libclc: Update asinh (#188219)
This was originally ported from rocm device libs in 2b4ef39b2f46acf29294f1fbb223ea5a243c2567. Merge in more recent changes.
This commit is contained in:
Matt Arsenault
GitHub
parent
25da0c8ddb
commit
80245f3b14
@ -8,15 +8,14 @@
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#include "clc/clc_convert.h"
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#include "clc/float/definitions.h"
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#include "clc/internal/clc.h"
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#include "clc/math/clc_ep_log.h"
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#include "clc/math/clc_asinh.h"
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#include "clc/math/clc_copysign.h"
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#include "clc/math/clc_ep.h"
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#include "clc/math/clc_fabs.h"
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#include "clc/math/clc_fma.h"
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#include "clc/math/clc_log.h"
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#include "clc/math/clc_log2_fast.h"
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#include "clc/math/clc_mad.h"
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#include "clc/math/clc_sqrt.h"
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#include "clc/math/math.h"
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#include "clc/relational/clc_isinf.h"
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#include "clc/math/clc_sqrt_fast.h"
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#include "clc/relational/clc_isfinite.h"
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#include "clc/relational/clc_isnan.h"
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#include "clc/relational/clc_select.h"
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@ -1,4 +1,5 @@
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//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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@ -7,304 +8,47 @@
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#if __CLC_FPSIZE == 32
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_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinh(__CLC_GENTYPE x) {
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__CLC_UINTN ux = __CLC_AS_UINTN(x);
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__CLC_UINTN ax = ux & EXSIGNBIT_SP32;
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__CLC_UINTN xsgn = ax ^ ux;
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_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_FLOATN __clc_asinh(__CLC_FLOATN x) {
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__CLC_FLOATN y = __clc_fabs(x);
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__CLC_INTN b = y >= 0x1.0p+64f;
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__CLC_FLOATN s = b ? 0x1.0p-64f : 1.0f;
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__CLC_FLOATN sy = y * s;
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__CLC_EP_PAIR a =
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__clc_ep_add(sy, __clc_ep_sqrt(__clc_ep_add(__clc_ep_sqr(sy), s * s)));
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__CLC_FLOATN z = __clc_ep_ln_hi(a, b ? 64 : 0);
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// |x| <= 2
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__CLC_GENTYPE t = x * x;
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__CLC_GENTYPE a =
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__clc_mad(t,
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__clc_mad(t,
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__clc_mad(t,
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__clc_mad(t, -1.177198915954942694e-4f,
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-4.162727710583425360e-2f),
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-5.063201055468483248e-1f),
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-1.480204186473758321f),
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-1.152965835871758072f);
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__CLC_GENTYPE b =
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__clc_mad(t,
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__clc_mad(t,
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__clc_mad(t,
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__clc_mad(t, 6.284381367285534560e-2f,
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1.260024978680227945f),
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6.582362487198468066f),
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11.99423176003939087f),
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6.917795026025976739f);
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z = y < 0x1.0p-12f ? y : z;
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z = y == __CLC_GENTYPE_INF ? y : z;
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__CLC_GENTYPE q = MATH_DIVIDE(a, b);
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__CLC_GENTYPE z1 = __clc_mad(x * t, q, x);
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// |x| > 2
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// Arguments greater than 1/sqrt(epsilon) in magnitude are
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// approximated by asinh(x) = ln(2) + ln(abs(x)), with sign of x
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// Arguments such that 4.0 <= abs(x) <= 1/sqrt(epsilon) are
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// approximated by asinhf(x) = ln(abs(x) + sqrt(x*x+1))
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// with the sign of x (see Abramowitz and Stegun 4.6.20)
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__CLC_GENTYPE absx = __clc_fabs(x);
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__CLC_INTN hi = ax > 0x46000000U;
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__CLC_GENTYPE y = __clc_sqrt(absx * absx + 1.0f) + absx;
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y = hi ? absx : y;
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__CLC_GENTYPE r = __clc_log(y) + (hi ? 0x1.62e430p-1f : 0.0f);
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__CLC_GENTYPE z2 = __CLC_AS_GENTYPE(xsgn | __CLC_AS_UINTN(r));
