.file "acoshl.s" // Copyright (c) 2000 - 2005, Intel Corporation // All rights reserved. // // Contributed 2000 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: // 10/01/01 Initial version // 10/10/01 Performance inproved // 12/11/01 Changed huges_logp to not be global // 01/02/02 Corrected .restore syntax // 05/20/02 Cleaned up namespace and sf0 syntax // 08/14/02 Changed mli templates to mlx // 02/06/03 Reorganized data tables // 03/31/05 Reformatted delimiters between data tables // //********************************************************************* // // API //============================================================== // long double acoshl(long double); // // Overview of operation //============================================================== // // There are 6 paths: // 1. x = 1 // Return acoshl(x) = 0; // // 2. x < 1 // Return acoshl(x) = Nan (Domain error, error handler call with tag 135); // // 3. x = [S,Q]Nan or +INF // Return acoshl(x) = x + x; // // 4. 'Near 1': 1 < x < 1+1/8 // Return acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)), // where y = 1, P(y)/Q(y) - rational approximation // // 5. 'Huges': x > 0.5*2^64 // Return acoshl(x) = (logl(2*x-1)); // // 6. 'Main path': 1+1/8 < x < 0.5*2^64 // b_hi + b_lo = x + sqrt(x^2 - 1); // acoshl(x) = logl_special(b_hi, b_lo); // // Algorithm description //============================================================== // // I. Near 1 path algorithm // ************************************************************** // The formula is acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)), // where y = 1, P(y)/Q(y) - rational approximation // // 1) y = x - 1, y2 = 2 * y // // 2) Compute in parallel sqrtl(2*y) and P(y)/Q(y) // a) sqrtl computation method described below (main path algorithm, item 2)) // As result we obtain (gg+gl) - multiprecision result // as pair of double extended values // b) P(y) and Q(y) calculated without any extra precision manipulations // c) P/Q division: // y = frcpa(Q) initial approximation of 1/Q // z = P*y initial approximation of P/Q // // e = 1 - b*y // e2 = e + e^2 // e1 = e^2 // y1 = y + y*e2 = y + y*(e+e^2) // // e3 = e + e1^2 // y2 = y + y1*e3 = y + y*(e+e^2+..+e^6) // // r = P - Q*z // e = 1 - Q*y2 // xx = z + r*y2 high part of a/b // // y3 = y2 + y2*e4 // r1 = P - Q*xx // xl = r1*y3 low part of a/b // // 3) res = sqrt(2*y) - sqrt(2*y)*(P(y)/Q(y)) = // = (gg+gl) - (gg + gl)*(xx+xl); // // a) hh = gg*xx; hl = gg*xl; lh = gl*xx; ll = gl*xl; // b) res = ((((gl + ll) + lh) + hl) + hh) + gg; // (exactly in this order) // // II. Main path algorithm // ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! ) // ********************************************************************** // // There are 3 parts of x+sqrt(x^2-1) computation: // // 1) m2 = (m2_hi+m2_lo) = x^2-1 obtaining // ------------------------------------ // m2_hi = x2_hi - 1, where x2_hi = x * x; // m2_lo = x2_lo + p1_lo, where // x2_lo = FMS(x*x-x2_hi), // p1_lo = (1 + m2_hi) - x2_hi; // // 2) g = (g_hi+g_lo) = sqrt(m2) = sqrt(m2_hi+m2_lo) // ---------------------------------------------- // r = invsqrt(m2_hi) (8-bit reciprocal square root approximation); // g = m2_hi * r (first 8 bit-approximation of sqrt); // // h = 0.5 * r; // e = 0.5 - g * h; // g = g * e + g (second 16 bit-approximation of sqrt); // // h = h * e + h; // e = 0.5 - g * h; // g = g * e + g (third 32 bit-approximation of sqrt); // // h = h * e + h; // e = 0.5 - g * h; // g_hi = g * e + g (fourth 64 bit-approximation of sqrt); // // Remainder computation: // h = h * e + h; // d = (m2_hi - g_hi * g_hi) + m2_lo; // g_lo = d * h; // // 3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2-1) // ------------------------------------------------------------------- // b_hi = (g_hi + x) + gl; // b_lo = (x - b_hi) + g_hi + gl; // // Now we pass b presented as sum b_hi + b_lo to special version // of logl function which accept a pair of arguments as // mutiprecision value. // // Special log algorithm overview // ================================ // Here we use a table lookup method. The basic idea is that in // order to compute logl(Arg) for an argument Arg in [1,2), // we construct a value G such that G*Arg is close to 1 and that // logl(1/G) is obtainable easily from a table of values calculated // beforehand. Thus // // logl(Arg) = logl(1/G) + logl((G*Arg - 1)) // // Because |G*Arg - 1| is small, the second term on the right hand // side can be approximated by a short polynomial. We elaborate // this method in four steps. // // Step 0: Initialization // // We need to calculate logl( X+1 ). Obtain N, S_hi such that // // X = 2^N * ( S_hi + S_lo ) exactly // // where S_hi in [1,2) and S_lo is a correction to S_hi in the sense // that |S_lo| <= ulp(S_hi). // // For the special version of logl: S_lo = b_lo // !-----------------------------------------------! // // Step 1: Argument Reduction // // Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate // // G := G_1 * G_2 * G_3 // r := (G * S_hi - 1) + G * S_lo // // These G_j's have the property that the product is exactly // representable and that |r| < 2^(-12) as a result. // // Step 2: Approximation // // logl(1 + r) is approximated by a short polynomial poly(r). // // Step 3: Reconstruction // // Finally, logl( X ) = logl( X+1 ) is given by // // logl( X ) = logl( 2^N * (S_hi + S_lo) ) // ~=~ N*logl(2) + logl(1/G) + logl(1 + r) // ~=~ N*logl(2) + logl(1/G) + poly(r). // // For detailed description see logl or log1pl function, regular path. // // Registers used //============================================================== // Floating Point registers used: // f8, input // f32 -> f95 (64 registers) // General registers used: // r32 -> r67 (36 registers) // Predicate registers used: // p7 -> p11 // p7 for 'NaNs, Inf' path // p8 for 'near 1' path // p9 for 'huges' path // p10 for x = 1 // p11 for x < 1 // //********************************************************************* // IEEE Special Conditions: // // acoshl(+inf) = +inf // acoshl(-inf) = QNaN // acoshl(1) = 0 // acoshl(x<1) = QNaN // acoshl(SNaN) = QNaN // acoshl(QNaN) = QNaN // // Data tables //============================================================== RODATA .align 64 // Near 1 path rational approximation coefficients LOCAL_OBJECT_START(Poly_P) data8 0xB0978143F695D40F, 0x3FF1 // .84205539791447100108478906277453574946e-4 data8 0xB9800D841A8CAD29, 0x3FF6 // .28305085180397409672905983082168721069e-2 data8 0xC889F455758C1725, 0x3FF9 // .24479844297887530847660233111267222945e-1 data8 0x9BE1DFF006F45F12, 0x3FFB // .76114415657565879842941751209926938306e-1 data8 0x9E34AF4D372861E0, 0x3FFB // .77248925727776366270605984806795850504e-1 data8 0xF3DC502AEE14C4AE, 0x3FA6 // .3077953476682583606615438814166025592e-26 LOCAL_OBJECT_END(Poly_P) // LOCAL_OBJECT_START(Poly_Q) data8 0xF76E3FD3C7680357, 0x3FF1 // .11798413344703621030038719253730708525e-3 data8 0xD107D2E7273263AE, 0x3FF7 // .63791065024872525660782716786703188820e-2 data8 0xB609BE5CDE206AEF, 0x3FFB // .88885771950814004376363335821980079985e-1 data8 0xF7DEACAC28067C8A, 0x3FFD // .48412074662702495416825113623936037072302 data8 0x8F9BE5890CEC7E38, 0x3FFF // 1.1219450873557867470217771071068369729526 data8 0xED4F06F3D2BC92D1, 0x3FFE // .92698710873331639524734537734804056798748 LOCAL_OBJECT_END(Poly_Q) // Q coeffs LOCAL_OBJECT_START(Constants_Q) data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 