.file "logl.s" // Copyright (c) 2000 - 2003, 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: // 05/21/01 Extracted logl and log10l from log1pl.s file, and optimized // all paths. // 06/20/01 Fixed error tag for x=-inf. // 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 // //********************************************************************* // //********************************************************************* // // Function: Combined logl(x) and log10l(x) where // logl(x) = ln(x), for double-extended precision x values // log10l(x) = log (x), for double-extended precision x values // 10 // //********************************************************************* // // Resources Used: // // Floating-Point Registers: f8 (Input and Return Value) // f34-f76 // // General Purpose Registers: // r32-r56 // r53-r56 (Used to pass arguments to error handling routine) // // Predicate Registers: p6-p14 // //********************************************************************* // // IEEE Special Conditions: // // Denormal fault raised on denormal inputs // Overflow exceptions cannot occur // Underflow exceptions raised when appropriate for log1p // (Error Handling Routine called for underflow) // Inexact raised when appropriate by algorithm // // logl(inf) = inf // logl(-inf) = QNaN // logl(+/-0) = -inf // logl(SNaN) = QNaN // logl(QNaN) = QNaN // logl(EM_special Values) = QNaN // log10l(inf) = inf // log10l(-inf) = QNaN // log10l(+/-0) = -inf // log10l(SNaN) = QNaN // log10l(QNaN) = QNaN // log10l(EM_special Values) = QNaN // //********************************************************************* // // Overview // // The method consists of two cases. // // If |X-1| < 2^(-7) use case log_near1; // else use case log_regular; // // Case log_near1: // // logl( 1 + X ) can be approximated by a simple polynomial // in W = X-1. This polynomial resembles the truncated Taylor // series W - W^/2 + W^3/3 - ... // // Case log_regular: // // 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) // = logl(1/G) + logl(1 + (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 ). Obtain N, S_hi such that // // X = 2^N * S_hi exactly // // where S_hi in [1,2) // // 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) // // 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 ) is given by // // logl( X ) = logl( 2^N * S_hi ) // ~=~ N*logl(2) + logl(1/G) + logl(1 + r) // ~=~ N*logl(2) + logl(1/G) + poly(r). // // **** Algorithm **** // // Case log_near1: // // Here we compute a simple polynomial. To exploit parallelism, we split // the polynomial into two portions. // // W := X - 1 // Wsq := W * W // W4 := Wsq*Wsq // W6 := W4*Wsq // Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4)) // Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8))) // // Case log_regular: // // We present the algorithm in four steps. // // Step 0. Initialization // ---------------------- // // Z := X // N := unbaised exponent of Z // S_hi := 2^(-N) * Z // // Step 1. Argument Reduction // -------------------------- // // Let // // Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63 // // We obtain G_1, G_2, G_3 by the following steps. // // // Define X_0 := 1.d_1 d_2 ... d_14. This is extracted // from S_hi. // // Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated // to lsb = 2^(-4). // // Define index_1 := [ d_1 d_2 d_3 d_4 ]. // // Fetch Z_1 := (1/A_1) rounded UP in fixed point with // fixed point lsb = 2^(-15). // Z_1 looks like z_0.z_1 z_2 ... z_15 // Note that the fetching is done using index_1. // A_1 is actually not needed in the implementation // and is used here only to explain how is the value // Z_1 defined. // // Fetch G_1 := (1/A_1) truncated to 21 sig. bits. // floating pt. Again, fetching is done using index_1. A_1 // explains how G_1 is defined. // // Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14) // = 1.0 0 0 0 d_5 ... d_14 // This is accomplished by integer multiplication. // It is proved that X_1 indeed always begin // with 1.0000 in fixed point. // // // Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1 // truncated to lsb = 2^(-8). Similar to A_1, // A_2 is not needed in actual implementation. It // helps explain how some of the values are defined. // // Define index_2 := [ d_5 d_6 d_7 d_8 ]. // // Fetch Z_2 := (1/A_2) rounded UP in fixed point with // fixed point lsb = 2^(-15). Fetch done using index_2. // Z_2 looks like z_0.z_1 