Lines Matching defs:z
79 * such that 0<x<T. Let k = [x] and z = x-[x]. Define
86 * Since x = k+z,
88 * -sin(x*pi) = -sin(k*pi+z*pi) = (-1) *sin(z*pi),
90 * we have -kpsin(x) = (-1) * kpsin(z). We can further
91 * reduce z to t by
92 * (I) t = z when 0.00000 <= z < 0.31830...
93 * (II) t = 0.5-z when 0.31830... <= z < 0.681690...
94 * (III) t = 1-z when 0.681690... <= z < 1.00000
96 * (I) kpsin(z) = kpsin(t) ... 0<= z < 0.3184
97 * (II) kpsin(z) = kpcos(t) ... |t| < 0.182
98 * (III) kpsin(z) = kpsin(t) ... 0<= t < 0.3184
191 * Let k = int(x), z = x-k.
192 * For z in (I)
196 * kpsin(z)*gamma(1+x)
198 * otherwise, for z in (II),
202 * kpcos(0.5-z)*gamma(1+x)
204 * otherwise, for z in (III),
208 * kpsin(1-z)*gamma(1+x)
490 * computing (x-1)*(x-2)*(x-3)*(x-4), if we compute (x-1)*(x-4) = z.h+z.l,
491 * then (x-2)(x-3) = z.h+2+z.l readily. In below, we list the expression
598 * Let x = 2**n * y, where 1 <= y < 2. Let Z={z(i),i=1,...,m}
600 * in [1, 2]. Let z(j) be the closest one to y, then
602 * = n*log(2)-1 + log(z(j)*y/z(j))
603 * = n*log(2)-1 + log(z(j)) + log(y/z(j))
606 * where T1(n) = n*log(2)-1 and T2(j) = log(z(j)). Both T1 and T2 can be
611 * y-z(i) y 1+s
613 * y+z(i) z(i) 1-s
626 * Base on this analysis, we choose Z = {z(i)|z(i)=1+i/64+1/128, 0<=i<=63}.
627 * For any y in [1,2), let j = [64*y] chopped to integer, then z(j) is
658 * 2s - v = --- * (2(y-z) - v*(y+z) )
659 * y+z
661 * = --- * ( [2(y-z) - v*(y+z)_h ] - v*(y+z)_l )
662 * y+z
663 * where (y+z)_h = (y+z) rounded to 24 bits by (double)(float),
664 * and (y+z)_l = ((z+z)-(y+z)_h)+(y-z). Note the the quantity
734 * z = (1/x), z2 = z*z, z4 = z2*z2;
735 * p = z*(GP0+z2*(GP1+....+z2*GP7))
736 * = z*(GP0+(z4*(GP2+z4*(GP4+z4*GP6))+z2*(GP1+z4*(GP3+z4*(GP5+z4*GP7)))))
823 * j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
825 * T2(j) = T2[2j,2j+1] = log(z[j]),
1151 double t3, t4, y, z;
1155 z = y * y;
1156 t3 = (z * (P10 + y * ((P11 + y * P12) + z * (P13 + y * P14)))) /
1157 (Q10 + y * ((Q11 + y * Q12) + z * ((Q13 + Q14 * y) + z * Q15)));
1170 double t3, y, z;
1174 z = y * y;
1175 t3 = (z * (P20 + y * P21 + z * (P22 + y * P23))) /
1176 (Q20 + (y * ((Q21 + Q22 * y) + z * Q23) +
1177 (z * z) * ((Q24 + Q25 * y) + z * Q26))) + GZ2_l;
1187 double t3, t4, y, z;
1191 z = y * y;
1192 t3 = (z * (P30 + y * ((P31 + y * P32) + z * (P33 + y * P34)))) /
1193 (Q30 + y * ((Q31 + y * Q32) + z * ((Q33 + Q34 * y) + z * Q35)));
1211 double z, t1, t2, t3, z2, t5, w, y, u, r, z4, v, t24 = 16777216.0,
1223 * j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
1225 * T2(j) = T2[2j,2j+1] = log(z[j]),
1250 __HI(z) = (ix & 0xffffc000) | 0x2000; /* z[j]=1+j/64+1/128 */
1251 __LO(z) = 0;
1253 t1 = y + z;
1254 t2 = y - z;
1257 u = r * t2; /* u = (y-z)/(y+z) */
1268 t2 = t5 + r * ((two * t2 - v * t1) - v * (y - (t1 - z)));
1278 z = one / x;
1282 z2 = z * z;
1289 w_l = z * (GP0 + t1) + w;
1305 z = w_h - w_l;
1306 z2 = z * z;
1309 t3 = w_h - (w_l - (t1 + z * t2));
1335 double z, t1, t2, t3, t4;
1338 z = x * x;
1340 t1 = z * x;
1341 t2 = z * z;
1343 t3 = (t1 * z) * ((ks[1] + z * ks[2] + t2 * ks[3]) + (z * t2) *
1344 (ks[4] + z * ks[5] + t2 * ks[6]));
1373 double z, t1, t2, t3, t4, x4, x8;
1376 z = x * x;
1379 x4 = z * z;
1380 t2 = npi_2_l * z + npi_2_h * (x + t1) * (x - t1);
1381 t3 = one_pi_l + x4 * ((kc[1] + z * kc[2]) + x4 * (kc[3] + z *
1408 double r1, r2, t2, z, xh, xl, yh, yl, zh, z1, z2, zl, x5, wh, wl;
1444 z = x + one; /* may not be exact */
1445 zh = (double) ((float) z);
1447 rr.l = z * yy.l + (x - (zh - one)) * yy.h;
1452 z = z1 * z2;
1453 xh = (double) ((float) z);
1457 rr.l = z * yy.l + xl * yy.h;
1467 z = z1 * z2;
1468 xh = (double) ((float) z);
1471 rr.l = z * yy.l + xl * yy.h;
1476 z = z1 * z2;
1478 yh = (double) ((float) z);
1480 z2 = z - 2.0;
1481 z *= z2;
1482 xh = (double) ((float) z);
1485 rr.l = z * yy.l + xl * yy.h;
1490 z = z1 * z2;
1492 yh = (double) ((float) z);
1495 z2 = z - 2.0;
1497 z *= z2;
1498 xh = (double) ((float) z);
1506 rr.l = z * wl + xl * wh;
1511 z = z2 * z1;
1513 yh = (double) ((float) z); /* yh+yl = (x+3)(x+4) */
1516 z2 = z - 2.0; /* z2 = (x+2)*(x+5) */
1517 z *= z2;
1518 xh = (double) ((float) z);
1526 rr.l = z * wl + xl * wh;
1534 double t, t1, t2, t3, t4, t5, w, y, z, z1, z2, z3, z5;
1550 z = x / tiny;
1551 return (z * z);
1605 z = tiny / x;
1607 z = -z;
1608 return (z * tiny);
1619 z = y - (double) j;
1620 if (z > 0.3183098861837906715377675)
1621 if (z > 0.6816901138162093284622325)
1622 ss = kpsin(one - z);
1624 ss = kpcos(0.5 - z);
1626 ss = kpsin(z);
1635 ww = gam_n(j + 1, z);
1646 ww = gam_n(j, z);
1674 z = t2 - z2;
1676 /* check whether z*2**-m underflow */
1678 hx = __HI(z);
1684 __HI(z) = ix ^ i;
1688 z = -tiny * tiny;
1690 z = tiny * tiny;
1697 __HI(z) = ix ^ i;
1698 z *= t;
1701 return (z);