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glibc/sysdeps/ia64/fpu/s_erfc.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

1197 lines
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.file "erfc.s"
// Copyright (c) 2001 - 2005, 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
//==============================================================
// 11/12/01 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header: .section, .global, .proc, .align
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// double erfc(double)
//
// Overview of operation
//==============================================================
// 1. 0 <= x <= 28.0
//
// erfc(x) = P14(z) * exp( -x^2 ), z = x - x(i).
//
// Comment:
//
// Let x(i) = -1.0 + 2^(i/4),i=0,...19. So we have 20 unequal
// argument intervals [x(i),x(i+1)] with length ratio q = 2^(1/4).
// Values x(i) we have in the table erfc_xb_table.
//
// Let x(i)<= x < x(i+1).
// We can find i as exponent of number (x + 1)^4.
//
// Let P14(z) - polynomial approximation of degree 14 for function
// erfc(z+x(i)) * exp( (z+x(i))^2) and 0 <= z <= x(i+1)-x(i).
// Polynomial coefficients we have in the table erfc_p_table.
//
// So we can find result for erfc(x) as above.
// Algorithm description for exp function see below.
//
// 2. -6 <= x < 0
//
// erfc(x) = 2.0 - erfc(-x)
//
// 3. x > 28.0
// erfc(x) ~=~ 0.0
//
// 4. x < -6.0
// erfc(x) ~=~ 2.0
// Special values
//==============================================================
// erfc(+0) = 1.0
// erfc(-0) = 1.0
// erfc(+qnan) = +qnan
// erfc(-qnan) = -qnan
// erfc(+snan) = +qnan
// erfc(-snan) = -qnan
// erfc(-inf) = 2.0
// erfc(+inf) = +0
//==============================================================
// Take double exp(double) from libm_64.
//
// Overview of operation
//==============================================================
// Take the input x. w is "how many log2/128 in x?"
// w = x * 128/log2
// n = int(w)
// x = n log2/128 + r + delta
// n = 128M + index_1 + 2^4 index_2
// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
// Construct 2^M
// Get 2^(index_1/128) from table_1;
// Get 2^(index_2/8) from table_2;
// Calculate exp(r) by series
// r = x - n (log2/128)_high
// delta = - n (log2/128)_low
// Calculate exp(delta) as 1 + delta
//==============================================================
// Comment for exp for erfc:
//
// We use quad precision for calculate input argument -x^2 and add
// result low bits to value delta in exp.
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f9 -> f15, f32 -> f93
// General registers used:
// r32 -> r68
// Predicate registers used:
// p6 -> p15
// Assembly macros
//==============================================================
exp_GR_rshf = r33
EXP_AD_TB1 = r34
EXP_AD_TB2 = r35
EXP_AD_P = r36
exp_GR_N = r37
exp_GR_index_1 = r38
exp_GR_index_2_16 = r39
exp_GR_biased_M = r40
EXP_AD_T1 = r41
EXP_AD_T2 = r42
exp_GR_sig_inv_ln2 = r43
exp_GR_17ones = r44
exp_TB1_size = r45
exp_TB2_size = r46
exp_GR_rshf_2to56 = r47
exp_GR_exp_2tom56 = r48
// GR for erfc(x)
//==============================================================
GR_POS_ARG_ASYMP = r49
GR_NEG_ARG_ASYMP = r50
GR_ARG_ASYMP = r51
GR_ERFC_XB_TB = r52
GR_ERFC_P_TB = r53
GR_IndxPlusBias = r54
GR_BIAS = r55
GR_P_A12 = r56
GR_P_A13 = r57
GR_AbsArg = r58
GR_ShftXBi = r59
GR_ShftPi = r60
GR_mBIAS = r61
GR_ShftPi_bias = r62
GR_ShftXBi_bias = r63
GR_ShftA12 = r64
GR_ShftA13 = r65
GR_EpsNorm = r66
GR_0x1 = r67
GR_ShftPi_8 = r68
// GR for __libm_support call
//==============================================================
GR_SAVE_B0 = r61
GR_SAVE_PFS = r62
GR_SAVE_GP = r63
GR_SAVE_SP = r64
GR_Parameter_X = r65
GR_Parameter_Y = r66
GR_Parameter_RESULT = r67
GR_Parameter_TAG = r68
// FR for exp(-x^2)
//==============================================================
FR_X = f10
FR_Y = f1
FR_RESULT = f8
EXP_2TOM56 = f6
EXP_INV_LN2_2TO63 = f7
EXP_W_2TO56_RSH = f9
EXP_RSHF_2TO56 = f10
exp_P4 = f11
exp_P3 = f12
exp_P2 = f13
exp_P1 = f14
exp_ln2_by_128_hi = f15
exp_ln2_by_128_lo = f32
EXP_RSHF = f33
EXP_Nfloat = f34
exp_r = f35
exp_f = f36
exp_rsq = f37
exp_rcube = f38
EXP_2M = f39
exp_S1 = f40
exp_T1 = f41
exp_rP4pP3 = f42
exp_P_lo = f43
exp_P_hi = f44
exp_P = f45
exp_S = f46
EXP_NORM_f8 = f47
exp_S2 = f48
exp_T2 = f49
// FR for erfc(x)
//==============================================================
FR_AbsArg = f50
FR_Tmp = f51
FR_Xb = f52
FR_A0 = f53
FR_A1 = f54
FR_A2 = f55
FR_A3 = f56
FR_A4 = f57
FR_A5 = f58
FR_A6 = f59
FR_A7 = f60
FR_A8 = f61
FR_A9 = f62
FR_A10 = f63
FR_A11 = f64
FR_A12 = f65
FR_A13 = f66
FR_A14 = f67
FR_P14_0_1 = f68
FR_P14_0_2 = f69
FR_P14_1_1 = f70
FR_P14_1_2 = f71
FR_P14_2_1 = f72
FR_P14_2_2 = f73
FR_P14_3_1 = f74
FR_P14_3_2 = f75
FR_P14_6_1 = f76
FR_P14_7_1 = f77
FR_P14_7_2 = f78
FR_P14_8_1 = f79
FR_P14_8_2 = f80
FR_P14_12_1 = f81
FR_P14_13_1 = f82
FR_P14_13_2 = f83
FR_Pol = f84
FR_Exp = f85
FR_2 = f86
f8_sq_lo = f87
FR_LocArg = f88
FR_Tmpf = f89
FR_Tmp1 = f90
FR_EpsNorm = f91
FR_UnfBound = f92
FR_NormX = f93
// Data tables