LOCAL_OBJECT_END(Constants_Q) // Z1 - 16 bit fixed LOCAL_OBJECT_START(Constants_Z_1) data4 0x00008000 data4 0x00007879 data4 0x000071C8 data4 0x00006BCB data4 0x00006667 data4 0x00006187 data4 0x00005D18 data4 0x0000590C data4 0x00005556 data4 0x000051EC data4 0x00004EC5 data4 0x00004BDB data4 0x00004925 data4 0x0000469F data4 0x00004445 data4 0x00004211 LOCAL_OBJECT_END(Constants_Z_1) // G1 and H1 - IEEE single and h1 - IEEE double LOCAL_OBJECT_START(Constants_G_H_h1) data4 0x3F800000,0x00000000 data8 0x0000000000000000 data4 0x3F70F0F0,0x3D785196 data8 0x3DA163A6617D741C data4 0x3F638E38,0x3DF13843 data8 0x3E2C55E6CBD3D5BB data4 0x3F579430,0x3E2FF9A0 data8 0xBE3EB0BFD86EA5E7 data4 0x3F4CCCC8,0x3E647FD6 data8 0x3E2E6A8C86B12760 data4 0x3F430C30,0x3E8B3AE7 data8 0x3E47574C5C0739BA data4 0x3F3A2E88,0x3EA30C68 data8 0x3E20E30F13E8AF2F data4 0x3F321640,0x3EB9CEC8 data8 0xBE42885BF2C630BD data4 0x3F2AAAA8,0x3ECF9927 data8 0x3E497F3497E577C6 data4 0x3F23D708,0x3EE47FC5 data8 0x3E3E6A6EA6B0A5AB data4 0x3F1D89D8,0x3EF8947D data8 0xBDF43E3CD328D9BE data4 0x3F17B420,0x3F05F3A1 data8 0x3E4094C30ADB090A data4 0x3F124920,0x3F0F4303 data8 0xBE28FBB2FC1FE510 data4 0x3F0D3DC8,0x3F183EBF data8 0x3E3A789510FDE3FA data4 0x3F088888,0x3F20EC80 data8 0x3E508CE57CC8C98F data4 0x3F042108,0x3F29516A data8 0xBE534874A223106C LOCAL_OBJECT_END(Constants_G_H_h1) // Z2 - 16 bit fixed LOCAL_OBJECT_START(Constants_Z_2) data4 0x00008000 data4 0x00007F81 data4 0x00007F02 data4 0x00007E85 data4 0x00007E08 data4 0x00007D8D data4 0x00007D12 data4 0x00007C98 data4 0x00007C20 data4 0x00007BA8 data4 0x00007B31 data4 0x00007ABB data4 0x00007A45 data4 0x000079D1 data4 0x0000795D data4 0x000078EB LOCAL_OBJECT_END(Constants_Z_2) // G2 and H2 - IEEE single and h2 - IEEE double LOCAL_OBJECT_START(Constants_G_H_h2) data4 0x3F800000,0x00000000 data8 0x0000000000000000 data4 0x3F7F00F8,0x3B7F875D data8 0x3DB5A11622C42273 data4 0x3F7E03F8,0x3BFF015B data8 0x3DE620CF21F86ED3 data4 0x3F7D08E0,0x3C3EE393 data8 0xBDAFA07E484F34ED data4 0x3F7C0FC0,0x3C7E0586 data8 0xBDFE07F03860BCF6 data4 0x3F7B1880,0x3C9E75D2 data8 0x3DEA370FA78093D6 data4 0x3F7A2328,0x3CBDC97A data8 0x3DFF579172A753D0 data4 0x3F792FB0,0x3CDCFE47 data8 0x3DFEBE6CA7EF896B data4 0x3F783E08,0x3CFC15D0 data8 0x3E0CF156409ECB43 data4 0x3F774E38,0x3D0D874D data8 0xBE0B6F97FFEF71DF data4 0x3F766038,0x3D1CF49B data8 0xBE0804835D59EEE8 data4 0x3F757400,0x3D2C531D data8 0x3E1F91E9A9192A74 data4 0x3F748988,0x3D3BA322 data8 0xBE139A06BF72A8CD data4 0x3F73A0D0,0x3D4AE46F data8 0x3E1D9202F8FBA6CF data4 0x3F72B9D0,0x3D5A1756 data8 0xBE1DCCC4BA796223 data4 0x3F71D488,0x3D693B9D data8 0xBE049391B6B7C239 LOCAL_OBJECT_END(Constants_G_H_h2) // G3 and H3 - IEEE single and h3 - IEEE double LOCAL_OBJECT_START(Constants_G_H_h3) data4 0x3F7FFC00,0x38800100 data8 0x3D355595562224CD data4 0x3F7FF400,0x39400480 data8 0x3D8200A206136FF6 data4 0x3F7FEC00,0x39A00640 data8 0x3DA4D68DE8DE9AF0 data4 0x3F7FE400,0x39E00C41 data8 0xBD8B4291B10238DC data4 0x3F7FDC00,0x3A100A21 data8 0xBD89CCB83B1952CA data4 0x3F7FD400,0x3A300F22 data8 0xBDB107071DC46826 data4 0x3F7FCC08,0x3A4FF51C data8 0x3DB6FCB9F43307DB data4 0x3F7FC408,0x3A6FFC1D data8 0xBD9B7C4762DC7872 data4 0x3F7FBC10,0x3A87F20B data8 0xBDC3725E3F89154A data4 0x3F7FB410,0x3A97F68B data8 0xBD93519D62B9D392 data4 0x3F7FAC18,0x3AA7EB86 data8 0x3DC184410F21BD9D data4 0x3F7FA420,0x3AB7E101 data8 0xBDA64B952245E0A6 data4 0x3F7F9C20,0x3AC7E701 data8 0x3DB4B0ECAABB34B8 data4 0x3F7F9428,0x3AD7DD7B data8 0x3D9923376DC40A7E data4 0x3F7F8C30,0x3AE7D474 data8 0x3DC6E17B4F2083D3 data4 0x3F7F8438,0x3AF7CBED data8 0x3DAE314B811D4394 data4 0x3F7F7C40,0x3B03E1F3 data8 0xBDD46F21B08F2DB1 data4 0x3F7F7448,0x3B0BDE2F data8 0xBDDC30A46D34522B