1 /* 2 * Double-precision SVE sinh(x) 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 "poly_sve_f64.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 static const struct data 14 { 15 float64_t poly[11]; 16 float64_t inv_ln2, m_ln2_hi, m_ln2_lo, shift; 17 uint64_t halff; 18 int64_t onef; 19 uint64_t large_bound; 20 } data = { 21 /* Generated using Remez, deg=12 in [-log(2)/2, log(2)/2]. */ 22 .poly = { 0x1p-1, 0x1.5555555555559p-3, 0x1.555555555554bp-5, 23 0x1.111111110f663p-7, 0x1.6c16c16c1b5f3p-10, 24 0x1.a01a01affa35dp-13, 0x1.a01a018b4ecbbp-16, 25 0x1.71ddf82db5bb4p-19, 0x1.27e517fc0d54bp-22, 26 0x1.af5eedae67435p-26, 0x1.1f143d060a28ap-29, }, 27 28 .inv_ln2 = 0x1.71547652b82fep0, 29 .m_ln2_hi = -0x1.62e42fefa39efp-1, 30 .m_ln2_lo = -0x1.abc9e3b39803fp-56, 31 .shift = 0x1.8p52, 32 33 .halff = 0x3fe0000000000000, 34 .onef = 0x3ff0000000000000, 35 /* 2^9. expm1 helper overflows for large input. */ 36 .large_bound = 0x4080000000000000, 37 }; 38 39 static inline svfloat64_t 40 expm1_inline (svfloat64_t x, svbool_t pg) 41 { 42 const struct data *d = ptr_barrier (&data); 43 44 /* Reduce argument: 45 exp(x) - 1 = 2^i * (expm1(f) + 1) - 1 46 where i = round(x / ln2) 47 and f = x - i * ln2 (f in [-ln2/2, ln2/2]). */ 48 svfloat64_t j 49 = svsub_x (pg, svmla_x (pg, sv_f64 (d->shift), x, d->inv_ln2), d->shift); 50 svint64_t i = svcvt_s64_x (pg, j); 51 svfloat64_t f = svmla_x (pg, x, j, d->m_ln2_hi); 52 f = svmla_x (pg, f, j, d->m_ln2_lo); 53 /* Approximate expm1(f) using polynomial. */ 54 svfloat64_t f2 = svmul_x (pg, f, f); 55 svfloat64_t f4 = svmul_x (pg, f2, f2); 56 svfloat64_t f8 = svmul_x (pg, f4, f4); 57 svfloat64_t p 58 = svmla_x (pg, f, f2, sv_estrin_10_f64_x (pg, f, f2, f4, f8, d->poly)); 59 /* t = 2^i. */ 60 svfloat64_t t = svscale_x (pg, sv_f64 (1), i); 61 /* expm1(x) ~= p * t + (t - 1). */ 62 return svmla_x (pg, svsub_x (pg, t, 1.0), p, t); 63 } 64 65 static svfloat64_t NOINLINE 66 special_case (svfloat64_t x, svbool_t pg) 67 { 68 return sv_call_f64 (sinh, x, x, pg); 69 } 70 71 /* Approximation for SVE double-precision sinh(x) using expm1. 72 sinh(x) = (exp(x) - exp(-x)) / 2. 73 The greatest observed error is 2.57 ULP: 74 _ZGVsMxv_sinh (0x1.a008538399931p-2) got 0x1.ab929fc64bd66p-2 75 want 0x1.ab929fc64bd63p-2. */ 76 svfloat64_t SV_NAME_D1 (sinh) (svfloat64_t x, svbool_t pg) 77 { 78 const struct data *d = ptr_barrier (&data); 79 80 svfloat64_t ax = svabs_x (pg, x); 81 svuint64_t sign 82 = sveor_x (pg, svreinterpret_u64 (x), svreinterpret_u64 (ax)); 83 svfloat64_t halfsign = svreinterpret_f64 (svorr_x (pg, sign, d->halff)); 84 85 svbool_t special = svcmpge (pg, svreinterpret_u64 (ax), d->large_bound); 86 87 /* Fall back to scalar variant for all lanes if any are special. */ 88 if (unlikely (svptest_any (pg, special))) 89 return special_case (x, pg); 90 91 /* Up to the point that expm1 overflows, we can use it to calculate sinh 92 using a slight rearrangement of the definition of sinh. This allows us to 93 retain acceptable accuracy for very small inputs. */ 94 svfloat64_t t = expm1_inline (ax, pg); 95 t = svadd_x (pg, t, svdiv_x (pg, t, svadd_x (pg, t, 1.0))); 96 return svmul_x (pg, t, halfsign); 97 } 98 99 PL_SIG (SV, D, 1, sinh, -10.0, 10.0) 100 PL_TEST_ULP (SV_NAME_D1 (sinh), 2.08) 101 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0, 0x1p-26, 1000) 102 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p-26, 0x1p9, 500000) 103 PL_TEST_SYM_INTERVAL (SV_NAME_D1 (sinh), 0x1p9, inf, 1000) 104