//==============================================================
RODATA
.align 16
// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
LOCAL_OBJECT_START(exp_table_1)
data8 0x403a8b12fc6e4892 , 0 // underflow boundary
data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
//
// Table 1 is 2^(index_1/128) where
// index_1 goes from 0 to 15
//
data8 0x8000000000000000 , 0x00003FFF
data8 0x80B1ED4FD999AB6C , 0x00003FFF
data8 0x8164D1F3BC030773 , 0x00003FFF
data8 0x8218AF4373FC25EC , 0x00003FFF
data8 0x82CD8698AC2BA1D7 , 0x00003FFF
data8 0x8383594EEFB6EE37 , 0x00003FFF
data8 0x843A28C3ACDE4046 , 0x00003FFF
data8 0x84F1F656379C1A29 , 0x00003FFF
data8 0x85AAC367CC487B15 , 0x00003FFF
data8 0x8664915B923FBA04 , 0x00003FFF
data8 0x871F61969E8D1010 , 0x00003FFF
data8 0x87DB357FF698D792 , 0x00003FFF
data8 0x88980E8092DA8527 , 0x00003FFF
data8 0x8955EE03618E5FDD , 0x00003FFF
data8 0x8A14D575496EFD9A , 0x00003FFF
data8 0x8AD4C6452C728924 , 0x00003FFF
LOCAL_OBJECT_END(exp_table_1)
// Table 2 is 2^(index_1/8) where
// index_2 goes from 0 to 7
LOCAL_OBJECT_START(exp_table_2)
data8 0x8000000000000000 , 0x00003FFF
data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
data8 0x9837F0518DB8A96F , 0x00003FFF
data8 0xA5FED6A9B15138EA , 0x00003FFF
data8 0xB504F333F9DE6484 , 0x00003FFF
data8 0xC5672A115506DADD , 0x00003FFF
data8 0xD744FCCAD69D6AF4 , 0x00003FFF
data8 0xEAC0C6E7DD24392F , 0x00003FFF
LOCAL_OBJECT_END(exp_table_2)
LOCAL_OBJECT_START(exp_p_table)
data8 0x3f8111116da21757 //P_4
data8 0x3fa55555d787761c //P_3
data8 0x3fc5555555555414 //P_2
data8 0x3fdffffffffffd6a //P_1
LOCAL_OBJECT_END(exp_p_table)
LOCAL_OBJECT_START(erfc_xb_table)
data8 0x0000000000000000, 0x00000000 //XB[0] = +0.00000000000000000000e-01L
data8 0xC1BF828C6DC54B7A, 0x00003FFC //XB[1] = +1.89207115002721066717e-01L
data8 0xD413CCCFE7799211, 0x00003FFD //XB[2] = +4.14213562373095048802e-01L
data8 0xAE89F995AD3AD5E8, 0x00003FFE //XB[3] = +6.81792830507429086062e-01L
data8 0x8000000000000000, 0x00003FFF //XB[4] = +1.00000000000000000000e+00L
data8 0xB06FE0A31B7152DF, 0x00003FFF //XB[5] = +1.37841423000544213343e+00L
data8 0xEA09E667F3BCC909, 0x00003FFF //XB[6] = +1.82842712474619009760e+00L
data8 0x9744FCCAD69D6AF4, 0x00004000 //XB[7] = +2.36358566101485817212e+00L
data8 0xC000000000000000, 0x00004000 //XB[8] = +3.00000000000000000000e+00L
data8 0xF06FE0A31B7152DF, 0x00004000 //XB[9] = +3.75682846001088426687e+00L
data8 0x9504F333F9DE6484, 0x00004001 //XB[10] = +4.65685424949238019521e+00L
data8 0xB744FCCAD69D6AF4, 0x00004001 //XB[11] = +5.72717132202971634425e+00L
data8 0xE000000000000000, 0x00004001 //XB[12] = +7.00000000000000000000e+00L
data8 0x8837F0518DB8A96F, 0x00004002 //XB[13] = +8.51365692002176853374e+00L
data8 0xA504F333F9DE6484, 0x00004002 //XB[14] = +1.03137084989847603904e+01L
data8 0xC744FCCAD69D6AF4, 0x00004002 //XB[15] = +1.24543426440594326885e+01L
data8 0xF000000000000000, 0x00004002 //XB[16] = +1.50000000000000000000e+01L
data8 0x9037F0518DB8A96F, 0x00004003 //XB[17] = +1.80273138400435370675e+01L
data8 0xAD04F333F9DE6484, 0x00004003 //XB[18] = +2.16274169979695207808e+01L
data8 0xCF44FCCAD69D6AF4, 0x00004003 //XB[19] = +2.59086852881188653770e+01L
LOCAL_OBJECT_END(erfc_xb_table)
LOCAL_OBJECT_START(erfc_p_table)
// Pol0
data8 0x8000000000000000, 0x00003FFF //A0 = +1.00000000000000000000e+00L
data8 0x906EBA8214DB688D, 0x0000BFFF //A1 = -1.12837916709551257389e+00L
data8 0xFFFFFFFFFFFFFFEB, 0x00003FFE //A2 = +9.99999999999999998841e-01L
data8 0xC093A3581BCF2925, 0x0000BFFE //A3 = -7.52252778063674869885e-01L
data8 0xFFFFFFFFFFF7CDBD, 0x00003FFD //A4 = +4.99999999999985440383e-01L
data8 0x9A0FB5E014AE3EFB, 0x0000BFFD //A5 = -3.00901111224757482205e-01L
data8 0xAAAAAAAA4672B0BD, 0x00003FFC //A6 = +1.66666666643879582201e-01L
data8 0xB011F45C9F590FC0, 0x0000BFFB //A7 = -8.59717455640916223912e-02L
data8 0xAAAAA89474161033, 0x00003FFA //A8 = +4.16666588928413935202e-02L
data8 0x9C818E2CE37D4214, 0x0000BFF9 //A9 = -1.91047455656271634308e-02L
data8 0x8885969315AB76A1, 0x00003FF8 //A10 = +8.33263115449753085659e-03L
data8 0xE36112A686F5165B, 0x0000BFF6 //A11 = -3.46953111013788405745e-03L
data8 0xB3DD6B2DB3307D2E, 0x00003FF5 //A12 = +1.37226041156280127011e-03L
data8 0x8018A34267FED226, 0x0000BFF4 //A13 = -4.88648380816410282971e-04L
data8 0xFBBA6A7AEBD3ABD9, 0x00003FF1 //A14 = +1.20033353451879025825e-04L
// Pol1
data8 0xD15A1EF03BB91E71, 0x00003FFE //A0 = +8.17781385088640600540e-01L
data8 0xD1A4ADDAC3337118, 0x0000BFFE //A1 = -8.18919053944410683867e-01L
data8 0xA9AF9FFA2AD18CB0, 0x00003FFE //A2 = +6.62836073471060947628e-01L
data8 0xECB77514F0F151B3, 0x0000BFFD //A3 = -4.62337168508812580002e-01L
data8 0x934AB35EA5CD5EEB, 0x00003FFD //A4 = +2.87679295829458273854e-01L
data8 0xA71410A68C1EF21C, 0x0000BFFC //A5 = -1.63162479558223113104e-01L
data8 0xAF506A335238094A, 0x00003FFB //A6 = +8.56025978958108330224e-02L
data8 0xABFDF67F968765A7, 0x0000BFFA //A7 = -4.19902447551140139048e-02L
data8 0x9F0B0165A6CDCA99, 0x00003FF9 //A8 = +1.94144274984979538382e-02L
