1 /* 2 * Helper for SVE routines which calculate log(1 + x) and do not 3 * need special-case handling 4 * 5 * Copyright (c) 2023-2024, Arm Limited. 6 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 7 */ 8 9 #ifndef MATH_SV_LOG1PF_INLINE_H 10 #define MATH_SV_LOG1PF_INLINE_H 11 12 #define SignExponentMask 0xff800000 13 14 static const struct sv_log1pf_data 15 { 16 float c0, c2, c4, c6; 17 float c1, c3, c5, c7; 18 float ln2, exp_bias, quarter; 19 uint32_t four, three_quarters; 20 } sv_log1pf_data = { 21 /* Do not store first term of polynomial, which is -0.5, as 22 this can be fmov-ed directly instead of including it in 23 the main load-and-mla polynomial schedule. */ 24 .c0 = 0x1.5555aap-2f, .c1 = -0x1.000038p-2f, .c2 = 0x1.99675cp-3f, 25 .c3 = -0x1.54ef78p-3f, .c4 = 0x1.28a1f4p-3f, .c5 = -0x1.0da91p-3f, 26 .c6 = 0x1.abcb6p-4f, .c7 = -0x1.6f0d5ep-5f, .ln2 = 0x1.62e43p-1f, 27 .exp_bias = 0x1p-23f, .quarter = 0x1p-2f, .four = 0x40800000, 28 .three_quarters = 0x3f400000, 29 }; 30 31 static inline svfloat32_t 32 sv_log1pf_inline (svfloat32_t x, svbool_t pg) 33 { 34 const struct sv_log1pf_data *d = ptr_barrier (&sv_log1pf_data); 35 36 /* With x + 1 = t * 2^k (where t = m + 1 and k is chosen such that m 37 is in [-0.25, 0.5]): 38 log1p(x) = log(t) + log(2^k) = log1p(m) + k*log(2). 39 40 We approximate log1p(m) with a polynomial, then scale by 41 k*log(2). Instead of doing this directly, we use an intermediate 42 scale factor s = 4*k*log(2) to ensure the scale is representable 43 as a normalised fp32 number. */ 44 svfloat32_t m = svadd_x (pg, x, 1); 45 46 /* Choose k to scale x to the range [-1/4, 1/2]. */ 47 svint32_t k 48 = svand_x (pg, svsub_x (pg, svreinterpret_s32 (m), d->three_quarters), 49 sv_s32 (SignExponentMask)); 50 51 /* Scale x by exponent manipulation. */ 52 svfloat32_t m_scale = svreinterpret_f32 ( 53 svsub_x (pg, svreinterpret_u32 (x), svreinterpret_u32 (k))); 54 55 /* Scale up to ensure that the scale factor is representable as normalised 56 fp32 number, and scale m down accordingly. */ 57 svfloat32_t s = svreinterpret_f32 (svsubr_x (pg, k, d->four)); 58 svfloat32_t fconst = svld1rq_f32 (svptrue_b32 (), &d->ln2); 59 m_scale = svadd_x (pg, m_scale, svmla_lane_f32 (sv_f32 (-1), s, fconst, 2)); 60 61 /* Evaluate polynomial on reduced interval. */ 62 svfloat32_t ms2 = svmul_x (svptrue_b32 (), m_scale, m_scale); 63 64 svfloat32_t c1357 = svld1rq_f32 (svptrue_b32 (), &d->c1); 65 svfloat32_t p01 = svmla_lane_f32 (sv_f32 (d->c0), m_scale, c1357, 0); 66 svfloat32_t p23 = svmla_lane_f32 (sv_f32 (d->c2), m_scale, c1357, 1); 67 svfloat32_t p45 = svmla_lane_f32 (sv_f32 (d->c4), m_scale, c1357, 2); 68 svfloat32_t p67 = svmla_lane_f32 (sv_f32 (d->c6), m_scale, c1357, 3); 69 70 svfloat32_t p = svmla_x (pg, p45, p67, ms2); 71 p = svmla_x (pg, p23, p, ms2); 72 p = svmla_x (pg, p01, p, ms2); 73 74 p = svmad_x (pg, m_scale, p, -0.5); 75 p = svmla_x (pg, m_scale, m_scale, svmul_x (pg, m_scale, p)); 76 77 /* The scale factor to be applied back at the end - by multiplying float(k) 78 by 2^-23 we get the unbiased exponent of k. */ 79 svfloat32_t scale_back = svmul_lane_f32 (svcvt_f32_x (pg, k), fconst, 1); 80 return svmla_lane_f32 (p, scale_back, fconst, 0); 81 } 82 83 #endif // SV_LOG1PF_INLINE_H 84