| .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 accomplised 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 accomplised 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# |