data4 0x3F7F6C50,0x3B13DAAA data8 0x3DCB0070B1F473DB data4 0x3F7F6458,0x3B1BD766 data8 0xBDD65DDC6AD282FD data4 0x3F7F5C68,0x3B23CC5C data8 0xBDCDAB83F153761A data4 0x3F7F5470,0x3B2BC997 data8 0xBDDADA40341D0F8F data4 0x3F7F4C78,0x3B33C711 data8 0x3DCD1BD7EBC394E8 data4 0x3F7F4488,0x3B3BBCC6 data8 0xBDC3532B52E3E695 data4 0x3F7F3C90,0x3B43BAC0 data8 0xBDA3961EE846B3DE data4 0x3F7F34A0,0x3B4BB0F4 data8 0xBDDADF06785778D4 data4 0x3F7F2CA8,0x3B53AF6D data8 0x3DCC3ED1E55CE212 data4 0x3F7F24B8,0x3B5BA620 data8 0xBDBA31039E382C15 data4 0x3F7F1CC8,0x3B639D12 data8 0x3D635A0B5C5AF197 data4 0x3F7F14D8,0x3B6B9444 data8 0xBDDCCB1971D34EFC data4 0x3F7F0CE0,0x3B7393BC data8 0x3DC7450252CD7ADA data4 0x3F7F04F0,0x3B7B8B6D data8 0xBDB68F177D7F2A42 LOCAL_OBJECT_END(Constants_G_H_h3) // Assembly macros //============================================================== // Floating Point Registers FR_Arg = f8 FR_Res = f8 FR_PP0 = f32 FR_PP1 = f33 FR_PP2 = f34 FR_PP3 = f35 FR_PP4 = f36 FR_PP5 = f37 FR_QQ0 = f38 FR_QQ1 = f39 FR_QQ2 = f40 FR_QQ3 = f41 FR_QQ4 = f42 FR_QQ5 = f43 FR_Q1 = f44 FR_Q2 = f45 FR_Q3 = f46 FR_Q4 = f47 FR_Half = f48 FR_Two = f49 FR_log2_hi = f50 FR_log2_lo = f51 FR_X2 = f52 FR_M2 = f53 FR_M2L = f54 FR_Rcp = f55 FR_GG = f56 FR_HH = f57 FR_EE = f58 FR_DD = f59 FR_GL = f60 FR_Tmp = f61 FR_XM1 = f62 FR_2XM1 = f63 FR_XM12 = f64 // Special logl registers FR_XLog_Hi = f65 FR_XLog_Lo = f66 FR_Y_hi = f67 FR_Y_lo = f68 FR_S_hi = f69 FR_S_lo = f70 FR_poly_lo = f71 FR_poly_hi = f72 FR_G = f73 FR_H = f74 FR_h = f75 FR_G2 = f76 FR_H2 = f77 FR_h2 = f78 FR_r = f79 FR_rsq = f80 FR_rcub = f81 FR_float_N = f82 FR_G3 = f83 FR_H3 = f84 FR_h3 = f85 FR_2_to_minus_N = f86 // Near 1 registers FR_PP = f65 FR_QQ = f66 FR_PV6 = f69 FR_PV4 = f70 FR_PV3 = f71 FR_PV2 = f72 FR_QV6 = f73 FR_QV4 = f74 FR_QV3 = f75 FR_QV2 = f76 FR_Y0 = f77 FR_Q0 = f78 FR_E0 = f79 FR_E2 = f80 FR_E1 = f81 FR_Y1 = f82 FR_E3 = f83 FR_Y2 = f84 FR_R0 = f85 FR_E4 = f86 FR_Y3 = f87 FR_R1 = f88 FR_X_Hi = f89 FR_X_lo = f90 FR_HH = f91 FR_LL = f92 FR_HL = f93 FR_LH = f94 // Error handler registers FR_Arg_X = f95 FR_Arg_Y = f0 // General Purpose Registers // General prolog registers GR_PFS = r32 GR_OneP125 = r33 GR_TwoP63 = r34 GR_Arg = r35 GR_Half = r36 // Near 1 path registers GR_Poly_P = r37 GR_Poly_Q = r38 // Special logl registers GR_Index1 = r39 GR_Index2 = r40 GR_signif = r41 GR_X_0 = r42 GR_X_1 = r43 GR_X_2 = r44 GR_minus_N = r45 GR_Z_1 = r46 GR_Z_2 = r47 GR_N = r48 GR_Bias = r49 GR_M = r50 GR_Index3 = r51 GR_exp_2tom80 = r52 GR_exp_mask = r53 GR_exp_2tom7 = r54 GR_ad_ln10 = r55 GR_ad_tbl_1 = r56 GR_ad_tbl_2 = r57 GR_ad_tbl_3 = r58 GR_ad_q = r59 GR_ad_z_1 = r60 GR_ad_z_2 = r61 GR_ad_z_3 = r62 // // Added for unwind support // GR_SAVE_PFS = r32 GR_SAVE_B0 = r33 GR_SAVE_GP = r34 GR_Parameter_X = r64 GR_Parameter_Y = r65 GR_Parameter_RESULT = r66 GR_Parameter_TAG = r67 .section .text GLOBAL_LIBM_ENTRY(acoshl) { .mfi alloc GR_PFS = ar.pfs,0,32,4,0 // Local frame allocation fcmp.lt.s1 p11, p0 = FR_Arg, f1 // if arg is less than 1 mov GR_Half = 0xfffe // 0.5's exp } { .mfi addl GR_Poly_Q = @ltoff(Poly_Q), gp // Address of Q-coeff table fma.s1 FR_X2 = FR_Arg, FR_Arg, f0 // Obtain x^2 addl GR_Poly_P = @ltoff(Poly_P), gp // Address of P-coeff table };; { .mfi getf.d GR_Arg = FR_Arg // get argument as double (int64) fma.s0 FR_Two = f1, f1, f1 // construct 2.0 addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp // logl tables } { .mlx nop.m 0 movl GR_TwoP63 = 0x43E8000000000000 // 0.5*2^63 (huge arguments) };; { .mfi ld8 GR_Poly_P = [GR_Poly_P] // get actual P-coeff table address fcmp.eq.s1 p10, p0 = FR_Arg, f1 // if arg == 1 (return 0) nop.i 0 } { .mlx ld8 GR_Poly_Q = [GR_Poly_Q] // get actual Q-coeff