data8 0x8B8197BFC346CDEA, 0x0000BFF8 //A9 = -8.51478404279186775501e-03L
data8 0xE950D763FE51AB1E, 0x00003FF6 //A10 = +3.56011637267641495904e-03L
data8 0xBA821A59FC05FBAD, 0x0000BFF5 //A11 = -1.42294475244146555952e-03L
data8 0x8D535042E11A0D89, 0x00003FF4 //A12 = +5.39113782651680545599e-04L
data8 0xBE589447DB26564E, 0x0000BFF2 //A13 = -1.81528103431449706486e-04L
data8 0xABC8C7EF636F5B0A, 0x00003FF0 //A14 = +4.09565689009869217620e-05L
// Pol2
data8 0xA9973ABB272898B2, 0x00003FFE //A0 = +6.62463827792779356910e-01L
data8 0x945F1A7993F7AADD, 0x0000BFFE //A1 = -5.79576162988785154930e-01L
data8 0xD84439C6609A8A62, 0x00003FFD //A2 = +4.22395520654665085222e-01L
data8 0x8A1BBAA7E9CB8C52, 0x0000BFFD //A3 = -2.69742806431984313298e-01L
data8 0x9F0F67364B466975, 0x00003FFC //A4 = +1.55332195938916594663e-01L
data8 0xA843F180287DAF7F, 0x0000BFFB //A5 = -8.21608416782158837025e-02L
data8 0xA59D71B7C690E545, 0x00003FFA //A6 = +4.04333536247671644540e-02L
data8 0x991A733518C74874, 0x0000BFF9 //A7 = -1.86893701691354422481e-02L
data8 0x85E7F91148F9F6D2, 0x00003FF8 //A8 = +8.17298243522623724858e-03L
data8 0xDEE0607CC9D6777E, 0x0000BFF6 //A9 = -3.40082507754089306495e-03L
data8 0xB145D2CC470B306B, 0x00003FF5 //A10 = +1.35248373238824318949e-03L
data8 0x86FAEBB4438A20FA, 0x0000BFF4 //A11 = -5.14908443679775343409e-04L
data8 0xC2503856CE48A657, 0x00003FF2 //A12 = +1.85311660448280465934e-04L
data8 0xF52642F22A26965B, 0x0000BFF0 //A13 = -5.84481856856861454591e-05L
data8 0xC98588E1A95FFDBD, 0x00003FEE //A14 = +1.20116245684500489648e-05L
// Pol3
data8 0x887CBA2C47B1E2B5, 0x00003FFE //A0 = +5.33153186617432643784e-01L
data8 0xCD81909CF194328E, 0x0000BFFD //A1 = -4.01379126699602646289e-01L
data8 0x84DCA15C52122372, 0x00003FFD //A2 = +2.59495775718310530164e-01L
data8 0x993AA9C76AD28157, 0x0000BFFC //A3 = -1.49637844845261107836e-01L
data8 0xA140CD8A96FADBA5, 0x00003FFB //A4 = +7.87368829650154013961e-02L
data8 0x9D36B25E76E56EEA, 0x0000BFFA //A5 = -3.83822410143975630292e-02L
data8 0x8F8BCC2C0536ECD3, 0x00003FF9 //A6 = +1.75227153523910189727e-02L
data8 0xF77EDC644BA17AF9, 0x0000BFF7 //A7 = -7.55296479527793552675e-03L
data8 0xCAB8AC76793C1151, 0x00003FF6 //A8 = +3.09328279988546711083e-03L
data8 0x9E8FCBC793D555AF, 0x0000BFF5 //A9 = -1.20972979110659888616e-03L
data8 0xEDC1328664A0CE79, 0x00003FF3 //A10 = +4.53481058502015766058e-04L
data8 0xAAE3CAAB9D117591, 0x0000BFF2 //A11 = -1.62973223928790256249e-04L
data8 0xE7704D06A3080C19, 0x00003FF0 //A12 = +5.51792801195012080688e-05L
data8 0x875A5B53E510F305, 0x0000BFEF //A13 = -1.61353297293572230995e-05L
data8 0xC8F10CDDB9CC9A42, 0x00003FEC //A14 = +2.99426321046583353559e-06L
// Pol4
data8 0xDAEC3C07CAB590C1, 0x00003FFD //A0 = +4.27583576155807004411e-01L
data8 0x8BE271F8BE0280AC, 0x0000BFFD //A1 = -2.73212014783898564863e-01L
data8 0x9E13941E19661429, 0x00003FFC //A2 = +1.54371561371908397882e-01L
data8 0xA241BFC48377449D, 0x0000BFFB //A3 = -7.92269689413235358504e-02L
data8 0x99E56877AD00D1AE, 0x00003FFA //A4 = +3.75722962151600767952e-02L
data8 0x887E78DA3BA57C80, 0x0000BFF9 //A5 = -1.66618690872055148862e-02L
data8 0xE465CAA9F4D54FD8, 0x00003FF7 //A6 = +6.97014232347351913821e-03L
data8 0xB57930370208D4A7, 0x0000BFF6 //A7 = -2.76906420823065422653e-03L
data8 0x89A90B5DF0C0C55E, 0x00003FF5 //A8 = +1.05026496655247749532e-03L
data8 0xC83DB867F08D93C6, 0x0000BFF3 //A9 = -3.81929578900287685559e-04L
data8 0x8C0C9113FC8061FA, 0x00003FF2 //A10 = +1.33561218944256209215e-04L
data8 0xBC17A73E9CA51313, 0x0000BFF0 //A11 = -4.48447217225392170834e-05L
data8 0xED10FE8FC0E44CAD, 0x00003FEE //A12 = +1.41302576244352578317e-05L
data8 0xFE49912328516F81, 0x0000BFEC //A13 = -3.78917710289305330220e-06L
data8 0xA8F6077E25DAFD33, 0x00003FEA //A14 = +6.29428967202166402369e-07L
// Pol5
data8 0xAF72220985BED710, 0x00003FFD //A0 = +3.42667640364081975844e-01L
data8 0xBC1CB559042410AB, 0x0000BFFC //A1 = -1.83703263815036934677e-01L
data8 0xB730BF62E0B63A3C, 0x00003FFB //A2 = +8.94484474229911741150e-02L
data8 0xA4F307B1D1A1534E, 0x0000BFFA //A3 = -4.02708340235238993824e-02L
data8 0x8B0327F5117861DB, 0x00003FF9 //A4 = +1.69692783752415790321e-02L
data8 0xDD4059307B2B081C, 0x0000BFF7 //A5 = -6.75205569219747369303e-03L
data8 0xA761D738974FECF6, 0x00003FF6 //A6 = +2.55404953403837072821e-03L
data8 0xF208F6D704F4B487, 0x0000BFF4 //A7 = -9.23290315545127419886e-04L
data8 0xA7F3658D34EC10B9, 0x00003FF3 //A8 = +3.20340668304962386053e-04L
data8 0xE079C35CEFD4E6D6, 0x0000BFF1 //A9 = -1.07038324953715640850e-04L
data8 0x90C5CDD19BB3DD2F, 0x00003FF0 //A10 = +3.45164947021915687751e-05L
data8 0xB3911863705825F6, 0x0000BFEE //A11 = -1.07030140392753204852e-05L
data8 0xD023CF5C3F915685, 0x00003FEC //A12 = +3.10152594473606007552e-06L
data8 0xCA7016FADFF584F5, 0x0000BFEA //A13 = -7.54139761055503416594e-07L
data8 0xEEBB5CC0901D2BB0, 0x00003FE7 //A14 = +1.11168196441717301549e-07L
// Pol6
data8 0x8CD1160326A754AF, 0x00003FFD //A0 = +2.75032699474947383325e-01L
data8 0xFB22A4C657119388, 0x0000BFFB //A1 = -1.22624671271190511269e-01L
