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|
.file "asinhf.s"
// Copyright (c) 2000 - 2003, Intel Corporation
// All rights reserved.
//
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// ==============================================================
// History
// ==============================================================
// 04/02/01 Initial version
// 04/19/01 Improved speed of the paths #1,2,3,4,5
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 05/21/03 Improved performance, fixed to handle unorms
//
// API
// ==============================================================
// float asinhf(float)
//
// Overview of operation
// ==============================================================
//
// There are 7 paths:
// 1. x = 0.0
// Return asinhf(x) = 0.0
// 2. 0.0 <|x| < 2^(-5)
// Return asinhf(x) = Pol5(x), where Pol5(x) = ((x^2)*C1 + C0)*x^3 + x
// 3. 2^(-5) <= |x| < 2^51
// Return asinhf(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
// To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
// (2 iterations)
// Algorithm description for log function see below.
//
// 4. 2^51 <= |x| < +INF
// Return asinhf(x) = sign(x)*log(2*|x|)
// Algorithm description for log function see below.
//
// 5. x = INF
// Return asinhf(x) = INF
//
// 6. x = [S,Q]NaN
// Return asinhf(x) = QNaN
//
// 7. x = denormal
// Return asinhf(x) = x
//
//==============================================================
// Algorithm Description for log(x) function
// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
// true for this asinh implementation
//
// Consider x = 2^N 1.f1 f2 f3 f4...f63
// Log(x) = log(frcpa(x) x/frcpa(x))
// = log(1/frcpa(x)) + log(frcpa(x) x)
// = -log(frcpa(x)) + log(frcpa(x) x)
//
// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
//
// -log(frcpa(x)) = -log(C)
// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C)
// = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C)
// = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
//
// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
//
// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
// Log(x) = +Nlog2 + T + log(frcpa(x) x)
//
// Log(x) = +Nlog2 + T + log(C x)
//
// Cx = 1 + r
//
// Log(x) = +Nlog2 + T + log(1+r)
// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
//
// 1.f1 f2 ... f8 has 256 entries.
// They are 1 + k/2^8, k = 0 ... 255
// These 256 values are the table entries.
//
// Implementation
//==============================================================
// C = frcpa(x)
// r = C * x - 1
//
// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
//
// x = f * 2*n where f is 1.f_1f_2f_3....f_63
// Nfloat = float(n) where n is the true unbiased exponent
// pre-index = f_1f_2....f_8
// index = pre_index * 8
// get the dxt table entry at index + offset = T
//
// result = (T + Nfloat * log(2)) + rseries
//
// The T table is calculated as follows
// Form x_k = 1 + k/2^8 where k goes from 0... 255
// y_k = frcpa(x_k)
// log(1/y_k) in quad and round to double-extended
//
//
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f9 -> f15, f32 -> f55
// General registers used:
// r14 -> r27
// Predicate registers used:
// p6 -> p14
// p6 to filter out case when x = [Q,S]NaN or INF or zero
// p7 to filter out case when x < 0.0
// p8 to select path #2
// p11 to filter out case when x >= 0
// p12 to filter out case when x = + denormal
// p13 to select path #4
// p14 to filtef out case when x = - denormal
// Assembly macros
//==============================================================
log_GR_exp_17_ones = r14
log_GR_signexp_f8 = r15
log_table_address2 = r16
log_GR_exp_16_ones = r17
log_GR_exp_f8 = r18
log_GR_true_exp_f8 = r19
log_GR_significand_f8 = r20
log_GR_index = r21
log_GR_comp2 = r22
asinh_GR_f8 = r23
asinh_GR_comp = r24
asinh_GR_f8 = r25
log_table_address3 = r26
NR_table_address = r27
//==============================================================
log_y = f9
NR1 = f10
NR2 = f11
log_y_rs = f12
log_y_rs_iter = f13
log_y_rs_iter1 = f14
fNormX = f15
asinh_w_sq = f32
log_arg_early = f33
log_y_rs_iter2 = f34
log_P3 = f35
log_P2 = f36
log_P1 = f37
log2 = f38
log_C0 = f39
log_C1 = f40
asinh_f8 = f41
log_C = f42
log_arg = f43
asinh_w_cube = f44
log_int_Nfloat = f45
log_r = f46
log_rsq = f47
asinh_w_1 = f48
log_rp_p32 = f49
log_rcube = f50
log_rp_p10 = f51
log_rp_p2 = f52
log_Nfloat = f53
log_T = f54
log_T_plus_Nlog2 = f55
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(log_table_1)
data8 0xbfd0001008f39d59 // p3
data8 0x3fd5556073e0c45a // p2
data8 0xbfdffffffffaea15 // p1
data8 0x3fe62e42fefa39ef // log(2)
LOCAL_OBJECT_END(log_table_1)
LOCAL_OBJECT_START(log_table_2)
data8 0x3FE0000000000000 // 0.5
data8 0x4008000000000000 // 3.0
data8 0x9979C79685A5EB16, 0x00003FFB // C1 3FFB9979C79685A5EB16
data8 0xAAAAA96F80786D62, 0x0000BFFC // C0 BFFCAAAAA96F80786D62
LOCAL_OBJECT_END(log_table_2)
LOCAL_OBJECT_START(log_table_3)
data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)
data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)
data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)
data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)
data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)
data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)
data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)
data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)
data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)
data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)
data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)
data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)
data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)
data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)
data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)
data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)
data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)
data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)
data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)
data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)
data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)
data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)
data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)
data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)
data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)
data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)
data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)
data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)
data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)
data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)
data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)
data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)
data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)
data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)
data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)
data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)
data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)
data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)
data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)
data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)
data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)
data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)
data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)
data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)
data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)
data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)
data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)
data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)
data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)
data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)
data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)
data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)
data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)
data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)
data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)
data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)
data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)
data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)
data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)
data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)
data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)
data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)
data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)
data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)
data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)
data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)