table address movl GR_OneP125 = 0x3FF2000000000000 // 1.125 (near 1 path bound) };; { .mfi ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 fclass.m p7,p0 = FR_Arg, 0xe3 // if arg NaN inf cmp.le p9, p0 = GR_TwoP63, GR_Arg // if arg > 0.5*2^63 ('huges') } { .mfb cmp.ge p8, p0 = GR_OneP125, GR_Arg // if arg<1.125 -near 1 path fms.s1 FR_XM1 = FR_Arg, f1, f1 // X0 = X-1 (for near 1 path) (p11) br.cond.spnt acoshl_lt_pone // error branch (less than 1) };; { .mmi setf.exp FR_Half = GR_Half // construct 0.5 (p9) setf.s FR_XLog_Lo = r0 // Low of logl arg=0 (Huges path) mov GR_exp_mask = 0x1FFFF // Create exponent mask };; { .mmf (p8) ldfe FR_PP5 = [GR_Poly_P],16 // Load P5 (p8) ldfe FR_QQ5 = [GR_Poly_Q],16 // Load Q5 fms.s1 FR_M2 = FR_X2, f1, f1 // m2 = x^2 - 1 };; { .mfi (p8) ldfe FR_QQ4 = [GR_Poly_Q],16 // Load Q4 fms.s1 FR_M2L = FR_Arg, FR_Arg, FR_X2 // low part of // m2 = fma(X*X - m2) add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 } { .mfb (p8) ldfe FR_PP4 = [GR_Poly_P],16 // Load P4 (p7) fma.s0 FR_Res = FR_Arg,f1,FR_Arg // r = a + a (Nan, Inf) (p7) br.ret.spnt b0 // return (Nan, Inf) };; { .mfi (p8) ldfe FR_PP3 = [GR_Poly_P],16 // Load P3 nop.f 0 add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P } { .mfb (p8) ldfe FR_QQ3 = [GR_Poly_Q],16 // Load Q3 (p9) fms.s1 FR_XLog_Hi = FR_Two, FR_Arg, f1 // Hi of log arg = 2*X-1 (p9) br.cond.spnt huges_logl // special version of log } ;; { .mfi (p8) ldfe FR_PP2 = [GR_Poly_P],16 // Load P2 (p8) fma.s1 FR_2XM1 = FR_Two, FR_XM1, f0 // 2X0 = 2 * X0 add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 } { .mfb (p8) ldfe FR_QQ2 = [GR_Poly_Q],16 // Load Q2 (p10) fma.s0 FR_Res = f0,f1,f0 // r = 0 (arg = 1) (p10) br.ret.spnt b0 // return (arg = 1) };; { .mmi (p8) ldfe FR_PP1 = [GR_Poly_P],16 // Load P1 (p8) ldfe FR_QQ1 = [GR_Poly_Q],16 // Load Q1 add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 } ;; { .mfi (p8) ldfe FR_PP0 = [GR_Poly_P] // Load P0 fma.s1 FR_Tmp = f1, f1, FR_M2 // Tmp = 1 + m2 add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 } { .mfb (p8) ldfe FR_QQ0 = [GR_Poly_Q] nop.f 0 (p8) br.cond.spnt near_1 // near 1 path };; { .mfi ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi nop.f 0 mov GR_Bias = 0x0FFFF // Create exponent bias };; { .mfi nop.m 0 frsqrta.s1 FR_Rcp, p0 = FR_M2 // Rcp = 1/m2 reciprocal appr. nop.i 0 };; { .mfi ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo fms.s1 FR_Tmp = FR_X2, f1, FR_Tmp // Tmp = x^2 - Tmp nop.i 0 };; { .mfi ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 fma.s1 FR_GG = FR_Rcp, FR_M2, f0 // g = Rcp * m2 // 8 bit Newton Raphson iteration nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp nop.i 0 };; { .mfi ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h nop.i 0 } { .mfi nop.m 0 fma.s1 FR_M2L = FR_Tmp, f1, FR_M2L // low part of m2 = Tmp+m2l nop.i 0 };; { .mfi ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g // 16 bit Newton Raphson iteration nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h nop.i 0 };; { .mfi ldfe FR_Q1 = [GR_ad_q] // Load Q1 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g // 32 bit Newton Raphson iteration nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g // 64 bit Newton Raphson iteration nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_DD = FR_GG, FR_GG, FR_M2 // Remainder d = g * g - p2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_XLog_Hi = FR_Arg, f1, FR_GG // bh = z + gh nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_DD = FR_DD, f1, FR_M2L // add p2l: d = d + p2l nop.i 0 };; { .mfi getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 nop.f 0 mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 };; { .mfi nop.m 0 fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif } { .mfi nop.m 0 fma.s1 FR_XLog_Hi = FR_DD, FR_HH, FR_XLog_Hi // bh = bh + gl nop.i 0 };; { .mmi shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif. };; { .mmi ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 nop.m 0 nop.i 0 };; { .mmi ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 nop.m 0 nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_XLog_Lo = FR_Arg, f1, FR_XLog_Hi // bl = x - bh pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 };; // WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL! // "DEAD" ZONE! { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1| nop.i 0 };; { .mmi getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 ldfd FR_h = [GR_ad_tbl_1] // Load h_1 nop.i 0 };; { .mfi nop.m 0 nop.f 0 extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 };; { .mfi shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GG // bl = bl + gg mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 } { .mfi shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 nop.f 0 sub GR_N = GR_N, GR_Bias // sub bias from exp };; { .mmi ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) };; { .mmi ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 nop.m 0 nop.i 0 };; { .mmi setf.sig FR_float_N = GR_N // Put integer N into rightmost sign setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 };; // WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!) // BECAUSE OF POSSIBLE 10 CLOCKS STALL! // (Just nops added - nothing to do here) { .mfi nop.m 0 fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GL // bl = bl + gl nop.i 0 };; { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 nop.f 0 extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 };; { .mfi shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 nop.f 0 nop.i 0 };; { .mfi ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 nop.f 0 nop.i 0 };; { .mfi ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 fcvt.xf FR_float_N = FR_float_N nop.i 0 };; { .mfi nop.m 0 fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 nop.i 0 } { .mfi nop.m 0 fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 nop.i 0 };; { .mfi nop.m 0 fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_S_lo = FR_XLog_Lo, FR_2_to_minus_N, f0 //S_lo=S_lo*2^(-N) nop.i 0 };; { .mfi nop.m 0 fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 nop.i 0 } { .mfi nop.m 0 fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 nop.i 0 };; { .mfi nop.m 0 fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h=N*log2_lo+h nop.i 0 } { .mfi nop.m 0 fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r=G*S_lo+(G*S_hi-1) nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 nop.i 0 } { .mfi nop.m 0 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h nop.i 0 };; { .mfi nop.m 0 fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo nop.i 0 };; { .mfb nop.m 0 fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi br.ret.sptk b0 // Common exit for 2^-7 < x < inf };; huges_logl: { .mmi getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 nop.i 0 };; { .mfi add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 nop.f 0 add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P } { .mfi add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 nop.f 0 add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 };; { .mfi add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 nop.f 0 extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif };; { .mfi shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 nop.f 0 extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif. };; { .mfi ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 nop.f 0 