data8 0xD02B2CA872A774E9, 0x00003FFA //A2 = +5.08224243596176920409e-02L
data8 0xA23302E146E9E406, 0x0000BFF9 //A3 = -1.97997146844646077750e-02L
data8 0xEF8918FEDE237C98, 0x00003FF7 //A4 = +7.31004448401605074486e-03L
data8 0xA8A8B598FA20D881, 0x0000BFF6 //A5 = -2.57353242430059589053e-03L
data8 0xE3964D9788BFF50F, 0x00003FF4 //A6 = +8.68175969920725727944e-04L
data8 0x93B83C10B7210AC7, 0x0000BFF3 //A7 = -2.81752903983413936245e-04L
data8 0xB913B752B0D56A42, 0x00003FF1 //A8 = +8.82515983758695613094e-05L
data8 0xE0623EFA0B1E8DE9, 0x0000BFEF //A9 = -2.67486302195396417310e-05L
data8 0x83C4D1A4019E1D2E, 0x00003FEE //A10 = +7.85403393879249335151e-06L
data8 0x950CBA5D80D8125E, 0x0000BFEC //A11 = -2.22101388436550539151e-06L
data8 0x9CE72C0409A3E800, 0x00003FEA //A12 = +5.84509280984781223375e-07L
data8 0x88CCD7A000D1C213, 0x0000BFE8 //A13 = -1.27405082040077425019e-07L
data8 0x8DF4EC84F093B1C0, 0x00003FE5 //A14 = +1.65259388738830506389e-08L
// Pol7
data8 0xE2BF82A153B1B82E, 0x00003FFC //A0 = +2.21433678719152843912e-01L
data8 0xA72A9AE0BD7F29D5, 0x0000BFFB //A1 = -8.16242313227913578068e-02L
data8 0xE98939292289EDBE, 0x00003FF9 //A2 = +2.85078159732432477516e-02L
data8 0x9B93E5E0EEFF9516, 0x0000BFF8 //A3 = -9.49571084105114051468e-03L
data8 0xC6B39897AABC47BC, 0x00003FF6 //A4 = +3.03194499398790451607e-03L
data8 0xF442AC7D84DDF1E0, 0x0000BFF4 //A5 = -9.31779649708690069328e-04L
data8 0x90FBD9F8B41DF23E, 0x00003FF3 //A6 = +2.76534642660360753287e-04L
data8 0xA6AC59077C78B437, 0x0000BFF1 //A7 = -7.94759910003852154521e-05L
data8 0xB9FC0BADD531E5E9, 0x00003FEF //A8 = +2.21710864553358009804e-05L
data8 0xC9CFC8CD93648856, 0x0000BFED //A9 = -6.01445608619100503330e-06L
data8 0xD4FA51B86A9B2494, 0x00003FEB //A10 = +1.58680833469323702924e-06L
data8 0xD8D0ED030032926D, 0x0000BFE9 //A11 = -4.03851487695924456733e-07L
data8 0xCCA1CA2AC3EB8973, 0x00003FE7 //A12 = +9.52891963880517988726e-08L
data8 0x9E26A080F9DA39DE, 0x0000BFE5 //A13 = -1.84111863600343741644e-08L
data8 0x8F3DC58F64A92C62, 0x00003FE2 //A14 = +2.08443519336792003049e-09L
// Pol8
data8 0xB74C13E914E9666F, 0x00003FFC //A0 = +1.79001151181389950418e-01L
data8 0xDEB57268A58B763B, 0x0000BFFA //A1 = -5.43722600071728705200e-02L
data8 0x821FF0D4C605A4CD, 0x00003FF9 //A2 = +1.58843711598712515609e-02L
data8 0x92C830DD423DB924, 0x0000BFF7 //A3 = -4.47943101836927657394e-03L
data8 0xA04E61767A095BB6, 0x00003FF5 //A4 = +1.22303905230942532198e-03L
data8 0xA9EF64E0F6654358, 0x0000BFF3 //A5 = -3.24125543666296226957e-04L
data8 0xAF39C8969BD163E8, 0x00003FF1 //A6 = +8.35541329311315562274e-05L
data8 0xB01273B34197330C, 0x0000BFEF //A7 = -2.09894273215824495783e-05L
data8 0xACAE4C820B99EBAC, 0x00003FED //A8 = +5.14629050848703676006e-06L
data8 0xA57BF2AEA52B92DF, 0x0000BFEB //A9 = -1.23295315941138567172e-06L
data8 0x9AD6FE7A852DA239, 0x00003FE9 //A10 = +2.88411640627675721042e-07L
data8 0x8BFE95FCD7B92763, 0x0000BFE7 //A11 = -6.51900079707465044843e-08L
data8 0xE9F15C8E7F58CF90, 0x00003FE4 //A12 = +1.36172642554216769522e-08L
data8 0x9E90F22B11FAF8B5, 0x0000BFE2 //A13 = -2.30744183054978535129e-09L
data8 0xF8CF74F1A138FBBA, 0x00003FDE //A14 = +2.26291720693360003233e-10L
// Pol9
data8 0x94D45274A831ED57, 0x00003FFC //A0 = +1.45341194505862183128e-01L
data8 0x94D4518B699A4A68, 0x0000BFFA //A1 = -3.63352952323113355459e-02L
data8 0x90C3B59FF403A916, 0x00003FF8 //A2 = +8.83572327421709216515e-03L
data8 0x893B796D0E9B4867, 0x0000BFF6 //A3 = -2.09399904729894563201e-03L
data8 0xFDFFA94903DCB8EA, 0x00003FF3 //A4 = +4.84464029001979577664e-04L
data8 0xE5CE7C2E4B05CF16, 0x0000BFF1 //A5 = -1.09580317663729186599e-04L
data8 0xCB88CC8F1146FDAE, 0x00003FEF //A6 = +2.42631878042764234194e-05L
data8 0xB0AA52C6F44E47C8, 0x0000BFED //A7 = -5.26503698764159271674e-06L
data8 0x966DD813170F8EBD, 0x00003FEB //A8 = +1.12078397189300511086e-06L
data8 0xFB75782788A6E378, 0x0000BFE8 //A9 = -2.34189317246047219283e-07L
data8 0xCDF787C4E5FDCF2A, 0x00003FE6 //A10 = +4.79554094892420966704e-08L
data8 0xA34CD3DFAC12AA45, 0x0000BFE4 //A11 = -9.50531730989412282035e-09L
data8 0xEEBB49645DE0E34C, 0x00003FE1 //A12 = +1.73700091999434388879e-09L
data8 0x8C86D8677DEACFBA, 0x0000BFDF //A13 = -2.55616650187281815453e-10L
data8 0xBDB223D0FE2A7D6B, 0x00003FDB //A14 = +2.15659223402509415592e-11L
// Pol10
data8 0xF2C1812715E4050A, 0x00003FFB //A0 = +1.18533143048567888157e-01L
data8 0xC7DA2C565ADAEE57, 0x0000BFF9 //A1 = -2.43960252726894623056e-02L
data8 0xA15CEFFD632F697D, 0x00003FF7 //A2 = +4.92440908672041077933e-03L
data8 0xFFCFF4D3FB118F69, 0x0000BFF4 //A3 = -9.75846593969603576904e-04L
data8 0xC73F437D2F226C56, 0x00003FF2 //A4 = +1.90016864347860462550e-04L
data8 0x989D7E1F60845811, 0x0000BFF0 //A5 = -3.63863004988760879054e-05L
data8 0xE615A5A669361BE1, 0x00003FED //A6 = +6.85705419984646959791e-06L
data8 0xAACD08E0BE6270F8, 0x0000BFEB //A7 = -1.27256599602163049440e-06L
data8 0xF9DEE9C1C02A3062, 0x00003FE8 //A8 = +2.32710274258898439253e-07L
data8 0xB420E960508A3003, 0x0000BFE6 //A9 = -4.19394488070741280136e-08L
