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Diffstat (limited to 'sysdeps/ia64/fpu/s_erfcl.S')
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diff --git a/sysdeps/ia64/fpu/s_erfcl.S b/sysdeps/ia64/fpu/s_erfcl.S new file mode 100644 index 0000000..aaa0bb0 --- /dev/null +++ b/sysdeps/ia64/fpu/s_erfcl.S @@ -0,0 +1,2063 @@ +.file "erfcl.s" + + +// Copyright (c) 2001 - 2005, Intel Corporation +// All rights reserved. +// +// Contributed 2001 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 +//============================================================== +// 11/12/01 Initial version +// 02/08/02 Added missing } +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/10/03 Reordered header: .section, .global, .proc, .align; +// used data8 for long double table values +// 03/31/05 Reformatted delimiters between data tables +// +// API +//============================================================== +// long double erfcl(long double) +// +// Implementation and Algorithm Notes: +//============================================================== +// 1. 0 <= x <= 107.0 +// +// erfcl(x) ~=~ P15(z) * expl( -x^2 )/(dx + x), z = x - xc(i). +// +// Comment: +// +// Let x(i) = -1.0 + 2^(i/4),i=0,...27. So we have 28 unequal +// argument intervals [x(i),x(i+1)] with length ratio q = 2^(1/4). +// Values xc(i) we have in the table erfc_xc_table,xc(i)=x(i)for i = 0 +// and xc(i)= 0.5*( x(i)+x(i+1) ) for i>0. +// +// Let x(i)<= x < x(i+1). +// We can find i as exponent of number (x + 1)^4. +// +// Let P15(z)= a0+ a1*z +..+a15*z^15 - polynomial approximation of degree 15 +// for function erfcl(z+xc(i)) * expl( (z+xc(i))^2)* (dx+z+xc(i)) and +// -0.5*[x(i+1)-x(i)] <= z <= 0.5*[x(i+1)-x(i)]. +// +// Let Q(z)= (P(z)- S)/S, S = a0, rounded to 16 bits. +// Polynomial coefficients for Q(z) we have in the table erfc_Q_table as +// long double values +// +// We use multi precision to calculate input argument -x^2 for expl and +// for u = 1/(dx + x). +// +// Algorithm description for expl function see below. In accordance with +// denotation of this algorithm we have for expl: +// +// expl(X) ~=~ 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r)), X = -x^2. +// +// Final calculations for erfcl: +// +// erfcl(x) ~=~ +// +// 2^K*T_1*(1+W_1)*T_2*(1+W_2)*(1+ poly(r))*(1-dy)*S*(1+Q(z))*u*(1+du), +// +// where dy - low bits of x^2 and u, u*du - hi and low bits of 1/(dx + x). +// +// The order of calculations is the next: +// +// 1) M = 2^K*T_1*T_2*S without rounding error, +// 2) W = W_1 + (W_2 + W_1*W_2), where 1+W ~=~ (1+W_1)(1+W_2), +// 3) H = W - dy, where 1+H ~=~ (1+W )(1-dy), +// 4) R = poly(r)*H + poly(r), +// 5) R = H + R , where 1+R ~=~ (1+H )(1+poly(r)), +// 6) G = Q(z)*R + Q(z), +// 7) R1 = R + du, where 1+R1 ~=~ (1+R)(1+du), +// 8) G1 = R1 + G, where 1+G1 ~=~ (1+R1)(1+Q(z)), +// 9) V = G1*M*u, +// 10) erfcl(x) ~=~ M*u + V +// +// 2. -6.5 <= x < 0 +// +// erfcl(x) = 2.0 - erfl(-x) +// +// 3. x > 107.0 +// erfcl(x) ~=~ 0.0 +// +// 4. x < -6.5 +// erfcl(x) ~=~ 2.0 + +// Special values +//============================================================== +// erfcl(+0) = 1.0 +// erfcl(-0) = 1.0 + +// erfcl(+qnan) = +qnan +// erfcl(-qnan) = -qnan +// erfcl(+snan) = +qnan +// erfcl(-snan) = -qnan + +// erfcl(-inf) = 2.0 +// erfcl(+inf) = +0 + +//============================================================== +// Algorithm description of used expl function. +// +// Implementation and Algorithm Notes: +// +// ker_exp_64( in_FR : X, +// out_FR : Y_hi, +// out_FR : Y_lo, +// out_FR : scale, +// out_PR : Safe ) +// +// On input, X is in register format +// +// On output, +// +// scale*(Y_hi + Y_lo) approximates exp(X) +// +// The accuracy is sufficient for a highly accurate 64 sig. +// bit implementation. Safe is set if there is no danger of +// overflow/underflow when the result is composed from scale, +// Y_hi and Y_lo. Thus, we can have a fast return if Safe is set. +// Otherwise, one must prepare to handle the possible exception +// appropriately. Note that SAFE not set (false) does not mean +// that overflow/underflow will occur; only the setting of SAFE +// guarantees the opposite. +// +// **** High Level Overview **** +// +// The method consists of three cases. +// +// If |X| < Tiny use case exp_tiny; +// else if |X| < 2^(-6) use case exp_small; +// else use case exp_regular; +// +// Case exp_tiny: +// +// 1 + X can be used to approximate exp(X) +// X + X^2/2 can be used to approximate exp(X) - 1 +// +// Case exp_small: +// +// Here, exp(X) and exp(X) - 1 can all be +// approximated by a relatively simple polynomial. +// +// This polynomial resembles the truncated Taylor series +// +// exp(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n! +// +// Case exp_regular: +// +// Here we use a table lookup method. The basic idea is that in +// order to compute exp(X), we accurately decompose X into +// +// X = N * log(2)/(2^12) + r, |r| <= log(2)/2^13. +// +// Hence +// +// exp(X) = 2^( N / 2^12 ) * exp(r). +// +// The value 2^( N / 2^12 ) is obtained by simple combinations +// of values calculated beforehand and stored in table; exp(r) +// is approximated by a short polynomial because |r| is small. +// +// We elaborate this method in 4 steps. +// +// Step 1: Reduction +// +// The value 2^12/log(2) is stored as a double-extended number +// L_Inv. +// +// N := round_to_nearest_integer( X * L_Inv ) +// +// The value log(2)/2^12 is stored as two numbers L_hi and L_lo so +// that r can be computed accurately via +// +// r := (X - N*L_hi) - N*L_lo +// +// We pick L_hi such that N*L_hi is representable in 64 sig. bits +// and thus the FMA X - N*L_hi is error free. So r is the +// 1 rounding error from an exact reduction with respect to +// +// L_hi + L_lo. +// +// In particular, L_hi has 30 significant bit and can be stored +// as a double-precision number; L_lo has 64 significant bits and +// stored as a double-extended number. +// +// Step 2: Approximation +// +// exp(r) - 1 is approximated by a short polynomial of the form +// +// r + A_1 r^2 + A_2 r^3 + A_3 r^4 . +// +// Step 3: Composition from Table Values +// +// The value 2^( N / 2^12 ) can be composed from a couple of tables +// of precalculated values. First, express N as three integers +// K, M_1, and M_2 as +// +// N = K * 2^12 + M_1 * 2^6 + M_2 +// +// Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative. +// When N is represented in 2's complement, M_2 is simply the 6 +// lsb's, M_1 is the next 6, and K is simply N shifted right +// arithmetically (sign extended) by 12 bits. +// +// Now, 2^( N / 2^12 ) is simply +// +// 2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 ) +// +// Clearly, 2^K needs no tabulation. The other two values are less +// trivial because if we store each accurately to more than working +// precision, than its product is too expensive to calculate. We +// use the following method. +// +// Define two mathematical values, delta_1 and delta_2, implicitly +// such that +// +// T_1 = exp( [M_1 log(2)/2^6] - delta_1 ) +// T_2 = exp( [M_2 log(2)/2^12] - delta_2 ) +// +// are representable as 24 significant bits. To illustrate the idea, +// we show how we define delta_1: +// +// T_1 := round_to_24_bits( exp( M_1 log(2)/2^6 ) ) +// delta_1 = (M_1 log(2)/2^6) - log( T_1 ) +// +// The last equality means mathematical equality. We then tabulate +// +// W_1 := exp(delta_1) - 1 +// W_2 := exp(delta_2) - 1 +// +// Both in double precision. +// +// From the tabulated values T_1, T_2, W_1, W_2, we compose the values +// T and W via +// +// T := T_1 * T_2 ...exactly +// W := W_1 + (1 + W_1)*W_2 +// +// W approximates exp( delta ) - 1 where delta = delta_1 + delta_2. +// The mathematical product of T and (W+1) is an accurate representation +// of 2^(M_1/2^6) * 2^(M_2/2^12). +// +// Step 4. Reconstruction +// +// Finally, we can reconstruct exp(X), exp(X) - 1. +// Because +// +// X = K * log(2) + (M_1*log(2)/2^6 - delta_1) +// + (M_2*log(2)/2^12 - delta_2) +// + delta_1 + delta_2 + r ...accurately +// We have +// +// exp(X) ~=~ 2^K * ( T + T*[exp(delta_1+delta_2+r) - 1] ) +// ~=~ 2^K * ( T + T*[exp(delta + r) - 1] ) +// ~=~ 2^K * ( T + T*[(exp(delta)-1) +// + exp(delta)*(exp(r)-1)] ) +// ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) ) +// ~=~ 2^K * ( Y_hi + Y_lo ) +// +// where Y_hi = T and Y_lo = T*(W + (1+W)*poly(r)) +// +// For exp(X)-1, we have +// +// exp(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1 +// ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) ) +// +// and we combine Y_hi + Y_lo - 2^(-N) into the form of two +// numbers Y_hi + Y_lo carefully. +// +// **** Algorithm Details **** +// +// A careful algorithm must be used to realize the mathematical ideas +// accurately. We describe each of the three cases. We assume SAFE +// is preset to be TRUE. +// +// Case exp_tiny: +// +// The important points are to ensure an accurate result under +// different rounding directions and a