1 /* 2 * Single-precision vector log(x + 1) function. 3 * 4 * Copyright (c) 2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "sv_math.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 #include "poly_sve_f32.h" 12 13 static const struct data 14 { 15 float poly[8]; 16 float ln2, exp_bias; 17 uint32_t four, three_quarters; 18 } data = {.poly = {/* Do not store first term of polynomial, which is -0.5, as 19 this can be fmov-ed directly instead of including it in 20 the main load-and-mla polynomial schedule. */ 21 0x1.5555aap-2f, -0x1.000038p-2f, 0x1.99675cp-3f, 22 -0x1.54ef78p-3f, 0x1.28a1f4p-3f, -0x1.0da91p-3f, 23 0x1.abcb6p-4f, -0x1.6f0d5ep-5f}, 24 .ln2 = 0x1.62e43p-1f, 25 .exp_bias = 0x1p-23f, 26 .four = 0x40800000, 27 .three_quarters = 0x3f400000}; 28 29 #define SignExponentMask 0xff800000 30 31 static svfloat32_t NOINLINE 32 special_case (svfloat32_t x, svfloat32_t y, svbool_t special) 33 { 34 return sv_call_f32 (log1pf, x, y, special); 35 } 36 37 /* Vector log1pf approximation using polynomial on reduced interval. Worst-case 38 error is 1.27 ULP very close to 0.5. 39 _ZGVsMxv_log1pf(0x1.fffffep-2) got 0x1.9f324p-2 40 want 0x1.9f323ep-2. */ 41 svfloat32_t SV_NAME_F1 (log1p) (svfloat32_t x, svbool_t pg) 42 { 43 const struct data *d = ptr_barrier (&data); 44 /* x < -1, Inf/Nan. */ 45 svbool_t special = svcmpeq (pg, svreinterpret_u32 (x), 0x7f800000); 46 special = svorn_z (pg, special, svcmpge (pg, x, -1)); 47 48 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m 49 is in [-0.25, 0.5]): 50 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). 51 52 We approximate log1p(m) with a polynomial, then scale by 53 k*log(2). Instead of doing this directly, we use an intermediate 54 scale factor s = 4*k*log(2) to ensure the scale is representable 55 as a normalised fp32 number. */ 56 svfloat32_t m = svadd_x (pg, x, 1); 57 58 /* Choose k to scale x to the range [-1/4, 1/2]. */ 59 svint32_t k 60 = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters), 61 sv_s32 (SignExponentMask)); 62 63 /* Scale x by exponent manipulation. */ 64 svfloat32_t m_scale = svreinterpret_f32 ( 65 svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k))); 66 67 /* Scale up to ensure that the scale factor is representable as normalised 68 fp32 number, and scale m down accordingly. */ 69 svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four)); 70 m_scale = svadd_x (pg, m_scale, svmla_x (pg, sv_f32 (-1), s, 0.25)); 71 72 /* Evaluate polynomial on reduced interval. */ 73 svfloat32_t ms2 = svmul_x (pg, m_scale, m_scale), 74 ms4 = svmul_x (pg, ms2, ms2); 75 svfloat32_t p = sv_estrin_7_f32_x (pg, m_scale, ms2, ms4, d->poly); 76 p = svmad_x (pg, m_scale, p, -0.5); 77 p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p)); 78 79 /* The scale factor to be applied back at the end - by multiplying float(k) 80 by 2^-23 we get the unbiased exponent of k. */ 81 svfloat32_t scale_back = svmul_x (pg, svcvt_f32_x (pg, k), d->exp_bias); 82 83 /* Apply the scaling back. */ 84 svfloat32_t y = svmla_x (pg, p, scale_back, d->ln2); 85 86 if (unlikely (svptest_any (pg, special))) 87 return special_case (x, y, special); 88 89 return y; 90 } 91 92 PL_SIG (SV, F, 1, log1p, -0.9, 10.0) 93 PL_TEST_ULP (SV_NAME_F1 (log1p), 0.77) 94 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (log1p), 0, 0x1p-23, 5000) 95 PL_TEST_SYM_INTERVAL (SV_NAME_F1 (log1p), 0x1p-23, 1, 5000) 96 PL_TEST_INTERVAL (SV_NAME_F1 (log1p), 1, inf, 10000) 97 PL_TEST_INTERVAL (SV_NAME_F1 (log1p), -1, -inf, 10) 98