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 "estrinf.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 #define C(i) __asinhf_data.coeffs[i] 20 21 float 22 optr_aor_log_f32 (float); 23 24 /* asinhf approximation using a variety of approaches on different intervals: 25 26 |x| < 2^-12: Return x. Function is exactly rounded in this region. 27 28 |x| < 1.0: Use custom order-8 polynomial. The largest observed 29 error in this region is 1.3ulps: 30 asinhf(0x1.f0f74cp-1) got 0x1.b88de4p-1 want 0x1.b88de2p-1. 31 32 |x| <= SqrtFltMax: Calculate the result directly using the 33 definition of asinh(x) = ln(x + sqrt(x*x + 1)). The largest 34 observed error in this region is 1.99ulps. 35 asinhf(0x1.00e358p+0) got 0x1.c4849ep-1 want 0x1.c484a2p-1. 36 37 |x| > SqrtFltMax: We cannot square x without overflow at a low 38 cost. At very large x, asinh(x) ~= ln(2x). At huge x we cannot 39 even double x without overflow, so calculate this as ln(x) + 40 ln(2). This largest observed error in this region is 3.39ulps. 41 asinhf(0x1.749e9ep+10) got 0x1.fffff8p+2 want 0x1.fffffep+2. */ 42 float 43 asinhf (float x) 44 { 45 uint32_t ix = asuint (x); 46 uint32_t ia = ix & AbsMask; 47 uint32_t ia12 = ia >> 20; 48 float ax = asfloat (ia); 49 uint32_t sign = ix & ~AbsMask; 50 51 if (unlikely (ia12 < ExpM12 || ia == 0x7f800000)) 52 return x; 53 54 if (unlikely (ia12 >= 0x7f8)) 55 return __math_invalidf (x); 56 57 if (ia12 < One) 58 { 59 float x2 = ax * ax; 60 float p = ESTRIN_7 (ax, x2, x2 * x2, C); 61 float y = fmaf (x2, p, ax); 62 return asfloat (asuint (y) | sign); 63 } 64 65 if (unlikely (ax > SqrtFltMax)) 66 { 67 return asfloat (asuint (optr_aor_log_f32 (ax) + Ln2) | sign); 68 } 69 70 return asfloat (asuint (optr_aor_log_f32 (ax + sqrtf (ax * ax + 1))) | sign); 71 } 72 73 PL_SIG (S, F, 1, asinh, -10.0, 10.0) 74 PL_TEST_ULP (asinhf, 2.9) 75 PL_TEST_INTERVAL (asinhf, 0, 0x1p-12, 5000) 76 PL_TEST_INTERVAL (asinhf, 0x1p-12, 1.0, 50000) 77 PL_TEST_INTERVAL (asinhf, 1.0, 0x1p11, 50000) 78 PL_TEST_INTERVAL (asinhf, 0x1p11, 0x1p127, 20000) 79