correct setting of the SAFE +// flag. +// +// If expm1 is 1, then +// SAFE := False ...possibility of underflow +// Scale := 1.0 +// Y_hi := X +// Y_lo := 2^(-17000) +// Else +// Scale := 1.0 +// Y_hi := 1.0 +// Y_lo := X ...for different rounding modes +// Endif +// +// Case exp_small: +// +// Here we compute a simple polynomial. To exploit parallelism, we split +// the polynomial into several portions. +// +// Let r = X +// +// If exp ...i.e. exp( argument ) +// +// rsq := r * r; +// r4 := rsq*rsq +// poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6)) +// poly_hi := r + rsq*(P_1 + r*P_2) +// Y_lo := poly_hi + r4 * poly_lo +// Y_hi := 1.0 +// Scale := 1.0 +// +// Else ...i.e. exp( argument ) - 1 +// +// rsq := r * r +// r4 := rsq * rsq +// r6 := rsq * r4 +// poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7)) +// poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4)) +// Y_lo := rsq*poly_hi + poly_lo +// Y_hi := X +// Scale := 1.0 +// +// Endif +// +// Case exp_regular: +// +// The previous description contain enough information except the +// computation of poly and the final Y_hi and Y_lo in the case for +// exp(X)-1. +// +// The computation of poly for Step 2: +// +// rsq := r*r +// poly := r + rsq*(A_1 + r*(A_2 + r*A_3)) +// +// For the case exp(X) - 1, we need to incorporate 2^(-K) into +// Y_hi and Y_lo at the end of Step 4. +// +// If K > 10 then +// Y_lo := Y_lo - 2^(-K) +// Else +// If K < -10 then +// Y_lo := Y_hi + Y_lo +// Y_hi := -2^(-K) +// Else +// Y_hi := Y_hi - 2^(-K) +// End If +// End If +// + +// Overview of operation +//============================================================== + +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f9 -> f14, f36 -> f126 + +// General registers used: +// r32 -> r71 + +// Predicate registers used: +// p6 -> p15 + +// Assembly macros +//============================================================== +// GR for exp(X) +GR_ad_Arg = r33 +GR_ad_C = r34 +GR_ERFC_S_TB = r35 +GR_signexp_x = r36 +GR_exp_x = r36 +GR_exp_mask = r37 +GR_ad_W1 = r38 +GR_ad_W2 = r39 +GR_M2 = r40 +GR_M1 = r41 +GR_K = r42 +GR_exp_2_k = r43 +GR_ad_T1 = r44 +GR_ad_T2 = r45 +GR_N_fix = r46 +GR_ad_P = r47 +GR_exp_bias = r48 +GR_BIAS = r48 +GR_exp_half = r49 +GR_sig_inv_ln2 = r50 +GR_rshf_2to51 = r51 +GR_exp_2tom51 = r52 +GR_rshf = r53 + +// GR for erfcl(x) +//============================================================== + +GR_ERFC_XC_TB = r54 +GR_ERFC_P_TB = r55 +GR_IndxPlusBias = r56 +GR_P_POINT_1 = r57 +GR_P_POINT_2 = r58 +GR_AbsArg = r59 +GR_ShftXBi = r60 +GR_ShftPi = r61 +GR_mBIAS = r62 +GR_ShftPi_bias = r63 +GR_ShftXBi_bias = r64 +GR_ShftA14 = r65 +GR_ShftA15 = r66 +GR_EpsNorm = r67 +GR_0x1 = r68 +GR_ShftPi_8 = r69 +GR_26PlusBias = r70 +GR_27PlusBias = r71 + +// GR for __libm_support call +//============================================================== +GR_SAVE_B0 = r64 +GR_SAVE_PFS = r65 +GR_SAVE_GP = r66 +GR_SAVE_SP = r67 + +GR_Parameter_X = r68 +GR_Parameter_Y = r69 +GR_Parameter_RESULT = r70 +GR_Parameter_TAG = r71 + +//============================================================== +// Floating Point Registers +// +FR_RSHF_2TO51 = f10 +FR_INV_LN2_2TO63 = f11 +FR_W_2TO51_RSH = f12 +FR_2TOM51 = f13 +FR_RSHF = f14 + +FR_scale = f36 +FR_float_N = f37 +FR_N_signif = f38 +FR_L_hi = f39 +FR_L_lo = f40 +FR_r = f41 +FR_W1 = f42 +FR_T1 = f43 +FR_W2 = f44 +FR_T2 = f45 +FR_rsq = f46 +FR_C2 = f47 +FR_C3 = f48 +FR_poly = f49 +FR_P6 = f49 +FR_T = f50 +FR_P5 = f50 +FR_P4 = f51 +FR_W = f51 +FR_P3 = f52 +FR_Wp1 = f52 +FR_P2 = f53 +FR_P1 = f54 +FR_Q7 = f56 +FR_Q6 = f57 +FR_Q5 = f58 +FR_Q4 = f59 +FR_Q3 = f60 +FR_Q2 = f61 +FR_Q1 = f62 +FR_C1 = f63 +FR_A15 = f64 +FR_ch_dx = f65 +FR_T_scale = f66 +FR_norm_x = f67 +FR_AbsArg = f68 +FR_POS_ARG_ASYMP = f69 +FR_NEG_ARG_ASYMP = f70 +FR_Tmp = f71 +FR_Xc = f72 +FR_A0 = f73 +FR_A1 = f74 +FR_A2 = f75 +FR_A3 = f76 +FR_A4 = f77 +FR_A5 = f78 +FR_A6 = f79 +FR_A7 = f80 +FR_A8 = f81 +FR_A9 = f82 +FR_A10 = f83 +FR_A11 = f84 +FR_A12 = f85 +FR_A13 = f86 +FR_A14 = f87 +FR_P15_0_1 = f88 +FR_P15_8_1 = f88 +FR_P15_1_1 = f89 +FR_P15_8_2 = f89 +FR_P15_1_2 = f90 +FR_P15_2_1 = f91 +FR_P15_2_2 = f92 +FR_P15_3_1 = f93 +FR_P15_3_2 = f94 +FR_P15_4_2 = f95 +FR_P15_7_1 = f96 +FR_P15_7_2 = f97 +FR_P15_9_1 = f98 +FR_P15_9_2 = f99 +FR_P15_13_1 = f100 +FR_P15_14_1 = f101 +FR_P15_14_2 = f102 +FR_Tmp2 = f103 +FR_Xpdx_lo = f104 +FR_2 = f105 +FR_xsq_lo = f106 +FR_LocArg = f107 +FR_Tmpf = f108 +FR_Tmp1 = f109 +FR_EpsNorm = f110 +FR_UnfBound = f111 +FR_NormX = f112 +FR_Xpdx_hi = f113 +FR_dU = f114 +FR_H = f115 +FR_G = f116 +FR_V = f117 +FR_M = f118 +FR_U = f119 +FR_Q = f120 +FR_S = f121 +FR_R = f122 +FR_res_pos_x_hi = f123 +FR_res_pos_x_lo = f124 +FR_dx = f125 +FR_dx1 = f126 + +// for error handler routine +FR_X = f9 +FR_Y = f0 +FR_RESULT = f8 + +// Data tables +//============================================================== +RODATA +.align 16 + +// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** +LOCAL_OBJECT_START(exp_table_1) + +data8 0xae89f995ad3ad5ea , 0x00003ffe // x = 0.681..,bound for dx = 0.875 +data8 0x405AC00000000000 , 0x401A000000000000 //ARG_ASYMP,NEG_ARG_ASYMP +data8 0x3FE4000000000000 , 0x3FEC000000000000 //0.625,0.875 +data8 0xD5126065B720A4e9 , 0x00004005 // underflow boundary +data8 0x8000000000000000 , 0x00000001 //FR_EpsNorm +LOCAL_OBJECT_END(exp_table_1) + +LOCAL_OBJECT_START(Constants_exp_64_Arg) +data8 0xB17217F400000000,0x00003FF2 //L_hi = hi part log(2)/2^12 +data8 0xF473DE6AF278ECE6,0x00003FD4 //L_lo = lo part log(2)/2^12 +LOCAL_OBJECT_END(Constants_exp_64_Arg) + +LOCAL_OBJECT_START(Constants_exp_64_C) +data8 0xAAAAAAABB1B736A0,0x00003FFA // C3 +data8 0xAAAAAAAB90CD6327,0x00003FFC // C2 +data8 0xFFFFFFFFFFFFFFFF,0x00003FFD // C1 +LOCAL_OBJECT_END(Constants_exp_64_C) + +LOCAL_OBJECT_START(Constants_exp_64_T1) +data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29 +data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5 +data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC +data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D +data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA +data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516 +data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A +data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4 +data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B +data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD +data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15 +data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B +data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5 +data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A +data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177 +data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C +LOCAL_OBJECT_END(Constants_exp_64_T1) + +LOCAL_OBJECT_START(Constants_exp_64_T2) +data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4 +data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7 +data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E +data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349 +data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987 +data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA +data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610 +data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A +data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8 +data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA +data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50 +data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA +data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07 +data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269 +data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE +data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37 +LOCAL_OBJECT_END(Constants_exp_64_T2) + +LOCAL_OBJECT_START(Constants_exp_64_W1) +data8 0x0000000000000000, 0xBE384454171EC4B4 +data8 0xBE6947414AA72766, 0xBE5D32B6D42518F8 +data8 0x3E68D96D3A319149, 0xBE68F4DA62415F36 +data8 0xBE6DDA2FC9C86A3B, 0x3E6B2E50F49228FE +data8 0xBE49C0C21188B886, 0x3E64BFC21A4C2F1F +data8 0xBE6A2FBB2CB98B54, 0x3E5DC5DE9A55D329 +data8 0x3E69649039A7AACE, 0x3E54728B5C66DBA5 +data8 0xBE62B0DBBA1C7D7D, 0x3E576E0409F1AF5F +data8 0x3E6125001A0DD6A1, 0xBE66A419795FBDEF +data8 0xBE5CDE8CE1BD41FC, 0xBE621376EA54964F +data8 0x3E6370BE476E76EE, 0x3E390D1A3427EB92 +data8 0x3E1336DE2BF82BF8, 0xBE5FF1CBD0F7BD9E +data8 0xBE60A3550CEB09DD, 0xBE5CA37E0980F30D +data8 0xBE5C541B4C082D25, 0xBE5BBECA3B467D29 +data8 0xBE400D8AB9D946C5, 0xBE5E2A0807ED374A +data8 0xBE66CB28365C8B0A, 0x3E3AAD5BD3403BCA +data8 0x3E526055C7EA21E0, 0xBE442C75E72880D6 +data8 0x3E58B2BB85222A43, 0xBE5AAB79522C42BF +data8 0xBE605CB4469DC2BC, 0xBE589FA7A48C40DC +data8 0xBE51C2141AA42614, 0xBE48D087C37293F4 +data8 0x3E367A1CA2D673E0, 0xBE51BEBB114F7A38 +data8 0xBE6348E5661A4B48, 0xBDF526431D3B9962 +data8 0x3E3A3B5E35A78A53, 0xBE46C46C1CECD788 +data8 0xBE60B7EC7857D689, 0xBE594D3DD14F1AD7 +data8 0xBE4F9C304C9A8F60, 0xBE52187302DFF9D2 +data8 0xBE5E4C8855E6D68F, 0xBE62140F667F3DC4 +data8 0xBE36961B3BF88747, 0x3E602861C96EC6AA +data8 0xBE3B5151D57FD718, 0x3E561CD0FC4A627B +data8 0xBE3A5217CA913FEA, 0x3E40A3CC9A5D193A +data8 0xBE5AB71310A9C312, 0x3E4FDADBC5F57719 +data8 0x3E361428DBDF59D5, 0x3E5DB5DB61B4180D +data8 0xBE42AD5F7408D856, 0x3E2A314831B2B707 +LOCAL_OBJECT_END(Constants_exp_64_W1) + +LOCAL_OBJECT_START(Constants_exp_64_W2) +data8 0x0000000000000000, 0xBE641F2537A3D7A2 +data8 0xBE68DD57AD028C40, 0xBE5C77D8F212B1B6 +data8 0x3E57878F1BA5B070, 0xBE55A36A2ECAE6FE +data8 0xBE620608569DFA3B, 0xBE53B50EA6D300A3 +data8 0x3E5B5EF2223F8F2C, 0xBE56A0D9D6DE0DF4 +data8 0xBE64EEF3EAE28F51, 0xBE5E5AE2367EA80B +data8 0x3E47CB1A5FCBC02D, 0xBE656BA09BDAFEB7 +data8 0x3E6E70C6805AFEE7, 0xBE6E0509A3415EBA +data8 0xBE56856B49BFF529, 0x3E66DD3300508651 +data8 0x3E51165FC114BC13, 0x3E53333DC453290F +data8 0x3E6A072B05539FDA, 0xBE47CD877C0A7696 +data8 0xBE668BF4EB05C6D9, 0xBE67C3E36AE86C93 +data8 0xBE533904D0B3E84B, 0x3E63E8D9556B53CE +data8 0x3E212C8963A98DC8, 0xBE33138F032A7A22 +data8 0x3E530FA9BC584008, 0xBE6ADF82CCB93C97 +data8 0x3E5F91138370EA39, 0x3E5443A4FB6A05D8 +data8 0x3E63DACD181FEE7A, 0xBE62B29DF0F67DEC +data8 0x3E65C4833DDE6307, 0x3E5BF030D40A24C1 +data8 0x3E658B8F14E437BE, 0xBE631C29ED98B6C7 +data8 0x3E6335D204CF7C71, 0x3E529EEDE954A79D +data8 0x3E5D9257F64A2FB8, 0xBE6BED1B854ED06C +data8 0x3E5096F6D71405CB, 0xBE3D4893ACB9FDF5 +data8 0xBDFEB15801B68349, 0x3E628D35C6A463B9 +data8 0xBE559725ADE45917, 0xBE68C29C042FC476 +data8 0xBE67593B01E511FA, 0xBE4A4313398801ED +data8 0x3E699571DA7C3300, 0x3E5349BE08062A9E +data8 0x3E5229C4755BB28E, 0x3E67E42677A1F80D +data8 0xBE52B33F6B69C352, 0xBE6B3550084DA57F +data8 0xBE6DB03FD1D09A20, 0xBE60CBC42161B2C1 +data8 0x3E56ED9C78A2B771, 0xBE508E319D0FA795 +data8 0xBE59482AFD1A54E9, 0xBE2A17CEB07FD23E +data8 0x3E68BF5C17365712, 0x3E3956F9B3785569 +LOCAL_OBJECT_END(Constants_exp_64_W2) + + +LOCAL_OBJECT_START(erfc_xc_table) + +data8 0x0000000000000000, 0x00000000 //XC[0] = +0.00000000000000000000e-01L +data8 0x9A79C70000000000, 0x00003FFD //XC[1] = +3.01710337400436401367e-01L +data8 0x8C49EF0000000000, 0x00003FFE //XC[2] = +5.48003137111663818359e-01L +data8 0xD744FC0000000000, 0x00003FFE //XC[3] = +8.40896368026733398438e-01L +data8 0x9837F00000000000, 0x00003FFF //XC[4] = +1.18920707702636718750e+00L +data8 0xCD3CE30000000000, 0x00003FFF //XC[5] = +1.60342061519622802734e+00L +data8 0x8624F70000000000, 0x00004000 //XC[6] = +2.09600615501403808594e+00L +data8 0xABA27E0000000000, 0x00004000 //XC[7] = +2.68179273605346679688e+00L +data8 0xD837F00000000000, 0x00004000 //XC[8] = +3.37841415405273437500e+00L +data8 0x869E710000000000, 0x00004001 //XC[9] = +4.20684099197387695313e+00L +data8 0xA624F70000000000, 0x00004001 //XC[10] = +5.19201231002807617188e+00L +data8 0xCBA27E0000000000, 0x00004001 //XC[11] = +6.36358547210693359375e+00L +data8 0xF837F00000000000, 0x00004001 //XC[12] = +7.75682830810546875000e+00L +data8 0x969E710000000000, 0x00004002 //XC[13] = +9.41368198394775390625e+00L +data8 0xB624F70000000000, 0x00004002 //XC[14] = +1.13840246200561523438e+01L +data8 0xDBA27E0000000000, 0x00004002 //XC[15] = +1.37271709442138671875e+01L +data8 0x841BF80000000000, 0x00004003 //XC[16] = +1.65136566162109375000e+01L +data8 0x9E9E710000000000, 0x00004003 //XC[17] = +1.98273639678955078125e+01L +data8 0xBE24F70000000000, 0x00004003 //XC[18] = +2.37680492401123046875e+01L +data8 0xE3A27E0000000000, 0x00004003 //XC[19] = +2.84543418884277343750e+01L +data8 0x881BF80000000000, 0x00004004 //XC[20] = +3.40273132324218750000e+01L +data8 0xA29E710000000000, 0x00004004 //XC[21] = +4.06547279357910156250e+01L +data8 0xC224F70000000000, 0x00004004 //XC[22] = +4.85360984802246093750e+01L +data8 0xE7A27E0000000000, 0x00004004 //XC[23] = +5.79086837768554687500e+01L +data8 0x8A1BF80000000000, 0x00004005 //XC[24] = +6.90546264648437500000e+01L +data8 0xA49E710000000000, 0x00004005 //XC[25] = +8.23094558715820312500e+01L +data8 0xC424F70000000000, 0x00004005 //XC[26] = +9.80721969604492187500e+01L +data8 0xD5A27E0000000000, 0x00004005 //XC[27] = +1.06817367553710937500e+02L +LOCAL_OBJECT_END(erfc_xc_table) + +LOCAL_OBJECT_START(erfc_s_table) + +data8 0xE000000000000000, 0x00003FFE //s[0] = +8.75000000000000000000e-01L +data8 0xDCEF000000000000, 0x00003FFE //s[1] = +8.63021850585937500000e-01L +data8 0xD79D000000000000, 0x00003FFE //s[2] = +8.42239379882812500000e-01L +data8 0xB25E000000000000, 0x00003FFE //s[3] = +6.96746826171875000000e-01L +data8 0xB0EA000000000000, 0x00003FFE //s[4] = +6.91070556640625000000e-01L +data8 0xAE3F000000000000, 0x00003FFE //s[5] = +6.80648803710937500000e-01L +data8 0xAB05000000000000, 0x00003FFE //s[6] = +6.68045043945312500000e-01L +data8 0xA7AC000000000000, 0x00003FFE //s[7] = +6.54968261718750000000e-01L +data8 0xA478000000000000, 0x00003FFE //s[8] = +6.42456054687500000000e-01L +data8 0xA18D000000000000, 0x00003FFE //s[9] = +6.31057739257812500000e-01L +data8 0x9EF8000000000000, 0x00003FFE //s[10] = +6.20971679687500000000e-01L +data8 0x9CBA000000000000, 0x00003FFE //s[11] = +6.12213134765625000000e-01L +data8 0x9ACD000000000000, 0x00003FFE //s[12] = +6.04690551757812500000e-01L +data8 0x992A000000000000, 0x00003FFE //s[13] = +5.98297119140625000000e-01L +data8 0x97C7000000000000, 0x00003FFE //s[14] = +5.92880249023437500000e-01L +data8 0x969C000000000000, 0x00003FFE //s[15] = +5.88317871093750000000e-01L +data8 0x95A0000000000000, 0x00003FFE //s[16] = +5.84472656250000000000e-01L +data8 0x94CB000000000000, 0x00003FFE //s[17] = +5.81222534179687500000e-01L +data8 0x9419000000000000, 0x00003FFE //s[18] = +5.78506469726562500000e-01L +data8 0x9383000000000000, 0x00003FFE //s[19] = +5.76217651367187500000e-01L +data8 0x9305000000000000, 0x00003FFE //s[20] = +5.74295043945312500000e-01L +data8 0x929B000000000000, 0x00003FFE //s[21] = +5.72677612304687500000e-01L +data8 0x9242000000000000, 0x00003FFE //s[22] = +5.71319580078125000000e-01L +data8 0x91F8000000000000, 0x00003FFE //s[23] = +5.70190429687500000000e-01L +data8 0x91B9000000000000, 0x00003FFE //s[24] = +5.69229125976562500000e-01L +data8 0x9184000000000000, 0x00003FFE //s[25] = +5.68420410156250000000e-01L +data8 0x9158000000000000, 0x00003FFE //s[26] = +5.67749023437500000000e-01L +data8 0x9145000000000000, 0x00003FFE //s[27] = +5.67459106445312500000e-01L +LOCAL_OBJECT_END(erfc_s_table) + +LOCAL_OBJECT_START(erfc_Q_table) +// Q(z)= (P(z)- S)/S +// +// Pol0 +data8 0x98325D50F9DC3499, 0x0000BFAA //A0 = +3.07358861423101280650e-26L +data8 0xED35081A2494DDD9, 0x00003FF8 //A1 = +1.44779757616302832466e-02L +data8 0x9443549BCD0F94CE, 0x0000BFFD //A2 = -2.89576190966300084405e-01L +data8 0xC7FD4B98ECF3DBBF, 0x00003FFD //A3 = +3.90604364793467799170e-01L +data8 0xB82CE31288B49759, 0x0000BFFD //A4 = -3.59717460644199233866e-01L +data8 0x8A8293447BEF69B5, 0x00003FFD //A5 = +2.70527460203054582368e-01L +data8 0xB5793E30EE36766C, 0x0000BFFC //A6 = -1.77220317589265674647e-01L +data8 0xD6066D16BBDECE17, 0x00003FFB //A7 = +1.04504444366724593714e-01L +data8 0xE7C783CE3C997BD8, 0x0000BFFA //A8 = -5.65867565781331646771e-02L +data8 0xE9969EBC2F5B2828, 0x00003FF9 //A9 = +2.85142040533900194955e-02L +data8 0xDD31D619F29AD7BF, 0x0000BFF8 //A10 = -1.35006514390540367929e-02L +data8 0xC63A20EB59768F3A, 0x00003FF7 //A11 = +6.04940993680332271481e-03L +data8 0xA8DEC641AACEB600, 0x0000BFF6 //A12 = -2.57675495383156581601e-03L +data8 0x87F0E77BA914FBEB, 0x00003FF5 //A13 = +1.03714776726541296794e-03L +data8 0xC306C2894C5CEF2D, 0x0000BFF3 //A14 = -3.71983348634136412407e-04L +data8 0xBDAB416A989D0697, 0x00003FF1 //A15 = +9.04412111877987292294e-05L +// Pol1 +data8 0x82808893DA2DD83F, 0x00003FEE //A0 = +7.77853035974467145290e-06L +data8 0xAE9CD9DCADC86113, 0x0000BFFB //A1 = -8.52601070853077921197e-02L +data8 0x9D429743E312AD9F, 0x0000BFFB //A2 = -7.67871682732076080494e-02L +data8 0x8637FC533AE805DC, 0x00003FFC //A3 = +1.31072943286859831330e-01L +data8 0xF68DBE3639ABCB6E, 0x0000BFFB //A4 = -1.20387540845703264588e-01L +data8 0xB168FFC3CFA71256, 0x00003FFB //A5 = +8.66260511047190247534e-02L +data8 0xDBC5078A7EA89236, 0x0000BFFA //A6 = -5.36546988077281230848e-02L +data8 0xF4331FEDB2CB838F, 0x00003FF9 //A7 = +2.98095344165515989564e-02L +data8 0xF909173C0E61C25D, 0x0000BFF8 //A8 = -1.51999213123642373375e-02L +data8 0xEC83560A2ACB23E9, 0x00003FF7 //A9 = +7.21780491979582106904e-03L +data8 0xD350D62C4FEAD8F5, 0x0000BFF6 //A10 = -3.22442272982896360044e-03L +data8 0xB2F44F4B3FD9B826, 0x00003FF5 //A11 = +1.36531322425499451283e-03L +data8 0x9078BC61927671C6, 0x0000BFF4 //A12 = -5.51115510818844954547e-04L +data8 0xDF67AC6287A63B03, 0x00003FF2 //A13 = +2.13055585989529858265e-04L +data8 0xA719CFEE67FCE1CE, 0x0000BFF1 //A14 = -7.96798844477905965933e-05L +data8 0xEF926367BABBB029, 0x00003FEF //A15 = +2.85591875675765038065e-05L +// Pol2 +data8 0x82B5E5A93B059C50, 0x00003FEF //A0 = +1.55819100856330860049e-05L +data8 0xDC856BC2542B1938, 0x0000BFFB //A1 = -1.07676355235999875911e-01L +data8 0xDF225EF5694F14AE, 0x0000BFF8 //A2 = -1.36190345125628043277e-02L +data8 0xDAF66A954ED22428, 0x00003FFA //A3 = +5.34576571853233908886e-02L +data8 0xD28AE4F21A392EC6, 0x0000BFFA //A4 = -5.14019911949062230820e-02L +data8 0x9441A95713F0DB5B, 0x00003FFA //A5 = +3.61954321717769771045e-02L +data8 0xB0957B5C483C7A04, 0x0000BFF9 //A6 = -2.15556535133667988704e-02L +data8 0xBB9260E812814F71, 0x00003FF8 //A7 = +1.14484735825400480057e-02L +data8 0xB68AB17287ABAB04, 0x0000BFF7 //A8 = -5.57073273108465072470e-03L +data8 0xA56A95E0BC0EF01B, 0x00003FF6 //A9 = +2.52405318381952650677e-03L +data8 0x8D19C7D286839C00, 0x0000BFF5 //A10 = -1.07651294935087466892e-03L +data8 0xE45DB3766711A0D3, 0x00003FF3 //A11 = +4.35573615323234291196e-04L +data8 0xB05949F947FA7AEF, 0x0000BFF2 //A12 = -1.68179306983868501372e-04L +data8 0x82901D055A0D5CB6, 0x00003FF1 //A13 = +6.22572626227726684168e-05L +data8 0xBB957698542D6FD0, 0x0000BFEF //A14 = -2.23617364009159182821e-05L +data8 0x810740E1DF572394, 0x00003FEE //A15 = +7.69068800065192940487e-06L +// Pol3 +data8 0x9526D1C87655AFA8, 0x00003FEC //A0 = +2.22253260814242012255e-06L +data8 0xA47E21EBFE73F72F, 0x0000BFF8 //A1 = -1.00398379581527733314e-02L +data8 0xDE65685FCDF7A913, 0x0000BFFA //A2 = -5.42959286802879105148e-02L +data8 0xED289CB8F97D4860, 0x00003FFA //A3 = +5.79000589346770417248e-02L +data8 0xAA3100D5A7D870F1, 0x0000BFFA //A4 = -4.15506394006027604387e-02L +data8 0xCA0567032C5308C0, 0x00003FF9 //A5 = +2.46607791863290331169e-02L +data8 0xD3E1794A50F31BEB, 0x0000BFF8 //A6 = -1.29321751094401754013e-02L +data8 0xCAA02CB4C87CC1F0, 0x00003FF7 //A7 = +6.18364508551740736863e-03L +data8 0xB3F126AF16B121F2, 0x0000BFF6 //A8 = -2.74569696838501870748e-03L +data8 0x962B2D64D3900510, 0x00003FF5 //A9 = +1.14569596409019883022e-03L +data8 0xED8785714A9A00FB, 0x0000BFF3 //A10 = -4.53051338046340380512e-04L +data8 0xB325DA4515D8B54C, 0x00003FF2 //A11 = +1.70848714622328427290e-04L +data8 0x8179C36354571747, 0x0000BFF1 //A12 = -6.17387951061077132522e-05L +data8 0xB40F241C01C907E9, 0x00003FEF //A13 = +2.14647227210702861416e-05L +data8 0xF436D84AD7D4D316, 0x0000BFED //A14 = -7.27815144835213913238e-06L +data8 0x9EB432503FB0B7BC, 0x00003FEC //A15 = +2.36487228755136968792e-06L +// Pol4 +data8 0xE0BA539E4AFC4741, 0x00003FED //A0 = +6.69741148991838024429e-06L +data8 0x8583BF71139452CF, 0x0000BFFA //A1 = -3.25963476363756051657e-02L +data8 0x8384FEF6D08AD6CE, 0x0000BFF9 //A2 = -1.60546283500634200479e-02L +data8 0xB1E67DFB84C97036, 0x00003FF9 //A3 = +2.17163525195697635702e-02L +data8 0xFB6ACEE6899E360D, 0x0000BFF8 //A4 = -1.53452892792759316229e-02L +data8 0x8D2B869EB9149905, 0x00003FF8 //A5 = +8.61633440480716870830e-03L +data8 0x8A90BFE0FD869A41, 0x0000BFF7 //A6 = -4.22868126950622376530e-03L +data8 0xF7536A76E59F54D2, 0x00003FF5 //A7 = +1.88694643606912107006e-03L +data8 0xCCF6FE58C16E1CC7, 0x0000BFF4 //A8 = -7.81878732767742447339e-04L +data8 0x9FCC6ED9914FAA24, 0x00003FF3 //A9 = +3.04791577214885118730e-04L +data8 0xEC7F5AAACAE593E8, 0x0000BFF1 //A10 = -1.12770784960291779798e-04L +data8 0xA72CE628A114C940, 0x00003FF0 //A11 = +3.98577182157456408782e-05L +data8 0xE2DCC5750FD769BA, 0x0000BFEE //A12 = -1.35220520471857266339e-05L +data8 0x9459160B1E6F1F8D, 0x00003FED //A13 = +4.42111470121432700283e-06L +data8 0xBE0A05701BD0DD42, 0x0000BFEB //A14 = -1.41590196994052764542e-06L +data8 0xE905D729105081BF, 0x00003FE9 //A15 = +4.34038814785401120999e-07L +// Pol5 +data8 0xA33649C3AB459832, 0x00003FEE //A0 = +9.72819704141525206634e-06L +data8 0x9E4EA2F44C9A24BD, 0x0000BFFA //A1 = -3.86492123987296806210e-02L +data8 0xE80C0B1280F357BF, 0x0000BFF2 //A2 = -2.21297306012713370124e-04L +data8 0xDAECCE90A4D45D9A, 0x00003FF7 //A3 = +6.68106161291482829670e-03L +data8 0xA4006572071BDD4B, 0x0000BFF7 //A4 = -5.00493005170532147076e-03L +data8 0xB07FD7EB1F4D8E8E, 0x00003FF6 //A5 = +2.69316693731732554959e-03L +data8 0xA1F471D42ADD73A1, 0x0000BFF5 //A6 = -1.23561753760779610478e-03L +data8 0x8611D0ED1B4C8176, 0x00003FF4 //A7 = +5.11434914439322741260e-04L +data8 0xCDADB789B487A541, 0x0000BFF2 //A8 = -1.96150380913036018825e-04L +data8 0x9470252731687FEE, 0x00003FF1 //A9 = +7.07807859951401721129e-05L +data8 0xCB9399AD1C376D85, 0x0000BFEF //A10 = -2.42682175234436724152e-05L +data8 0x858D815F9CA0A9F7, 0x00003FEE //A11 = +7.96036454038012144300e-06L +data8 0xA878D338E6E6A079, 0x0000BFEC //A12 = -2.51042802626063073967e-06L +data8 0xCD2C2F079D2FCB36, 0x00003FEA //A13 = +7.64327468786076941271e-07L +data8 0xF5EF4A4B2EA426F2, 0x0000BFE8 //A14 = -2.29044563492386125272e-07L +data8 0x8CE52181393820FC, 0x00003FE7 //A15 = +6.56093668622712763489e-08L +// Pol6 +data8 0xB2015D7F1864B7CF, 0x00003FEC //A0 = +2.65248615880090351276e-06L +data8 0x954EA7A861B4462A, 0x0000BFFA //A1 = -3.64519642954351295215e-02L +data8 0x9E46F2A4D9157E69, 0x00003FF7 //A2 = +4.83023498390681965101e-03L +data8 0xA0D12B422FFD5BAD, 0x00003FF5 //A3 = +1.22693684633643883352e-03L +data8 0xB291D16A560A740E, 0x0000BFF5 //A4 = -1.36237794246703606647e-03L +data8 0xC138941BC8AF4A9D, 0x00003FF4 //A5 = +7.37079658343628747256e-04L +data8 0xA761669D61B405CF, 0x0000BFF3 //A6 = -3.19252914480518163396e-04L +data8 0x8053680F1C84607E, 0x00003FF2 //A7 = +1.22381025852939439541e-04L +data8 0xB518F4B6F25015F9, 0x0000BFF0 //A8 = -4.31770048258291369742e-05L +data8 0xEFF526AC70B9411E, 0x00003FEE //A9 = +1.43025887824433324525e-05L +data8 0x970B2A848DF5B5C2, 0x0000BFED //A10 = -4.50145058393497252604e-06L +data8 0xB614D2E61DB86963, 0x00003FEB //A11 = +1.35661172167726780059e-06L +data8 0xD34EA4D283EC33FA, 0x0000BFE9 //A12 = -3.93590335713880681528e-07L +data8 0xED209EBD68E1145F, 0x00003FE7 //A13 = +1.10421060667544991323e-07L +data8 0x83A126E22A17568D, 0x0000BFE6 //A14 = -3.06473811074239684132e-08L +data8 0x8B778496EDE9F415, 0x00003FE4 //A15 = +8.11804009754249175736e-09L +// Pol7 +data8 0x8E152F522501B7B9, 0x00003FEE //A0 = +8.46879203970927626532e-06L +data8 0xFD22F92EE21F491E, 0x0000BFF9 //A1 = -3.09004656656418947425e-02L +data8 0xAF0C41847D89EC14, 0x00003FF7 //A2 = +5.34203719233189217519e-03L +data8 0xB7C539C400445956, 0x0000BFF3 //A3 = -3.50514245383356287965e-04L +data8 0x8428C78B2B1E3622, 0x0000BFF3 //A4 = -2.52073850239006530978e-04L +data8 0xAFC0CCC7D1A05F5B, 0x00003FF2 //A5 = +1.67611241057491801028e-04L +data8 0x95DC7272C5695A5A, 0x0000BFF1 //A6 = -7.14593512262564106636e-05L +data8 0xD6FCA68A61F0E835, 0x00003FEF //A7 = +2.56284375437771117850e-05L +data8 0x8B71C74DEA936C66, 0x0000BFEE //A8 = -8.31153675277218441096e-06L +data8 0xA8AC71E2A56AA2C9, 0x00003FEC //A9 = +2.51343269277107451413e-06L +data8 0xC15DED6C44B46046, 0x0000BFEA //A10 = -7.20347851650066610771e-07L +data8 0xD42BA1DFBD1277AC, 0x00003FE8 //A11 = +1.97599119274780745741e-07L +data8 0xE03A81F2C976D11A, 0x0000BFE6 //A12 = -5.22072765405802337371e-08L +data8 0xE56A19A67DD66100, 0x00003FE4 //A13 = +1.33536787408751203998e-08L +data8 0xE964D255CB31DFFA, 0x0000BFE2 //A14 = -3.39632729387679010008e-09L +data8 0xE22E62E932B704D4, 0x00003FE0 //A15 = +8.22842400379225526299e-10L +// Pol8 +data8 0xB8B835882D46A6C8, 0x00003FEF //A0 = +2.20202883282415435401e-05L +data8 0xC9D1F63F89B74E90, 0x0000BFF9 //A1 = -2.46362504515706189782e-02L +data8 0x8E376748B1274F30, 0x00003FF7 //A2 = +4.34010070001387441657e-03L +data8 0x98174C7EA49B5B37, 0x0000BFF4 //A3 = -5.80181163659971286762e-04L +data8 0x8D2C40506AE9FF97, 0x00003FEF //A4 = +1.68291159100251734927e-05L +data8 0xD9A580C115B9D150, 0x00003FEF //A5 = +2.59454841475194555896e-05L +data8 0xDB35B21F1C3F99CE, 0x0000BFEE //A6 = -1.30659192305072674545e-05L +data8 0x99FAADAE17A3050E, 0x00003FED //A7 = +4.58893813631592314881e-06L +data8 0xBA1D259BCD6987A9, 0x0000BFEB //A8 = -1.38665627771423394637e-06L +data8 0xCDD7FF5BEA0145C2, 0x00003FE9 //A9 = +3.83413844219813384124e-07L +data8 0xD60857176CE6AB9D, 0x0000BFE7 //A10 = -9.96666862214499946343e-08L +data8 0xD446A2402112DF4C, 0x00003FE5 //A11 = +2.47121687566658908126e-08L +data8 0xCA87133235F1F495, 0x0000BFE3 //A12 = -5.89433000014933371980e-09L +data8 0xBB15B0021581C8B6, 0x00003FE1 //A13 = +1.36122047057936849125e-09L +data8 0xAC9D6585D4AF505E, 0x0000BFDF //A14 = -3.13984547328132268695e-10L +data8 0x975A1439C3795183, 0x00003FDD //A15 = +6.88268624429648826457e-11L +// Pol9 +data8 0x99A7676284CDC9FE, 0x00003FEF //A0 = +1.83169747921764176475e-05L +data8 0x9AD0AE249A02896C, 0x0000BFF9 //A1 = -1.88983346204739151909e-02L +data8 0xCB89B4AEC19898BE, 0x00003FF6 //A2 = +3.10574208447745576452e-03L +data8 0xEBBC47E30E1AC2C2, 0x0000BFF3 //A3 = -4.49629730048297442064e-04L +data8 0xD1E35B7FCE1CF859, 0x00003FF0 //A4 = +5.00412261289558493438e-05L +data8 0xB40743664EF24552, 0x0000BFEB //A5 = -1.34131589671166307319e-06L +data8 0xCAD2F5C596FFE1B4, 0x0000BFEB //A6 = -1.51115702599728593837e-06L +data8 0xAE42B6D069DFDDF2, 