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Diffstat (limited to 'sysdeps/ia64/fpu/s_erfcf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_erfcf.S | 983 |
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diff --git a/sysdeps/ia64/fpu/s_erfcf.S b/sysdeps/ia64/fpu/s_erfcf.S deleted file mode 100644 index 2e3eeab3c7..0000000000 --- a/sysdeps/ia64/fpu/s_erfcf.S +++ /dev/null @@ -1,983 +0,0 @@ -.file "erfcf.s" - - -// Copyright (c) 2002 - 2005, Intel Corporation -// All rights reserved. -// -// Contributed 2002 by the Intel Numerics Group, Intel Corporation -// -// 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 -//============================================================== -// 01/17/02 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 -//============================================================== -// float erfcf(float) -// -// Overview of operation -//============================================================== -// 1. 0 <= x <= 10.06 -// -// erfcf(x) = P15(x) * exp( -x^2 ) -// -// Comment: -// -// Let x(0)=0, x(i) = 2^(i), i=1,...3, x(4)= 10.06 -// -// Let x(i)<= x < x(i+1). -// We can find i as exponent of argument x (let i = 0 for 0<= x < 2 ) -// -// Let P15(x) - polynomial approximation of degree 15 for function -// erfcf(x) * exp( x^2) and x(i) <= x <= x(i+1), i = 0,1,2,3 -// Polynomial coeffitients we have in the table erfc_p_table. -// -// So we can find result for erfcf(x) as above. -// Algorithm description for exp function see below. -// -// 2. -4.4 <= x < 0 -// -// erfcf(x) = 2.0 - erfcf(-x) -// -// 3. x > 10.06 -// -// erfcf(x) ~=~ 0.0 -// -// 4. x < -4.4 -// -// erfcf(x) ~=~ 2.0 - -// Special values -//============================================================== -// erfcf(+0) = 1.0 -// erfcf(-0) = 1.0 - -// erfcf(+qnan) = +qnan -// erfcf(-qnan) = -qnan -// erfcf(+snan) = +qnan -// erfcf(-snan) = -qnan - -// erfcf(-inf) = 2.0 -// erfcf(+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 erfcf: -// -// Let exp(r) = 1 + x + 0.5*x^2 + (1/6)*x^3 -// Let delta = 0. -//============================================================== -// -// Registers used -//============================================================== -// Floating Point registers used: -// f8, input -// f6,f7,f9 -> f11, f32 -> f92 - -// General registers used: -// r14 -> r22,r32 -> r50 - -// Predicate registers used: -// p6 -> p15 - -// Assembly macros -//============================================================== -EXP_AD_TB1 = r14 -exp_GR_sig_inv_ln2 = r15 -exp_TB1_size = r16 -exp_GR_rshf_2to56 = r17 -exp_GR_exp_2tom56 = r18 - -exp_GR_rshf = r33 -EXP_AD_TB2 = r34 -EXP_AD_P = r35 -exp_GR_N = r36 -exp_GR_index_1 = r37 -exp_GR_index_2_16 = r38 -exp_GR_biased_M = r39 -EXP_AD_T1 = r40 -EXP_AD_T2 = r41 -exp_TB2_size = r42 - -// GR for erfcf(x) -//============================================================== -GR_IndxPlusBias = r19 -GR_ExpMask = r20 -GR_BIAS = r21 -GR_ShftPi_bias = r22 - -GR_P_POINT_1 = r43 -GR_P_POINT_2 = r44 -GR_P_POINT_3 = r45 -GR_P_POINT_4 = r46 - -GR_ShftPi = r47 -GR_EpsNorm = r48 - -GR_05 = r49 -GR_1_by_6 = r50 - -// GR for __libm_support call -//============================================================== - -GR_SAVE_B0 = r43 -GR_SAVE_PFS = r44 -GR_SAVE_GP = r45 -GR_SAVE_SP = r46 - -GR_Parameter_X = r47 -GR_Parameter_Y = r48 -GR_Parameter_RESULT = r49 -GR_Parameter_TAG = r50 - - -// 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_ln2_by_128_hi = f11 - -EXP_RSHF_2TO56 = f32 -exp_ln2_by_128_lo = f33 -EXP_RSHF = f34 -EXP_Nfloat = f35 -exp_r = f36 -exp_rsq = f37 -EXP_2M = f38 -exp_S1 = f39 -exp_T1 = f40 -exp_P = f41 -exp_S = f42 -EXP_NORM_f8 = f43 -exp_S2 = f44 -exp_T2 = f45 - -// FR for erfcf(x) -//============================================================== -FR_AbsArg = f46 -FR_Tmp = f47 -FR_Tmp1 = f48 -FR_Tmpf = f49 -FR_NormX = f50 - -FR_A15 = f51 -FR_A14 = f52 - -FR_A13 = f53 -FR_A12 = f54 - -FR_A11 = f55 -FR_A10 = f56 - -FR_A9 = f57 -FR_A8 = f58 - -FR_A7 = f59 -FR_A6 = f60 - -FR_A5 = f61 -FR_A4 = f62 - -FR_A3 = f63 -FR_A2 = f64 - -FR_A1 = f65 -FR_A0 = f66 - -FR_P15_0_1 = f67 -FR_P15_1_1 = f68 -FR_P15_1_2 = f69 -FR_P15_2_1 = f70 -FR_P15_2_2 = f71 -FR_P15_3_1 = f72 -FR_P15_3_2 = f73 -FR_P15_4_1 = f74 -FR_P15_4_2 = f75 -FR_P15_7_1 = f76 -FR_P15_7_2 = f77 -FR_P15_8_1 = f78 -FR_P15_9_1 = f79 -FR_P15_9_2 = f80 -FR_P15_13_1 = f81 -FR_P15_14_1 = f82 -FR_P15_14_2 = f83 - -FR_2 = f84 -FR_05 = f85 -FR_1_by_6 = f86 -FR_Pol = f87 -FR_Exp = f88 - -FR_POS_ARG_ASYMP = f89 -FR_NEG_ARG_ASYMP = f90 - -FR_UnfBound = f91 -FR_EpsNorm = f92 - -// Data tables -//============================================================== -RODATA -.align 16 - -// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** - -// double-extended 1/ln(2) -// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 -// 3fff b8aa 3b29 5c17 f0bc -// For speed the significand will be loaded directly with a movl and setf.sig -// and the exponent will be bias+63 instead of bias+0. Thus subsequent -// computations need to scale appropriately. -// The constant 128/ln(2) is needed for the computation of w. This is also -// obtained by scaling the computations. -// -// Two shifting constants are loaded directly with movl and setf.d. -// 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7) -// This constant is added to x*1/ln2 to shift the integer part of -// x*128/ln2 into the rightmost bits of the significand. -// The result of this fma is EXP_W_2TO56_RSH. -// 2. EXP_RSHF = 1.1000..00 * 2^(63) -// This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give -// the integer part of w, n, as a floating-point number. -// The result of this fms is EXP_Nfloat. - - -LOCAL_OBJECT_START(exp_table_1) - -data4 0x4120f5c3, 0x408ccccd //POS_ARG_ASYMP = 10.06, NEG_ARG_ASYMP = 4.4 -data4 0x41131Cdf, 0x00800000 //UnfBound ~=~ 9.1, EpsNorm ~=~ 1.1754944e-38 -// -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(erfc_p_table) - -// Pol_0 -data8 0xBEA3260C63CB0446 //A15 = -5.70673541831883454676e-07 -data8 0x3EE63D6178077654 //A14 = +1.06047480138940182343e-05 -data8 0xBF18646BC5FC70A7 //A13 = -9.30491237309283694347e-05 -data8 0x3F40F92F909117FE //A12 = +5.17986512144075019133e-04 -data8 0xBF611344289DE1E6 //A11 = -2.08438217390159994419e-03 -data8 0x3F7AF9FE6AD16DC0 //A10 = +6.58606893292862351928e-03 -data8 0xBF91D219E196CBA7 //A9 = -1.74030345858217321001e-02 -data8 0x3FA4AFDDA355854C //A8 = +4.04042493708041968315e-02 -data8 0xBFB5D465BB7025AE //A7 = -8.52721769916999425445e-02 -data8 0x3FC54C15A95B717D //A6 = +1.66384418195672549029e-01 -data8 0xBFD340A75B4B1AB5 //A5 = -3.00821150926292166899e-01 -data8 