1 /* 2 * Single-precision vector/SVE log2 function. 3 * 4 * Copyright (c) 2022-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 12 static const struct data 13 { 14 float poly_02468[5]; 15 float poly_1357[4]; 16 uint32_t off, lower; 17 } data = { 18 .poly_1357 = { 19 /* Coefficients copied from the AdvSIMD routine, then rearranged so that coeffs 20 1, 3, 5 and 7 can be loaded as a single quad-word, hence used with _lane 21 variant of MLA intrinsic. */ 22 -0x1.715458p-1f, -0x1.7171a4p-2f, -0x1.e5143ep-3f, -0x1.c675bp-3f 23 }, 24 .poly_02468 = { 0x1.715476p0f, 0x1.ec701cp-2f, 0x1.27a0b8p-2f, 25 0x1.9d8ecap-3f, 0x1.9e495p-3f }, 26 .off = 0x3f2aaaab, 27 /* Lower bound is the smallest positive normal float 0x00800000. For 28 optimised register use subnormals are detected after offset has been 29 subtracted, so lower bound is 0x0080000 - offset (which wraps around). */ 30 .lower = 0x00800000 - 0x3f2aaaab 31 }; 32 33 #define Thresh (0x7f000000) /* asuint32(inf) - 0x00800000. */ 34 #define MantissaMask (0x007fffff) 35 36 static svfloat32_t NOINLINE 37 special_case (svuint32_t u_off, svfloat32_t p, svfloat32_t r2, svfloat32_t y, 38 svbool_t cmp) 39 { 40 return sv_call_f32 ( 41 log2f, svreinterpret_f32 (svadd_x (svptrue_b32 (), u_off, data.off)), 42 svmla_x (svptrue_b32 (), p, r2, y), cmp); 43 } 44 45 /* Optimised implementation of SVE log2f, using the same algorithm 46 and polynomial as AdvSIMD log2f. 47 Maximum error is 2.48 ULPs: 48 SV_NAME_F1 (log2)(0x1.558174p+0) got 0x1.a9be84p-2 49 want 0x1.a9be8p-2. */ 50 svfloat32_t SV_NAME_F1 (log2) (svfloat32_t x, const svbool_t pg) 51 { 52 const struct data *d = ptr_barrier (&data); 53 54 svuint32_t u_off = svreinterpret_u32 (x); 55 56 u_off = svsub_x (pg, u_off, d->off); 57 svbool_t special = svcmpge (pg, svsub_x (pg, u_off, d->lower), Thresh); 58 59 /* x = 2^n * (1+r), where 2/3 < 1+r < 4/3. */ 60 svfloat32_t n = svcvt_f32_x ( 61 pg, svasr_x (pg, svreinterpret_s32 (u_off), 23)); /* Sign-extend. */ 62 svuint32_t u = svand_x (pg, u_off, MantissaMask); 63 u = svadd_x (pg, u, d->off); 64 svfloat32_t r = svsub_x (pg, svreinterpret_f32 (u), 1.0f); 65 66 /* y = log2(1+r) + n. */ 67 svfloat32_t r2 = svmul_x (svptrue_b32 (), r, r); 68 69 /* Evaluate polynomial using pairwise Horner scheme. */ 70 svfloat32_t p_1357 = svld1rq (svptrue_b32 (), &d->poly_1357[0]); 71 svfloat32_t q_01 = svmla_lane (sv_f32 (d->poly_02468[0]), r, p_1357, 0); 72 svfloat32_t q_23 = svmla_lane (sv_f32 (d->poly_02468[1]), r, p_1357, 1); 73 svfloat32_t q_45 = svmla_lane (sv_f32 (d->poly_02468[2]), r, p_1357, 2); 74 svfloat32_t q_67 = svmla_lane (sv_f32 (d->poly_02468[3]), r, p_1357, 3); 75 svfloat32_t y = svmla_x (pg, q_67, r2, sv_f32 (d->poly_02468[4])); 76 y = svmla_x (pg, q_45, r2, y); 77 y = svmla_x (pg, q_23, r2, y); 78 y = svmla_x (pg, q_01, r2, y); 79 80 if (unlikely (svptest_any (pg, special))) 81 return special_case (u_off, n, r, y, special); 82 return svmla_x (svptrue_b32 (), n, r, y); 83 } 84 85 TEST_SIG (SV, F, 1, log2, 0.01, 11.1) 86 TEST_ULP (SV_NAME_F1 (log2), 1.99) 87 TEST_DISABLE_FENV (SV_NAME_F1 (log2)) 88 TEST_INTERVAL (SV_NAME_F1 (log2), -0.0, -0x1p126, 4000) 89 TEST_INTERVAL (SV_NAME_F1 (log2), 0.0, 0x1p-126, 4000) 90 TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-126, 0x1p-23, 50000) 91 TEST_INTERVAL (SV_NAME_F1 (log2), 0x1p-23, 1.0, 50000) 92 TEST_INTERVAL (SV_NAME_F1 (log2), 1.0, 100, 50000) 93 TEST_INTERVAL (SV_NAME_F1 (log2), 100, inf, 50000) 94 CLOSE_SVE_ATTR 95