1 /* 2 * Double-precision cosh(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 SpecialBound \ 15 0x40861da04cbafe44 /* 0x1.61da04cbafe44p+9, above which exp overflows. */ 16 17 static double 18 specialcase (double x, uint64_t iax) 19 { 20 if (iax == 0x7ff0000000000000) 21 return INFINITY; 22 if (iax > 0x7ff0000000000000) 23 return __math_invalid (x); 24 /* exp overflows above SpecialBound. At this magnitude cosh(x) is dominated 25 by exp(x), so we can approximate cosh(x) by (exp(|x|/2)) ^ 2 / 2. */ 26 double t = exp_inline (asdouble (iax) / 2, 0); 27 return (0.5 * t) * t; 28 } 29 30 /* Approximation for double-precision cosh(x). 31 cosh(x) = (exp(x) + exp(-x)) / 2. 32 The greatest observed error is in the special region, 1.93 ULP: 33 cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021 34 want 0x1.fdf28623ef923p+1021. 35 36 The greatest observed error in the non-special region is 1.03 ULP: 37 cosh(0x1.502cd8e56ab3bp+0) got 0x1.fe54962842d0ep+0 38 want 0x1.fe54962842d0fp+0. */ 39 double 40 cosh (double x) 41 { 42 uint64_t ix = asuint64 (x); 43 uint64_t iax = ix & AbsMask; 44 45 /* exp overflows a little bit before cosh, so use special-case handler for 46 the gap, as well as special values. */ 47 if (unlikely (iax >= SpecialBound)) 48 return specialcase (x, iax); 49 50 double ax = asdouble (iax); 51 /* Use double-precision exp helper to calculate exp(x), then: 52 cosh(x) = exp(|x|) / 2 + 1 / (exp(|x| * 2). */ 53 double t = exp_inline (ax, 0); 54 return 0.5 * t + 0.5 / t; 55 } 56 57 TEST_SIG (S, D, 1, cosh, -10.0, 10.0) 58 TEST_ULP (cosh, 1.43) 59 TEST_SYM_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000) 60 TEST_SYM_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000) 61 TEST_SYM_INTERVAL (cosh, 0x1p10, inf, 100) 62