z_2 ... z_15 // // Fetch G_2 := (1/A_2) truncated to 21 sig. bits. // floating pt. // // Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14) // = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14 // This is accomplished by integer multiplication. // It is proved that X_2 indeed always begin // with 1.00000000 in fixed point. // // // Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1. // This is 2^(-14) + X_2 truncated to lsb = 2^(-13). // // Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ]. // // Fetch G_3 := (1/A_3) truncated to 21 sig. bits. // floating pt. Fetch is done using index_3. // // Compute G := G_1 * G_2 * G_3. // // This is done exactly since each of G_j only has 21 sig. bits. // // Compute // // r := (G*S_hi - 1) // // // Step 2. Approximation // --------------------- // // This step computes an approximation to logl( 1 + r ) where r is the // reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13); // thus logl(1+r) can be approximated by a short polynomial: // // logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5 // // // Step 3. Reconstruction // ---------------------- // // This step computes the desired result of logl(X): // // logl(X) = logl( 2^N * S_hi ) // = N*logl(2) + logl( S_hi ) // = N*logl(2) + logl(1/G) + // logl(1 + G*S_hi - 1 ) // // logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers: // log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are // single-precision numbers and the low parts are double precision // numbers. These have the property that // // N*log2_hi + SUM ( log1byGj_hi ) // // is computable exactly in double-extended precision (64 sig. bits). // Finally // // Y_hi := N*log2_hi + SUM ( log1byGj_hi ) // Y_lo := poly_hi + [ poly_lo + // ( SUM ( log1byGj_lo ) + N*log2_lo ) ] // RODATA .align 64 // ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* // P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1 LOCAL_OBJECT_START(Constants_P) data8 0xE3936754EFD62B15,0x00003FFB data8 0x8003B271A5E56381,0x0000BFFC data8 0x9249248C73282DB0,0x00003FFC data8 0xAAAAAA9F47305052,0x0000BFFC data8 0xCCCCCCCCCCD17FC9,0x00003FFC data8 0x8000000000067ED5,0x0000BFFD data8 0xAAAAAAAAAAAAAAAA,0x00003FFD data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD LOCAL_OBJECT_END(Constants_P) // log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1 LOCAL_OBJECT_START(Constants_Q) data8 0xB172180000000000,0x00003FFE data8 0x82E308654361C4C6,0x0000BFE2 data8 0xCCCCCAF2328833CB,0x00003FFC data8 0x80000077A9D4BAFB,0x0000BFFD data8 0xAAAAAAAAAAABE3D2,0x00003FFD data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD LOCAL_OBJECT_END(Constants_Q) // 1/ln10_hi, 1/ln10_lo LOCAL_OBJECT_START(Constants_1_by_LN10) data8 0xDE5BD8A937287195,0x00003FFD data8 0xD56EAABEACCF70C8,0x00003FBB LOCAL_OBJECT_END(Constants_1_by_LN10) // 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) // Floating Point Registers FR_Input_X = f8 FR_Y_hi = f34 FR_Y_lo = f35 FR_Scale = f36 FR_X_Prime = f37 FR_S_hi = f38 FR_W = f39 FR_G = f40 FR_H = f41 FR_wsq = f42 FR_w4 = f43 FR_h = f44 FR_w6 = f45 FR_G2 = f46 FR_H2 = f47 FR_poly_lo = f48 FR_P8 = f49 FR_poly_hi = f50 FR_P7 = f51 FR_h2 = f52 FR_rsq = f53 FR_P6 = f54 FR_r = f55 FR_log2_hi = f56 FR_log2_lo = f57 FR_p87 = f58 FR_p876 = f58 FR_p8765 = f58 FR_float_N = f59 FR_Q4 = f60 FR_p43 = f61 FR_p432 = f61 FR_p4321 = f61 FR_P4 = f62 FR_G3 = f63 FR_H3 = f64 FR_h3 = f65 FR_Q3 = f66 FR_P3 = f67 FR_Q2 = f68 FR_P2 = f69 FR_1LN10_hi = f70 FR_Q1 = f71 FR_P1 = f72 FR_1LN10_lo = f73 FR_P5 = f74 FR_rcub = f75 FR_Output_X_tmp = f76 FR_X = f8 FR_Y = f0 FR_RESULT = f76 // General Purpose Registers GR_ad_p = r33 GR_Index1 = r34 GR_Index2 = r35 GR_signif = r36 GR_X_0 = r37 GR_X_1 = r38 GR_X_2 = r39 GR_Z_1 = r40 GR_Z_2 = r41 GR_N = r42 GR_Bias = r43 GR_M = r44 GR_Index3 = r45 GR_ad_p2 = r46 GR_exp_mask = r47 GR_exp_2tom7 = r48 GR_ad_ln10 = r49 GR_ad_tbl_1 = r50 GR_ad_tbl_2 = r51 GR_ad_tbl_3 = r52 GR_ad_q = r53 GR_ad_z_1 = r54 GR_ad_z_2 = r55 GR_ad_z_3 = r56 // // Added for unwind support // GR_SAVE_PFS = r50 GR_SAVE_B0 = r51 GR_SAVE_GP = r52 GR_Parameter_X = r53 GR_Parameter_Y = r54 GR_Parameter_RESULT = r55 GR_Parameter_TAG = r56 .section .text GLOBAL_IEEE754_ENTRY(logl) { .mfi alloc r32 = ar.pfs,0,21,4,0 fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf cmp.eq p7, p14 = r0, r0 // Set p7 if logl } { .mfb addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x