1 /*
2 * Double-precision vector sin 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 Pi1 v_f64 (0x1.921fb54442d18p+1)
35 #define Pi2 v_f64 (0x1.1a62633145c06p-53)
36 #define Pi3 v_f64 (0x1.c1cd129024e09p-106)
37 #define Shift v_f64 (0x1.8p52)
38 #define RangeVal v_f64 (0x1p23)
39 #define AbsMask v_u64 (0x7fffffffffffffff)
40
41 VPCS_ATTR
42 __attribute__ ((noinline)) static v_f64_t
specialcase(v_f64_t x,v_f64_t y,v_u64_t cmp)43 specialcase (v_f64_t x, v_f64_t y, v_u64_t cmp)
44 {
45 return v_call_f64 (sin, x, y, cmp);
46 }
47
48 VPCS_ATTR
49 v_f64_t
V_NAME(sin)50 V_NAME(sin) (v_f64_t x)
51 {
52 v_f64_t n, r, r2, y;
53 v_u64_t sign, odd, cmp;
54
55 r = v_as_f64_u64 (v_as_u64_f64 (x) & AbsMask);
56 sign = 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). */
60 n = v_fma_f64 (InvPi, r, Shift);
61 odd = v_as_u64_f64 (n) << 63;
62 n -= Shift;
63
64 /* r = |x| - n*pi (range reduction into -pi/2 .. pi/2). */
65 r = v_fma_f64 (-Pi1, n, r);
66 r = v_fma_f64 (-Pi2, n, r);
67 r = v_fma_f64 (-Pi3, n, r);
68
69 /* sin(r) poly approx. */
70 r2 = r * r;
71 y = v_fma_f64 (C7, r2, C6);
72 y = v_fma_f64 (y, r2, C5);
73 y = v_fma_f64 (y, r2, C4);
74 y = v_fma_f64 (y, r2, C3);
75 y = v_fma_f64 (y, r2, C2);
76 y = v_fma_f64 (y, r2, C1);
77 y = v_fma_f64 (y * r2, r, r);
78
79 /* sign. */
80 y = v_as_f64_u64 (v_as_u64_f64 (y) ^ sign ^ odd);
81
82 if (unlikely (v_any_u64 (cmp)))
83 return specialcase (x, y, cmp);
84 return y;
85 }
86 VPCS_ALIAS
87 #endif
88