1 /* e_lgammaf_r.c -- float version of e_lgamma_r.c.
28  * Domain y in [0x1p-27, 0.27], range ~[-3.4599e-10, 3.4590e-10]:
29  * |(lgamma(2 - y) + 0.5 * y) / y - a(y)| < 2**-31.4
31 a0  =  7.72156641e-02, /* 0x3d9e233f */
32 a1  =  3.22467119e-01, /* 0x3ea51a69 */
33 a2  =  6.73484802e-02, /* 0x3d89ee00 */
34 a3  =  2.06395667e-02, /* 0x3ca9144f */
35 a4  =  6.98275631e-03, /* 0x3be4cf9b */
36 a5  =  4.11768444e-03, /* 0x3b86eda4 */
38  * Domain x in [tc-0.24, tc+0.28], range ~[-5.6577e-10, 5.5677e-10]:
39  * |(lgamma(x) - tf) - t(x - tc)| < 2**-30.8.
42 tf  = -1.21486291e-01, /* 0xbdf8cdce */
43 t0  = -2.94064460e-11, /* 0xae0154b7 */
44 t1  = -2.35939837e-08, /* 0xb2caabb8 */
45 t2  =  4.83836412e-01, /* 0x3ef7b968 */
46 t3  = -1.47586212e-01, /* 0xbe1720d7 */
47 t4  =  6.46013096e-02, /* 0x3d844db1 */
48 t5  = -3.28450352e-02, /* 0xbd068884 */
49 t6  =  1.86483748e-02, /* 0x3c98c47a */
50 t7  = -9.89206228e-03, /* 0xbc221251 */
52  * Domain y in [-0.1, 0.232], range ~[-8.4931e-10, 8.7794e-10]:
53  * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-31.2
55 u0  = -7.72156641e-02, /* 0xbd9e233f */
56 u1  =  7.36789703e-01, /* 0x3f3c9e40 */
57 u2  =  4.95649040e-01, /* 0x3efdc5b6 */
59 v2  =  2.10598111e-01, /* 0x3e57a708 */
60 v3  = -1.02995494e-02, /* 0xbc28bf71 */
62  * Domain x in (2, 3], range ~[-5.5189e-11, 5.2317e-11]:
63  * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-35.0
64  * with y = x - 2.
66 s0 = -7.72156641e-02, /* 0xbd9e233f */
67 s1 =  2.69987404e-01, /* 0x3e8a3bca */
68 s2 =  1.42851010e-01, /* 0x3e124789 */
69 s3 =  1.19389519e-02, /* 0x3c439b98 */
70 r1 =  6.79650068e-01, /* 0x3f2dfd8c */
71 r2 =  1.16058730e-01, /* 0x3dedb033 */
72 r3 =  3.75673687e-03, /* 0x3b763396 */
74  * Domain z in [8, 0x1p24], range ~[-1.2640e-09, 1.2640e-09]:
75  * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-29.6.
