| 1 | /* |
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| 2 | * Single-precision vector 2^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: 1.962 ulp. */ |
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| 15 | 0x1.59977ap-10f, |
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| 16 | 0x1.3ce9e4p-7f, |
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| 17 | 0x1.c6bd32p-5f, |
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| 18 | 0x1.ebf9bcp-3f, |
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| 19 | 0x1.62e422p-1f, |
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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 | |
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| 29 | VPCS_ATTR |
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| 30 | static v_f32_t |
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| 31 | specialcase (v_f32_t poly, v_f32_t n, v_u32_t e, v_f32_t absn, v_u32_t cmp1, v_f32_t scale) |
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| 32 | { |
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| 33 | /* 2^n may overflow, break it up into s1*s2. */ |
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| 34 | v_u32_t b = v_cond_u32 (n <= v_f32 (0.0f)) & v_u32 (0x82000000); |
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| 35 | v_f32_t s1 = v_as_f32_u32 (v_u32 (0x7f000000) + b); |
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| 36 | v_f32_t s2 = v_as_f32_u32 (e - b); |
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| 37 | v_u32_t cmp2 = v_cond_u32 (absn > v_f32 (192.0f)); |
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| 38 | v_u32_t r2 = v_as_u32_f32 (s1 * s1); |
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| 39 | v_u32_t r1 = v_as_u32_f32 (v_fma_f32 (poly, s2, s2) * s1); |
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| 40 | /* Similar to r1 but avoids double rounding in the subnormal range. */ |
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| 41 | v_u32_t r0 = v_as_u32_f32 (v_fma_f32 (poly, scale, scale)); |
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| 42 | return v_as_f32_u32 ((cmp2 & r2) | (~cmp2 & cmp1 & r1) | (~cmp1 & r0)); |
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| 43 | } |
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| 44 | |
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| 45 | VPCS_ATTR |
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| 46 | v_f32_t |
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| 47 | V_NAME(exp2f) (v_f32_t x) |
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| 48 | { |
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| 49 | v_f32_t n, r, r2, scale, p, q, poly, absn; |
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| 50 | v_u32_t cmp, e; |
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| 51 | |
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| 52 | /* exp2(x) = 2^n (1 + poly(r)), with 1 + poly(r) in [1/sqrt(2),sqrt(2)] |
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| 53 | x = n + r, with r in [-1/2, 1/2]. */ |
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| 54 | #if 0 |
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| 55 | v_f32_t z; |
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| 56 | z = x + Shift; |
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| 57 | n = z - Shift; |
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| 58 | r = x - n; |
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| 59 | e = v_as_u32_f32 (z) << 23; |
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| 60 | #else |
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| 61 | n = v_round_f32 (x); |
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| 62 | r = x - n; |
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| 63 | e = v_as_u32_s32 (v_round_s32 (x)) << 23; |
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| 64 | #endif |
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| 65 | scale = v_as_f32_u32 (e + v_u32 (0x3f800000)); |
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| 66 | absn = v_abs_f32 (n); |
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| 67 | cmp = v_cond_u32 (absn > v_f32 (126.0f)); |
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| 68 | r2 = r * r; |
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| 69 | p = v_fma_f32 (C0, r, C1); |
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| 70 | q = v_fma_f32 (C2, r, C3); |
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| 71 | q = v_fma_f32 (p, r2, q); |
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| 72 | p = C4 * r; |
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| 73 | poly = v_fma_f32 (q, r2, p); |
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| 74 | if (unlikely (v_any_u32 (cmp))) |
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| 75 | return specialcase (poly, n, e, absn, cmp, scale); |
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| 76 | return v_fma_f32 (poly, scale, scale); |
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| 77 | } |
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| 78 | VPCS_ALIAS |
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| 79 | #endif |
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| 80 | |
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