0x00003FEA //A7 = +6.49171330116787223873e-07L +data8 0xD0739A05BB43A714, 0x0000BFE8 //A8 = -1.94135651872623440782e-07L +data8 0xD745B854AB601BD7, 0x00003FE6 //A9 = +5.01219983943456578062e-08L +data8 0xCC4066E13E338B13, 0x0000BFE4 //A10 = -1.18890061172430768892e-08L +data8 0xB6EAADB55A6C3CB4, 0x00003FE2 //A11 = +2.66178850259168707794e-09L +data8 0x9CC6C178AD3F96AD, 0x0000BFE0 //A12 = -5.70349182959704086428e-10L +data8 0x81D0E2AA27DEB74A, 0x00003FDE //A13 = +1.18066926578104076645e-10L +data8 0xD75FB9049190BEFD, 0x0000BFDB //A14 = -2.44851795398843967972e-11L +data8 0xA9384A51D48C8703, 0x00003FD9 //A15 = +4.80951837368635202609e-12L +// Pol10 +data8 0xD2B3482EE449C535, 0x00003FEE //A0 = +1.25587177382575655080e-05L +data8 0xE7939B2D0607DFCF, 0x0000BFF8 //A1 = -1.41343131436717436429e-02L +data8 0x8810EB4AC5F0F1CE, 0x00003FF6 //A2 = +2.07620377002350121270e-03L +data8 0x9546589602AEB955, 0x0000BFF3 //A3 = -2.84719065122144294949e-04L +data8 0x9333434342229798, 0x00003FF0 //A4 = +3.50952732796136549298e-05L +data8 0xEB36A98FD81D3DEB, 0x0000BFEC //A5 = -3.50495464815398722482e-06L +data8 0xAC370EFA025D0477, 0x00003FE8 //A6 = +1.60387784498518639254e-07L +data8 0xC8DF7F8ACA099426, 0x00003FE6 //A7 = +4.67693991699936842330e-08L +data8 0xAC694AD4921C02CF, 0x0000BFE5 //A8 = -2.00713167514877937714e-08L +data8 0xB6E29F2FDE2D8C1A, 0x00003FE3 //A9 = +5.32266106167252495164e-09L +data8 0xA41F8EEA75474358, 0x0000BFE1 //A10 = -1.19415398856537468324e-09L +data8 0x869D778A1C56D3D6, 0x00003FDF //A11 = +2.44863450057778470469e-10L +data8 0xD02658BF31411F4C, 0x0000BFDC //A12 = -4.73277831746128372261e-11L +data8 0x9A4A95EE59127779, 0x00003FDA //A13 = +8.77044784978207256260e-12L +data8 0xE518330AF013C2F6, 0x0000BFD7 //A14 = -1.62781453276882333209e-12L +data8 0xA036A9DF71BD108A, 0x00003FD5 //A15 = +2.84596398987114375607e-13L +// Pol11 +data8 0x9191CFBF001F3BB3, 0x00003FEE //A0 = +8.67662287973472452343e-06L +data8 0xAA47E0CF01AE9730, 0x0000BFF8 //A1 = -1.03931136509584404513e-02L +data8 0xAEABE7F17B01D18F, 0x00003FF5 //A2 = +1.33263784731775399430e-03L +data8 0xAC0D6A309D04E5DB, 0x0000BFF2 //A3 = -1.64081956462118568288e-04L +data8 0xA08357DF458054D0, 0x00003FEF //A4 = +1.91346477952797715021e-05L +data8 0x8A1596B557440FE0, 0x0000BFEC //A5 = -2.05761687274453412571e-06L +data8 0xCDA0EAE0A5615E9A, 0x00003FE8 //A6 = +1.91506542215670149741e-07L +data8 0xD36A08FB4E104F9A, 0x0000BFE4 //A7 = -1.23059260396551086769e-08L +data8 0xD7433F91E78A7A11, 0x0000BFDF //A8 = -3.91560549815575091188e-10L +data8 0xC2F5308FD4F5CE62, 0x00003FDF //A9 = +3.54626121852421163117e-10L +data8 0xC83876915F49D630, 0x0000BFDD //A10 = -9.10497688901018285126e-11L +data8 0xA11C605DEAE1FE9C, 0x00003FDB //A11 = +1.83161825409194847892e-11L +data8 0xE7977BC1342D19BF, 0x0000BFD8 //A12 = -3.29111645807102123274e-12L +data8 0x9BC3A7D6396C6756, 0x00003FD6 //A13 = +5.53385887288503961220e-13L +data8 0xD0110D5683740B8C, 0x0000BFD3 //A14 = -9.24001363293241428519e-14L +data8 0x81786D7856A5CC92, 0x00003FD1 //A15 = +1.43741041714595023996e-14L +// Pol12 +data8 0xB85654F6033B3372, 0x00003FEF //A0 = +2.19747106911869287049e-05L +data8 0xF78B40078736B406, 0x0000BFF7 //A1 = -7.55444170413862312647e-03L +data8 0xDA8FDE84D88E5D5D, 0x00003FF4 //A2 = +8.33747822263358628569e-04L +data8 0xBC2D3F3891721AA9, 0x0000BFF1 //A3 = -8.97296647669960333635e-05L +data8 0x9D15ACFD3BF50064, 0x00003FEE //A4 = +9.36297600601039610762e-06L +data8 0xFBED3D03F3C1B671, 0x0000BFEA //A5 = -9.38500137149172923985e-07L +data8 0xBEE615E3B2FA16C8, 0x00003FE7 //A6 = +8.88941676851808958175e-08L +data8 0x843D32692CF5662A, 0x0000BFE4 //A7 = -7.69732580860195238520e-09L +data8 0x99E74472FD94E22B, 0x00003FE0 //A8 = +5.59897264617128952416e-10L +data8 0xCEF63DABF4C32E15, 0x0000BFDB //A9 = -2.35288414996279313219e-11L +data8 0xA2D86C25C0991123, 0x0000BFD8 //A10 = -2.31417232327307408235e-12L +data8 0xF50C1B31D2E922BD, 0x00003FD6 //A11 = +8.70582858983364191159e-13L +data8 0xC0F093DEC2B019A1, 0x0000BFD4 //A12 = -1.71364927865227509533e-13L +data8 0xFC1441C4CD105981, 0x00003FD1 //A13 = +2.79864052545369490865e-14L +data8 0x9CC959853267F026, 0x0000BFCF //A14 = -4.35170017302700609509e-15L +data8 0xB06BA14016154F1E, 0x00003FCC //A15 = +6.12081320471295704631e-16L +// Pol13 +data8 0xA59E74BF544F2422, 0x00003FEF //A0 = +1.97433196215210145261e-05L +data8 0xB2814F4EDAE15330, 0x0000BFF7 //A1 = -5.44754383528015875700e-03L +data8 0x867C249D378F0A23, 0x00003FF4 //A2 = +5.13019308804593120161e-04L +data8 0xC76644393388AB68, 0x0000BFF0 //A3 = -4.75405403392600215101e-05L +data8 0x91143AD5CCA229FE, 0x00003FED //A4 = +4.32369180778264703719e-06L +data8 0xCE6A11FB6840A974, 0x0000BFE9 //A5 = -3.84476663329551178495e-07L +data8 0x8EC29F66C59DE243, 0x00003FE6 //A6 = +3.32389596787155456596e-08L +data8 0xBE3FCDDCA94CA24E, 0x0000BFE2 //A7 = -2.76849073931513325199e-09L +data8 0xF06A84BDC70A0B0D, 0x00003FDE //A8 = +2.18657158231304988330e-10L +data8 0x8B8E6969D056D124, 0x0000BFDB //A9 = -1.58657139740906811035e-11L +data8 0x8984985AA29A0567, 0x00003FD7 //A10 = +9.77123802231106533829e-13L +data8 0xA53ABA084300137C, 0x0000BFD2 //A11 = -3.66882970952892030306e-14L +data8 0xA90EC851E91C3319, 0x0000BFCE //A12 = -2.34614750044359490986e-15L +data8 0xEC9CAF64237B5060, 0x00003FCC //A13 = +8.20912960028437475035e-16L +data8 0xA9156668FCF01479, 0x0000BFCA //A14 = -1.46656639874123613261e-16L +data8 0xBAEF58D8118DD5D4, 0x00003FC7 //A15 = +2.02675278255254907493e-17L +// Pol14 +data8 0xC698952E9CEAA800, 0x00003FEF //A0 = +2.36744912073515619263e-05L +data8 0x800395F8C7B4FA00, 0x0000BFF7 //A1 = -3.90667746392883642897e-03L +data8 0xA3B2467B6B391831, 0x00003FF3 //A2 = +3.12226081793919541155e-04L +data8 0xCF2061122A69D72B, 0x0000BFEF //A3 = -2.46914006692526122176e-05L +data8 0x817FAB6B5DEB9924, 0x00003FEC //A4 = +1.92968114320180123521e-06L +data8 0x9FC190F5827740E7, 0x0000BFE8 //A5 = -1.48784479265231093475e-07L +data8 0xC1FE5C1835C8AFCD, 0x00003FE4 //A6 = +1.12919132662720380018e-08L +data8 0xE7216A9FBB204DA3, 0x0000BFE0 //A7 = -8.40847981461949000003e-10L +data8 0x867566ED95C5C64F, 0x00003FDD //A8 = +6.11446929759298780795e-11L +data8 0x97A8BFA723F0F014, 0x0000BFD9 //A9 = -4.31041298699752869577e-12L +data8 0xA3D24B7034984522, 0x00003FD5 //A10 = +2.91005377301348717042e-13L +data8 0xA5AAA371C22F3741, 0x0000BFD1 //A11 = -1.83926825395757259128e-14L +data8 0x95352E5597EACC23, 0x00003FCD //A12 = +1.03533666540077850452e-15L +data8 0xCCEBE3043B689428, 0x0000BFC8 //A13 = -4.44352525147076912166e-17L +data8 0xA779DAB4BE1F80BB, 0x0000BFBC //A14 = -8.86610526981738255206e-21L +data8 0xB171271F3517282C, 0x00003FC1 //A15 = +3.00598445879282370850e-19L +// Pol15 +data8 0xB7AC727D1C3FEB05, 0x00003FEE //A0 = +1.09478009914822049780e-05L +data8 0xB6E6274485C10B0A, 0x0000BFF6 //A1 = -2.79081782038927199588e-03L +data8 0xC5CAE2122D009506, 0x00003FF2 //A2 = +1.88629638738336219173e-04L +data8 0xD466E7957D0A3362, 0x0000BFEE //A3 = -1.26601440424012313479e-05L +data8 0xE2593D798DA20E2E, 0x00003FEA //A4 = +8.43214222346512003230e-07L +data8 0xEF2D2BBA7D2882CC, 0x0000BFE6 //A5 = -5.56876064495961858535e-08L +data8 0xFA5819BB4AE974C2, 0x00003FE2 //A6 = +3.64298674151704370449e-09L +data8 0x819BB0CE825FBB28, 0x0000BFDF //A7 = -2.35755881668932259913e-10L +data8 0x84871099BF728B8F, 0x00003FDB //A8 = +1.50666434199945890414e-11L +data8 0x858188962DFEBC9F, 0x0000BFD7 //A9 = -9.48617116568458677088e-13L +data8 0x840F38FF2FBAE753, 0x00003FD3 //A10 = +5.86461827778372616657e-14L +data8 0xFF47EAF69577B213, 0x0000BFCE //A11 = -3.54273456410181081472e-15L +data8 0xEF402CCB4D29FAF8, 0x00003FCA //A12 = +2.07516888659313950588e-16L +data8 0xD6B789E01141231B, 0x0000BFC6 //A13 = -1.16398290506765191078e-17L +data8 0xB5EEE343E9CFE3EC, 0x00003FC2 //A14 = +6.16413506924643419723e-19L +data8 0x859B41A39D600346, 0x0000BFBE //A15 = -2.82922705825870414438e-20L +// Pol16 +data8 0x85708B69FD184E11, 0x00003FED //A0 = +3.97681079176353356199e-06L +data8 0x824D92BC60A1F70A, 0x0000BFF6 //A1 = -1.98826630037499070532e-03L +data8 0xEDCF7D3576BB5258, 0x00003FF1 //A2 = +1.13396885054265675352e-04L +data8 0xD7FC59226A947CDF, 0x0000BFED //A3 = -6.43687650810478871875e-06L +data8 0xC32C51B574E2651E, 0x00003FE9 //A4 = +3.63538268539251809118e-07L +data8 0xAF67910F5681401F, 0x0000BFE5 //A5 = -2.04197779750247395258e-08L +data8 0x9CB3E8D7DCD1EA9D, 0x00003FE1 //A6 = +1.14016272459029850306e-09L +data8 0x8B14ECFBF7D4F114, 0x0000BFDD //A7 = -6.32470533185766848692e-11L +data8 0xF518253AE4A3AE72, 0x00003FD8 //A8 = +3.48299974583453268369e-12L +data8 0xD631A5699AA2F334, 0x0000BFD4 //A9 = -1.90242426474085078079e-13L +data8 0xB971AD4C30C56E5D, 0x00003FD0 //A10 = +1.02942127356740047925e-14L +data8 0x9ED0065A601F3160, 0x0000BFCC //A11 = -5.50991880383698965959e-16L +data8 0x863A04008E12867C, 0x00003FC8 //A12 = +2.91057593756148904838e-17L +data8 0xDF62F9F44F5C7170, 0x0000BFC3 //A13 = -1.51372666097522872780e-18L +data8 0xBA4E118E88CFDD31, 0x00003FBF //A14 = +7.89032177282079635722e-20L +data8 0x942AD897FC4D2F2A, 0x0000BFBB //A15 = -3.92195756076319409245e-21L +// Pol17 +data8 0xCB8514540566C717, 0x00003FEF //A0 = +2.42614557068144130848e-05L +data8 0xB94F08D6816E0CD4, 0x0000BFF5 //A1 = -1.41379340061829929314e-03L +data8 0x8E7C342C2DABB51B, 0x00003FF1 //A2 = +6.79422240687700109911e-05L +data8 0xDA69DAFF71E30D5B, 0x0000BFEC //A3 = -3.25461473899657142468e-06L +data8 0xA6D5B2DB69B4B3F6, 0x00003FE8 //A4 = +1.55376978584082701045e-07L +data8 0xFDF4F76BC1D1BD47, 0x0000BFE3 //A5 = -7.39111857092131684572e-09L +data8 0xC08BC52C95B12C2D, 0x00003FDF //A6 = +3.50239092565793882444e-10L +data8 0x91624BF6D3A3F6C9, 0x0000BFDB //A7 = -1.65282439890232458821e-11L +data8 0xDA91F7A450DE4270, 0x00003FD6 //A8 = +7.76517285902715940501e-13L +data8 0xA380ADF55416E624, 0x0000BFD2 //A9 = -3.63048822989374426852e-14L +data8 0xF350FC0CEDEE0FD6, 0x00003FCD //A10 = +1.68834630987974622269e-15L +data8 0xB3FA19FBDC8F023C, 0x0000BFC9 //A11 = -7.80525639701804380489e-17L +data8 0x8435328C80940126, 0x00003FC5 //A12 = +3.58349966898667910204e-18L +data8 0xC0D22F655BA5EF39, 0x0000BFC0 //A13 = -1.63325770165403860181e-19L +data8 0x8F14B9EBD5A9AB25, 0x00003FBC //A14 = +7.57464305512080733773e-21L +data8 0xCD4804BBF6DC1B6F, 0x0000BFB7 //A15 = -3.39609459750208886298e-22L +// Pol18 +data8 0xE251DFE45AB0C22E, 0x00003FEE //A0 = +1.34897126299700418200e-05L +data8 0x83943CC7D59D4215, 0x0000BFF5 //A1 = -1.00386850310061655307e-03L +data8 0xAA57896951134BCA, 0x00003FF0 //A2 = +4.06126834109940757047e-05L +data8 0xDC0A67051E1C4A2C, 0x0000BFEB //A3 = -1.63943048164477430317e-06L +data8 0x8DCB3C0A8CD07BBE, 0x00003FE7 //A4 = +6.60279229777753829876e-08L +data8 0xB64DE81C24F7F265, 0x0000BFE2 //A5 = -2.65287705357477481067e-09L +data8 0xE9CBB7A990DBA8B5, 0x00003FDD //A6 = +1.06318007608620426224e-10L +data8 0x9583D4B85C2ADC6F, 0x0000BFD9 //A7 = -4.24947087941505088222e-12L +data8 0xBEB0EE8114EEDF77, 0x00003FD4 //A8 = +1.69367754741562774916e-13L +data8 0xF2791BB8F06BDA93, 0x0000BFCF //A9 = -6.72997988617021128704e-15L +data8 0x99A907F6A92195B4, 0x00003FCB //A10 = +2.66558091161711891239e-16L +data8 0xC213E5E6F833BB93, 0x0000BFC6 //A11 = -1.05209746502719578617e-17L +data8 0xF41FBBA6B343960F, 0x00003FC1 //A12 = +4.13562069721140021224e-19L +data8 0x98F194AEE31D188D, 0x0000BFBD //A13 = -1.61935414722333263347e-20L +data8 0xC42F5029BB622157, 0x00003FB8 //A14 = +6.49121108201931196678e-22L +data8 0xF43BD08079E50E0F, 0x0000BFB3 //A15 = -2.52531675510242468317e-23L +// Pol19 +data8 0x82557B149A04D08E, 0x00003FEF //A0 = +1.55370127331027842820e-05L +data8 0xBAAB433307CE614B, 0x0000BFF4 //A1 = -7.12085701486669872724e-04L +data8 0xCB52D9DBAC16FE82, 0x00003FEF //A2 = +2.42380662859334411743e-05L +data8 0xDD214359DBBCE7D1, 0x0000BFEA //A3 = -8.23773197624244883859e-07L +data8 0xF01E8E968139524C, 0x00003FE5 //A4 = +2.79535729459988509676e-08L +data8 0x82286A057E0916CE, 0x0000BFE1 //A5 = -9.47023128967039348510e-10L +data8 0x8CDDDC4E8D013365, 0x00003FDC //A6 = +3.20293663356974901319e-11L +data8 0x982FEEE90D4E8751, 0x0000BFD7 //A7 = -1.08135537312234452657e-12L +data8 0xA41D1E84083B8FD6, 0x00003FD2 //A8 = +3.64405720894915411836e-14L +data8 0xB0A1B6111B72E159, 0x0000BFCD //A9 = -1.22562851790685744085e-15L +data8 0xBDB77DE6B650FFA2, 0x00003FC8 //A10 = +4.11382657214908334175e-17L +data8 0xCB54E95CDB66978A, 0x0000BFC3 //A11 = -1.37782909696752432371e-18L +data8 0xD959E428A62B1B6C, 0x00003FBE //A12 = +4.60258936838597812582e-20L +data8 0xE7D49EC23F1A16A0, 0x0000BFB9 //A13 = -1.53412587409583783059e-21L +data8 0xFDE429BC9947B2BE, 0x00003FB4 //A14 = +5.25034823750902928092e-23L +data8 0x872137A062C042EF, 0x0000BFB0 //A15 = -1.74651114923000080365e-24L +// Pol20 +data8 0x8B9B185C6A2659AC, 0x00003FEF //A0 = +1.66423130594825442963e-05L +data8 0x84503AD52588A1E8, 0x0000BFF4 //A1 = -5.04735556466270303549e-04L +data8 0xF26C7C2B566388E1, 0x00003FEE //A2 = +1.44495826764677427386e-05L +data8 0xDDDA15FEE262BB47, 0x0000BFE9 //A3 = -4.13231361893675488873e-07L +data8 0xCACEBC73C90C2FE0, 0x00003FE4 //A4 = +1.18049538609157282958e-08L +data8 0xB9314D00022B41DD, 0x0000BFDF //A5 = -3.36863342776746896664e-10L +data8 0xA8E9FBDC714638B9, 0x00003FDA //A6 = +9.60164921624768038366e-12L +data8 0x99E246C0CC8CA6F6, 0x0000BFD5 //A7 = -2.73352704217713596798e-13L +data8 0x8C04E7B5DF372EA1, 0x00003FD0 //A8 = +7.77262480048865685174e-15L +data8 0xFE7B90CAA0B6D5F7, 0x0000BFCA //A9 = -2.20728537958846147109e-16L +data8 0xE6F40BAD4EC6CB4F, 0x00003FC5 //A10 = +6.26000182616999972048e-18L +data8 0xD14F4E0538F0F992, 0x0000BFC0 //A11 = -1.77292283439752259258e-19L +data8 0xBD5A7FAA548CC749, 0x00003FBB //A12 = +5.01214569023722089225e-21L +data8 0xAB15D69425373A67, 0x0000BFB6 //A13 = -1.41518447770061562822e-22L +data8 0x9EF95456F75B4DF4, 0x00003FB1 //A14 = +4.10938011540250142351e-24L +data8 0x8FADCC45E81433E7, 0x0000BFAC //A15 = -1.16062889679749879834e-25L +// Pol21 +data8 0xB47A917B0F7B50AE, 0x00003FEF //A0 = +2.15147474240529518138e-05L +data8 0xBB77DC3BA0C937B3, 0x0000BFF3 //A1 = -3.57567223048598672970e-04L +data8 0x90694DFF4EBF7370, 0x00003FEE //A2 = +8.60758700336677694536e-06L +data8 0xDE5379AA90A98F3F, 0x0000BFE8 //A3 = -2.07057292787309736495e-07L +data8 0xAB0322293F1F9CA0, 0x00003FE3 //A4 = +4.97711123919916694625e-09L +data8 0x837119E59D3B7AC2, 0x0000BFDE //A5 = -1.19545621970063369582e-10L +data8 0xC9E5B74A38ECF3FC, 0x00003FD8 //A6 = +2.86913359605586285967e-12L +data8 0x9AEF5110C6885352, 0x0000BFD3 //A7 = -6.88048865490621757799e-14L +data8 0xED988D52189CE6A3, 0x00003FCD //A8 = +1.64865278639132278935e-15L +data8 0xB6063CECD8012B6D, 0x0000BFC8 //A9 = -3.94702428606368525374e-17L +data8 0x8B541EB15E79CEEC, 0x00003FC3 //A10 = +9.44127272399408815784e-19L +data8 0xD51A136D8C75BC25, 0x0000BFBD //A11 = -2.25630369561137931232e-20L +data8 0xA2C1C5E19CC79E6F, 0x00003FB8 //A12 = +5.38517493921589837361e-22L +data8 0xF86F9772306F56C1, 0x0000BFB2 //A13 = -1.28438352359240135735e-23L +data8 0xC32F6FEEDE86528E, 0x00003FAD //A14 = +3.15338862172962186458e-25L +data8 0x9534ED189744D7D4, 0x0000BFA8 //A15 = -7.53301543611470014315e-27L +// Pol22 +data8 0xCBA0A2DB94A2C494, 0x00003FEF //A0 = +2.42742878212752702946e-05L +data8 0x84C089154A49E0E8, 0x0000BFF3 //A1 = -2.53204520651046300034e-04L +data8 0xABF5665BD0D8B0CD, 0x00003FED //A2 = +5.12476542947092361490e-06L +data8 0xDEA1C518E3EEE872, 0x0000BFE7 //A3 = -1.03671063536324831083e-07L +data8 0x900B77F271559AE8, 0x00003FE2 //A4 = +2.09612770408581408652e-09L +data8 0xBA4C74A262BE3E4E, 0x0000BFDC //A5 = -4.23594098489216166935e-11L +data8 0xF0D1680FCC1EAF97, 0x00003FD6 //A6 = +8.55557381760467917779e-13L +data8 0x9B8F8E033BB83A24, 0x0000BFD1 //A7 = -1.72707138247091685914e-14L +data8 0xC8DCA6A691DB8335, 0x00003FCB //A8 = +3.48439884388851942939e-16L +data8 0x819A6CB9CEA5E9BD, 0x0000BFC6 //A9 = -7.02580471688245511753e-18L +data8 0xA726B4F622585BEA, 0x00003FC0 //A10 = +1.41582572516648501043e-19L +data8 0xD7727648A4095986, 0x0000BFBA //A11 = -2.85141885626054217632e-21L +data8 0x8AB627E09CF45997, 0x00003FB5 //A12 = +5.73697507862703019314e-23L +data8 0xB28C15C117CC604F, 0x0000BFAF //A13 = -1.15383428132352407085e-24L +data8 0xECB8428626DA072C, 0x00003FA9 //A14 = +2.39025879246942839796e-26L +data8 0x98B731BCFA2CE2B2, 0x0000BFA4 //A15 = -4.81885474332093262902e-28L +// Pol23 +data8 0xC6D013811314D31B, 0x00003FED //A0 = +5.92508308918577687876e-06L +data8 0xBBF3057B8DBACBCF, 0x0000BFF2 //A1 = -1.79242422493281965934e-04L +data8 0xCCADECA501162313, 0x00003FEC //A2 = +3.04996061562356504918e-06L +data8 0xDED1FDBE8CCAF3DB, 0x0000BFE6 //A3 = -5.18793887648024117154e-08L +data8 0xF27B74EDDCA65859, 0x00003FE0 //A4 = +8.82145297317787820675e-10L +data8 0x83E4415687F01A0C, 0x0000BFDB //A5 = -1.49943414247603665601e-11L +data8 0x8F6CB350861CE446, 0x00003FD5 //A6 = +2.54773288906376920377e-13L +data8 0x9BE8456A30CBFC02, 0x0000BFCF //A7 = -4.32729710913845745148e-15L +data8 0xA9694F7E1033977D, 0x00003FC9 //A8 = +7.34704698157502347441e-17L +data8 0xB8035A3D5AF82D85, 0x0000BFC3 //A9 = -1.24692123826025468001e-18L +data8 0xC7CB4B3ACB905FDA, 0x00003FBD //A10 = +2.11540249352095943317e-20L +data8 0xD8D70AEB2E58D729, 0x0000BFB7 //A11 = -3.58731705184186608576e-22L +data8 0xEB27A61B1D5C7697, 0x00003FB1 //A12 = +6.07861113430709162243e-24L +data8 0xFEF9ED74D4F4C9B0, 0x0000BFAB //A13 = -1.02984099170876754831e-25L +data8 0x8E6F410068C12043, 0x00003FA6 //A14 = +1.79777721804459361762e-27L +data8 0x9AE2F6705481630E, 0x0000BFA0 //A15 = -3.05459905177379058768e-29L +// Pol24 +data8 0xD2D858D5B01C9434, 0x00003FEE //A0 = +1.25673476165670766128e-05L +data8 0x8505330F8B4FDE49, 0x0000BFF2 //A1 = -1.26858053564784963985e-04L +data8 0xF39171C8B1D418C2, 0x00003FEB //A2 = +1.81472407620770441249e-06L +data8 0xDEF065C3D7BFD26E, 0x0000BFE5 //A3 = -2.59535215807652675043e-08L +data8 0xCC0199EA6ACA630C, 0x00003FDF //A4 = +3.71085215769339916703e-10L +data8 0xBAA25319F01ED248, 0x0000BFD9 //A5 = -5.30445960650683029105e-12L +data8 0xAAB28A84F8CFE4D1, 0x00003FD3 //A6 = +7.58048850973457592162e-14L +data8 0x9C14B931AEB311A8, 0x0000BFCD //A7 = -1.08302915828084288776e-15L +data8 0x8EADA745715A0714, 0x00003FC7 //A8 = +1.54692159263197000533e-17L +data8 0x82643F3F722CE6B5, 0x0000BFC1 //A9 = -2.20891945694400066611e-19L +data8 0xEE42ECDE465A99E4, 0x00003FBA //A10 = +3.15336372779307614198e-21L +data8 0xD99FC74326ACBFC0, 0x0000BFB4 //A11 = -4.50036161691276556269e-23L +data8 0xC6A4DCACC554911E, 0x00003FAE //A12 = +6.41853356148678957077e-25L +data8 0xB550CEA09DA96F44, 0x0000BFA8 //A13 = -9.15410112414783078242e-27L +data8 0xAA9149317996F32F, 0x00003FA2 //A14 = +1.34554050666508391264e-28L +data8 0x9C3008EFE3F52F19, 0x0000BF9C //A15 = -1.92516125328592532359e-30L +// Pol25 +data8 0xA68E78218806283F, 0x00003FEF //A0 = +1.98550844852103406280e-05L +data8 0xBC41423996DC8A37, 0x0000BFF1 //A1 = -8.97669395268764751516e-05L +data8 0x90E55AE31A2F8271, 0x00003FEB //A2 = +1.07955871580069359702e-06L +data8 0xDF022272DA4A3BEF, 0x0000BFE4 //A3 = -1.29807937275957214439e-08L +data8 0xAB95DCBFFB0BAAB8, 0x00003FDE //A4 = +1.56056011861921437794e-10L +data8 0x83FF2547BA9011FF, 0x0000BFD8 //A5 = -1.87578539510813332135e-12L +data8 0xCB0C353560EEDC45, 0x00003FD1 //A6 = +2.25428217090412574481e-14L +data8 0x9C24CEB86E76D2C5, 0x0000BFCB //A7 = -2.70866279585559299821e-16L +data8 0xF01AFA23DDFDAE0E, 0x00003FC4 //A8 = +3.25403467375734083376e-18L +data8 0xB892BDFBCF1D9740, 0x0000BFBE //A9 = -3.90848978133441513662e-20L +data8 0x8DDBBF34415AAECA, 0x00003FB8 //A10 = +4.69370027479731756829e-22L +data8 0xDA04170D07458C3B, 0x0000BFB1 //A11 = -5.63558091177482043435e-24L +data8 0xA76F391095A9563A, 0x00003FAB //A12 = +6.76262416498584003290e-26L +data8 0x8098FA125C18D8DB, 0x0000BFA5 //A13 = -8.11564737276592661642e-28L +data8 0xCB9E4D5C08923227, 0x00003F9E //A14 = +1.00391606269366059664e-29L +data8 0x9CEC3BF7A0BE2CAF, 0x0000BF98 //A15 = -1.20888920108938909316e-31L +// Pol26 +data8 0xC17AB25E269272F7, 0x00003FEE //A0 = +1.15322640047234590651e-05L +data8 0x85310509E633FEF2, 0x0000BFF1 //A1 = -6.35106483144690768696e-05L +data8 0xAC5E4C4DCB2D940C, 0x00003FEA //A2 = +6.42122148740412561597e-07L +data8 0xDF0AAD0571FFDD48, 0x0000BFE3 //A3 = -6.49136789710824396482e-09L +data8 0x9049D8440AFD180F, 0x00003FDD //A4 = +6.56147932223174570008e-11L +data8 0xBAA936477C5FA9D7, 0x0000BFD6 //A5 = -6.63153032879993841863e-13L +data8 0xF17261294EAB1443, 0x00003FCF //A6 = +6.70149477756803680009e-15L +data8 0x9C22F87C31DB007A, 0x0000BFC9 //A7 = -6.77134581402030645534e-17L +data8 0xC9E98E633942AC12, 0x00003FC2 //A8 = +6.84105580182052870823e-19L +data8 0x828998181309642C, 0x0000BFBC //A9 = -6.91059649300859944955e-21L +data8 0xA8C3D4DCE1ECBAB6, 0x00003FB5 //A10 = +6.97995542988331257517e-23L +data8 0xDA288D52CC4C351A, 0x0000BFAE //A11 = -7.04907829139578377009e-25L +data8 0x8CEEACB790B5F374, 0x00003FA8 //A12 = +7.11526399101774993883e-27L +data8 0xB61C8A29D98F24C0, 0x0000BFA1 //A13 = -7.18303147470398859453e-29L +data8 0xF296F69FE45BDA7D, 0x00003F9A //A14 = +7.47537230021540031251e-31L +data8 0x9D4B25BF6FB7234B, 0x0000BF94 //A15 = -7.57340869663212138051e-33L +// Pol27 +data8 0xC7772CC326D6FBB8, 0x00003FEE //A0 = +1.18890718679826004395e-05L +data8 0xE0F9D5410565D55D, 0x0000BFF0 //A1 = -5.36384368533203585378e-05L +data8 0x85C0BE825680E148, 0x00003FEA //A2 = +4.98268406609692971520e-07L +data8 0x9F058A389D7BA177, 0x0000BFE3 //A3 = -4.62813885933188677790e-09L +data8 0xBD0B751F0A6BAC7A, 0x00003FDC //A4 = +4.29838009673609430305e-11L +data8 0xE0B6823570502E9D, 0x0000BFD5 //A5 = -3.99170340031272728535e-13L +data8 0x858A9C52FC426D86, 0x00003FCF //A6 = +3.70651975271664045723e-15L +data8 0x9EB4438BFDF1928D, 0x0000BFC8 //A7 = -3.44134780748056488222e-17L +data8 0xBC968DCD8C06D74E, 0x00003FC1 //A8 = +3.19480670422195579127e-19L +data8 0xE0133A405F782125, 0x0000BFBA //A9 = -2.96560935615546392028e-21L +data8 0x851AFEBB70D07E79, 0x00003FB4 //A10 = +2.75255617931932536111e-23L +data8 0x9E1E21A841BF8738, 0x0000BFAD //A11 = -2.55452923487640676799e-25L +data8 0xBBCF2EF1C6E72327, 0x00003FA6 //A12 = +2.37048675755308004410e-27L +data8 0xDF0D320CF12B8BCB, 0x0000BF9F //A13 = -2.19945804585962185550e-29L +data8 0x8470A76DE5FCADD8, 0x00003F99 //A14 = +2.04056213851532266258e-31L +data8 0x9D41C15F6A6FBB04, 0x0000BF92 //A15 = -1.89291056020108587823e-33L +LOCAL_OBJECT_END(erfc_Q_table) + + +.section .text +GLOBAL_LIBM_ENTRY(erfcl) + +{ .mfi + alloc r32 = ar.pfs, 0, 36, 4, 0 + fma.s1 FR_Tmp = f1, f1, f8 // |x|+1, if x >= 0 + nop.i 0 +} +{ .mfi + addl GR_ad_Arg = @ltoff(exp_table_1), gp + fms.s1 FR_Tmp1 = f1, f1, f8 // |x|+1, if x < 0 + mov GR_rshf_2to51 = 0x4718 // begin 1.10000 2^(63+51) +} +;; + +{ .mfi + ld8 GR_ad_Arg = [GR_ad_Arg] // Point to Arg table + fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0 + shl GR_rshf_2to51 = GR_rshf_2to51,48 // end 1.10000 2^(63+51) +} +{ .mlx + mov GR_rshf = 0x43e8 // begin 1.1000 2^63 for right shift + movl GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // signif. of 1/ln2 +} +;; + +{ .mfi + mov GR_exp_2tom51 = 0xffff-51 + fclass.m p8,p0 = f8,0x07 // p8: x = 0 + shl GR_rshf = GR_rshf,48 // end 1.1000 2^63 for right shift +} +{ .mfi + nop.m 0 + fnma.s1 FR_norm_x = f8, f8, f0 //high bits for -x^2 + nop.i 0 +} +;; + +.pred.rel "mutex",p6,p7 +{ .mfi + setf.sig FR_INV_LN2_2TO63 = GR_sig_inv_ln2 // form 1/ln2 * 2^63 +(p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x|, if x >= 0 + nop.i 0 +} +{ .mfi + setf.d FR_RSHF_2TO51 = GR_rshf_2to51 //const 1.10 * 2^(63+51) +(p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x|, if x < 0 + mov GR_exp_mask = 0x1FFFF // Form exponent mask +} +;; + +{ .mfi + ldfe FR_ch_dx = [GR_ad_Arg], 16 + fclass.m p10,p0 = f8, 0x21 // p10: x = +inf + mov GR_exp_bias = 0x0FFFF // Set exponent bias +} +{ .mlx + setf.d FR_RSHF = GR_rshf // Right shift const 1.1000 * 2^63 + movl GR_ERFC_XC_TB = 0x650 +} +;; + +.pred.rel "mutex",p6,p7 +{ .mfi + setf.exp FR_2TOM51 = GR_exp_2tom51 // 2^-51 for scaling float_N +(p6) fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^2,x >=0 + nop.i 0 +} +{ .mfi + ldfpd FR_POS_ARG_ASYMP,FR_NEG_ARG_ASYMP = [GR_ad_Arg], 16 +(p7) fma.s1 FR_Tmp = FR_Tmp1, FR_Tmp1, f0 // (|x|+1)^2, x<0 + mov GR_0x1 = 0x1 +} +;; + +//p8: y = 1.0, x = 0.0,quick exit +{ .mfi + ldfpd FR_dx,FR_dx1 = [GR_ad_Arg], 16 + fclass.m p9,p0 = f8, 0x22 // p9: x = -inf + nop.i 0 + +} +{ .mfb + nop.m 0 +(p8) fma.s0 f8 = f1, f1, f0 +(p8) br.ret.spnt b0 +} +;; + +{ .mfi + ldfe FR_UnfBound = [GR_ad_Arg], 16 + fclass.m p11,p0 = f8, 0xc3 // p11: x = nan + mov GR_BIAS = 0x0FFFF +} +{ .mfi + nop.m 0 + fma.s1 FR_NormX = f8,f1,f0 + nop.i 0 +} +;; + +{ .mfi + ldfe FR_EpsNorm = [GR_ad_Arg], 16 + fmerge.s FR_X = f8,f8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_xsq_lo = f8, f8, FR_norm_x // low bits for -x^2 + nop.i 0 +} +;; + +{ .mfi + add GR_ad_C = 0x20, GR_ad_Arg // Point to C table + nop.f 0 + add GR_ad_T1 = 0x50, GR_ad_Arg // Point to T1 table +} +{ .mfi + add GR_ad_T2 = 0x150, GR_ad_Arg // Point to T2 table + nop.f 0 + add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ad_Arg //poin.to XB_TBL +} +;; + +{ .mfi + getf.exp GR_signexp_x = FR_norm_x // Extr. sign and exponent of x + fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^4 + add GR_ad_W1 = 0x100, GR_ad_T2 // Point to W1 table +} +{ .mfi + ldfe FR_L_hi = [GR_ad_Arg],16 // Get L_hi + nop.f 0 + add GR_ad_W2 = 0x300, GR_ad_T2 // Point to W2 table +} +;; + +// p9: y = 2.0, x = -inf, quick exit +{ .mfi + sub GR_mBIAS = r0, GR_BIAS + fma.s1 FR_2 = f1, f1, f1 + nop.i 0 +} +{ .mfb + ldfe FR_L_lo = [GR_ad_Arg],16 // Get L_lo +(p9) fma.s0 f8 = f1, f1, f1 +(p9) br.ret.spnt b0 +} +;; + +// p10: y = 0.0, x = +inf, quick exit +{ .mfi + adds GR_ERFC_P_TB = 0x380, GR_ERFC_XC_TB // pointer to P_TBL + fma.s1 FR_N_signif = FR_norm_x, FR_INV_LN2_2TO63, FR_RSHF_2TO51 + and GR_exp_x = GR_signexp_x, GR_exp_mask +} +{ .mfb + adds GR_ERFC_S_TB = 0x1C0, GR_ERFC_XC_TB // pointer to S_TBL +(p10) fma.s0 f8 = f0, f1, f0 +(p10) br.ret.spnt b0 +} +;; + +// p12: |x| < 0.681... -> dx = 0.875 (else dx = 0.625 ) +// p11: y = x, x = nan, quick exit +{ .mfi + ldfe FR_C3 = [GR_ad_C],16 // Get C3 for normal path + fcmp.lt.s1 p12,p0 = FR_AbsArg, FR_ch_dx + shl GR_ShftPi_bias = GR_BIAS, 8 // BIAS * 256 +} +{ .mfb + sub GR_exp_x = GR_exp_x, GR_exp_bias // Get exponent +(p11) fma.s0 f8 = f8, f1, f0 +(p11) br.ret.spnt b0 + +} +;; + +{ .mfi + ldfe FR_C2 = [GR_ad_C],16 // Get A2 for main path + nop.f 0 + nop.i 0 +} +;; + +//p15: x > POS_ARG_ASYMP = 107.0 -> erfcl(x) ~=~ 0.0 +{ .mfi + ldfe FR_C1 = [GR_ad_C],16 // Get C1 for main path +(p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP // p6: x >= 0 + nop.i 0 +} +{ .mfb + nop.m 0 +(p12) fma.s1 FR_dx = FR_dx1, f1, f0 //p12: dx = 0.875 for x < 0.681 + nop.b 0 +} +;; + +//p14: x < - NEG_ARG_ASYMP = -6.5 -> erfcl(x) ~=~ 2.0 +{ .mfi + nop.m 0 +(p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg,FR_NEG_ARG_ASYMP // p7: x < 0 + shladd GR_ShftXBi_bias = GR_mBIAS, 4, r0 +} +;; + +{ .mfi + nop.m 0 + fma.s0 FR_Tmpf = f1, f1, FR_EpsNorm // flag i + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 FR_float_N = FR_N_signif, FR_2TOM51, FR_RSHF + nop.i 0 +} +;; + +// p8: x < UnfBound ~=~ 106.53... -> result without underflow error +// p14: y ~=~ 2, x < -6.5,quick exit +{ .