 0x3f38d0c5 */
-r3 = 1.7193385959e-01, /* 0x3e300f6e */
-r4 = 1.8645919859e-02, /* 0x3c98bf54 */
-r5 = 7.7794247773e-04, /* 0x3a4beed6 */
-r6 = 7.3266842264e-06, /* 0x36f5d7bd */
-w0 = 4.1893854737e-01, /* 0x3ed67f1d */
-w1 = 8.3333335817e-02, /* 0x3daaaaab */
-w2 = -2.7777778450e-03, /* 0xbb360b61 */
-w3 = 7.9365057172e-04, /* 0x3a500cfd */
-w4 = -5.9518753551e-04, /* 0xba1c065c */
-w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
-w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
+/*
+ * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]:
+ * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4
+ */
+a0 = 7.72156641e-02, /* 0x3d9e233f */
+a1 = 3.22467119e-01, /* 0x3ea51a69 */
+a2 = 6.73484802e-02, /* 0x3d89ee00 */
+a3 = 2.06395667e-02, /* 0x3ca9144f */
+a4 = 6.98275631e-03, /* 0x3be4cf9b */
+a5 = 4.11768444e-03, /* 0x3b86eda4 */
+/*
+ * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]:
+ * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8.
+ */
+tc = 1.46163213e+00, /* 0x3fbb16c3 */
+tf = -1.21486291e-01, /* 0xbdf8cdce */
+t0 = -2.94064460e-11, /* 0xae0154b7 */
+t1 = -2.35939837e-08, /* 0xb2caabb8 */
+t2 = 4.83836412e-01, /* 0x3ef7b968 */
+t3 = -1.47586212e-01, /* 0xbe1720d7 */
+t4 = 6.46013096e-02, /* 0x3d844db1 */
+t5 = -3.28450352e-02, /* 0xbd068884 */
+t6 = 1.86483748e-02, /* 0x3c98c47a */
+t7 = -9.89206228e-03, /* 0xbc221251 */
+/*
+ * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]:
+ * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2
+ */
+u0 = -7.72156641e-02, /* 0xbd9e233f */
+u1 = 7.36789703e-01, /* 0x3f3c9e40 */
+u2 = 4.95649040e-01, /* 0x3efdc5b6 */
+v1 = 1.10958421e+00, /* 0x3f8e06db */
+v2 = 2.10598111e-01, /* 0x3e57a708 */
+v3 = -1.02995494e-02, /* 0xbc28bf71 */
+/*
+ * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]:
+ * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0
+ * with y = x - 2.
+ */
+s0 = -7.72156641e-02, /* 0xbd9e233f */
+s1 = 2.69987404e-01, /* 0x3e8a3bca */
+s2 = 1.42851010e-01, /* 0x3e124789 */
+s3 = 1.19389519e-02, /* 0x3c439b98 */
+r1 = 6.79650068e-01, /* 0x3f2dfd8c */
+r2 = 1.16058730e-01, /* 0x3dedb033 */
+r3 = 3.75673687e-03, /* 0x3b763396 */
+/*
+ * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]:
+ * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6.
+ */
+w0 = 4.18938547e-01, /* 0x3ed67f1d */
+w1 = 8.33332464e-02, /* 0x3daaaa9f */
+w2 = -2.76129087e-03; /* 0xbb34f6c6 */
static float
sin_pif(float x)
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return x*x;
- if(ix==0) return one/vzero;
+ if(ix==0) {
+ if(hx<0)
+ *signgamp = -1;
+ return one/vzero;
+ }
if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
else {y = x; i=2;}
} else {
r = zero;
- if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */
+ if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */
else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */
else {y=x-one;i=2;}
}
switch(i) {
case 0:
z = y*y;
- 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)))));
+ p1 = a0+z*(a2+z*a4);
+ p2 = z*(a1+z*(a3+z*a5));
p = y*p1+p2;
- r += (p-(float)0.5*y); break;
+ r += (p-y/2); break;
case 1:
- z = y*y;
- w = z*y;
- p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
- p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
- p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
- p = z*p1-(tt-w*(p2+y*p3));
+ p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7)))));
r += (tf + p); 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);
+ p1 = y*(u0+y*(u1+y*u2));
+ p2 = one+y*(v1+y*(v2+y*v3));
+ r += (p1/p2-y/2);
}
}
else if(ix<0x41000000) { /* x < 8.0 */
- i = (int)x;
- 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;
+ i = x;
+ y = x-i;
+ p = y*(s0+y*(s1+y*(s2+y*s3)));
+ q = one+y*(r1+y*(r2+y*r3));
+ r = y/2+p/q;
z = one; /* 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); /* FALLTHRU */
+ case 6: z *= (y+5); /* FALLTHRU */
+ case 5: z *= (y+4); /* FALLTHRU */
+ case 4: z *= (y+3); /* FALLTHRU */
+ case 3: z *= (y+2); /* FALLTHRU */
r += __ieee754_logf(z); break;
}
- /* 8.0 <= x < 2**58 */
- } else if (ix < 0x5c800000) {
+ /* 8.0 <= x < 2**24 */
+ } else if (ix < 0x4b800000) {
t = __ieee754_logf(x);
z = one/x;
y = z*z;
- w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
+ w = w0+z*(w1+y*w2);
r = (x-half)*(t-one)+w;
} else
- /* 2**58 <= x <= inf */
+ /* 2**24 <= x <= inf */
r = x*(__ieee754_logf(x)-one);
if(hx<0) r = nadj - r;
return r;