data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)
data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)
data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)
data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)
data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)
data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)
data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)
data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)
data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)
data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)
data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)
data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)
data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)
data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)
data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)
data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)
data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)
data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)
data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)
data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)
data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)
data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)
data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)
data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)
data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)
data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)
data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)
data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)
data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)
data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)
data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)
data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)
data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)
data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)
data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)
data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)
data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)
data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)
data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)
data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)
data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)
data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)
data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)
data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)
data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)
data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)
data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)
data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)
data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)
data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)
data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)
data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)
data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)
data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)
data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)
data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)
data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)
data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)
data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)
data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)
data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)
data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)
data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)
data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)
data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)
data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)
data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)
data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)
data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)
data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)
data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)
data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)
data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)
data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)
data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)
data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)
data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)
data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)
data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)
data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)
data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)
data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)
data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)
data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)
data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)
data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)
data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)
data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)
data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)
data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)
data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)
data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)
data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)
data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)
data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)
data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)
data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)
data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)
data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)
data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)
data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)
data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)
data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)
data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)
data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)
data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)
data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)
data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)
data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)
data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)
data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)
data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)
data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)
data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)
data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)
data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)
data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)
data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)
data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)
data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)
data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)
data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)
data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)
data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)
data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)
data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)
data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)
data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)
data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)
data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)
data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)
data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)
data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)
data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)
data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)
data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)
data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)
data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)
data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)
data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)
data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)
data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)
data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)
data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)
data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)
data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)
data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)
data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)
data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)