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__CLC_GENTYPE z = ax <= 0x40000000 ? z1 : z2;
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z = __clc_select(z, x, ax < 0x39800000U || __clc_isinf(x) || __clc_isnan(x));
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return z;
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return __clc_copysign(z, x);
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}
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#elif __CLC_FPSIZE == 64
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#define NA0 -0.12845379283524906084997e0
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#define NA1 -0.21060688498409799700819e0
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#define NA2 -0.10188951822578188309186e0
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#define NA3 -0.13891765817243625541799e-1
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#define NA4 -0.10324604871728082428024e-3
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_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_DOUBLEN __clc_asinh(__CLC_DOUBLEN x) {
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__CLC_DOUBLEN y = __clc_fabs(x);
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__CLC_LONGN b = y >= 0x1.0p+512;
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__CLC_DOUBLEN s = b ? 0x1.0p-512 : 1.0;
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__CLC_DOUBLEN sy = y * s;
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__CLC_EP_PAIR a =
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__clc_ep_add(sy, __clc_ep_sqrt(__clc_ep_add(__clc_ep_sqr(sy), s * s)));
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__CLC_DOUBLEN z = __clc_ep_ln_hi(a, __CLC_CONVERT_INTN(b) ? 512 : 0);
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#define DA0 0.77072275701149440164511e0
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#define DA1 0.16104665505597338100747e1
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#define DA2 0.11296034614816689554875e1
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#define DA3 0.30079351943799465092429e0
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#define DA4 0.235224464765951442265117e-1
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z = y < 0x1.0p-27 ? y : z;
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z = y == __CLC_GENTYPE_INF ? y : z;
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#define NB0 -0.12186605129448852495563e0
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#define NB1 -0.19777978436593069928318e0
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#define NB2 -0.94379072395062374824320e-1
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#define NB3 -0.12620141363821680162036e-1
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#define NB4 -0.903396794842691998748349e-4
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#define DB0 0.73119630776696495279434e0
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#define DB1 0.15157170446881616648338e1
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#define DB2 0.10524909506981282725413e1
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#define DB3 0.27663713103600182193817e0
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#define DB4 0.21263492900663656707646e-1
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#define NC0 -0.81210026327726247622500e-1
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#define NC1 -0.12327355080668808750232e0
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#define NC2 -0.53704925162784720405664e-1
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#define NC3 -0.63106739048128554465450e-2
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#define NC4 -0.35326896180771371053534e-4
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#define DC0 0.48726015805581794231182e0
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#define DC1 0.95890837357081041150936e0
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#define DC2 0.62322223426940387752480e0
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#define DC3 0.15028684818508081155141e0
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#define DC4 0.10302171620320141529445e-1
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#define ND0 -0.4638179204422665073e-1
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#define ND1 -0.7162729496035415183e-1
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#define ND2 -0.3247795155696775148e-1
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#define ND3 -0.4225785421291932164e-2
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#define ND4 -0.3808984717603160127e-4
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#define ND5 0.8023464184964125826e-6
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#define DD0 0.2782907534642231184e0
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#define DD1 0.5549945896829343308e0
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#define DD2 0.3700732511330698879e0
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#define DD3 0.9395783438240780722e-1
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#define DD4 0.7200057974217143034e-2
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#define NE0 -0.121224194072430701e-4
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#define NE1 -0.273145455834305218e-3
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#define NE2 -0.152866982560895737e-2
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#define NE3 -0.292231744584913045e-2
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#define NE4 -0.174670900236060220e-2
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#define NE5 -0.891754209521081538e-12
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#define DE0 0.499426632161317606e-4
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#define DE1 0.139591210395547054e-2
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#define DE2 0.107665231109108629e-1
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#define DE3 0.325809818749873406e-1
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#define DE4 0.415222526655158363e-1
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#define DE5 0.186315628774716763e-1
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#define NF0 -0.195436610112717345e-4
