1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Double-precision cosh(x) function. 3*f3087befSAndrew Turner * 4*f3087befSAndrew Turner * Copyright (c) 2022-2024, Arm Limited. 5*f3087befSAndrew Turner * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception 6*f3087befSAndrew Turner */ 7*f3087befSAndrew Turner 8*f3087befSAndrew Turner #include "math_config.h" 9*f3087befSAndrew Turner #include "test_sig.h" 10*f3087befSAndrew Turner #include "test_defs.h" 11*f3087befSAndrew Turner #include "exp_inline.h" 12*f3087befSAndrew Turner 13*f3087befSAndrew Turner #define AbsMask 0x7fffffffffffffff 14*f3087befSAndrew Turner #define SpecialBound \ 15*f3087befSAndrew Turner 0x40861da04cbafe44 /* 0x1.61da04cbafe44p+9, above which exp overflows. */ 16*f3087befSAndrew Turner 17*f3087befSAndrew Turner static double 18*f3087befSAndrew Turner specialcase (double x, uint64_t iax) 19*f3087befSAndrew Turner { 20*f3087befSAndrew Turner if (iax == 0x7ff0000000000000) 21*f3087befSAndrew Turner return INFINITY; 22*f3087befSAndrew Turner if (iax > 0x7ff0000000000000) 23*f3087befSAndrew Turner return __math_invalid (x); 24*f3087befSAndrew Turner /* exp overflows above SpecialBound. At this magnitude cosh(x) is dominated 25*f3087befSAndrew Turner by exp(x), so we can approximate cosh(x) by (exp(|x|/2)) ^ 2 / 2. */ 26*f3087befSAndrew Turner double t = exp_inline (asdouble (iax) / 2, 0); 27*f3087befSAndrew Turner return (0.5 * t) * t; 28*f3087befSAndrew Turner } 29*f3087befSAndrew Turner 30*f3087befSAndrew Turner /* Approximation for double-precision cosh(x). 31*f3087befSAndrew Turner cosh(x) = (exp(x) + exp(-x)) / 2. 32*f3087befSAndrew Turner The greatest observed error is in the special region, 1.93 ULP: 33*f3087befSAndrew Turner cosh(0x1.628af341989dap+9) got 0x1.fdf28623ef921p+1021 34*f3087befSAndrew Turner want 0x1.fdf28623ef923p+1021. 35*f3087befSAndrew Turner 36*f3087befSAndrew Turner The greatest observed error in the non-special region is 1.03 ULP: 37*f3087befSAndrew Turner cosh(0x1.502cd8e56ab3bp+0) got 0x1.fe54962842d0ep+0 38*f3087befSAndrew Turner want 0x1.fe54962842d0fp+0. */ 39*f3087befSAndrew Turner double 40*f3087befSAndrew Turner cosh (double x) 41*f3087befSAndrew Turner { 42*f3087befSAndrew Turner uint64_t ix = asuint64 (x); 43*f3087befSAndrew Turner uint64_t iax = ix & AbsMask; 44*f3087befSAndrew Turner 45*f3087befSAndrew Turner /* exp overflows a little bit before cosh, so use special-case handler for 46*f3087befSAndrew Turner the gap, as well as special values. */ 47*f3087befSAndrew Turner if (unlikely (iax >= SpecialBound)) 48*f3087befSAndrew Turner return specialcase (x, iax); 49*f3087befSAndrew Turner 50*f3087befSAndrew Turner double ax = asdouble (iax); 51*f3087befSAndrew Turner /* Use double-precision exp helper to calculate exp(x), then: 52*f3087befSAndrew Turner cosh(x) = exp(|x|) / 2 + 1 / (exp(|x| * 2). */ 53*f3087befSAndrew Turner double t = exp_inline (ax, 0); 54*f3087befSAndrew Turner return 0.5 * t + 0.5 / t; 55*f3087befSAndrew Turner } 56*f3087befSAndrew Turner 57*f3087befSAndrew Turner TEST_SIG (S, D, 1, cosh, -10.0, 10.0) 58*f3087befSAndrew Turner TEST_ULP (cosh, 1.43) 59*f3087befSAndrew Turner TEST_SYM_INTERVAL (cosh, 0, 0x1.61da04cbafe44p+9, 100000) 60*f3087befSAndrew Turner TEST_SYM_INTERVAL (cosh, 0x1.61da04cbafe44p+9, 0x1p10, 1000) 61*f3087befSAndrew Turner TEST_SYM_INTERVAL (cosh, 0x1p10, inf, 100) 62