data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)
data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)
data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)
data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)
data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)
data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)
data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)
data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)
data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)
data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)
data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)
data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)
data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)
data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)
data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)
data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)
data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)
data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)
data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)
data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)
data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)
data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)
data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)
data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)
data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)
data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)
data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)
data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)
data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)
data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)
data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)
data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)
data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)
data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)
data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)
data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)
data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)
data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)
data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)
data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)
data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
LOCAL_OBJECT_END(log_table_3)
.section .text
GLOBAL_LIBM_ENTRY(asinhf)
{ .mfi
getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
fclass.m p12,p0 = f8, 0x0b // Test x unorm
mov log_GR_exp_17_ones = 0x1ffff
}
{ .mfi
addl NR_table_address = @ltoff(log_table_1), gp
fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
mov asinh_GR_comp = 0xfffa
}
;;
{ .mfi
mov log_GR_exp_16_ones = 0xffff //BIAS
fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
mov log_GR_comp2 = 0x10032
}
{ .mfi
ld8 NR_table_address = [NR_table_address]
fma.s1 asinh_w_sq = f8,f8,f0 // x^2
nop.i 0
}
;;
{ .mfi
nop.m 0
fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
nop.i 0
}
{ .mfb
nop.m 0
fnorm.s1 fNormX = f8 // Normalize x
(p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
}
;;
ASINH_COMMON:
// Return here if x=unorm and not denorm
{ .mfi
//to get second table address
adds log_table_address2 = 0x20, NR_table_address
fma.s1 log_arg = f8,f1,f8
}
{ .mfb
nop.m 0
(p6) fma.s.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
(p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
}
;;
{ .mfi
ldfpd NR1,NR2 = [log_table_address2],16
frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
nop.i 0
}
;;
{ .mfi
ldfe log_C1 = [log_table_address2],16
nop.f 0
and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
}
;;
{ .mib
ldfe log_C0 = [log_table_address2],16
cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
(p13) br.cond.spnt LOG_COMMON1 // Branch if path 4: |x| >= 2^51
}
;;
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) mov asinh_f8 = fNormX
nop.i 0
}
{ .mfb
cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
(p7) fnma.s1 asinh_f8 = fNormX,f1,f0
(p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2: 0 < |x| < 2^-5
}
;;
// Here if main path, 2^-5 <= |x| < 2^51
///////////////////////////////// The first iteration /////////////////////////
{ .mfi
ldfpd log_P3,log_P2 = [NR_table_address],16
fnma.s1 log_y_rs_iter2 = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
nop.i 0
}
;;
{ .mfi
ldfpd log_P1,log2 = [NR_table_address],16
// (0.5*z)*(3-(y*z)*z)
fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter2,f0
nop.i 0
}
{ .mfi
nop.m 0
// (0.5*z)*(3-(y*z)*z)
fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs_iter2,f0
nop.i 0
}
;;
////////////////////////////////// The second iteration ////////////////////////
{ .mfi
nop.m 0
fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
nop.i 0
}
;;
{ .mfi
nop.m 0
fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
frcpa.s1 log_C,p0 = f1,log_arg_early
nop.i 0
}
;;
{ .mfi
getf.exp log_GR_signexp_f8 = log_arg_early
nop.f 0
nop.i 0
}
;;
{ .mfi
getf.sig log_GR_significand_f8 = log_arg_early
// (0.5*z)*(3-(y*z)*z)*y + |x|
fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
//to get third table address
adds log_table_address3 = 0x30, NR_table_address
}
;;
/////////////////////////////////////////// The end NR iterations /////////////
{ .mfi
nop.m 0
nop.f 0
//significant bit destruction
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
}
;;
{ .mfi
//BIAS subtraction
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
(p7) fnma.s1 log2 = log2,f1,f0
nop.i 0
}
;;
{ .mfi
setf.sig log_int_Nfloat = log_GR_true_exp_f8
fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
}
;;
{ .mmi
//pre-index*16 + index
shladd log_table_address3 = log_GR_index,3,log_table_address3
;;
ldfd log_T = [log_table_address3]
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rsq = log_r, log_r, f0 //r^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p10 = log_P1, log_r, f1
nop.i 0
}
;;
{ .mfi
nop.m 0
//convert N to the floating-point format
fcvt.xf log_Nfloat = log_int_Nfloat
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
nop.i 0
}
;;
{ .mfi
nop.m 0
(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
nop.i 0
}
{ .mfb
nop.m 0
(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
br.ret.sptk b0 // Exit main path, path 3: 2^-5 <= |x| < 2^51
}
;;
// Here if path 4, |x| >= 2^51
LOG_COMMON1:
{ .mfi
ldfpd log_P3,log_P2 = [NR_table_address],16
nop.f 0
nop.i 0
}
;;
{ .mfi
ldfpd log_P1,log2 = [NR_table_address],16
frcpa.s1 log_C,p0 = f1,log_arg
nop.i 0
}
;;
{ .mfi
getf.exp log_GR_signexp_f8 = log_arg
nop.f 0
//to get third table address
adds log_table_address3 = 0x30, NR_table_address
}
;;
{ .mfi
getf.sig log_GR_significand_f8 = log_arg
nop.f 0
nop.i 0
}
;;
{ .mfi
nop.m 0
nop.f 0
//to destroy the most bit in the significant area
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
}
;;
{ .mmf
nop.m 0
//BIAS subtraction
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
}
;;
{ .mfi
setf.sig log_int_Nfloat = log_GR_true_exp_f8
nop.f 0
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
}
;;
{ .mmi
//pre-index*16 + index
shladd log_table_address3 = log_GR_index,3,log_table_address3
;;
ldfd log_T = [log_table_address3]
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rsq = log_r, log_r, f0 //r^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
nop.i 0
}
;;
{ .mfi
nop.m 0
fma.s1 log_rp_p10 = log_P1, log_r, f1
nop.i 0
}
{ .mfi
nop.m 0
(p7) fnma.s1 log2 = log2,f1,f0
nop.i 0
}
;;
{ .mfi
nop.m 0
//convert N to the floating-point format
fcvt.xf log_Nfloat = log_int_Nfloat
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10
nop.i 0
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
nop.i 0
}
;;
{ .mfi
nop.m 0
(p11) fma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
nop.i 0
}
{ .mfb
nop.m 0
(p7) fnma.s.s0 f8 = log_rp_p2,log_r,log_T_plus_Nlog2
br.ret.sptk b0 // Exit path 4, |x| >= 2^51
}
;;
// Here if path 2, 0 < |x| < 2^-5
ASINH_NEAR_ZERO:
{ .mfi
nop.m 0
fma.s1 asinh_w_1 = asinh_w_sq,log_C1,log_C0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
nop.i 0
}
;;
{ .mfb
nop.m 0
fma.s.s0 f8 = asinh_w_1,asinh_w_cube,fNormX
br.ret.sptk b0 // Exit path 2, 0 < |x| < 2^-5
}
;;
ASINH_UNORM:
// Here if x=unorm
{ .mfi
getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
nop.i 0
}
;;
{ .mfb
nop.m 0
fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
(p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
}
;;
.pred.rel "mutex",p7,p11
{ .mfi
nop.m 0
(p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
nop.i 0
}
{ .mfb
nop.m 0
(p11) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
br.ret.spnt b0 // Exit if denorm
}
;;
GLOBAL_LIBM_END(asinhf)
libm_alias_float_other (asinh, asinh)
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