br.cond.sptk LOGL_BEGIN } ;; GLOBAL_IEEE754_END(logl) GLOBAL_IEEE754_ENTRY(log10l) { .mfi alloc r32 = ar.pfs,0,21,4,0 fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf cmp.ne p7, p14 = r0, r0 // Set p14 if log10l } { .mfb addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x nop.b 999 } ;; // Common code for logl and log10 LOGL_BEGIN: { .mfi ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 fclass.m p10, p0 = FR_Input_X, 0x0b // Test for denormal mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 } ;; { .mfb getf.sig GR_signif = FR_Input_X // Get significand of x fcmp.eq.s1 p9, p0 = FR_Input_X, f1 // Test for x=1.0 (p6) br.cond.spnt LOGL_64_special // Branch for nan, inf, natval } ;; { .mfi add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 fcmp.lt.s1 p13, p0 = FR_Input_X, f0 // Test for x<0 add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P } { .mib add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 (p10) br.cond.spnt LOGL_64_denormal // Branch for denormal } ;; LOGL_64_COMMON: { .mfi add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q fcmp.eq.s1 p8, p0 = FR_Input_X, f0 // Test for x=0 extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif } { .mfb add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 (p9) fma.s0 f8 = FR_Input_X, f0, f0 // If x=1, return +0.0 (p9) br.ret.spnt b0 // Exit if x=1 } ;; { .mfi shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand } { .mfi ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path fsub.s1 FR_W = FR_X_Prime, f1 // W = x - 1 add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10 } ;; { .mfi ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 nop.f 999 mov GR_exp_mask = 0x1FFFF // Create exponent mask } { .mib shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 mov GR_Bias = 0x0FFFF // Create exponent bias (p13) br.cond.spnt LOGL_64_negative // Branch if x<0 } ;; { .mfb ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 fmerge.se FR_S_hi = f1,FR_X_Prime // Form |x| (p8) br.cond.spnt LOGL_64_zero // Branch if x=0 } ;; { .mmb getf.exp GR_N = FR_X_Prime // Get N = exponent of x ldfd FR_h = [GR_ad_tbl_1] // Load h_1 (p10) br.cond.spnt LOGL_64_unsupported // Branch for unsupported type } ;; { .mfi ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 } ;; // // For performance, don't use result of pmpyshr2.u for 4 cycles. // { .mmi ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo (p14) ldfe FR_1LN10_hi = [GR_ad_ln10],16 // If log10l, load 1/ln10_hi sub GR_N = GR_N, GR_Bias } ;; { .mmi ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 (p14) ldfe FR_1LN10_lo = [GR_ad_ln10] // If log10l, load 1/ln10_lo nop.i 999 } ;; { .mmi ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 setf.sig FR_float_N = GR_N // Put integer N into rightmost significand nop.i 999 } ;; { .mmi getf.exp GR_M = FR_W // Get signexp of w = x - 1 ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 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 add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4 } ;; { .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 and GR_M = GR_exp_mask, GR_M // Get exponent of w = x - 1 } ;; { .mmi ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x-1| < 2^-7 nop.i 999 } ;; // Paths are merged. // p8 is for the near1 path: |x-1| < 2^-7 // p9 is for regular path: |x-1| >= 2^-7 { .mmi ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 nop.m 999 nop.i 999 } ;; { .mmi (p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path (p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path (p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 } ;; // // For performance, don't use result of pmpyshr2.u for 4 cycles. // { .mmi (p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path (p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path nop.i 999 } ;; { .mmf (p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path (p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path (p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path } ;; { .mmi (p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path nop.m 999 (p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 } ;; { .mfi (p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 (p9) fcvt.xf FR_float_N = FR_float_N nop.i 999 } ;; { .mfi (p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 nop.f 999 nop.i 999 } ;; { .mfi (p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 (p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 nop.i 999 } { .mfi nop.m 999 (p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 nop.i 999 } ;; { .mmf nop.m 999 nop.m 999 (p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 } ;; { .mfi nop.m 999 (p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7 nop.i 999 } ;; { .mfi nop.m 999 (p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3 nop.i 999 } ;; { .mfi nop.m 999 (p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 nop.i 999 } { .mfi nop.m 999 (p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 nop.i 999 } ;; { .mfi nop.m 999 (p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 nop.i 999 } { .mfi nop.m 999 (p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path nop.i 999 } ;; { .mfi nop.m 999 (p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6 nop.i 999 } ;; { .mfi nop.m 999 (p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H nop.i 999 } ;; { .mfi nop.m 999 (p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h nop.i 999 } ;; { .mfi nop.m 999 (p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5 nop.i 999 } ;; { .mfi nop.m 999 (p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 nop.i 999 } { .mfi nop.m 999 (p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r nop.i 999 } ;; { .mfi nop.m 999 (p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321 nop.i 999 } { .mfi nop.m 999 (p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path nop.i 999 } ;; { .mfi nop.m 999 (p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2 nop.i 999 } { .mfi nop.m 999 (p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 nop.i 999 } ;; { .mfi nop.m 999 (p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321 nop.i 999 } ;; { .mfi nop.m 999 (p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r nop.i 999 } ;; { .mfi nop.m 999 (p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h nop.i 999 } ;; { .mfi nop.m 999 (p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo nop.i 999 } ;; // Remainder of code is common for near1 and regular paths { .mfi nop.m 999 (p7) fadd.s0 f8 = FR_Y_lo,FR_Y_hi // If logl, result=Y_lo+Y_hi nop.i 999 } { .mfi nop.m 999 (p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi nop.i 999 } ;; { .mfi nop.m 999 (p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp nop.i 999 } ;; { .mfb nop.m 999 (p14) fma.s0 f8 = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp br.ret.sptk b0 // Common exit for 0 < x < inf } ;; // Here if x=+-0 LOGL_64_zero: // // If x=+-0 raise divide by zero and return -inf // { .mfi (p7) mov GR_Parameter_TAG = 0 fsub.s1 FR_Output_X_tmp = f0, f1 nop.i 999 } ;; { .mfb (p14) mov GR_Parameter_TAG = 6 frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 br.cond.sptk __libm_error_region } ;; LOGL_64_special: { .mfi nop.m 999 fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf nop.i 999 } ;; // // For SNaN raise invalid and return QNaN. // For QNaN raise invalid and return QNaN. // For +Inf return +Inf. // { .mfb nop.m 999 (p8) fmpy.s0 f8 = FR_Input_X, f1 (p8) br.ret.sptk b0 // Return for natval, nan, +inf } ;; // // For -Inf raise invalid and return QNaN. // { .mmi (p7) mov GR_Parameter_TAG = 1 nop.m 999 nop.i 999 } ;; { .mfb (p14) mov GR_Parameter_TAG = 7 fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 br.cond.sptk __libm_error_region } ;; // Here if x denormal or unnormal LOGL_64_denormal: { .mmi getf.sig GR_signif = FR_X_Prime // Get significand of normalized input nop.m 999 nop.i 999 } ;; { .mmb getf.exp GR_N = FR_X_Prime // Get exponent of normalized input nop.m 999 br.cond.sptk LOGL_64_COMMON // Branch back to common code } ;; LOGL_64_unsupported: // // Return generated NaN or other value. // { .mfb nop.m 999 fmpy.s0 f8 = FR_Input_X, f0 br.ret.sptk b0 } ;; // Here if -inf < x < 0 LOGL_64_negative: // // Deal with x < 0 in a special way - raise // invalid and produce QNaN indefinite. // { .mfi (p7) mov GR_Parameter_TAG = 1 frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 nop.i 999 } ;; { .mib (p14) mov GR_Parameter_TAG = 7 nop.i 999 br.cond.sptk __libm_error_region } ;; GLOBAL_IEEE754_END(log10l) 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 // Save 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 nop.b 0 // Parameter 3 address } { .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 999 nop.m 999 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#