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1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8 9#if __CLC_FPSIZE == 3210 11_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acosh(__CLC_GENTYPE x) {12 __CLC_UINTN ux = __CLC_AS_UINTN(x);13 14 // Arguments greater than 1/sqrt(epsilon) in magnitude are approximated by15 // acosh(x) = ln(2) + ln(x)16 // For 2.0 <= x <= 1/sqrt(epsilon) the approximation is:17 // acosh(x) = ln(x + sqrt(x * x - 1))18 __CLC_INTN high = ux > 0x46000000U;19 __CLC_INTN med = ux > 0x40000000U;20 21 __CLC_GENTYPE w = x - 1.0f;22 __CLC_GENTYPE s = w * w + 2.0f * w;23 __CLC_GENTYPE t = x * x - 1.0f;24 __CLC_GENTYPE r = __clc_sqrt(med ? t : s) + (med ? x : w);25 __CLC_GENTYPE v = (high ? x : r) - (med ? 1.0f : 0.0f);26 __CLC_GENTYPE z = __clc_log1p(v) + (high ? 0x1.62e430p-1f : 0.0f);27 28 z = __clc_select(z, x, __clc_isnan(x) || __clc_isinf(x));29 z = x < 1.0f ? __CLC_GENTYPE_NAN : z;30 31 return z;32}33 34#elif __CLC_FPSIZE == 6435 36_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acosh(__CLC_GENTYPE x) {37 // 1/sqrt(eps) = 9.49062656242515593767e+0738 const __CLC_GENTYPE recrteps = 0x1.6a09e667f3bcdp+26;39 // log2_lead and log2_tail sum to an extra-precise version of log(2)40 const __CLC_GENTYPE log2_lead = 0x1.62e42ep-1;41 const __CLC_GENTYPE log2_tail = 0x1.efa39ef35793cp-25;42 43 // Handle x >= 128 here44 __CLC_LONGN xlarge = x > recrteps;45 __CLC_GENTYPE r = x + __clc_sqrt(__clc_fma(x, x, -1.0));46 r = xlarge ? x : r;47 48 __CLC_INTN xexp;49 __CLC_GENTYPE r1, r2;50 __clc_ep_log(r, &xexp, &r1, &r2);51 52 __CLC_GENTYPE dxexp = __CLC_CONVERT_GENTYPE(53 __CLC_CONVERT_LONGN(xexp) + (xlarge ? (__CLC_LONGN)1 : (__CLC_LONGN)0));54 r1 = __clc_fma(dxexp, log2_lead, r1);55 r2 = __clc_fma(dxexp, log2_tail, r2);56 57 __CLC_GENTYPE ret1 = r1 + r2;58 59 // Handle 1 < x < 128 here60 // We compute the value61 // t = x - 1.0 + sqrt(2.0*(x - 1.0) + (x - 1.0)*(x - 1.0))62 // using simulated quad precision.63 __CLC_GENTYPE t = x - 1.0;64 __CLC_GENTYPE u1 = t * 2.0;65 66 // (t,0) * (t,0) -> (v1, v2)67 __CLC_GENTYPE v1 = t * t;68 __CLC_GENTYPE v2 = __clc_fma(t, t, -v1);69 70 // (u1,0) + (v1,v2) -> (w1,w2)71 r = u1 + v1;72 __CLC_GENTYPE s = (((u1 - r) + v1) + v2);73 __CLC_GENTYPE w1 = r + s;74 __CLC_GENTYPE w2 = (r - w1) + s;75 76 // sqrt(w1,w2) -> (u1,u2)77 __CLC_GENTYPE p1 = __clc_sqrt(w1);78 __CLC_GENTYPE a1 = p1 * p1;79 __CLC_GENTYPE a2 = __clc_fma(p1, p1, -a1);80 __CLC_GENTYPE temp = (((w1 - a1) - a2) + w2);81 __CLC_GENTYPE p2 = MATH_DIVIDE(temp * 0.5, p1);82 u1 = p1 + p2;83 __CLC_GENTYPE u2 = (p1 - u1) + p2;84 85 // (u1,u2) + (t,0) -> (r1,r2)86 r = u1 + t;87 s = ((u1 - r) + t) + u2;88 // r1 = r + s;89 // r2 = (r - r1) + s;90 // t = r1 + r2;91 t = r + s;92 93 // For arguments 1.13 <= x <= 1.5 the log1p function is good enough94 __CLC_GENTYPE ret2 = __clc_log1p(t);95 96 __CLC_GENTYPE ret = x >= 128.0 ? ret1 : ret2;97 98 ret = (__clc_isinf(x) || __clc_isnan(x)) ? x : ret;99 ret = x == 1.0 ? 0.0 : ret;100 ret = x < 1.0 ? __CLC_GENTYPE_NAN : ret;101 102 return ret;103}104 105#elif __CLC_FPSIZE == 16106 107_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_acosh(__CLC_GENTYPE x) {108 return __CLC_CONVERT_GENTYPE(__clc_acosh(__CLC_CONVERT_FLOATN(x)));109}110 111#endif112