mov GR_exp_mask = 0x1FFFF // Create exponent mask } { .mfi shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 nop.f 0 mov GR_Bias = 0x0FFFF // Create exponent bias };; { .mfi ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x| nop.i 0 };; { .mmi getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 ldfd FR_h = [GR_ad_tbl_1] // Load h_1 nop.i 0 };; { .mfi ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi nop.f 0 pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 };; { .mmi ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo sub GR_N = GR_N, GR_Bias mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 };; { .mfi ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 nop.f 0 sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) };; { .mmf ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 setf.sig FR_float_N = GR_N // Put integer N into rightmost sign nop.f 0 };; { .mmi ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 nop.m 0 extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 };; { .mmi ldfe FR_Q1 = [GR_ad_q] // Load Q1 shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 nop.i 0 };; { .mmi ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 nop.i 0 };; { .mmi ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 nop.m 0 nop.i 0 };; { .mmf ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) nop.f 0 };; { .mfi nop.m 0 nop.f 0 pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1*Z_2 };; // WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!) // BECAUSE OF POSSIBLE 10 CLOCKS STALL! // (Just nops added - nothing to do here) { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 nop.f 0 nop.i 0 };; { .mfi nop.m 0 nop.f 0 extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 };; { .mfi shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 fcvt.xf FR_float_N = FR_float_N nop.i 0 };; { .mfi ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 nop.f 0 nop.i 0 };; { .mfi ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 nop.i 0 } { .mfi nop.m 0 fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 nop.i 0 };; { .mmf nop.m 0 nop.m 0 fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 };; { .mfi nop.m 0 fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2)*G_3 nop.i 0 } { .mfi nop.m 0 fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2)+H_3 nop.i 0 };; { .mfi nop.m 0 fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N*log2_lo+h nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 nop.i 0 } { .mfi nop.m 0 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 nop.i 0 } { .mfi nop.m 0 fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h nop.i 0 };; { .mfi nop.m 0 fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo nop.i 0 };; { .mfb nop.m 0 fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi br.ret.sptk b0 // Common exit };; // NEAR ONE INTERVAL near_1: { .mfi nop.m 0 frsqrta.s1 FR_Rcp, p0 = FR_2XM1 // Rcp = 1/x reciprocal appr. &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_PV6 = FR_PP5, FR_XM1, FR_PP4 // pv6 = P5*xm1+P4 $POLY$ nop.i 0 } { .mfi nop.m 0 fma.s1 FR_QV6 = FR_QQ5, FR_XM1, FR_QQ4 // qv6 = Q5*xm1+Q4 $POLY$ nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_PV4 = FR_PP3, FR_XM1, FR_PP2 // pv4 = P3*xm1+P2 $POLY$ nop.i 0 } { .mfi nop.m 0 fma.s1 FR_QV4 = FR_QQ3, FR_XM1, FR_QQ2 // qv4 = Q3*xm1+Q2 $POLY$ nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_XM12 = FR_XM1, FR_XM1, f0 // xm1^2 = xm1 * xm1 $POLY$ nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_PV2 = FR_PP1, FR_XM1, FR_PP0 // pv2 = P1*xm1+P0 $POLY$ nop.i 0 } { .mfi nop.m 0 fma.s1 FR_QV2 = FR_QQ1, FR_XM1, FR_QQ0 // qv2 = Q1*xm1+Q0 $POLY$ nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_Rcp, FR_2XM1, f0 // g = Rcp * x &SQRT& nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_PV3 = FR_XM12, FR_PV6, FR_PV4//pv3=pv6*xm1^2+pv4 $POLY$ nop.i 0 } { .mfi nop.m 0 fma.s1 FR_QV3 = FR_XM12, FR_QV6, FR_QV4//qv3=qv6*xm1^2+qv4 $POLY$ nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_PP = FR_XM12, FR_PV3, FR_PV2 //pp=pv3*xm1^2+pv2 $POLY$ nop.i 0 } { .mfi nop.m 0 fma.s1 FR_QQ = FR_XM12, FR_QV3, FR_QV2 //qq=qv3*xm1^2+qv2 $POLY$ nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT& nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& nop.i 0 };; { .mfi nop.m 0 frcpa.s1 FR_Y0,p0 = f1,FR_QQ // y = frcpa(b) #DIV# nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g*h &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Q0 = FR_PP,FR_Y0,f0 // q = a*y #DIV# nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_E0 = FR_Y0,FR_QQ,f1 // e = 1 - b*y #DIV# nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT& nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2 #DIV# nop.i 0 } { .mfi nop.m 0 fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2 #DIV# nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT& nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2 #DIV# nop.i 0 } { .mfi nop.m 0 fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2 #DIV# nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GG = FR_DD, FR_HH, FR_GG // g = d * h + g &SQRT& nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3 #DIV# nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_R0 = FR_QQ,FR_Q0,FR_PP // r = a-b*q #DIV# nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT& nop.i 0 };; { .mfi nop.m 0 fnma.s1 FR_E4 = FR_QQ,FR_Y2,f1 // e4 = 1-b*y2 #DIV# nop.i 0 } { .mfi nop.m 0 fma.s1 FR_X_Hi = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2 #DIV# nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h &SQRT& nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4 #DIV# nop.i 0 } { .mfi nop.m 0 fnma.s1 FR_R1 = FR_QQ,FR_X_Hi,FR_PP // r1 = a-b*x #DIV# nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_HH = FR_GG, FR_X_Hi, f0 // hh = gg * x_hi nop.i 0 } { .mfi nop.m 0 fma.s1 FR_LH = FR_GL, FR_X_Hi, f0 // lh = gl * x_hi nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3 #DIV# nop.i 0 };; { .mfi nop.m 0 fma.s1 FR_LL = FR_GL, FR_X_lo, f0 // ll = gl*x_lo nop.i 0 } { .mfi nop.m 0 fma.s1 FR_HL = FR_GG, FR_X_lo, f0 // hl = gg * x_lo nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Res = FR_GL, f1, FR_LL // res = gl + ll nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Res = FR_Res, f1, FR_LH // res = res + lh nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Res = FR_Res, f1, FR_HL // res = res + hl nop.i 0 };; { .mfi nop.m 0 fms.s1 FR_Res = FR_Res, f1, FR_HH // res = res + hh nop.i 0 };; { .mfb nop.m 0 fma.s0 FR_Res = FR_Res, f1, FR_GG // result = res + gg br.ret.sptk b0 // Exit for near 1 path };; // NEAR ONE INTERVAL END acoshl_lt_pone: { .mfi nop.m 0 fmerge.s FR_Arg_X = FR_Arg, FR_Arg nop.i 0 };; { .mfb mov GR_Parameter_TAG = 135 frcpa.s0 FR_Res,p0 = f0,f0 // get QNaN,and raise invalid br.cond.sptk __libm_error_region // exit if x < 1.0 };; GLOBAL_LIBM_END(acoshl) 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_Arg_Y,16 // Parameter 2 to 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_Arg_X // Parameter 1 to stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 } { .mib stfe [GR_Parameter_Y] = FR_Res // Parameter 3 to stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk b0 = __libm_error_support# // Error handling function };; { .mmi nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp };; { .mmi ldfe f8 = [GR_Parameter_RESULT] // Get return res .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#