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#define NF1 -0.233315515113382977e-3
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#define NF2 -0.645380957611087587e-3
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#define NF3 -0.478948863920281252e-3
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#define NF4 -0.805234112224091742e-12
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#define NF5 0.246428598194879283e-13
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#define DF0 0.822166621698664729e-4
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#define DF1 0.135346265620413852e-2
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#define DF2 0.602739242861830658e-2
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#define DF3 0.972227795510722956e-2
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#define DF4 0.510878800983771167e-2
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#define NG0 -0.209689451648100728e-6
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#define NG1 -0.219252358028695992e-5
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#define NG2 -0.551641756327550939e-5
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#define NG3 -0.382300259826830258e-5
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#define NG4 -0.421182121910667329e-17
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#define NG5 0.492236019998237684e-19
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#define DG0 0.889178444424237735e-6
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#define DG1 0.131152171690011152e-4
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#define DG2 0.537955850185616847e-4
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#define DG3 0.814966175170941864e-4
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#define DG4 0.407786943832260752e-4
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#define NH0 -0.178284193496441400e-6
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#define NH1 -0.928734186616614974e-6
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#define NH2 -0.923318925566302615e-6
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#define NH3 -0.776417026702577552e-19
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#define NH4 0.290845644810826014e-21
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#define DH0 0.786694697277890964e-6
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#define DH1 0.685435665630965488e-5
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#define DH2 0.153780175436788329e-4
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#define DH3 0.984873520613417917e-5
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#define NI0 -0.538003743384069117e-10
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#define NI1 -0.273698654196756169e-9
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#define NI2 -0.268129826956403568e-9
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#define NI3 -0.804163374628432850e-29
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#define DI0 0.238083376363471960e-9
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#define DI1 0.203579344621125934e-8
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#define DI2 0.450836980450693209e-8
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#define DI3 0.286005148753497156e-8
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_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinh(__CLC_GENTYPE x) {
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const __CLC_GENTYPE rteps = 0x1.6a09e667f3bcdp-27;
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const __CLC_GENTYPE recrteps = 0x1.6a09e667f3bcdp+26;
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// log2_lead and log2_tail sum to an extra-precise version of log(2)
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const __CLC_GENTYPE log2_lead = 0x1.62e42ep-1;
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const __CLC_GENTYPE log2_tail = 0x1.efa39ef35793cp-25;
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__CLC_GENTYPE absx = __clc_fabs(x);
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__CLC_GENTYPE t = x * x;
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__CLC_GENTYPE pn, tn, pd, td;
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// XXX we are betting here that we can evaluate 8 pairs of
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// polys faster than we can grab 12 coefficients from a table
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// This also uses fewer registers
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// |x| >= 8
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pn = __clc_fma(t, __clc_fma(t, __clc_fma(t, NI3, NI2), NI1), NI0);
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pd = __clc_fma(t, __clc_fma(t, __clc_fma(t, DI3, DI2), DI1), DI0);
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tn = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NH4, NH3), NH2), NH1), NH0);
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td = __clc_fma(t, __clc_fma(t, __clc_fma(t, DH3, DH2), DH1), DH0);
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pn = absx < 8.0 ? tn : pn;
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pd = absx < 8.0 ? td : pd;
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tn = __clc_fma(
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t,
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__clc_fma(t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NG5, NG4), NG3), NG2),
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NG1),
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NG0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DG4, DG3), DG2), DG1), DG0);
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pn = absx < 4.0 ? tn : pn;
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pd = absx < 4.0 ? td : pd;
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tn = __clc_fma(
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t,
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__clc_fma(t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NF5, NF4), NF3), NF2),
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NF1),
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NF0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DF4, DF3), DF2), DF1), DF0);