data8 0xFF5E3ECA229CB0C7, 0x00003FE3 //A10 = +7.43219121339261970485e-09L
data8 0xAF86504D78D35E89, 0x0000BFE1 //A11 = -1.27711000692808421573e-09L
data8 0xDE1CE78ADB6DDF04, 0x00003FDE //A12 = +2.02010513073041015283e-10L
data8 0xE124FFAA267301A5, 0x0000BFDB //A13 = -2.55959692063871343080e-11L
data8 0x81F1BEBEFBE168D2, 0x00003FD8 //A14 = +1.84661980716000872722e-12L
// Pol11
data8 0xC6CE5D7D18203EAA, 0x00003FFB //A0 = +9.70732978630764996752e-02L
data8 0x86E8A30A76923C88, 0x0000BFF9 //A1 = -1.64683517829920230086e-02L
data8 0xB4A1CBB7576B4183, 0x00003FF6 //A2 = +2.75622581042760461528e-03L
data8 0xEEB782FBC8BB352B, 0x0000BFF3 //A3 = -4.55316242981110299585e-04L
data8 0x9BC489CC00C7E63A, 0x00003FF1 //A4 = +7.42758405750422020216e-05L
data8 0xC8D418A9F2A78515, 0x0000BFEE //A5 = -1.19703114831817055481e-05L
data8 0xFFE671DCEE8665A8, 0x00003FEB //A6 = +1.90660487794668853072e-06L
data8 0xA1313247D3E35365, 0x0000BFE9 //A7 = -3.00243820009225833104e-07L
data8 0xC8D5A87C970712B1, 0x00003FE6 //A8 = +4.67604496871825103188e-08L
data8 0xF77258CEF4675E25, 0x0000BFE3 //A9 = -7.20164586117313631144e-09L
data8 0x96549D79C0F33C27, 0x00003FE1 //A10 = +1.09379854902340983112e-09L
data8 0xB16A6CC5A3AE6E01, 0x0000BFDE //A11 = -1.61358659378896671620e-10L
data8 0xC0970F2551C52F96, 0x00003FDB //A12 = +2.18949565869759698947e-11L
data8 0xA6E029ABB3BB500C, 0x0000BFD8 //A13 = -2.37144541649446501026e-12L
data8 0xA3E43F3857D1B6A5, 0x00003FD4 //A14 = +1.45564973108152568130e-13L
// Pol12
data8 0xA36E35FC807B3E64, 0x00003FFB //A0 = +7.98000543291529334886e-02L
data8 0xB725A29237C8F94F, 0x0000BFF8 //A1 = -1.11784064873715046550e-02L
data8 0xCB51EF23EAD5F327, 0x00003FF5 //A2 = +1.55120891755237931425e-03L
data8 0xDFA838770AE711A2, 0x0000BFF2 //A3 = -2.13296043002775850891e-04L
data8 0xF3D7B777730B202D, 0x00003FEF //A4 = +2.90683082614108095819e-05L
data8 0x83C5FF0D475796DD, 0x0000BFED //A5 = -3.92715403535014263671e-06L
data8 0x8D37B41345244FD5, 0x00003FEA //A6 = +5.26076523514903487927e-07L
data8 0x9616B7E9C40C1DCC, 0x0000BFE7 //A7 = -6.98905176445499510102e-08L
data8 0x9E38FDF61B26699A, 0x00003FE4 //A8 = +9.20976891314475742405e-09L
data8 0xA565DFE27AEA03A1, 0x0000BFE1 //A9 = -1.20342845518628622757e-09L
data8 0xAAEB9EFB497EC812, 0x00003FDE //A10 = +1.55451193328690040046e-10L
data8 0xABD305A38349EAEB, 0x0000BFDB //A11 = -1.95341618552982314342e-11L
data8 0x9EDB00104DB66DD9, 0x00003FD8 //A12 = +2.25747200093121867690e-12L
data8 0xE9F80AF513F2B8AB, 0x0000BFD4 //A13 = -2.07806143133802417637e-13L
data8 0xC2B840C3859AB166, 0x00003FD0 //A14 = +1.08091168358477817812e-14L
// Pol13
data8 0x86CD0BF01914407A, 0x00003FFB //A0 = +6.58207829138836028568e-02L
data8 0xF9F4A17FA70807C3, 0x0000BFF7 //A1 = -7.62803922344113067603e-03L
data8 0xE63BF84EDE20EDAA, 0x00003FF4 //A2 = +8.78273993036530088653e-04L
data8 0xD2B746011B39D879, 0x0000BFF1 //A3 = -1.00477176633442906101e-04L
data8 0xBFA4F1F66023C975, 0x00003FEE //A4 = +1.14228914411837438985e-05L
data8 0xAD3A05E1F1F0EA8F, 0x0000BFEB //A5 = -1.29063913420827451449e-06L
data8 0x9BA1F2E56DBE1B49, 0x00003FE8 //A6 = +1.44944165416032280452e-07L
data8 0x8AFE93AF627BAFA6, 0x0000BFE5 //A7 = -1.61810825806733824014e-08L
data8 0xF6CEAB6E78304875, 0x00003FE1 //A8 = +1.79575947795401009493e-09L
data8 0xD9BFD64FD9166ECF, 0x0000BFDE //A9 = -1.98041892772535870322e-10L
data8 0xBE482C8AEA403737, 0x00003FDB //A10 = +2.16325508593741350803e-11L
data8 0xA1FB98FA19E62A4F, 0x0000BFD8 //A11 = -2.30191407969654156362e-12L
data8 0xFDB2E0599016AD1E, 0x00003FD4 //A12 = +2.25329742249079975388e-13L
data8 0x9E179A99CDD4BF4B, 0x0000BFD1 //A13 = -1.75517603530017718494e-14L
data8 0xDE4DE992A707C7BC, 0x00003FCC //A14 = +7.71273133169032472595e-16L
// Pol14
data8 0xDF0639E60CF6E96C, 0x00003FFA //A0 = +5.44492971101228988138e-02L
data8 0xAB6737B6065BD1C2, 0x0000BFF7 //A1 = -5.23081035867078490333e-03L
data8 0x8322CC0765FD9C27, 0x00003FF4 //A2 = +5.00243857322493802503e-04L
data8 0xC7C37C447AABC9BE, 0x0000BFF0 //A3 = -4.76273572257807668623e-05L
data8 0x977C068C67DD09B3, 0x00003FED //A4 = +4.51458915834329225528e-06L
data8 0xE4C00648054CBD72, 0x0000BFE9 //A5 = -4.26080256412742187632e-07L
data8 0xABF9032C426C0F54, 0x00003FE6 //A6 = +4.00405155179176153559e-08L
data8 0x80BD82177111B70D, 0x0000BFE3 //A7 = -3.74683488305340664541e-09L
data8 0xBFEFB2BBFC4AAE16, 0x00003FDF //A8 = +3.49130134089615132836e-10L
data8 0x8E68BCEC2A2F6025, 0x0000BFDC //A9 = -3.23800879252444001040e-11L
data8 0xD19FEF92B2157585, 0x00003FD8 //A10 = +2.97894685764287382560e-12L
data8 0x967A0ECC142382D9, 0x0000BFD5 //A11 = -2.67300472044743953909e-13L
data8 0xC6D8869855133985, 0x00003FD1 //A12 = +2.20763189681614758000e-14L
data8 0xD10AC0B228ABCECC, 0x0000BFCD //A13 = -1.45052027893524847250e-15L
data8 0xF7C6DEB4522487A3, 0x00003FC8 //A14 = +5.37280367113168366711e-17L
// Pol15
data8 0xB8F57DECFAC3B255, 0x00003FFA //A0 = +4.51559943173131409760e-02L
data8 0xEC1B8A6C822C036F, 0x0000BFF6 //A1 = -3.60271577347565115947e-03L
data8 0x963A6DD66951B72E, 0x00003FF3 //A2 = +2.86537625289770759336e-04L
