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63640cb7 | 1 | /* Double-precision floating point 2^x. |
0ac5ae23 UD |
2 | Copyright (C) 1997,1998,2000,2001,2005,2006,2011 |
3 | Free Software Foundation, Inc. | |
63640cb7 UD |
4 | This file is part of the GNU C Library. |
5 | Contributed by Geoffrey Keating <geoffk@ozemail.com.au> | |
6 | ||
7 | The GNU C Library is free software; you can redistribute it and/or | |
41bdb6e2 AJ |
8 | modify it under the terms of the GNU Lesser General Public |
9 | License as published by the Free Software Foundation; either | |
10 | version 2.1 of the License, or (at your option) any later version. | |
63640cb7 UD |
11 | |
12 | The GNU C Library is distributed in the hope that it will be useful, | |
13 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
14 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
41bdb6e2 | 15 | Lesser General Public License for more details. |
63640cb7 | 16 | |
41bdb6e2 AJ |
17 | You should have received a copy of the GNU Lesser General Public |
18 | License along with the GNU C Library; if not, write to the Free | |
19 | Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA | |
20 | 02111-1307 USA. */ | |
63640cb7 UD |
21 | |
22 | /* The basic design here is from | |
23 | Shmuel Gal and Boris Bachelis, "An Accurate Elementary Mathematical | |
24 | Library for the IEEE Floating Point Standard", ACM Trans. Math. Soft., | |
25 | 17 (1), March 1991, pp. 26-45. | |
26 | It has been slightly modified to compute 2^x instead of e^x. | |
27 | */ | |
28 | #ifndef _GNU_SOURCE | |
29 | #define _GNU_SOURCE | |
30 | #endif | |
31 | #include <stdlib.h> | |
32 | #include <float.h> | |
33 | #include <ieee754.h> | |
34 | #include <math.h> | |
35 | #include <fenv.h> | |
36 | #include <inttypes.h> | |
37 | #include <math_private.h> | |
38 | ||
39 | #include "t_exp2.h" | |
40 | ||
403a6325 UD |
41 | /* XXX I know the assembler generates a warning about incorrect section |
42 | attributes. But without the attribute here the compiler places the | |
43 | constants in the .data section. Ideally the constant is placed in | |
44 | .rodata.cst8 so that it can be merged, but gcc sucks, it ICEs when | |
45 | we try to force this section on it. --drepper */ | |
8ff16245 UD |
46 | static const volatile double TWO1023 = 8.988465674311579539e+307; |
47 | static const volatile double TWOM1000 = 9.3326361850321887899e-302; | |
63640cb7 UD |
48 | |
49 | double | |
50 | __ieee754_exp2 (double x) | |
51 | { | |
52 | static const double himark = (double) DBL_MAX_EXP; | |
601d2942 | 53 | static const double lomark = (double) (DBL_MIN_EXP - DBL_MANT_DIG - 1); |
63640cb7 UD |
54 | |
55 | /* Check for usual case. */ | |
601d2942 | 56 | if (isless (x, himark) && isgreaterequal (x, lomark)) |
63640cb7 UD |
57 | { |
58 | static const double THREEp42 = 13194139533312.0; | |
59 | int tval, unsafe; | |
60 | double rx, x22, result; | |
61 | union ieee754_double ex2_u, scale_u; | |
62 | fenv_t oldenv; | |
63 | ||
64 | feholdexcept (&oldenv); | |
65 | #ifdef FE_TONEAREST | |
66 | /* If we don't have this, it's too bad. */ | |
67 | fesetround (FE_TONEAREST); | |
68 | #endif | |
69 | ||
70 | /* 1. Argument reduction. | |
71 | Choose integers ex, -256 <= t < 256, and some real | |
72 | -1/1024 <= x1 <= 1024 so that | |
73 | x = ex + t/512 + x1. | |
74 | ||
75 | First, calculate rx = ex + t/512. */ | |
76 | rx = x + THREEp42; | |
77 | rx -= THREEp42; | |
78 | x -= rx; /* Compute x=x1. */ | |
79 | /* Compute tval = (ex*512 + t)+256. | |
80 | Now, t = (tval mod 512)-256 and ex=tval/512 [that's mod, NOT %; and | |
81 | /-round-to-nearest not the usual c integer /]. */ | |
82 | tval = (int) (rx * 512.0 + 256.0); | |
83 | ||
84 | /* 2. Adjust for accurate table entry. | |
85 | Find e so that | |
86 | x = ex + t/512 + e + x2 | |
87 | where -1e6 < e < 1e6, and | |
88 | (double)(2^(t/512+e)) | |
89 | is accurate to one part in 2^-64. */ | |
90 | ||
91 | /* 'tval & 511' is the same as 'tval%512' except that it's always | |
92 | positive. | |
93 | Compute x = x2. */ | |
94 | x -= exp2_deltatable[tval & 511]; | |
95 | ||
96 | /* 3. Compute ex2 = 2^(t/512+e+ex). */ | |
97 | ex2_u.d = exp2_accuratetable[tval & 511]; | |
98 | tval >>= 9; | |
99 | unsafe = abs(tval) >= -DBL_MIN_EXP - 1; | |
100 | ex2_u.ieee.exponent += tval >> unsafe; | |
101 | scale_u.d = 1.0; | |
102 | scale_u.ieee.exponent += tval - (tval >> unsafe); | |
103 | ||
104 | /* 4. Approximate 2^x2 - 1, using a fourth-degree polynomial, | |
105 | with maximum error in [-2^-10-2^-30,2^-10+2^-30] | |
106 | less than 10^-19. */ | |
107 | ||
108 | x22 = (((.0096181293647031180 | |
109 | * x + .055504110254308625) | |
110 | * x + .240226506959100583) | |
111 | * x + .69314718055994495) * ex2_u.d; | |
112 | ||
113 | /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ | |
114 | fesetenv (&oldenv); | |
115 | ||
116 | result = x22 * x + ex2_u.d; | |
117 | ||
118 | if (!unsafe) | |
119 | return result; | |
120 | else | |
121 | return result * scale_u.d; | |
122 | } | |
123 | /* Exceptional cases: */ | |
124 | else if (isless (x, himark)) | |
125 | { | |
126 | if (__isinf (x)) | |
127 | /* e^-inf == 0, with no error. */ | |
128 | return 0; | |
129 | else | |
130 | /* Underflow */ | |
131 | return TWOM1000 * TWOM1000; | |
132 | } | |
133 | else | |
134 | /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ | |
135 | return TWO1023*x; | |
136 | } | |
0ac5ae23 | 137 | strong_alias (__ieee754_exp2, __exp2_finite) |