1 /* 2 * Single-precision vector tanpi(x) function. 3 * 4 * Copyright (c) 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_sig.h" 10 #include "test_defs.h" 11 12 const static struct v_tanpif_data 13 { 14 float32x4_t c0, c2, c4, c6; 15 float c1, c3, c5, c7; 16 } tanpif_data = { 17 /* Coefficents for tan(pi * x). */ 18 .c0 = V4 (0x1.921fb4p1f), .c1 = 0x1.4abbcep3f, .c2 = V4 (0x1.466b8p5f), 19 .c3 = 0x1.461c72p7f, .c4 = V4 (0x1.42e9d4p9f), .c5 = 0x1.69e2c4p11f, 20 .c6 = V4 (0x1.e85558p11f), .c7 = 0x1.a52e08p16f, 21 }; 22 23 /* Approximation for single-precision vector tanpi(x) 24 The maximum error is 3.34 ULP: 25 _ZGVnN4v_tanpif(0x1.d6c09ap-2) got 0x1.f70aacp+2 26 want 0x1.f70aa6p+2. */ 27 float32x4_t VPCS_ATTR NOINLINE V_NAME_F1 (tanpi) (float32x4_t x) 28 { 29 const struct v_tanpif_data *d = ptr_barrier (&tanpif_data); 30 31 float32x4_t n = vrndnq_f32 (x); 32 33 /* inf produces nan that propagates. */ 34 float32x4_t xr = vsubq_f32 (x, n); 35 float32x4_t ar = vabdq_f32 (x, n); 36 uint32x4_t flip = vcgtq_f32 (ar, v_f32 (0.25f)); 37 float32x4_t r = vbslq_f32 (flip, vsubq_f32 (v_f32 (0.5f), ar), ar); 38 39 /* Order-7 pairwise Horner polynomial evaluation scheme. */ 40 float32x4_t r2 = vmulq_f32 (r, r); 41 float32x4_t r4 = vmulq_f32 (r2, r2); 42 43 float32x4_t odd_coeffs = vld1q_f32 (&d->c1); 44 float32x4_t p01 = vfmaq_laneq_f32 (d->c0, r2, odd_coeffs, 0); 45 float32x4_t p23 = vfmaq_laneq_f32 (d->c2, r2, odd_coeffs, 1); 46 float32x4_t p45 = vfmaq_laneq_f32 (d->c4, r2, odd_coeffs, 2); 47 float32x4_t p67 = vfmaq_laneq_f32 (d->c6, r2, odd_coeffs, 3); 48 float32x4_t p = vfmaq_f32 (p45, r4, p67); 49 p = vfmaq_f32 (p23, r4, p); 50 p = vfmaq_f32 (p01, r4, p); 51 52 p = vmulq_f32 (r, p); 53 float32x4_t p_recip = vdivq_f32 (v_f32 (1.0f), p); 54 float32x4_t y = vbslq_f32 (flip, p_recip, p); 55 56 uint32x4_t sign 57 = veorq_u32 (vreinterpretq_u32_f32 (xr), vreinterpretq_u32_f32 (ar)); 58 return vreinterpretq_f32_u32 (vorrq_u32 (vreinterpretq_u32_f32 (y), sign)); 59 } 60 61 HALF_WIDTH_ALIAS_F1 (tanpi) 62 63 #if WANT_TRIGPI_TESTS 64 TEST_DISABLE_FENV (V_NAME_F1 (tanpi)) 65 TEST_ULP (V_NAME_F1 (tanpi), 2.84) 66 TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0, 0x1p-31, 50000) 67 TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0x1p-31, 0.5, 100000) 68 TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0.5, 0x1p23f, 100000) 69 TEST_SYM_INTERVAL (V_NAME_F1 (tanpi), 0x1p23f, inf, 100000) 70 #endif 71