data8 0xBE93F9E80DF4AE0A, 0x0000BFEF //A3 = -2.27186718010906557773e-05L
data8 0xF10589FC10D908E0, 0x00003FEB //A4 = +1.79575113004740124999e-06L
data8 0x97F1A2435C7877EF, 0x0000BFE8 //A5 = -1.41508767557208714648e-07L
data8 0xBEFF2FB5F00E9327, 0x00003FE4 //A6 = +1.11174782364058338591e-08L
data8 0xEF5E09DC714DF198, 0x0000BFE0 //A7 = -8.70813302639377671664e-10L
data8 0x958A6EB9408970A4, 0x00003FDD //A8 = +6.80032608255179732632e-11L
data8 0xBA31F40954675710, 0x0000BFD9 //A9 = -5.29198388081297293593e-12L
data8 0xE63B9CEEDC4CF0E6, 0x00003FD5 //A10 = +4.08975721481205179918e-13L
data8 0x8AF8F1E3FED32CEC, 0x0000BFD2 //A11 = -3.08580807479307213059e-14L
data8 0x9A88033A08842BEA, 0x00003FCE //A12 = +2.14455258045503137285e-15L
data8 0x88BCF775B7B3A939, 0x0000BFCA //A13 = -1.18601440246395438386e-16L
data8 0x88687B63A5B7135E, 0x00003FC5 //A14 = +3.69734984736162880476e-18L
// Pol16
data8 0x99B8A501204BF3E7, 0x00003FFA //A0 = +3.75296063885057657456e-02L
data8 0xA33FA20D2867C79C, 0x0000BFF6 //A1 = -2.49097544033960143953e-03L
data8 0xACFD14CA6AA55829, 0x00003FF2 //A2 = +1.64974783411741182991e-04L
data8 0xB6E9B4ED9B378B09, 0x0000BFEE //A3 = -1.09024594422859744844e-05L
data8 0xC0FD95D38ADCF301, 0x00003FEA //A4 = +7.18945888498730738040e-07L
data8 0xCB302F7AAFFFA074, 0x0000BFE6 //A5 = -4.73084450875945514829e-08L
data8 0xD578674188198402, 0x00003FE2 //A6 = +3.10640208133938026422e-09L
data8 0xDFCC6ED4219E7FC4, 0x0000BFDE //A7 = -2.03543610142159316364e-10L
data8 0xEA1F448AA373E4A9, 0x00003FDA //A8 = +1.33083028465054001215e-11L
data8 0xF44780B8EACD37B5, 0x0000BFD6 //A9 = -8.67854438613319891312e-13L
data8 0xFD55794492F53AEE, 0x00003FD2 //A10 = +5.62514216652784597182e-14L
data8 0x805C040421E7A098, 0x0000BFCF //A11 = -3.56269003968981157635e-15L
data8 0xEFCCD20DE93A138E, 0x00003FCA //A12 = +2.07993414310230172191e-16L
data8 0xB259764466732080, 0x0000BFC6 //A13 = -9.66834364652262630640e-18L
data8 0x9597C1DB6AF830E4, 0x00003FC1 //A14 = +2.53420063550355940811e-19L
// Pol17
data8 0xFFFCBD66BAA4368C, 0x00003FF9 //A0 = +3.12484454387527380657e-02L
data8 0xE28174723762D197, 0x0000BFF5 //A1 = -1.72810121976742793952e-03L
data8 0xC81D832836019EC4, 0x00003FF1 //A2 = +9.54224026432644399736e-05L
data8 0xB0885530C7D7AB5B, 0x0000BFED //A3 = -5.26107996417947739207e-06L
data8 0x9B7EA64F62F6FD06, 0x00003FE9 //A4 = +2.89631495607631932854e-07L
data8 0x88C24ACAA9042166, 0x0000BFE5 //A5 = -1.59208376111789845204e-08L
data8 0xF033E5CD9B7F2822, 0x00003FE0 //A6 = +8.73852423930118273815e-10L
data8 0xD2A1B161FB4DFBFE, 0x0000BFDC //A7 = -4.78920839886600387264e-11L
data8 0xB86B27FCBB5A1E9D, 0x00003FD8 //A8 = +2.62074563162805723295e-12L
data8 0xA124E1303F08E508, 0x0000BFD4 //A9 = -1.43124677534734729453e-13L
data8 0x8C0B270950D7C697, 0x00003FD0 //A10 = +7.77397948226387851915e-15L
data8 0xEE034E350C65D2D9, 0x0000BFCB //A11 = -4.12886586201102092942e-16L
data8 0xBA94473E52495304, 0x00003FC7 //A12 = +2.02289587087169937807e-17L
data8 0xE913D34CBB853CEE, 0x0000BFC2 //A13 = -7.89697093687557412061e-19L
data8 0xA44576A85E8CAB59, 0x00003FBD //A14 = +1.73929048516879172258e-20L
// Pol18
data8 0xD579A3FE4622DED2, 0x00003FF9 //A0 = +2.60589793198885278242e-02L
data8 0x9D97EB84E7CD89C8, 0x0000BFF5 //A1 = -1.20234251012583627659e-03L
data8 0xE86EFDC2CCA5C47B, 0x00003FF0 //A2 = +5.54164790116744315389e-05L
data8 0xAB39FA5621E39B15, 0x0000BFEC //A3 = -2.55147332073979814633e-06L
data8 0xFC0244F58F8D8097, 0x00003FE7 //A4 = +1.17350772365097747003e-07L
data8 0xB941D44B71B14FE2, 0x0000BFE3 //A5 = -5.39169255673480031672e-09L
data8 0x880B4A40B6F2C901, 0x00003FDF //A6 = +2.47462779512141204748e-10L
data8 0xC7998AE5652CDCFC, 0x0000BFDA //A7 = -1.13459336509953900777e-11L
data8 0x92438AA45915CD95, 0x00003FD6 //A8 = +5.19633524685027215673e-13L
data8 0xD6067243AD3AEAE6, 0x0000BFD1 //A9 = -2.37615683835509918256e-14L
data8 0x9BD0722A07669E4D, 0x00003FCD //A10 = +1.08117849400479298186e-15L
data8 0xDDF6F1B79F50E3C4, 0x0000BFC8 //A11 = -4.81309059042573202592e-17L
data8 0x91F283C0351A9ACA, 0x00003FC4 //A12 = +1.97795505638619048412e-18L
data8 0x990BC4FAFA9C7542, 0x0000BFBF //A13 = -6.48174913943425248713e-20L
data8 0xB536865B89676892, 0x00003FB9 //A14 = +1.19916696090758913485e-21L
// Pol19
data8 0xB241CEB1B7C953F1, 0x00003FF9 //A0 = +2.17598950382519671244e-02L
data8 0xDBD6FBA9B11B85E1, 0x0000BFF4 //A1 = -8.38622198373701898430e-04L
data8 0x877605B1AD082441, 0x00003FF0 //A2 = +3.22964249573360786077e-05L
data8 0xA6D04DC067A5D310, 0x0000BFEB //A3 = -1.24285881515578912302e-06L
data8 0xCD458A72BC161315, 0x00003FE6 //A4 = +4.77935289502172654216e-08L
data8 0xFC6902CFB5DE90A2, 0x0000BFE1 //A5 = -1.83652591038905929358e-09L
data8 0x9B12B0707DFE615C, 0x00003FDD //A6 = +7.05190381049444126079e-11L
data8 0xBE67972F2C8EE5AE, 0x0000BFD8 //A7 = -2.70581282732878853626e-12L
data8 0xE99D8CAF9A3FFE02, 0x00003FD3 //A8 = +1.03746090805854376435e-13L
data8 0x8F35F5BBEF9E4299, 0x0000BFCF //A9 = -3.97489765699919189983e-15L
data8 0xAF6E62C3C91B7178, 0x00003FCA //A10 = +1.52162305785839987182e-16L
