1*f3087befSAndrew Turner /* 2*f3087befSAndrew Turner * Single-precision sinh(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 "mathlib.h" 9*f3087befSAndrew Turner #include "math_config.h" 10*f3087befSAndrew Turner #include "test_sig.h" 11*f3087befSAndrew Turner #include "test_defs.h" 12*f3087befSAndrew Turner 13*f3087befSAndrew Turner #define AbsMask 0x7fffffff 14*f3087befSAndrew Turner #define Half 0x3f000000 15*f3087befSAndrew Turner /* 0x1.62e43p+6, 2^7*ln2, minimum value for which expm1f overflows. */ 16*f3087befSAndrew Turner #define Expm1OFlowLimit 0x42b17218 17*f3087befSAndrew Turner /* 0x1.65a9fap+6, minimum positive value for which sinhf should overflow. */ 18*f3087befSAndrew Turner #define OFlowLimit 0x42b2d4fd 19*f3087befSAndrew Turner 20*f3087befSAndrew Turner /* Approximation for single-precision sinh(x) using expm1. 21*f3087befSAndrew Turner sinh(x) = (exp(x) - exp(-x)) / 2. 22*f3087befSAndrew Turner The maximum error is 2.26 ULP: 23*f3087befSAndrew Turner sinhf(0x1.e34a9ep-4) got 0x1.e469ep-4 want 0x1.e469e4p-4. */ 24*f3087befSAndrew Turner float 25*f3087befSAndrew Turner sinhf (float x) 26*f3087befSAndrew Turner { 27*f3087befSAndrew Turner uint32_t ix = asuint (x); 28*f3087befSAndrew Turner uint32_t iax = ix & AbsMask; 29*f3087befSAndrew Turner float ax = asfloat (iax); 30*f3087befSAndrew Turner uint32_t sign = ix & ~AbsMask; 31*f3087befSAndrew Turner float halfsign = asfloat (Half | sign); 32*f3087befSAndrew Turner 33*f3087befSAndrew Turner if (unlikely (iax >= Expm1OFlowLimit)) 34*f3087befSAndrew Turner { 35*f3087befSAndrew Turner /* Special values and overflow. */ 36*f3087befSAndrew Turner if (iax >= 0x7fc00001 || iax == 0x7f800000) 37*f3087befSAndrew Turner return x; 38*f3087befSAndrew Turner if (iax >= 0x7f800000) 39*f3087befSAndrew Turner return __math_invalidf (x); 40*f3087befSAndrew Turner if (iax >= OFlowLimit) 41*f3087befSAndrew Turner return __math_oflowf (sign); 42*f3087befSAndrew Turner 43*f3087befSAndrew Turner /* expm1f overflows a little before sinhf, (~88.7 vs ~89.4). We have to 44*f3087befSAndrew Turner fill this gap by using a different algorithm, in this case we use a 45*f3087befSAndrew Turner double-precision exp helper. For large x sinh(x) dominated by exp(x), 46*f3087befSAndrew Turner however we cannot compute exp without overflow either. We use the 47*f3087befSAndrew Turner identity: 48*f3087befSAndrew Turner exp(a) = (exp(a / 2)) ^ 2. 49*f3087befSAndrew Turner to compute sinh(x) ~= (exp(|x| / 2)) ^ 2 / 2 for x > 0 50*f3087befSAndrew Turner ~= (exp(|x| / 2)) ^ 2 / -2 for x < 0. 51*f3087befSAndrew Turner Greatest error in this region is 1.89 ULP: 52*f3087befSAndrew Turner sinhf(0x1.65898cp+6) got 0x1.f00aep+127 want 0x1.f00adcp+127. */ 53*f3087befSAndrew Turner float e = expf (ax / 2); 54*f3087befSAndrew Turner return (e * halfsign) * e; 55*f3087befSAndrew Turner } 56*f3087befSAndrew Turner 57*f3087befSAndrew Turner /* Use expm1f to retain acceptable precision for small numbers. 58*f3087befSAndrew Turner Let t = e^(|x|) - 1. */ 59*f3087befSAndrew Turner float t = expm1f (ax); 60*f3087befSAndrew Turner /* Then sinh(x) = (t + t / (t + 1)) / 2 for x > 0 61*f3087befSAndrew Turner (t + t / (t + 1)) / -2 for x < 0. */ 62*f3087befSAndrew Turner return (t + t / (t + 1)) * halfsign; 63*f3087befSAndrew Turner } 64*f3087befSAndrew Turner 65*f3087befSAndrew Turner TEST_SIG (S, F, 1, sinh, -10.0, 10.0) 66*f3087befSAndrew Turner TEST_ULP (sinhf, 1.76) 67*f3087befSAndrew Turner TEST_SYM_INTERVAL (sinhf, 0, 0x1.62e43p+6, 100000) 68*f3087befSAndrew Turner TEST_SYM_INTERVAL (sinhf, 0x1.62e43p+6, 0x1.65a9fap+6, 100) 69*f3087befSAndrew Turner TEST_SYM_INTERVAL (sinhf, 0x1.65a9fap+6, inf, 100) 70