1 /* 2 * Single-precision cosh(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 "math_config.h" 9 #include "pl_sig.h" 10 #include "pl_test.h" 11 12 #define AbsMask 0x7fffffff 13 #define TinyBound 0x20000000 /* 0x1p-63: Round to 1 below this. */ 14 #define SpecialBound \ 15 0x42ad496c /* 0x1.5a92d8p+6: expf overflows above this, so have to use \ 16 special case. */ 17 18 float 19 optr_aor_exp_f32 (float); 20 21 static NOINLINE float 22 specialcase (float x, uint32_t iax) 23 { 24 if (iax == 0x7f800000) 25 return INFINITY; 26 if (iax > 0x7f800000) 27 return __math_invalidf (x); 28 if (iax <= TinyBound) 29 /* For tiny x, avoid underflow by just returning 1. */ 30 return 1; 31 /* Otherwise SpecialBound <= |x| < Inf. x is too large to calculate exp(x) 32 without overflow, so use exp(|x|/2) instead. For large x cosh(x) is 33 dominated by exp(x), so return: 34 cosh(x) ~= (exp(|x|/2))^2 / 2. */ 35 float t = optr_aor_exp_f32 (asfloat (iax) / 2); 36 return (0.5 * t) * t; 37 } 38 39 /* Approximation for single-precision cosh(x) using exp. 40 cosh(x) = (exp(x) + exp(-x)) / 2. 41 The maximum error is 1.89 ULP, observed for |x| > SpecialBound: 42 coshf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127. 43 The maximum error observed for TinyBound < |x| < SpecialBound is 1.02 ULP: 44 coshf(0x1.50a3cp+0) got 0x1.ff21dcp+0 want 0x1.ff21dap+0. */ 45 float 46 coshf (float x) 47 { 48 uint32_t ix = asuint (x); 49 uint32_t iax = ix & AbsMask; 50 float ax = asfloat (iax); 51 52 if (unlikely (iax <= TinyBound || iax >= SpecialBound)) 53 { 54 /* x is tiny, large or special. */ 55 return specialcase (x, iax); 56 } 57 58 /* Compute cosh using the definition: 59 coshf(x) = exp(x) / 2 + exp(-x) / 2. */ 60 float t = optr_aor_exp_f32 (ax); 61 return 0.5f * t + 0.5f / t; 62 } 63 64 PL_SIG (S, F, 1, cosh, -10.0, 10.0) 65 PL_TEST_ULP (coshf, 1.89) 66 PL_TEST_INTERVAL (coshf, 0, 0x1p-63, 100) 67 PL_TEST_INTERVAL (coshf, 0, 0x1.5a92d8p+6, 80000) 68 PL_TEST_INTERVAL (coshf, 0x1.5a92d8p+6, inf, 2000) 69 PL_TEST_INTERVAL (coshf, -0, -0x1p-63, 100) 70 PL_TEST_INTERVAL (coshf, -0, -0x1.5a92d8p+6, 80000) 71 PL_TEST_INTERVAL (coshf, -0x1.5a92d8p+6, -inf, 2000) 72