0x3FDFFFC0BFCD247F //A4 = +4.99984919839853542841e-01 -data8 0xBFE81270C361852B //A3 = -7.52251035312075583309e-01 -data8 0x3FEFFFFFC67295FC //A2 = +9.99999892800303301771e-01 -data8 0xBFF20DD74F8CD2BF //A1 = -1.12837916445020868099e+00 -data8 0x3FEFFFFFFFFE7C1D //A0 = +9.99999999988975570714e-01 -// Pol_1 -data8 0xBDE8EC4BDD953B56 //A15 = -1.81338928934942767144e-10 -data8 0x3E43607F269E2A1C //A14 = +9.02309090272196442358e-09 -data8 0xBE8C4D9E69C10E02 //A13 = -2.10875261143659275328e-07 -data8 0x3EC9CF2F84566725 //A12 = +3.07671055805877356583e-06 -data8 0xBF007980B1B46A4D //A11 = -3.14228438702169818945e-05 -data8 0x3F2F4C3AD6DEF24A //A10 = +2.38783056770846320260e-04 -data8 0xBF56F5129F8D30FA //A9 = -1.40120333363130546426e-03 -data8 0x3F7AA6C7ABFC38EE //A8 = +6.50671002200751820429e-03 -data8 0xBF98E7522CB84BEF //A7 = -2.43199195666185511109e-02 -data8 0x3FB2F68EB1C3D073 //A6 = +7.40746673580490638637e-02 -data8 0xBFC7C16055AC6385 //A5 = -1.85588876564704611769e-01 -data8 0x3FD8A707AEF5A440 //A4 = +3.85194702967570635211e-01 -data8 0xBFE547BFE39AE2EA //A3 = -6.65008492032112467310e-01 -data8 0x3FEE7C91BDF13578 //A2 = +9.52706213932898128515e-01 -data8 0xBFF1CB5B61F8C589 //A1 = -1.11214769621105541214e+00 -data8 0x3FEFEA56BC81FD37 //A0 = +9.97355812243688815239e-01 -// Pol_2 -data8 0xBD302724A12F46E0 //A15 = -5.73866382814058809406e-14 -data8 0x3D98889B75D3102E //A14 = +5.57829983681360947356e-12 -data8 0xBDF16EA15074A1E9 //A13 = -2.53671153922423457844e-10 -data8 0x3E3EC6E688CFEE5F //A12 = +7.16581828336436419561e-09 -data8 0xBE82E5ED44C52609 //A11 = -1.40802202239825487803e-07 -data8 0x3EC120BE5CE42353 //A10 = +2.04180535157522081699e-06 -data8 0xBEF7B8B0311A1911 //A9 = -2.26225266204633600888e-05 -data8 0x3F29A281F43FC238 //A8 = +1.95577968156184077632e-04 -data8 0xBF55E19858B3B7A4 //A7 = -1.33552434527526534043e-03 -data8 0x3F7DAC8C3D12E5FD //A6 = +7.24463253680473816303e-03 -data8 0xBF9FF9C04613FB47 //A5 = -3.12261622211693854028e-02 -data8 0x3FBB3D5DBF9D9366 //A4 = +1.06405123978743883370e-01 -data8 0xBFD224DE9F62C258 //A3 = -2.83500342989133623476e-01 -data8 0x3FE28A95CB8C6D3E //A2 = +5.79417131000276437708e-01 -data8 0xBFEC21205D358672 //A1 = -8.79043752717008257224e-01 -data8 0x3FEDAE44D5EDFE5B //A0 = +9.27523057776805771830e-01 -// Pol_3 -data8 0xBCA3BCA734AC82F1 //A15 = -1.36952437983096410260e-16 -data8 0x3D16740DC3990612 //A14 = +1.99425676175410093285e-14 -data8 0xBD77F4353812C46A //A13 = -1.36162367755616790260e-12 -data8 0x3DCFD0BE13C73DB4 //A12 = +5.78718761040355136007e-11 -data8 0xBE1D728DF71189B4 //A11 = -1.71406885583934105120e-09 -data8 0x3E64252C8CB710B5 //A10 = +3.75233795940731111303e-08 -data8 0xBEA514B93180F33D //A9 = -6.28261292774310809962e-07 -data8 0x3EE1381118CC7151 //A8 = +8.21066421390821904504e-06 -data8 0xBF1634404FB0FA72 //A7 = -8.47019436358372148764e-05 -data8 0x3F46B2CBBCF0EB32 //A6 = +6.92700845213200923490e-04 -data8 0xBF725C2B445E6D81 //A5 = -4.48243046949004063741e-03 -data8 0x3F974E7CFA4D89D9 //A4 = +2.27603462002522228717e-02 -data8 0xBFB6D7BAC2E342D1 //A3 = -8.92292714882032736443e-02 -data8 0x3FD0D156AD9CE2A6 //A2 = +2.62777013343603696631e-01 -data8 0xBFE1C228572AADB0 //A1 = -5.54950876471982857725e-01 -data8 0x3FE8A739F48B9A3B //A0 = +7.70413377406675619766e-01 -LOCAL_OBJECT_END(erfc_p_table) - - -.section .text -GLOBAL_LIBM_ENTRY(erfcf) - -// Form index i for table erfc_p_table as exponent of x -// We use i + bias in real calculations -{ .mlx - getf.exp GR_IndxPlusBias = f8 // (sign + exp + bias) of x - movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif.of 1/ln2 -} -{ .mlx - addl EXP_AD_TB1 = @ltoff(exp_table_1), gp - movl exp_GR_rshf_2to56 = 0x4768000000000000 // 1.100 2^(63+56) -} -;; - -// Form argument EXP_NORM_f8 for exp(-x^2) -{ .mfi - ld8 EXP_AD_TB1 = [EXP_AD_TB1] - fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0 - mov GR_BIAS = 0x0FFFF -} -{ .mfi - mov exp_GR_exp_2tom56 = 0xffff-56 - fnma.s1 EXP_NORM_f8 = f8, f8, f0 // -x^2 - mov GR_ExpMask = 0x1ffff -} -;; - -// Form two constants we need -// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 -// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand - -// p9: x = 0,+inf,-inf,nan,unnorm. -// p10: x!= 0,+inf,-inf,nan,unnorm. -{ .mfi - setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // Form 1/ln2*2^63 - fclass.m p9,p10 = f8,0xef - shl GR_ShftPi_bias = GR_BIAS, 7 -} -{ .mfi - setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 //Const 1.10*2^(63+56) - nop.f 0 - and GR_IndxPlusBias = GR_IndxPlusBias, GR_ExpMask // i + bias -} -;; - -{ .mfi - alloc r32 = ar.pfs, 0, 15, 4, 0 -(p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x| if x >= 0 - cmp.lt p15,p0 = GR_IndxPlusBias, GR_BIAS//p15: i < 0 (for |x|<1) -} -{ .mlx - setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 //2^-56 for scaling Nfloat - movl exp_GR_rshf = 0x43e8000000000000 //1.10 2^63,right shift. -} -;; - -{ .mfi - ldfps FR_POS_ARG_ASYMP, FR_NEG_ARG_ASYMP = [EXP_AD_TB1],8 - nop.f 0 -(p15) mov GR_IndxPlusBias = GR_BIAS //Let i = 0 if i < 0 -} -{ .mlx - mov GR_P_POINT_3 = 0x1A0 - movl GR_05 = 0x3fe0000000000000 -} -;; - -// Form shift GR_ShftPi from the beginning of erfc_p_table -// to the polynomial with number i -{ .mfi - ldfps FR_UnfBound, FR_EpsNorm = [EXP_AD_TB1],8 - nop.f 0 - shl GR_ShftPi = GR_IndxPlusBias, 7 -} -{ .mfi - setf.d EXP_RSHF = exp_GR_rshf // Form right shift 1.100 * 2^63 -(p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x| if x < 0 - mov exp_TB1_size = 0x100 -} -;; - -// Form pointer GR_P_POINT_3 to the beginning of erfc_p_table -{ .mfi - setf.d FR_05 = GR_05 - nop.f 0 - sub GR_ShftPi = GR_ShftPi,GR_ShftPi_bias -} -{ .mfb - add GR_P_POINT_3 = GR_P_POINT_3, EXP_AD_TB1 - nop.f 0 -(p9) br.cond.spnt SPECIAL // For x = 0,+inf,-inf,nan,unnorm -} -;; - -{ .mfi - add GR_P_POINT_1 = GR_P_POINT_3, GR_ShftPi - nop.f 0 - add GR_P_POINT_2 = GR_P_POINT_3, GR_ShftPi -} -{ .mfi - ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16 - fma.s1 FR_NormX = f8,f1,f0 - add GR_P_POINT_3 = GR_P_POINT_3, GR_ShftPi -} -;; - -// Load coefficients for polynomial P15(x) -{ .mfi - ldfpd FR_A15, FR_A14 = [GR_P_POINT_1], 16 - nop.f 0 - add GR_P_POINT_3 = 0x30, GR_P_POINT_3 -} -{ .mfi - ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16 - nop.f 0 - add GR_P_POINT_2 = 0x20, GR_P_POINT_2 -} -;; - -// Now EXP_AD_TB1 points to the beginning of table 1 -{ .mlx - ldfpd FR_A13, FR_A12 = [GR_P_POINT_1] - movl GR_1_by_6 = 0x3FC5555555555555 -} -{ .mfi - add GR_P_POINT_4 = 0x30, GR_P_POINT_2 - nop.f 0 - nop.i 0 -} -;; - -{ .mfi - ldfpd FR_A11, FR_A10 = [GR_P_POINT_2] - fma.s1 FR_2 = f1, f1, f1 - mov exp_TB2_size = 0x80 -} -{ .mfi - ldfpd FR_A9, FR_A8 = [GR_P_POINT_3],16 - nop.f 0 - add GR_P_POINT_1 = 0x60 ,GR_P_POINT_1 -} -;; - -// W = X * Inv_log2_by_128 -// By adding 1.10...0*2^63 we shift and get round_int(W) in significand. -// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing. -{ .mfi - ldfpd FR_A7, FR_A6 = [GR_P_POINT_3] - fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56 - add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1 - -} -{ .mfi - ldfpd FR_A5, FR_A4 = [GR_P_POINT_4], 16 - nop.f 0 - nop.i 0 -} -;; - -{ .mfi - ldfpd FR_A3, FR_A2 = [GR_P_POINT_4] - fmerge.s FR_X = f8,f8 - nop.i 0 -} -{ .mfi - ldfpd FR_A1, FR_A0 = [GR_P_POINT_1] - nop.f 0 - nop.i 0 -} -;; - -//p14: x < - NEG_ARG_ASYMP = -4.4 -> erfcf(x) ~=~ 2.0 -{ .mfi - setf.d FR_1_by_6 = GR_1_by_6 -(p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg, FR_NEG_ARG_ASYMP //p7: x < 0 - nop.i 0 -} -;; - -//p15: x > POS_ARG_ASYMP = 10.06 -> erfcf(x) ~=~ 0.0 -{ .mfi - nop.m 0 -(p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP //p6: x > 0 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fcmp.le.s1 p8,p0 = FR_NormX, FR_UnfBound // p8: x <= UnfBound - nop.i 0 -} -{ .mfb - nop.m 0 -(p14) fnma.s.s0 FR_RESULT = FR_EpsNorm, FR_EpsNorm, FR_2//y = 2 if x <-4.4 -(p14) br.ret.spnt b0 -} -;; - -// Nfloat = round_int(W) -// The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W, -// as a twos complement number in the lower bits (that is, it may be negative). -// That twos complement number (called N) is put into exp_GR_N. - -// Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56 -// before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat. -// Thus, EXP_Nfloat contains the floating point version of N - -{ .mfi - nop.m 0 - fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF - nop.i 0 -} -{ .mfb -(p15) mov GR_Parameter_TAG = 209 -(p15) fma.s.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 //Result.for x>10.06 -(p15) br.cond.spnt __libm_error_region -} -;; - -// Now we can calculate polynomial P15(x) -{ .mfi - nop.m 0 - fma.s1 FR_P15_1_1 = FR_AbsArg, FR_AbsArg, f0 // x ^2 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_0_1 = FR_A15, FR_AbsArg, FR_A14 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_P15_1_2 = FR_A13, FR_AbsArg, FR_A12 - nop.i 0 -} -;; - -{ .mfi - getf.sig exp_GR_N = EXP_W_2TO56_RSH - fma.s1 FR_P15_2_1 = FR_A9, FR_AbsArg, FR_A8 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_2_2 = FR_A11, FR_AbsArg, FR_A10 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_P15_3_1 = FR_A5, FR_AbsArg, FR_A4 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_3_2 = FR_A7, FR_AbsArg, FR_A6 - nop.i 0 -} -;; - -// exp_GR_index_1 has index_1 -// exp_GR_index_2_16 has index_2 * 16 -// exp_GR_biased_M has M -// exp_GR_index_1_16 has index_1 * 16 - -// r2 has true M -{ .mfi - and exp_GR_index_1 = 0x0f, exp_GR_N - fma.s1 FR_P15_4_1 = FR_A1, FR_AbsArg, FR_A0 - shr r2 = exp_GR_N, 0x7 - -} -{ .mfi - and exp_GR_index_2_16 = 0x70, exp_GR_N - fma.s1 FR_P15_4_2 = FR_A3, FR_AbsArg, FR_A2 - nop.i 0 -} -;; - -// EXP_AD_T1 has address of T1 -// EXP_AD_T2 has address if T2 - -{ .mfi - add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16 - nop.f 0 - shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1 -} -{ .mfi - addl