xref: /freebsd/contrib/arm-optimized-routines/pl/math/v_acoshf_3u1.c (revision f81cdf24ba5436367377f7c8e8f51f6df2a75ca7)
1 /*
2  * Single-precision vector acosh(x) function.
3  * Copyright (c) 2023, Arm Limited.
4  * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception
5  */
6 
7 #include "v_math.h"
8 #include "pl_sig.h"
9 #include "pl_test.h"
10 
11 #define SignMask 0x80000000
12 #define One 0x3f800000
13 #define SquareLim 0x5f800000 /* asuint(0x1p64).  */
14 
15 #if V_SUPPORTED
16 
17 #include "v_log1pf_inline.h"
18 
19 static NOINLINE VPCS_ATTR v_f32_t
20 special_case (v_f32_t x, v_f32_t y, v_u32_t special)
21 {
22   return v_call_f32 (acoshf, x, y, special);
23 }
24 
25 /* Vector approximation for single-precision acosh, based on log1p. Maximum
26    error depends on WANT_SIMD_EXCEPT. With SIMD fp exceptions enabled, it
27    is 2.78 ULP:
28    __v_acoshf(0x1.07887p+0) got 0x1.ef9e9cp-3
29 			   want 0x1.ef9ea2p-3.
30    With exceptions disabled, we can compute u with a shorter dependency chain,
31    which gives maximum error of 3.07 ULP:
32   __v_acoshf(0x1.01f83ep+0) got 0x1.fbc7fap-4
33 			   want 0x1.fbc7f4p-4.  */
34 
35 VPCS_ATTR v_f32_t V_NAME (acoshf) (v_f32_t x)
36 {
37   v_u32_t ix = v_as_u32_f32 (x);
38   v_u32_t special = v_cond_u32 ((ix - One) >= (SquareLim - One));
39 
40 #if WANT_SIMD_EXCEPT
41   /* Mask special lanes with 1 to side-step spurious invalid or overflow. Use
42      only xm1 to calculate u, as operating on x will trigger invalid for NaN. */
43   v_f32_t xm1 = v_sel_f32 (special, v_f32 (1), x - 1);
44   v_f32_t u = v_fma_f32 (xm1, xm1, 2 * xm1);
45 #else
46   v_f32_t xm1 = x - 1;
47   v_f32_t u = xm1 * (x + 1.0f);
48 #endif
49   v_f32_t y = log1pf_inline (xm1 + v_sqrt_f32 (u));
50 
51   if (unlikely (v_any_u32 (special)))
52     return special_case (x, y, special);
53   return y;
54 }
55 VPCS_ALIAS
56 
57 PL_SIG (V, F, 1, acosh, 1.0, 10.0)
58 #if WANT_SIMD_EXCEPT
59 PL_TEST_ULP (V_NAME (acoshf), 2.29)
60 #else
61 PL_TEST_ULP (V_NAME (acoshf), 2.58)
62 #endif
63 PL_TEST_EXPECT_FENV (V_NAME (acoshf), WANT_SIMD_EXCEPT)
64 PL_TEST_INTERVAL (V_NAME (acoshf), 0, 1, 500)
65 PL_TEST_INTERVAL (V_NAME (acoshf), 1, SquareLim, 100000)
66 PL_TEST_INTERVAL (V_NAME (acoshf), SquareLim, inf, 1000)
67 PL_TEST_INTERVAL (V_NAME (acoshf), -0, -inf, 1000)
68 #endif
69