1 /* 2 * Single-precision vector 2^x function. 3 * 4 * Copyright (c) 2019-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "v_math.h" 9 #include "test_defs.h" 10 11 static const struct data 12 { 13 float32x4_t c0, c1, c2, c3, c4, c5, shift; 14 uint32x4_t exponent_bias; 15 float32x4_t special_bound, scale_thresh; 16 uint32x4_t special_offset, special_bias; 17 } data = { 18 .shift = V4 (0x1.8p23f), 19 .exponent_bias = V4 (0x3f800000), 20 .special_bound = V4 (126.0f), 21 .scale_thresh = V4 (192.0f), 22 .special_offset = V4 (0x82000000), 23 .special_bias = V4 (0x7f000000), 24 /* maxerr: 0.878 ulp. */ 25 .c0 = V4 (0x1.416b5ep-13f), 26 .c1 = V4 (0x1.5f082ep-10f), 27 .c2 = V4 (0x1.3b2dep-7f), 28 .c3 = V4 (0x1.c6af7cp-5f), 29 .c4 = V4 (0x1.ebfbdcp-3f), 30 .c5 = V4 (0x1.62e43p-1f), 31 }; 32 33 static float32x4_t VPCS_ATTR NOINLINE 34 specialcase (float32x4_t p, float32x4_t n, uint32x4_t e, const struct data *d) 35 { 36 /* 2^n may overflow, break it up into s1*s2. */ 37 uint32x4_t b = vandq_u32 (vclezq_f32 (n), d->special_offset); 38 float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, d->special_bias)); 39 float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b)); 40 uint32x4_t cmp = vcagtq_f32 (n, d->scale_thresh); 41 float32x4_t r1 = vmulq_f32 (s1, s1); 42 float32x4_t r0 = vmulq_f32 (vmulq_f32 (p, s1), s2); 43 return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1)) 44 | (~cmp & vreinterpretq_u32_f32 (r0))); 45 } 46 47 float32x4_t VPCS_ATTR 48 _ZGVnN4v_exp2f_1u (float32x4_t x) 49 { 50 /* exp2(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] 51 x = n + r, with r in [-1/2, 1/2]. */ 52 const struct data *d = ptr_barrier (&data); 53 float32x4_t n = vrndaq_f32 (x); 54 float32x4_t r = x - n; 55 uint32x4_t e = vreinterpretq_u32_s32 (vcvtaq_s32_f32 (x)) << 23; 56 float32x4_t scale = vreinterpretq_f32_u32 (e + d->exponent_bias); 57 uint32x4_t cmp = vcagtq_f32 (n, d->special_bound); 58 59 float32x4_t p = vfmaq_f32 (d->c1, d->c0, r); 60 p = vfmaq_f32 (d->c2, p, r); 61 p = vfmaq_f32 (d->c3, p, r); 62 p = vfmaq_f32 (d->c4, p, r); 63 p = vfmaq_f32 (d->c5, p, r); 64 p = vfmaq_f32 (v_f32 (1.0f), p, r); 65 if (unlikely (v_any_u32 (cmp))) 66 return specialcase (p, n, e, d); 67 return scale * p; 68 } 69 70 TEST_ULP (_ZGVnN4v_exp2f_1u, 0.4) 71 TEST_DISABLE_FENV (_ZGVnN4v_exp2f_1u) 72 TEST_INTERVAL (_ZGVnN4v_exp2f_1u, 0, 0xffff0000, 10000) 73 TEST_SYM_INTERVAL (_ZGVnN4v_exp2f_1u, 0x1p-14, 0x1p8, 500000) 74