1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-precision vector e^x function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2019-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner #include "v_math.h" 8*f3087befSAndrew Turner #include "test_defs.h" 9*f3087befSAndrew Turner 10*f3087befSAndrew Turner static const struct data 11*f3087befSAndrew Turner { 12*f3087befSAndrew Turner float32x4_t shift, inv_ln2; 13*f3087befSAndrew Turner uint32x4_t exponent_bias; 14*f3087befSAndrew Turner float32x4_t c1, c2, c3, c4; 15*f3087befSAndrew Turner float32x4_t special_bound, scale_thresh; 16*f3087befSAndrew Turner uint32x4_t special_offset, special_bias; 17*f3087befSAndrew Turner float ln2_hi, ln2_lo, c0, nothing; 18*f3087befSAndrew Turner } data = { 19*f3087befSAndrew Turner .ln2_hi = 0x1.62e4p-1f, 20*f3087befSAndrew Turner .ln2_lo = 0x1.7f7d1cp-20f, 21*f3087befSAndrew Turner .shift = V4 (0x1.8p23f), 22*f3087befSAndrew Turner .inv_ln2 = V4 (0x1.715476p+0f), 23*f3087befSAndrew Turner .exponent_bias = V4 (0x3f800000), 24*f3087befSAndrew Turner .special_bound = V4 (126.0f), 25*f3087befSAndrew Turner .scale_thresh = V4 (192.0f), 26*f3087befSAndrew Turner .special_offset = V4 (0x83000000), 27*f3087befSAndrew Turner .special_bias = V4 (0x7f000000), 28*f3087befSAndrew Turner /* maxerr: 0.36565 +0.5 ulp. */ 29*f3087befSAndrew Turner .c0 = 0x1.6a6000p-10f, 30*f3087befSAndrew Turner .c1 = V4 (0x1.12718ep-7f), 31*f3087befSAndrew Turner .c2 = V4 (0x1.555af0p-5f), 32*f3087befSAndrew Turner .c3 = V4 (0x1.555430p-3f), 33*f3087befSAndrew Turner .c4 = V4 (0x1.fffff4p-2f), 34*f3087befSAndrew Turner }; 35*f3087befSAndrew Turner 36*f3087befSAndrew Turner static float32x4_t VPCS_ATTR NOINLINE 37*f3087befSAndrew Turner specialcase (float32x4_t p, float32x4_t n, uint32x4_t e, const struct data *d) 38*f3087befSAndrew Turner { 39*f3087befSAndrew Turner /* 2^n may overflow, break it up into s1*s2. */ 40*f3087befSAndrew Turner uint32x4_t b = vandq_u32 (vclezq_f32 (n), d->special_offset); 41*f3087befSAndrew Turner float32x4_t s1 = vreinterpretq_f32_u32 (vaddq_u32 (b, d->special_bias)); 42*f3087befSAndrew Turner float32x4_t s2 = vreinterpretq_f32_u32 (vsubq_u32 (e, b)); 43*f3087befSAndrew Turner uint32x4_t cmp = vcagtq_f32 (n, d->scale_thresh); 44*f3087befSAndrew Turner float32x4_t r1 = vmulq_f32 (s1, s1); 45*f3087befSAndrew Turner float32x4_t r0 = vmulq_f32 (vmulq_f32 (p, s1), s2); 46*f3087befSAndrew Turner return vreinterpretq_f32_u32 ((cmp & vreinterpretq_u32_f32 (r1)) 47*f3087befSAndrew Turner | (~cmp & vreinterpretq_u32_f32 (r0))); 48*f3087befSAndrew Turner } 49*f3087befSAndrew Turner 50*f3087befSAndrew Turner float32x4_t VPCS_ATTR 51*f3087befSAndrew Turner _ZGVnN4v_expf_1u (float32x4_t x) 52*f3087befSAndrew Turner { 53*f3087befSAndrew Turner const struct data *d = ptr_barrier (&data); 54*f3087befSAndrew Turner float32x4_t ln2_c0 = vld1q_f32 (&d->ln2_hi); 55*f3087befSAndrew Turner 56*f3087befSAndrew Turner /* exp(x) = 2^n * poly(r), with poly(r) in [1/sqrt(2),sqrt(2)] 57*f3087befSAndrew Turner x = ln2*n + r, with r in [-ln2/2, ln2/2]. */ 58*f3087befSAndrew Turner float32x4_t z = vmulq_f32 (x, d->inv_ln2); 59*f3087befSAndrew Turner float32x4_t n = vrndaq_f32 (z); 60*f3087befSAndrew Turner float32x4_t r = vfmsq_laneq_f32 (x, n, ln2_c0, 0); 61*f3087befSAndrew Turner r = vfmsq_laneq_f32 (r, n, ln2_c0, 1); 62*f3087befSAndrew Turner uint32x4_t e = vshlq_n_u32 (vreinterpretq_u32_s32 (vcvtaq_s32_f32 (z)), 23); 63*f3087befSAndrew Turner float32x4_t scale = vreinterpretq_f32_u32 (e + d->exponent_bias); 64*f3087befSAndrew Turner uint32x4_t cmp = vcagtq_f32 (n, d->special_bound); 65*f3087befSAndrew Turner float32x4_t p = vfmaq_laneq_f32 (d->c1, r, ln2_c0, 2); 66*f3087befSAndrew Turner p = vfmaq_f32 (d->c2, p, r); 67*f3087befSAndrew Turner p = vfmaq_f32 (d->c3, p, r); 68*f3087befSAndrew Turner p = vfmaq_f32 (d->c4, p, r); 69*f3087befSAndrew Turner p = vfmaq_f32 (v_f32 (1.0f), p, r); 70*f3087befSAndrew Turner p = vfmaq_f32 (v_f32 (1.0f), p, r); 71*f3087befSAndrew Turner if (unlikely (v_any_u32 (cmp))) 72*f3087befSAndrew Turner return specialcase (p, n, e, d); 73*f3087befSAndrew Turner return scale * p; 74*f3087befSAndrew Turner } 75*f3087befSAndrew Turner 76*f3087befSAndrew Turner TEST_ULP (_ZGVnN4v_expf_1u, 0.4) 77*f3087befSAndrew Turner TEST_DISABLE_FENV (_ZGVnN4v_expf_1u) 78*f3087befSAndrew Turner TEST_INTERVAL (_ZGVnN4v_expf_1u, 0, 0xffff0000, 10000) 79*f3087befSAndrew Turner TEST_SYM_INTERVAL (_ZGVnN4v_expf_1u, 0x1p-14, 0x1p8, 500000) 80