1 /* 2 * Single-precision asinh(x) function. 3 * 4 * Copyright (c) 2022-2023, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "poly_scalar_f32.h" 9 #include "math_config.h" 10 #include "pl_sig.h" 11 #include "pl_test.h" 12 13 #define AbsMask (0x7fffffff) 14 #define SqrtFltMax (0x1.749e96p+10f) 15 #define Ln2 (0x1.62e4p-1f) 16 #define One (0x3f8) 17 #define ExpM12 (0x398) 18 19 float 20 optr_aor_log_f32 (float); 21 22 /* asinhf approximation using a variety of approaches on different intervals: 23 24 |x| < 2^-12: Return x. Function is exactly rounded in this region. 25 26 |x| < 1.0: Use custom order-8 polynomial. The largest observed 27 error in this region is 1.3ulps: 28 asinhf(0x1.f0f74cp-1) got 0x1.b88de4p-1 want 0x1.b88de2p-1. 29 30 |x| <= SqrtFltMax: Calculate the result directly using the 31 definition of asinh(x) = ln(x + sqrt(x*x + 1)). The largest 32 observed error in this region is 1.99ulps. 33 asinhf(0x1.00e358p+0) got 0x1.c4849ep-1 want 0x1.c484a2p-1. 34 35 |x| > SqrtFltMax: We cannot square x without overflow at a low 36 cost. At very large x, asinh(x) ~= ln(2x). At huge x we cannot 37 even double x without overflow, so calculate this as ln(x) + 38 ln(2). This largest observed error in this region is 3.39ulps. 39 asinhf(0x1.749e9ep+10) got 0x1.fffff8p+2 want 0x1.fffffep+2. */ 40 float 41 asinhf (float x) 42 { 43 uint32_t ix = asuint (x); 44 uint32_t ia = ix & AbsMask; 45 uint32_t ia12 = ia >> 20; 46 float ax = asfloat (ia); 47 uint32_t sign = ix & ~AbsMask; 48 49 if (unlikely (ia12 < ExpM12 || ia == 0x7f800000)) 50 return x; 51 52 if (unlikely (ia12 >= 0x7f8)) 53 return __math_invalidf (x); 54 55 if (ia12 < One) 56 { 57 float x2 = ax * ax; 58 float p = estrin_7_f32 (ax, x2, x2 * x2, __asinhf_data.coeffs); 59 float y = fmaf (x2, p, ax); 60 return asfloat (asuint (y) | sign); 61 } 62 63 if (unlikely (ax > SqrtFltMax)) 64 { 65 return asfloat (asuint (optr_aor_log_f32 (ax) + Ln2) | sign); 66 } 67 68 return asfloat (asuint (optr_aor_log_f32 (ax + sqrtf (ax * ax + 1))) | sign); 69 } 70 71 PL_SIG (S, F, 1, asinh, -10.0, 10.0) 72 PL_TEST_ULP (asinhf, 2.9) 73 PL_TEST_INTERVAL (asinhf, 0, 0x1p-12, 5000) 74 PL_TEST_INTERVAL (asinhf, 0x1p-12, 1.0, 50000) 75 PL_TEST_INTERVAL (asinhf, 1.0, 0x1p11, 50000) 76 PL_TEST_INTERVAL (asinhf, 0x1p11, 0x1p127, 20000) 77