exp_GR_biased_M = 0xffff, r2 - fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8 - nop.i 0 -} -;; - -// Create Scale = 2^M -// r = x - Nfloat * ln2_by_128_hi - -{ .mfi - setf.exp EXP_2M = exp_GR_biased_M - fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2 - nop.i 0 -} -{ .mfi - ldfe exp_T2 = [EXP_AD_T2] - nop.f 0 - nop.i 0 -} -;; - -// Load T1 and T2 - -{ .mfi - ldfe exp_T1 = [EXP_AD_T1] - fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // x^4 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_P15_4_1 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 exp_P = FR_1_by_6, exp_r, FR_05 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 exp_rsq = exp_r, exp_r, f0 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // x^8 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 exp_P = exp_P, exp_rsq, exp_r - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 exp_S1 = EXP_2M, exp_T2, f0 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 FR_Pol = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1 // P15(x) - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fma.s1 exp_S = exp_S1, exp_T1, f0 - 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.s.s0 FR_Tmpf = f8, f1, f0 // Flag d - nop.i 0 -} -;; - -//p6: result for 0 < x < = POS_ARG_ASYMP -//p7: result for - NEG_ARG_ASYMP <= x < 0 -//p8: exit for - NEG_ARG_ASYMP <= x <= UnfBound, x!=0 -.pred.rel "mutex",p6,p7 -{ .mfi - nop.m 0 -(p6) fma.s.s0 f8 = FR_Exp, FR_Pol, f0 - nop.i 0 -} -{ .mfb - mov GR_Parameter_TAG = 209 -(p7) fnma.s.s0 f8 = FR_Exp, FR_Pol, FR_2 -(p8) br.ret.sptk b0 -} -;; - -//p10: branch for UnfBound < x < = POS_ARG_ASYMP -{ .mfb - nop.m 0 - nop.f 0 -(p10) br.cond.spnt __libm_error_region -} -;; - -//Only via (p9) br.cond.spnt SPECIAL for x = 0,+inf,-inf,nan,unnorm -SPECIAL: - -{ .mfi - nop.m 0 - fclass.m.unc p10,p0 = f8,0x07 // p10: x = 0 - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fclass.m.unc p11,p0 = f8,0x21 // p11: x = +inf - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fclass.m.unc p12,p0 = f8,0x22 // p12 x = -inf - nop.i 0 -} -{ .mfb - nop.m 0 -(p10) fma.s.s0 f8 = f1, f1, f0 -(p10) br.ret.sptk b0 // Quick exit for x = 0 -} -;; - -{ .mfi - nop.m 0 - fclass.m.unc p13,p0 = f8,0xc3 // p13: x = nan - nop.i 0 -} -{ .mfb - nop.m 0 -(p11) fma.s.s0 f8 = f0, f1, f0 -(p11) br.ret.spnt b0 // Quick exit for x = +inf -} -;; -{ .mfi - nop.m 0 - fclass.m.unc p14,p0 = f8,0x0b // P14: x = unnormalized - nop.i 0 -} -{ .mfb - nop.m 0 -(p12) fma.s.s0 f8 = f1, f1, f1 -(p12) br.ret.spnt b0 // Quick exit for x = -inf -} -;; - -{ .mfb - nop.m 0 -(p13) fma.s.s0 f8 = f8, f1, f0 -(p13) br.ret.sptk b0 // Quick exit for x = nan -} -;; - -{ .mfb - nop.m 0 -(p14) fnma.s.s0 f8 = f8, f1, f1 -(p14) br.ret.sptk b0 // Quick exit for x = unnormalized -} -;; - -GLOBAL_LIBM_END(erfcf) - - -// Call via (p10) br.cond.spnt __libm_error_region -// for UnfBound < x < = POS_ARG_ASYMP -// and -// -// call via (p15) br.cond.spnt __libm_error_region -// for x > POS_ARG_ASYMP - -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 - stfs [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 - stfs [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 - stfs [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 - ldfs 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# - - - |