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 +} +{ .mfb + nop.m 0 +(p14) fnma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,FR_2 +(p14) br.ret.spnt b0 + +} +;; + +// p15: y ~=~ 0.0 (result with underflow error), x > POS_ARG_ASYMP = 107.0, +// call __libm_error_region +{ .mfb +(p15) mov GR_Parameter_TAG = 207 +(p15) fma.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 +(p15) br.cond.spnt __libm_error_region +} +;; + +{ .mfi + getf.sig GR_N_fix = FR_N_signif // Get N from significand + nop.f 0 + shl GR_ShftPi = GR_IndxPlusBias, 8 + +} +{ .mfi + shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias + nop.f 0 + nop.i 0 +} +;; + +{ .mmi + add GR_ERFC_S_TB = GR_ERFC_S_TB, GR_ShftXBi //poin.to S[i] + add GR_ERFC_XC_TB = GR_ERFC_XC_TB, GR_ShftXBi //poin.to XC[i] + sub GR_ShftPi = GR_ShftPi, GR_ShftPi_bias // 256*i +} +;; + +{ .mfi + ldfe FR_Xc = [GR_ERFC_XC_TB] + fma.s1 FR_Xpdx_hi = FR_AbsArg, f1, FR_dx // x + dx + add GR_ShftA14 = 0xE0, GR_ShftPi // pointer shift for A14 + + +} +{ .mfi + ldfe FR_S = [GR_ERFC_S_TB] + fnma.s1 FR_r = FR_L_hi, FR_float_N, FR_norm_x//r= -L_hi*float_N+x + add GR_ShftA15 = 0xF0, GR_ShftPi // pointer shift for A15 +} +;; + +{ .mfi + add GR_P_POINT_1 = GR_ERFC_P_TB, GR_ShftA14 // pointer to A14 + fcmp.gt.s1 p9,p10 = FR_AbsArg, FR_dx //p9: x > dx, p10: x <= dx + extr.u GR_M1 = GR_N_fix, 6, 6 // Extract index M_1 +} +{ .mfi + add GR_P_POINT_2 = GR_ERFC_P_TB, GR_ShftA15 // pointer to A15 + nop.f 0 + nop.i 0 + +} +;; + +{ .mfi + ldfe FR_A14 = [GR_P_POINT_1], -32 + nop.f 0 + extr.u GR_M2 = GR_N_fix, 0, 6 // Extract index M_2 +} +{ .mfi + ldfe FR_A15 = [GR_P_POINT_2], -32 + nop.f 0 + shladd GR_ad_W1 = GR_M1,3,GR_ad_W1 // Point to W1 +} +;; + +{ .mfi + ldfe FR_A12 = [GR_P_POINT_1], -64 + nop.f 0 + extr GR_K = GR_N_fix, 12, 32 // Extract limite range K +} +{ .mfi + ldfe FR_A13 = [GR_P_POINT_2], -64 + nop.f 0 + shladd GR_ad_T1 = GR_M1,2,GR_ad_T1 // Point to T1 +} +;; + +{ .mfi + ldfe FR_A8 = [GR_P_POINT_1], 32 + nop.f 0 + add GR_exp_2_k = GR_exp_bias, GR_K // Form exponent of 2^k +} +{ .mfi + ldfe FR_A9 = [GR_P_POINT_2], 32 + nop.f 0 + shladd GR_ad_W2 = GR_M2,3,GR_ad_W2 // Point to W2 +} +;; + +{ .mfi + ldfe FR_A10 = [GR_P_POINT_1], -96 + nop.f 0 + shladd GR_ad_T2 = GR_M2,2,GR_ad_T2 // Point to T2 +} +{ .mfi + ldfe FR_A11 = [GR_P_POINT_2], -96 + fnma.s1 FR_r = FR_L_lo, FR_float_N, FR_r //r = -L_lo*float_N + r + nop.i 0 +} +;; + +{ .mfi + ldfe FR_A4 = [GR_P_POINT_1], 32 +(p10) fms.s1 FR_Tmp = FR_dx,f1, FR_Xpdx_hi //for lo of x+dx, x<=dx + nop.i 0 +} +{ .mfi + ldfe FR_A5 = [GR_P_POINT_2], 32 +(p9) fms.s1 FR_Tmp = FR_AbsArg, f1, FR_Xpdx_hi //for lo of x+dx, x>dx + nop.i 0 +} +;; + +{ .mfi + ldfe FR_A6 = [GR_P_POINT_1], -64 + frcpa.s1 FR_U,p11 = f1, FR_Xpdx_hi // hi of 1 /(x + dx) + nop.i 0 +} +{ .mfi + ldfe FR_A7 = [GR_P_POINT_2], -64 + nop.f 0 + nop.i 0 +} +;; + +{ .mfi + ldfe FR_A2 = [GR_P_POINT_1], -32 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe FR_A3 = [GR_P_POINT_2], -32 + nop.f 0 + nop.i 0 +} +;; + +{ .mfi + ldfe FR_A0 = [GR_P_POINT_1], 224 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfe FR_A1 = [GR_P_POINT_2] + fms.s1 FR_LocArg = FR_AbsArg, f1, FR_Xc // xloc = x - x[i] + nop.i 0 +} +;; + +{ .mfi + ldfd FR_W1 = [GR_ad_W1],0 // Get W1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfd FR_W2 = [GR_ad_W2],0 // Get W2 + fma.s1 FR_poly = FR_r, FR_C3, FR_C2 // poly = r * A3 + A2 + nop.i 0 +} +;; + +{ .mfi + ldfs FR_T1 = [GR_ad_T1],0 // Get T1 +(p10) fma.s1 FR_Xpdx_lo = FR_AbsArg,f1, FR_Tmp//lo of x + dx , x <= dx + nop.i 0 +} +{ .mfi + ldfs FR_T2 = [GR_ad_T2],0 // Get T2 +(p9) fma.s1 FR_Xpdx_lo = FR_dx,f1, FR_Tmp // lo of x + dx, x > dx + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fnma.s1 FR_Tmp1 = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N1 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r + nop.i 0 +} +;; + +{ .mfi + setf.exp FR_scale = GR_exp_2_k // Set scale = 2^k + fma.s1 FR_P15_1_1 = FR_LocArg, FR_LocArg, f0 // xloc ^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P15_0_1 = FR_A15, FR_LocArg, FR_A14 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_1_2 = FR_A13, FR_LocArg, FR_A12 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_poly = FR_r, FR_poly, FR_C1 // poly = r * poly + A1 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_2_1 = FR_A9, FR_LocArg, FR_A8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P15_2_2 = FR_A11, FR_LocArg, FR_A10 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_U = FR_U, FR_Tmp1, f0 // N-R, iter. N1 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_3_1 = FR_A5, FR_LocArg, FR_A4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P15_3_2 = FR_A7, FR_LocArg, FR_A6 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_4_2 = FR_A3, FR_LocArg, FR_A2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_W = FR_W1, FR_W2, FR_W2 // W = W1 * W2 + W2 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fmpy.s1 FR_T = FR_T1, FR_T2 // T = T1 * T2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // xloc^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 + fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N2 + nop.i 0 +} + +{ .mfi + nop.m 0 + fma.s1 FR_poly = FR_rsq, FR_poly, FR_r // poly = rsq * poly + r + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_A0 + 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 FR_W = FR_W, f1, FR_W1 // W = W + W1 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_T_scale = FR_T, FR_scale, f0 // T_scale = T * scale + 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_U = FR_U, FR_Tmp, f0 // N-R, iter. N2 + 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 // xloc^8 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_M = FR_T_scale, FR_S, f0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, FR_2 // N-R, iter. N3 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_Q = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fms.s1 FR_H = FR_W, f1, FR_xsq_lo // H = W - xsq_lo + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_U = FR_U, FR_Tmp, f0 // N-R, iter. N3 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_Q = FR_A1, FR_LocArg, FR_Q + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fnma.s1 FR_Tmp = FR_Xpdx_hi, FR_U, f1 // for du + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_R = FR_H, FR_poly, FR_poly + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_res_pos_x_hi = FR_M, FR_U, f0 // M *U + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_R = FR_R, f1, FR_H // R = H + P(r) + H*P(r) + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s0 FR_Tmpf = f8, f1, f0 // flag d + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fnma.s1 FR_dU = FR_Xpdx_lo, FR_U, FR_Tmp + nop.i 0 +} +;; + +// p7: we begin to calculate y(x) = 2 - erfcl(-x) in multi precision +// for -6.5 <= x < 0 +{ .mfi + nop.m 0 + fms.s1 FR_res_pos_x_lo = FR_M, FR_U, FR_res_pos_x_hi + nop.i 0 + +} +{ .mfi + nop.m 0 +(p7) fnma.s1 FR_Tmp1 = FR_res_pos_x_hi, f1, FR_2 //p7: x < 0 + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_G = FR_R, FR_Q, FR_Q + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_Tmp = FR_R, f1, FR_dU // R + du + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 +(p7) fnma.s1 FR_Tmp2 = FR_Tmp1, f1, FR_2 //p7: x < 0 + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_G = FR_G, f1, FR_Tmp + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 +(p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_hi, f1, FR_Tmp2 //p7: x < 0 + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 + fma.s1 FR_V = FR_G, FR_res_pos_x_hi, f0 // V = G * M *U + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 +(p7) fma.s1 FR_res_pos_x_lo = FR_res_pos_x_lo, f1, FR_V //p7: x < 0 + nop.i 0 + +} +;; + +{ .mfi + nop.m 0 +(p7) fnma.s1 FR_Tmp2 = FR_res_pos_x_lo, f1, FR_Tmp2 //p7: x < 0 + 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 + +ERFC_RESULT: +.pred.rel "mutex",p6,p7 +{ .mfi + nop.m 0 +(p6) fma.s0 f8 = FR_M, FR_U, FR_V // p6: x >= 0 + nop.i 0 +} +{ .mfb + mov GR_Parameter_TAG = 207 +(p7) fma.s0 f8 = FR_Tmp2, f1, FR_Tmp1 // p7: x < 0 +(p8) br.ret.sptk b0 +};; + +GLOBAL_LIBM_END(erfcl) + +// call via (p15) br.cond.spnt __libm_error_region +// for x > POS_ARG_ASYMP +// or +// +// after .endp erfcl for UnfBound < = 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 + stfe [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 + stfe [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 + stfe [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 + ldfe 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# |