data8 0xD6636229C1646963, 0x0000BFC5 //A11 = -5.81100425482928485309e-18L
data8 0x810331BF289E068F, 0x00003FC1 //A12 = +2.18555638648715837944e-19L
data8 0x8E3D07CA59546B83, 0x0000BFBC //A13 = -7.53003820427900359431e-21L
data8 0xD5970B291ED73560, 0x00003FB6 //A14 = +1.76677518655145552907e-22L
LOCAL_OBJECT_END(erfc_p_table)
.section .text
GLOBAL_LIBM_ENTRY(erfc)
{ .mfi
alloc r32 = ar.pfs, 0, 33, 4, 0
fma.s1 FR_Tmp = f1, f1, f8 // |x|+1, if x >= 0
nop.i 0
}
{ .mfi
addl EXP_AD_TB1 = @ltoff(exp_table_1), gp
fms.s1 FR_Tmp1 = f1, f1, f8 // |x|+1, if x < 0
mov exp_GR_rshf_2to56 = 0x4768 // begin 1.1 2^(63+56)
};;
{ .mfi
ld8 EXP_AD_TB1 = [EXP_AD_TB1]
fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
mov exp_GR_rshf_2to56 = 0x4768 // begin 1.1 2^(63+56)
}
{ .mlx
mov exp_TB1_size = 0x100
movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif. of 1/ln2
};;
{ .mfi
nop.m 0
fclass.m p8,p0 = f8,0x07 // p8: x = 0
shl exp_GR_rshf_2to56 = exp_GR_rshf_2to56, 48 //end 1.1 2^(63+56)
}
{ .mfi
mov exp_GR_exp_2tom56 = 0xffff-56
fnma.s1 EXP_NORM_f8 = f8, f8, f0 // high bits for -x^2
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // form 1/ln2 * 2^63
(p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x|, if x >= 0
mov GR_POS_ARG_ASYMP = 0x403C
}
{ .mfi
mov GR_NEG_ARG_ASYMP = 0x4018
(p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x|, if x < 0
mov exp_GR_rshf = 0x43e8 // begin 1.1 2^63 for right shift
};;
{ .mfi
setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 // 2^-56 for scaling Nfloat
fclass.m p10,p0 = f8, 0x21 // p10: x = +inf
mov exp_GR_17ones = 0x1FFFF
}
{ .mlx
setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 // const 1.10*2^(63+56)
movl GR_ERFC_XB_TB = 0x1A0
};;
.pred.rel "mutex",p6,p7
{ .mfi
ldfd FR_UnfBound = [EXP_AD_TB1], 16
(p6) fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^2,x >=0
shl exp_GR_rshf = exp_GR_rshf, 48 //end 1.1 2^63 for right shift
}
{ .mfi
nop.m 0
(p7) fma.s1 FR_Tmp = FR_Tmp1, FR_Tmp1, f0 // (|x|+1)^2, x<0
mov GR_0x1 = 0x1
};;
{ .mfi
mov GR_BIAS = 0x0FFFF
fclass.m p9,p0 = f8, 0x22 // p9: x = -inf
shl GR_EpsNorm = GR_0x1,53
}
{ .mfb
mov exp_TB2_size = 0x80
(p8) fma.d.s0 f8 = f1, f1, f0 //p8: y = 1.0, x = 0
(p8) br.ret.spnt b0 //p8: quick exit for x = 0
};;
{ .mfi
nop.m 0
fclass.m p11,p0 = f8, 0xc3 // p11: x = nan
nop.i 0
}
{ .mfi
setf.d EXP_RSHF = exp_GR_rshf //Form right shift const 1.100 * 2^63
fma.s1 FR_NormX = f8,f1,f0
nop.i 0
};;
{ .mfi
setf.d FR_EpsNorm = GR_EpsNorm
nop.f 0
(p6) shl GR_ARG_ASYMP = GR_POS_ARG_ASYMP, 48//p6:ARG_ASYMP= 28.0,x>=0
}
{ .mfi
nop.m 0
fma.s1 FR_2 = f1, f1, f1
nop.i 0
};;
{ .mfi
ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16
fma.s1 f8_sq_lo = f8, f8, EXP_NORM_f8 // low bits for -x^2
(p7) shl GR_ARG_ASYMP = GR_NEG_ARG_ASYMP, 48//p6:ARG_ASYMP= 6.0,x < 0
};;
{ .mfi
sub GR_mBIAS = r0, GR_BIAS
fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^4
nop.i 0
}
{ .mfi
ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16
nop.f 0
nop.i 0
};;
{ .mfi
getf.d GR_AbsArg = FR_AbsArg
nop.f 0
add GR_ERFC_XB_TB = GR_ERFC_XB_TB, EXP_AD_TB1//pointer to XB_TBL
}
{ .mfb
shladd GR_ShftPi_bias = GR_BIAS, 4, GR_mBIAS // BIAS * 2^4 - BIAS
(p9) fma.d.s0 f8 = f1, f1, f1 // p9: y = 2 for x = -inf
(p9) br.ret.spnt b0 // p9: quick exit for x = -inf
};;
{ .mfi
add GR_ERFC_P_TB = 0x140, GR_ERFC_XB_TB // pointer to P_TBL
fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56
shladd GR_ShftPi_bias = GR_ShftPi_bias, 4, r0 // BIAS * 240
}
{ .mfb
nop.m 0
(p10) fma.d.s0 f8 = f0, f1, f0 // p10: y = 0 for x = +inf
(p10) br.ret.spnt b0 // p10: quick exit for x = +inf
};;
.pred.rel "mutex",p6,p7
{ .mfi
(p6) cmp.gt.unc p15,p0 = GR_AbsArg,GR_ARG_ASYMP //p15: x > 28.0,p6: x >= 0
nop.f 0
(p7) cmp.gt.unc p14,p0 = GR_AbsArg, GR_ARG_ASYMP //p14: x < - 6.0,p7: x < 0
}
{ .mfb
add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1
(p11) fma.d.s0 f8 = f8, f1, f0 //p11: y = x for x = nan
(p11) br.ret.spnt b0 //p11: quick exit for x = nan
};;
{ .mfi
add EXP_AD_P = exp_TB2_size, EXP_AD_TB2
fms.s1 f8_sq_lo = f1, f1, f8_sq_lo // 1 - low bits for -x^2
nop.i 0
};;
{ .mfi
ldfpd exp_P4, exp_P3 = [EXP_AD_P], 16
fmerge.s FR_X = f8,f8
shladd GR_ShftXBi_bias = GR_mBIAS, 4, r0
}
{ .mfb
nop.m 0
(p14) fnma.d.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,FR_2 //p14:y ~=~ 2,x< -6.0
(p14) br.ret.spnt b0 //p14: quick exit for x < -6.0
};;
//p15: y ~=~ 0.0(result with underflow error), x > ARG_ASYMP = 28,
{ .mfi
ldfpd exp_P2, exp_P1 = [EXP_AD_P]
fma.d.s0 FR_Tmpf = f1, f1, FR_EpsNorm // flag i
nop.i 0
}
{ .mfb
(p15) mov GR_Parameter_TAG = 208
(p15) fma.d.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0
(p15) br.cond.spnt __libm_error_region
};;
//p8: x < 27.0, result without ungerflow error
{ .mfi
getf.exp GR_IndxPlusBias = FR_Tmp // exp + bias for (|x|+1)^4
fcmp.lt.s1 p8,p0 = FR_NormX,FR_UnfBound
nop.i 0
}
{ .mfi
nop.m 0
fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
nop.i 0
};;
{ .mmi
shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias
shladd GR_ShftPi = GR_IndxPlusBias, 4, GR_ShftPi_bias
