1 | /* |
2 | * IBM Accurate Mathematical Library |
3 | * written by International Business Machines Corp. |
4 | * Copyright (C) 2001-2024 Free Software Foundation, Inc. |
5 | * |
6 | * This program is free software; you can redistribute it and/or modify |
7 | * it under the terms of the GNU Lesser General Public License as published by |
8 | * the Free Software Foundation; either version 2.1 of the License, or |
9 | * (at your option) any later version. |
10 | * |
11 | * This program is distributed in the hope that it will be useful, |
12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
14 | * GNU Lesser General Public License for more details. |
15 | * |
16 | * You should have received a copy of the GNU Lesser General Public License |
17 | * along with this program; if not, see <https://www.gnu.org/licenses/>. |
18 | */ |
19 | /*********************************************************************/ |
20 | /* MODULE_NAME: uroot.c */ |
21 | /* */ |
22 | /* FUNCTION: usqrt */ |
23 | /* */ |
24 | /* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */ |
25 | /* uroot.tbl */ |
26 | /* */ |
27 | /* An ultimate sqrt routine. Given an IEEE double machine number x */ |
28 | /* it computes the correctly rounded (to nearest) value of square */ |
29 | /* root of x. */ |
30 | /* Assumption: Machine arithmetic operations are performed in */ |
31 | /* round to nearest mode of IEEE 754 standard. */ |
32 | /* */ |
33 | /*********************************************************************/ |
34 | |
35 | #include <math_private.h> |
36 | #include <libm-alias-finite.h> |
37 | |
38 | typedef union {int64_t i[2]; long double x; double d[2]; } mynumber; |
39 | |
40 | static const double |
41 | t512 = 0x1p512, |
42 | tm256 = 0x1p-256, |
43 | two54 = 0x1p54, /* 0x4350000000000000 */ |
44 | twom54 = 0x1p-54; /* 0x3C90000000000000 */ |
45 | |
46 | /*********************************************************************/ |
47 | /* An ultimate sqrt routine. Given an IEEE double machine number x */ |
48 | /* it computes the correctly rounded (to nearest) value of square */ |
49 | /* root of x. */ |
50 | /*********************************************************************/ |
51 | long double __ieee754_sqrtl(long double x) |
52 | { |
53 | static const long double big = 134217728.0, big1 = 134217729.0; |
54 | long double t,s,i; |
55 | mynumber a,c; |
56 | uint64_t k, l; |
57 | int64_t m, n; |
58 | double d; |
59 | |
60 | a.x=x; |
61 | k=a.i[0] & INT64_C(0x7fffffffffffffff); |
62 | /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/ |
63 | if (k>INT64_C(0x000fffff00000000) && k<INT64_C(0x7ff0000000000000)) { |
64 | if (x < 0) return (big1-big1)/(big-big); |
65 | l = (k&INT64_C(0x001fffffffffffff))|INT64_C(0x3fe0000000000000); |
66 | if ((a.i[1] & INT64_C(0x7fffffffffffffff)) != 0) { |
67 | n = (int64_t) ((l - k) * 2) >> 53; |
68 | m = (a.i[1] >> 52) & 0x7ff; |
69 | if (m == 0) { |
70 | a.d[1] *= two54; |
71 | m = ((a.i[1] >> 52) & 0x7ff) - 54; |
72 | } |
73 | m += n; |
74 | if (m > 0) |
75 | a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); |
76 | else if (m <= -54) { |
77 | a.i[1] &= INT64_C(0x8000000000000000); |
78 | } else { |
79 | m += 54; |
80 | a.i[1] = (a.i[1] & INT64_C(0x800fffffffffffff)) | (m << 52); |
81 | a.d[1] *= twom54; |
82 | } |
83 | } |
84 | a.i[0] = l; |
85 | s = a.x; |
86 | d = __ieee754_sqrt (a.d[0]); |
87 | c.i[0] = INT64_C(0x2000000000000000)+((k&INT64_C(0x7fe0000000000000))>>1); |
88 | c.i[1] = 0; |
89 | i = d; |
90 | t = 0.5L * (i + s / i); |
91 | i = 0.5L * (t + s / t); |
92 | return c.x * i; |
93 | } |
94 | else { |
95 | if (k>=INT64_C(0x7ff0000000000000)) |
96 | /* sqrt (-Inf) = NaN, sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */ |
97 | return x * x + x; |
98 | if (x == 0) return x; |
99 | if (x < 0) return (big1-big1)/(big-big); |
100 | return tm256*__ieee754_sqrtl(x: x*t512); |
101 | } |
102 | } |
103 | libm_alias_finite (__ieee754_sqrtl, __sqrtl) |
104 | |