| 1 | /* |
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| 2 | * Single-precision vector e^x function. |
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| 3 | * |
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| 4 | * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions. |
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| 5 | * See https://llvm.org/LICENSE.txt for license information. |
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| 6 | * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception |
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| 7 | */ |
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| 8 | |
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| 9 | #include "mathlib.h" |
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| 10 | #include "v_math.h" |
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| 11 | #if V_SUPPORTED |
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| 12 | |
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| 13 | static const float Poly[] = { |
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| 14 | /* maxerr: 0.36565 +0.5 ulp. */ |
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| 15 | 0x1.6a6000p-10f, |
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| 16 | 0x1.12718ep-7f, |
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| 17 | 0x1.555af0p-5f, |
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| 18 | 0x1.555430p-3f, |
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| 19 | 0x1.fffff4p-2f, |
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| 20 | }; |
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| 21 | #define C0 v_f32 (Poly[0]) |
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| 22 | #define C1 v_f32 (Poly[1]) |
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| 23 | #define C2 v_f32 (Poly[2]) |
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| 24 | #define C3 v_f32 (Poly[3]) |
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| 25 | #define C4 v_f32 (Poly[4]) |
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| 26 | |
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| 27 | #define Shift v_f32 (0x1.8p23f) |
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| 28 | #define InvLn2 v_f32 (0x1.715476p+0f) |
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| 29 | #define Ln2hi v_f32 (0x1.62e4p-1f) |
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| 30 | #define Ln2lo v_f32 (0x1.7f7d1cp-20f) |
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| 31 | |
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| 32 | VPCS_ATTR |
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| 33 | static v_f32_t |
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| 34 | specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn) |
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| 35 | { |
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| 36 | /* 2^n may overflow, break it up into s1*s2. */ |
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| 37 | v_u32_t b = v_cond_u32 (x: n <= v_f32 (x: 0.0f)) & v_u32 (x: 0x83000000); |
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| 38 | v_f32_t s1 = v_as_f32_u32 (x: v_u32 (x: 0x7f000000) + b); |
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| 39 | v_f32_t s2 = v_as_f32_u32 (x: e - b); |
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| 40 | v_u32_t cmp = v_cond_u32 (x: absn > v_f32 (x: 192.0f)); |
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| 41 | v_f32_t r1 = s1 * s1; |
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| 42 | v_f32_t r0 = poly * s1 * s2; |
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| 43 | return v_as_f32_u32 (x: (cmp & v_as_u32_f32 (x: r1)) | (~cmp & v_as_u32_f32 (x: r0))); |
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| 44 | } |
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| 45 | |
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| 46 | VPCS_ATTR |
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| 47 | v_f32_t |
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| 48 | V_NAME(expf_1u) (v_f32_t x) |
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| 49 | { |
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| 50 | v_f32_t n, r, scale, poly, absn, z; |
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| 51 | v_u32_t cmp, e; |
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| 52 | |
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| 53 | /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] |
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| 54 | x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ |
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| 55 | #if 1 |
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| 56 | z = v_fma_f32 (x, InvLn2, Shift); |
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| 57 | n = z - Shift; |
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| 58 | r = v_fma_f32 (x: n, y: -Ln2hi, z: x); |
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| 59 | r = v_fma_f32 (x: n, y: -Ln2lo, z: r); |
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| 60 | e = v_as_u32_f32 (x: z) << 23; |
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| 61 | #else |
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| 62 | z = x * InvLn2; |
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| 63 | n = v_round_f32 (z); |
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| 64 | r = v_fma_f32 (n, -Ln2hi, x); |
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| 65 | r = v_fma_f32 (n, -Ln2lo, r); |
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| 66 | e = v_as_u32_s32 (v_round_s32 (z)) << 23; |
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| 67 | #endif |
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| 68 | scale = v_as_f32_u32 (x: e + v_u32 (x: 0x3f800000)); |
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| 69 | absn = v_abs_f32 (x: n); |
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| 70 | cmp = v_cond_u32 (x: absn > v_f32 (x: 126.0f)); |
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| 71 | poly = v_fma_f32 (C0, y: r, C1); |
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| 72 | poly = v_fma_f32 (x: poly, y: r, C2); |
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| 73 | poly = v_fma_f32 (x: poly, y: r, C3); |
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| 74 | poly = v_fma_f32 (x: poly, y: r, C4); |
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| 75 | poly = v_fma_f32 (x: poly, y: r, z: v_f32 (x: 1.0f)); |
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| 76 | poly = v_fma_f32 (x: poly, y: r, z: v_f32 (x: 1.0f)); |
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| 77 | if (unlikely (v_any_u32 (cmp))) |
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| 78 | return specialcase (poly, n, e, absn); |
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| 79 | return scale * poly; |
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| 80 | } |
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| 81 | #endif |
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| 82 | |
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