77 w0 =  4.18938547e-01, /* 0x3ed67f1d */
78 w1 =  8.33332464e-02, /* 0x3daaaa9f */
79 w2 = -2.76129087e-03; /* 0xbb34f6c6 */
85 	float y,z;  in sin_pif()  local
88 	y = -x;  in sin_pif()
90 	vz = y+0x1p23F;			/* depend on 0 <= y < 0x1p23 */  in sin_pif()
91 	z = vz-0x1p23F;			/* rintf(y) for the above range */  in sin_pif()
92 	if (z == y)  in sin_pif()
95 	vz = y+0x1p21F;  in sin_pif()
96 	GET_FLOAT_WORD(n,vz);		/* bits for rounded y (units 0.25) */  in sin_pif()
97 	z = vz-0x1p21F;			/* y rounded to a multiple of 0.25 */  in sin_pif()
98 	if (z > y) {  in sin_pif()
99 	    z -= 0.25F;			/* adjust to round down */  in sin_pif()
100 	    n--;  in sin_pif()
102 	n &= 7;				/* octant of y mod 2 */  in sin_pif()
103 	y = y - z + n * 0.25F;		/* y mod 2 */  in sin_pif()
106 	    case 0:   y =  __kernel_sindf(pi*y); break;  in sin_pif()
108 	    case 2:   y =  __kernel_cosdf(pi*((float)0.5-y)); break;  in sin_pif()
110 	    case 4:   y =  __kernel_sindf(pi*(one-y)); break;  in sin_pif()
112 	    case 6:   y = -__kernel_cosdf(pi*(y-(float)1.5)); break;  in sin_pif()
113 	    default:  y =  __kernel_sindf(pi*(y-(float)2.0)); break;  in sin_pif()
115 	return -y;  in sin_pif()
122 	float nadj,p,p1,p2,q,r,t,w,y,z;  in lgammaf_r()  local
128     /* purge +-Inf and NaNs */  in lgammaf_r()
133     /* purge +-0 and tiny arguments */  in lgammaf_r()
134 	*signgamp = 1-2*((uint32_t)hx>>31);  in lgammaf_r()
135 	if(ix<0x32000000) {		/* |x|<2**-27, return -log(|x|) */  in lgammaf_r()
138 	    return -logf(fabsf(x));  in lgammaf_r()
144 	    if(ix>=0x4b000000) 		/* |x|>=2**23, must be -integer */  in lgammaf_r()
147 	    if(t==zero) return one/vzero; /* -integer */  in lgammaf_r()
149 	    if(t<zero) *signgamp = -1;  in lgammaf_r()
150 	    x = -x;  in lgammaf_r()
157 	    if(ix<=0x3f666666) { 	/* lgamma(x) = lgamma(x+1)-log(x) */  in lgammaf_r()
158 		r = -logf(x);  in lgammaf_r()
159 		if(ix>=0x3f3b4a20) {y = one-x; i= 0;}  in lgammaf_r()
160 		else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;}  in lgammaf_r()
161 	  	else {y = x; i=2;}  in lgammaf_r()
164 	        if(ix>=0x3fdda618) {y=2-x;i=0;} /* [1.7316,2] */  in lgammaf_r()
165 	        else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */  in lgammaf_r()
166 		else {y=x-one;i=2;}  in lgammaf_r()
170 		z = y*y;  in lgammaf_r()
173 		p  = y*p1+p2;  in lgammaf_r()
174 		r  += p-y/2; break;  in lgammaf_r()
176 		p = t0+y*t1+y*y*(t2+y*(t3+y*(t4+y*(t5+y*(t6+y*t7)))));  in lgammaf_r()
179 		p1 = y*(u0+y*(u1+y*u2));  in lgammaf_r()
180 		p2 = one+y*(v1+y*(v2+y*v3));  in lgammaf_r()
181 		r += p1/p2-y/2;  in lgammaf_r()
187 	    y = x-i;  in lgammaf_r()
188 	    p = y*(s0+y*(s1+y*(s2+y*s3)));  in lgammaf_r()
189 	    q = one+y*(r1+y*(r2+y*r3));  in lgammaf_r()
190 	    r = y/2+p/q;  in lgammaf_r()
193 	    case 7: z *= (y+6);		/* FALLTHRU */  in lgammaf_r()
194 	    case 6: z *= (y+5);		/* FALLTHRU */  in lgammaf_r()
195 	    case 5: z *= (y+4);		/* FALLTHRU */  in lgammaf_r()
196 	    case 4: z *= (y+3);		/* FALLTHRU */  in lgammaf_r()
197 	    case 3: z *= (y+2);		/* FALLTHRU */  in lgammaf_r()
204 	    y = z*z;  in lgammaf_r()
205 	    w = w0+z*(w1+y*w2);  in lgammaf_r()
206 	    r = (x-half)*(t-one)+w;  in lgammaf_r()
209 	    r =  x*(logf(x)-one);  in lgammaf_r()
210 	if(hx<0) r = nadj - r;  in lgammaf_r()