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Diffstat (limited to 'ports/sysdeps/ia64/fpu/s_erfcf.S')
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1 files changed, 983 insertions, 0 deletions
diff --git a/ports/sysdeps/ia64/fpu/s_erfcf.S b/ports/sysdeps/ia64/fpu/s_erfcf.S new file mode 100644 index 0000000000..ce6be8db62 --- /dev/null +++ b/ports/sysdeps/ia64/fpu/s_erfcf.S @@ -0,0 +1,983 @@ +.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# + + + |