1 /* 2 * Double-precision sinh(x) function. 3 * 4 * Copyright (c) 2022-2024, Arm Limited. 5 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6 */ 7 8 #include "math_config.h" 9 #include "test_sig.h" 10 #include "test_defs.h" 11 #include "exp_inline.h" 12 13 #define AbsMask 0x7fffffffffffffff 14 #define Half 0x3fe0000000000000 15 /* 0x1.62e42fefa39fp+9, above which using expm1 results in NaN. */ 16 #define OFlowBound 0x40862e42fefa39f0 17 18 /* Approximation for double-precision sinh(x) using expm1. 19 sinh(x) = (exp(x) - exp(-x)) / 2. 20 The greatest observed error is 2.57 ULP: 21 __v_sinh(0x1.9fb1d49d1d58bp-2) got 0x1.ab34e59d678dcp-2 22 want 0x1.ab34e59d678d9p-2. */ 23 double 24 sinh (double x) 25 { 26 uint64_t ix = asuint64 (x); 27 uint64_t iax = ix & AbsMask; 28 double ax = asdouble (iax); 29 uint64_t sign = ix & ~AbsMask; 30 double halfsign = asdouble (Half | sign); 31 32 if (unlikely (iax >= OFlowBound)) 33 { 34 /* Special values and overflow. */ 35 if (unlikely (iax > 0x7ff0000000000000)) 36 return __math_invalidf (x); 37 /* expm1 overflows a little before sinh. We have to fill this 38 gap by using a different algorithm, in this case we use a 39 double-precision exp helper. For large x sinh(x) is dominated 40 by exp(x), however we cannot compute exp without overflow 41 either. We use the identity: exp(a) = (exp(a / 2)) ^ 2 42 to compute sinh(x) ~= (exp(|x| / 2)) ^ 2 / 2 for x > 0 43 ~= (exp(|x| / 2)) ^ 2 / -2 for x < 0. */ 44 double e = exp_inline (ax / 2, 0); 45 return (e * halfsign) * e; 46 } 47 48 /* Use expm1f to retain acceptable precision for small numbers. 49 Let t = e^(|x|) - 1. */ 50 double t = expm1 (ax); 51 /* Then sinh(x) = (t + t / (t + 1)) / 2 for x > 0 52 (t + t / (t + 1)) / -2 for x < 0. */ 53 return (t + t / (t + 1)) * halfsign; 54 } 55 56 TEST_SIG (S, D, 1, sinh, -10.0, 10.0) 57 TEST_ULP (sinh, 2.08) 58 TEST_SYM_INTERVAL (sinh, 0, 0x1p-51, 100) 59 TEST_SYM_INTERVAL (sinh, 0x1p-51, 0x1.62e42fefa39fp+9, 100000) 60 TEST_SYM_INTERVAL (sinh, 0x1.62e42fefa39fp+9, inf, 1000) 61