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pn = absx < 2.0 ? tn : pn;
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pd = absx < 2.0 ? td : pd;
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tn = __clc_fma(
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t,
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__clc_fma(t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NE5, NE4), NE3), NE2),
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NE1),
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NE0);
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td = __clc_fma(
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t,
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__clc_fma(t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DE5, DE4), DE3), DE2),
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DE1),
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DE0);
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pn = absx < 1.5 ? tn : pn;
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pd = absx < 1.5 ? td : pd;
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tn = __clc_fma(
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t,
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__clc_fma(t, __clc_fma(t, __clc_fma(t, __clc_fma(t, ND5, ND4), ND3), ND2),
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ND1),
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ND0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DD4, DD3), DD2), DD1), DD0);
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pn = absx <= 1.0 ? tn : pn;
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pd = absx <= 1.0 ? td : pd;
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tn = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NC4, NC3), NC2), NC1), NC0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DC4, DC3), DC2), DC1), DC0);
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pn = absx < 0.75 ? tn : pn;
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pd = absx < 0.75 ? td : pd;
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tn = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NB4, NB3), NB2), NB1), NB0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DB4, DB3), DB2), DB1), DB0);
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pn = absx < 0.5 ? tn : pn;
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pd = absx < 0.5 ? td : pd;
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tn = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, NA4, NA3), NA2), NA1), NA0);
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td = __clc_fma(
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t, __clc_fma(t, __clc_fma(t, __clc_fma(t, DA4, DA3), DA2), DA1), DA0);
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pn = absx < 0.25 ? tn : pn;
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pd = absx < 0.25 ? td : pd;
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__CLC_GENTYPE pq = MATH_DIVIDE(pn, pd);
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// |x| <= 1
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__CLC_GENTYPE result1 = __clc_fma(absx * t, pq, absx);
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// Other ranges
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__CLC_LONGN xout = absx <= 32.0 || absx > recrteps;
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__CLC_GENTYPE y = absx + __clc_sqrt(__clc_fma(absx, absx, 1.0));
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y = xout ? absx : y;
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__CLC_GENTYPE r1, r2;
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__CLC_INTN xexp;
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__clc_ep_log(y, &xexp, &r1, &r2);
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__CLC_GENTYPE dxexp = __CLC_CONVERT_GENTYPE(
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__CLC_CONVERT_LONGN(xexp) + (xout ? (__CLC_LONGN)1 : (__CLC_LONGN)0));
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r1 = __clc_fma(dxexp, log2_lead, r1);
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r2 = __clc_fma(dxexp, log2_tail, r2);
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// 1 < x <= 32
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__CLC_GENTYPE v2 = (pq + 0.25) / t;
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__CLC_GENTYPE r = v2 + r1;
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__CLC_GENTYPE s = ((r1 - r) + v2) + r2;
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__CLC_GENTYPE v1 = r + s;
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v2 = (r - v1) + s;
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__CLC_GENTYPE result2 = v1 + v2;
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// x > 32
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__CLC_GENTYPE result3 = r1 + r2;
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__CLC_GENTYPE ret = absx > 1.0 ? result2 : result1;
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ret = absx > 32.0 ? result3 : ret;
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ret = x < 0.0 ? -ret : ret;
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// NaN, +-Inf, or x small enough that asinh(x) = x
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ret = __clc_select(
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ret, x,
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__CLC_CONVERT_LONGN(__clc_isnan(x) || __clc_isinf(x) || absx < rteps));
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||||
return ret;
|
||||
return __clc_copysign(z, x);
|
||||
}
|
||||
|
||||
#elif __CLC_FPSIZE == 16
|
||||
|
||||
_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_asinh(__CLC_GENTYPE x) {
|
||||
return __CLC_CONVERT_GENTYPE(__clc_asinh(__CLC_CONVERT_FLOATN(x)));
|
||||
_CLC_DEF _CLC_OVERLOAD _CLC_CONST __CLC_HALFN __clc_asinh(__CLC_HALFN hx) {
|
||||
__CLC_FLOATN x = __CLC_CONVERT_FLOATN(__clc_fabs(hx));
|
||||
__CLC_FLOATN t = x + __clc_sqrt_fast(__clc_mad(x, x, 1.0f));
|
||||
__CLC_HALFN ret = __clc_copysign(
|
||||
__CLC_CONVERT_HALFN(__clc_log2_fast(t) * 0x1.62e430p-1f), hx);
|
||||
|
||||
return __clc_isfinite(hx) ? ret : hx;
|
||||
}
|
||||
|
||||
#endif
|
||||
|
||||
Loading…
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Reference in New Issue
Block a user