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[glibc.git] / sysdeps / ieee754 / ldbl-128 / x2y2m1l.c
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1 /* Compute x^2 + y^2 - 1, without large cancellation error.
2 Copyright (C) 2012-2014 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
19 #include <math.h>
20 #include <math_private.h>
21 #include <float.h>
22 #include <stdlib.h>
24 /* Calculate X + Y exactly and store the result in *HI + *LO. It is
25 given that |X| >= |Y| and the values are small enough that no
26 overflow occurs. */
28 static inline void
29 add_split (long double *hi, long double *lo, long double x, long double y)
31 /* Apply Dekker's algorithm. */
32 *hi = x + y;
33 *lo = (x - *hi) + y;
36 /* Calculate X * Y exactly and store the result in *HI + *LO. It is
37 given that the values are small enough that no overflow occurs and
38 large enough (or zero) that no underflow occurs. */
40 static inline void
41 mul_split (long double *hi, long double *lo, long double x, long double y)
43 #ifdef __FP_FAST_FMAL
44 /* Fast built-in fused multiply-add. */
45 *hi = x * y;
46 *lo = __builtin_fmal (x, y, -*hi);
47 #elif defined FP_FAST_FMAL
48 /* Fast library fused multiply-add, compiler before GCC 4.6. */
49 *hi = x * y;
50 *lo = __fmal (x, y, -*hi);
51 #else
52 /* Apply Dekker's algorithm. */
53 *hi = x * y;
54 # define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
55 long double x1 = x * C;
56 long double y1 = y * C;
57 # undef C
58 x1 = (x - x1) + x1;
59 y1 = (y - y1) + y1;
60 long double x2 = x - x1;
61 long double y2 = y - y1;
62 *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
63 #endif
66 /* Compare absolute values of floating-point values pointed to by P
67 and Q for qsort. */
69 static int
70 compare (const void *p, const void *q)
72 long double pld = fabsl (*(const long double *) p);
73 long double qld = fabsl (*(const long double *) q);
74 if (pld < qld)
75 return -1;
76 else if (pld == qld)
77 return 0;
78 else
79 return 1;
82 /* Return X^2 + Y^2 - 1, computed without large cancellation error.
83 It is given that 1 > X >= Y >= epsilon / 2, and that either X >=
84 0.75 or Y >= 0.5. */
86 long double
87 __x2y2m1l (long double x, long double y)
89 long double vals[4];
90 SET_RESTORE_ROUNDL (FE_TONEAREST);
91 mul_split (&vals[1], &vals[0], x, x);
92 mul_split (&vals[3], &vals[2], y, y);
93 if (x >= 0.75L)
94 vals[1] -= 1.0L;
95 else
97 vals[1] -= 0.5L;
98 vals[3] -= 0.5L;
100 qsort (vals, 4, sizeof (long double), compare);
101 /* Add up the values so that each element of VALS has absolute value
102 at most equal to the last set bit of the next nonzero
103 element. */
104 for (size_t i = 0; i <= 2; i++)
106 add_split (&vals[i + 1], &vals[i], vals[i + 1], vals[i]);
107 qsort (vals + i + 1, 3 - i, sizeof (long double), compare);
109 /* Now any error from this addition will be small. */
110 return vals[3] + vals[2] + vals[1] + vals[0];