1 /*
2 * Double-precision vector cos function.
3 *
4 * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 * See https://llvm.org/LICENSE.txt for license information.
6 * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 */
8
9 #include "mathlib.h"
10 #include "v_math.h"
11 #if V_SUPPORTED
12
13 static const double Poly[] = {
14 /* worst-case error is 3.5 ulp.
15 abs error: 0x1.be222a58p-53 in [-pi/2, pi/2]. */
16 -0x1.9f4a9c8b21dc9p-41,
17 0x1.60e88a10163f2p-33,
18 -0x1.ae6361b7254e7p-26,
19 0x1.71de382e8d62bp-19,
20 -0x1.a01a019aeb4ffp-13,
21 0x1.111111110b25ep-7,
22 -0x1.55555555554c3p-3,
23 };
24
25 #define C7 v_f64 (Poly[0])
26 #define C6 v_f64 (Poly[1])
27 #define C5 v_f64 (Poly[2])
28 #define C4 v_f64 (Poly[3])
29 #define C3 v_f64 (Poly[4])
30 #define C2 v_f64 (Poly[5])
31 #define C1 v_f64 (Poly[6])
32
33 #define InvPi v_f64 (0x1.45f306dc9c883p-2)
34 #define HalfPi v_f64 (0x1.921fb54442d18p+0)
35 #define Pi1 v_f64 (0x1.921fb54442d18p+1)
36 #define Pi2 v_f64 (0x1.1a62633145c06p-53)
37 #define Pi3 v_f64 (0x1.c1cd129024e09p-106)
38 #define Shift v_f64 (0x1.8p52)
39 #define RangeVal v_f64 (0x1p23)
40 #define AbsMask v_u64 (0x7fffffffffffffff)
41
42 VPCS_ATTR
43 __attribute__ ((noinline)) static v_f64_t
specialcase(v_f64_t x,v_f64_t y,v_u64_t cmp)44 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
45 {
46 return v_call_f64 (cos, x, y, cmp);
47 }
48
49 VPCS_ATTR
50 v_f64_t
V_NAME(cos)51 V_NAME(cos) (v_f64_t x)
52 {
53 v_f64_t n, r, r2, y;
54 v_u64_t odd, cmp;
55
56 r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
57 cmp = v_cond_u64 (v_as_u64_f64 (r) >= v_as_u64_f64 (RangeVal));
58
59 /* n = rint((|x|+pi/2)/pi) - 0.5. */
60 n = v_fma_f64 (InvPi, r + HalfPi, Shift);
61 odd = v_as_u64_f64 (n) << 63;
62 n -= Shift;
63 n -= v_f64 (0.5);
64
65 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
66 r = v_fma_f64 (-Pi1, n, r);
67 r = v_fma_f64 (-Pi2, n, r);
68 r = v_fma_f64 (-Pi3, n, r);
69
70 /* sin(r) poly approx. */
71 r2 = r * r;
72 y = v_fma_f64 (C7, r2, C6);
73 y = v_fma_f64 (y, r2, C5);
74 y = v_fma_f64 (y, r2, C4);
75 y = v_fma_f64 (y, r2, C3);
76 y = v_fma_f64 (y, r2, C2);
77 y = v_fma_f64 (y, r2, C1);
78 y = v_fma_f64 (y * r2, r, r);
79
80 /* sign. */
81 y = v_as_f64_u64 (v_as_u64_f64 (y) ^ odd);
82
83 if (unlikely (v_any_u64 (cmp)))
84 return specialcase (x, y, cmp);
85 return y;
86 }
87 VPCS_ALIAS
88 #endif
89