shl GR_ShftPi_8 = GR_IndxPlusBias, 8
};;
{ .mmi
getf.sig exp_GR_N = EXP_W_2TO56_RSH
add GR_ERFC_XB_TB = GR_ERFC_XB_TB, GR_ShftXBi// pointer to XB[i]
sub GR_ShftPi = GR_ShftPi_8, GR_ShftPi // (256-16)*i
};;
{ .mmi
ldfe FR_Xb = [GR_ERFC_XB_TB]
add GR_ShftA12 = 0xC0, GR_ShftPi // pointer shift for A12
add GR_ShftA13 = 0xD0, GR_ShftPi // pointer shift for A13
};;
{ .mfi
add GR_P_A13 = GR_ERFC_P_TB, GR_ShftA13 // pointer to A13
nop.f 0
and exp_GR_index_1 = 0x0f, exp_GR_N
}
{ .mfi
add GR_P_A12 = GR_ERFC_P_TB, GR_ShftA12 // pointer to A12
fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
nop.i 0
};;
{ .mfi
ldfe FR_A12 = [GR_P_A12], -64
nop.f 0
and exp_GR_index_2_16 = 0x70, exp_GR_N
}
{ .mfi
ldfe FR_A13 = [GR_P_A13], -64
nop.f 0
shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
};;
{ .mmi
ldfe FR_A8 = [GR_P_A12], 32
ldfe FR_A9 = [GR_P_A13], 32
add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
};;
{ .mmi
ldfe FR_A10 = [GR_P_A12], -96
ldfe FR_A11 = [GR_P_A13], -96
nop.i 0
};;
{ .mmi
ldfe FR_A4 = [GR_P_A12], 32
ldfe FR_A5 = [GR_P_A13], 32
shr r2 = exp_GR_N, 0x7
};;
{ .mfi
ldfe FR_A6 = [GR_P_A12], -64
fma.s1 exp_rP4pP3 = exp_r, exp_P4, exp_P3
nop.i 0
}
{ .mfi
ldfe FR_A7 = [GR_P_A13], -64
fma.s1 exp_rsq = exp_r, exp_r, f0
nop.i 0
};;
{ .mmi
ldfe FR_A2 = [GR_P_A12], -32
ldfe FR_A3 = [GR_P_A13], -32
addl exp_GR_biased_M = 0xffff, r2
};;
{ .mmi
ldfe FR_A0 = [GR_P_A12], 224
ldfe FR_A1 = [GR_P_A13]
nop.i 0
};;
{ .mfi
ldfe FR_A14 = [GR_P_A12]
fms.s1 FR_LocArg = FR_AbsArg, f1, FR_Xb // xloc = x - x[i]
nop.i 0
};;
{ .mmi
setf.exp EXP_2M = exp_GR_biased_M
ldfe exp_T1 = [EXP_AD_T1]
nop.i 0
};;
{ .mfi
ldfe exp_T2 = [EXP_AD_T2]
fma.s1 exp_P_hi = exp_rsq, exp_P1, exp_r
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_rcube = exp_r, exp_rsq, f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 exp_P_lo = exp_r, exp_rP4pP3, exp_P2
nop.i 0
};;
{ .mfi
nop.m 0
fnma.s1 exp_f = EXP_Nfloat, exp_ln2_by_128_lo, f8_sq_lo
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_0_1 = FR_LocArg, FR_LocArg, f0 // xloc ^2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_0_2 = FR_A13, FR_LocArg, FR_A12
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_1_1 = FR_A9, FR_LocArg, FR_A8
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_1_2 = FR_A11, FR_LocArg, FR_A10
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_2_1 = FR_A5, FR_LocArg, FR_A4
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_2_2 = FR_A7, FR_LocArg, FR_A6
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_3_1 = FR_A1, FR_LocArg, FR_A0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_3_2 = FR_A3, FR_LocArg, FR_A2
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_6_1 = FR_P14_0_1, FR_A14, FR_P14_0_2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_7_2 = FR_P14_0_1, FR_P14_0_1, f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_7_1 = FR_P14_0_1, FR_P14_1_2, FR_P14_1_1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 exp_S2 = exp_f, exp_T2, f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_S1 = EXP_2M, exp_T1, f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_8_1 = FR_P14_0_1, FR_P14_3_2, FR_P14_3_1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_8_2 = FR_P14_0_1, FR_P14_2_2, FR_P14_2_1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_12_1 = FR_P14_7_2, FR_P14_6_1, FR_P14_7_1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 exp_S = exp_S1, exp_S2, f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 exp_P = exp_rcube, exp_P_lo, exp_P_hi
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_P14_13_1 = FR_P14_7_2, FR_P14_8_2, FR_P14_8_1
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_P14_13_2 = FR_P14_7_2, FR_P14_7_2, f0 // xloc^8
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_Exp = exp_S, exp_P, exp_S // exp(-x^2)
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_Pol = FR_P14_13_2, FR_P14_12_1, FR_P14_13_1
nop.i 0
};;
{ .mfi
nop.m 0
fma.d.s0 FR_Tmpf = f8, f1, f0 // flag d
nop.i 0
};;
//p6: result for 0 < x < = 28.0,
//p7: result for -6.0 <= x < 0,
//p8: exit for - 6.0 <= x < UnfBound ~=~ 26.54..
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fma.d.s0 f8 = FR_Exp, FR_Pol, f0
nop.i 0
}
{ .mfb
mov GR_Parameter_TAG = 208
(p7) fnma.d.s0 f8 = FR_Exp, FR_Pol, FR_2
(p8) br.ret.sptk b0
};;
GLOBAL_LIBM_END(erfc)
libm_alias_double_other (erfc, erfc)
// call via (p15) br.cond.spnt __libm_error_region
// for x > ARG_ASYMP = 28.0
// or
//
// after .endp erfc for UnfBound < = x < = ARG_ASYMP = 28.0
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
.save ar.pfs,GR_SAVE_PFS
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
add sp=-64,sp // Create new stack
nop.f 0
mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
nop.b 0
}
{ .mib
stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .mib
mov gp = GR_SAVE_GP // Restore gp
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
br.ret.sptk b0 // Return
};;
LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
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