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Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pl.S')
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diff --git a/sysdeps/ia64/fpu/s_log1pl.S b/sysdeps/ia64/fpu/s_log1pl.S new file mode 100644 index 0000000..3c8be02 --- /dev/null +++ b/sysdeps/ia64/fpu/s_log1pl.S @@ -0,0 +1,1200 @@ +.file "log1pl.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: +// 02/02/00 Initial version +// 04/04/00 Unwind support added +// 08/15/00 Bundle added after call to __libm_error_support to properly +// set [the previously overwritten] GR_Parameter_RESULT. +// 05/21/01 Removed logl and log10l, putting them in a separate file +// 06/29/01 Improved speed of all paths +// 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: log1pl(x) = ln(x+1), for double-extended precision x values +// +//********************************************************************* +// +// Resources Used: +// +// Floating-Point Registers: f8 (Input and Return Value) +// f34-f82 +// +// General Purpose Registers: +// r32-r56 +// r53-r56 (Used to pass arguments to error handling routine) +// +// Predicate Registers: p6-p13 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// Denormal fault raised on denormal inputs +// Overflow exceptions cannot occur +// Underflow exceptions raised when appropriate for log1p +// Inexact raised when appropriate by algorithm +// +// log1pl(inf) = inf +// log1pl(-inf) = QNaN +// log1pl(+/-0) = +/-0 +// log1pl(-1) = -inf +// log1pl(SNaN) = QNaN +// log1pl(QNaN) = QNaN +// log1pl(EM_special Values) = QNaN +// +//********************************************************************* +// +// Overview +// +// The method consists of three cases. +// +// If |X| < 2^(-80) use case log1p_small; +// else |X| < 2^(-7) use case log_near1; +// else use case log_regular; +// +// Case log1p_small: +// +// log1pl( X ) = logl( X+1 ) can be approximated by X +// +// Case log_near1: +// +// log1pl( X ) = log( X+1 ) can be approximated by a simple polynomial +// in W = X. 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) = log1pl (Arg-1) 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+1 ). Obtain N, S_hi such that +// +// X+1 = 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). +// +// 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, log1pl( X ) = logl( X+1 ) is given by +// +// logl( X+1 ) = logl( 2^N * (S_hi + S_lo) ) +// ~=~ N*logl(2) + logl(1/G) + logl(1 + r) +// ~=~ N*logl(2) + logl(1/G) + poly(r). +// +// **** Algorithm **** +// +// Case log1p_small: +// +// Although log1pl(X) is basically X, we would like to preserve the inexactness +// nature as well as consistent behavior under different rounding modes. +// We can do this by computing the result as +// +// log1pl(X) = X - X*X +// +// +// Case log_near1: +// +// Here we compute a simple polynomial. To exploit parallelism, we split +// the polynomial into two portions. +// +// W := X +// 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 + 1 +// N := unbaised exponent of Z +// S_hi := 2^(-N) * Z +// S_lo := 2^(-N) * { (max(X,1)-Z) + min(X,1) } +// +// 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) + G*S_lo using 2 FMA operations. +// +// Thus r approximates G*(S_hi + S_lo) - 1 to within a couple of +// rounding errors. +// +// +// 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+1): +// +// logl(X+1) = logl( 2^N * (S_hi + S_lo) ) +// = N*logl(2) + logl( S_hi + S_lo) ) +// = N*logl(2) + logl(1/G) + +// logl(1 + G * ( S_hi + S_lo ) - 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) +//data4 0xEFD62B15,0xE3936754,0x00003FFB,0x00000000 +//data4 0xA5E56381,0x8003B271,0x0000BFFC,0x00000000 +//data4 0x73282DB0,0x9249248C,0x00003FFC,0x00000000 +//data4 0x47305052,0xAAAAAA9F,0x0000BFFC,0x00000000 +//data4 0xCCD17FC9,0xCCCCCCCC,0x00003FFC,0x00000000 +//data4 0x00067ED5,0x80000000,0x0000BFFD,0x00000000 +//data4 0xAAAAAAAA,0xAAAAAAAA,0x00003FFD,0x00000000 +//data4 0xFFFFFFFE,0xFFFFFFFF,0x0000BFFD,0x00000000 +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) +//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 +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) +//data4 0x37287195,0xDE5BD8A9,0x00003FFD,0x00000000 +//data4 0xACCF70C8,0xD56EAABE,0x00003FBB,0x00000000 +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_Neg_One = f77 +FR_Z = f78 +FR_AA = f79 +FR_BB = f80 +FR_S_lo = f81 +FR_2_to_minus_N = f82 + +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_minus_N = r39 +GR_Z_1 = r40 +GR_Z_2 = r41 +GR_N = r42 +GR_Bias = r43 +GR_M = r44 +GR_Index3 = r45 +GR_exp_2tom80 = 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 +GR_minus_N = r39 + +// +// 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(log1pl) +{ .mfi + alloc r32 = ar.pfs,0,21,4,0 + fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf + nop.i 999 +} +{ .mfi + addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp + fma.s1 FR_Z = FR_Input_X, f1, f1 // x+1 + nop.i 999 +} +;; + +{ .mfi + nop.m 999 + fmerge.ns FR_Neg_One = f1, f1 // Form -1.0 + nop.i 999 +} +{ .mfi + nop.m 999 + fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x + nop.i 999 +} +;; + +{ .mfi + ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 + nop.f 999 + mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 +} +;; + +{ .mfb + getf.sig GR_signif = FR_Z // Get significand of x+1 + fcmp.eq.s1 p9, p0 = FR_Input_X, f0 // Test for x=0 +(p6) br.cond.spnt LOG1P_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_X_Prime, FR_Neg_One // Test for x<-1 + add GR_ad_p = -0x100, 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 999 + add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 +} +;; + +{ .mfi + add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q + fcmp.eq.s1 p8, p0 = FR_X_Prime, FR_Neg_One // Test for x=-1 + 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 + nop.f 999 +(p9) br.ret.spnt b0 // Exit if x=0, return input +} +;; + +{ .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, f0 // W = x + 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 + fmax.s1 FR_AA = FR_X_Prime, f1 // For S_lo, form AA = max(X,1.0) + 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 LOG1P_LT_Minus_1 // Branch if x<-1 +} +;; + +{ .mfb + ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 + fmerge.se FR_S_hi = f1,FR_Z // Form |x+1| +(p8) br.cond.spnt LOG1P_EQ_Minus_1 // Branch if x=-1 +} +;; + +{ .mmb + getf.exp GR_N = FR_Z // Get N = exponent of x+1 + ldfd FR_h = [GR_ad_tbl_1] // Load h_1 +(p10) br.cond.spnt LOG1P_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 + 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 + fms.s1 FR_S_lo = FR_AA, f1, FR_Z // Form S_lo = AA - Z + 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 significand + fmin.s1 FR_BB = FR_X_Prime, f1 // For S_lo, form BB = min(X,1.0) +} +;; + +{ .mmi + getf.exp GR_M = FR_W // Get signexp of w = x + 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 +} +;; + +{ .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| < 2^-7 + cmp.lt p7, p0 = GR_M, GR_exp_2tom80 // Test |x| < 2^-80 +} +;; + +// Small path is separate code +// p7 is for the small path: |x| < 2^-80 +// near1 and regular paths are merged. +// p8 is for the near1 path: |x| < 2^-7 +// p9 is for regular path: |x| >= 2^-7 + +{ .mfi + ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 + nop.f 999 + nop.i 999 +} +{ .mfb +(p9) setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) +(p7) fnma.s0 f8 = FR_X_Prime, FR_X_Prime, FR_X_Prime // Result x - x*x +(p7) br.ret.spnt b0 // Branch if |x| < 2^-80 +} +;; + +{ .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. +// +{ .mmf +(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 +(p9) fma.s1 FR_S_lo = FR_S_lo, f1, FR_BB // S_lo = S_lo + BB +} +;; + +{ .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 +(p9) fma.s1 FR_S_lo = FR_S_lo, FR_2_to_minus_N, f0 // S_lo = S_lo * 2^(-N) + 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 +(p9) fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r = G * S_lo + (G * S_hi - 1) + 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 +{ .mfb + nop.m 999 + fadd.s0 f8 = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi + br.ret.sptk b0 // Common exit for 2^-80 < x < inf +} +;; + + +// Here if x=-1 +LOG1P_EQ_Minus_1: +// +// If x=-1 raise divide by zero and return -inf +// +{ .mfi + mov GR_Parameter_TAG = 138 + fsub.s1 FR_Output_X_tmp = f0, f1 + nop.i 999 +} +;; + +{ .mfb + nop.m 999 + frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0 + br.cond.sptk __libm_error_region +} +;; + +LOG1P_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. +// +{ .mfb + mov GR_Parameter_TAG = 139 + fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0 + br.cond.sptk __libm_error_region +} +;; + + +LOG1P_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 < -1 +LOG1P_LT_Minus_1: +// +// Deal with x < -1 in a special way - raise +// invalid and produce QNaN indefinite. +// +{ .mfb + mov GR_Parameter_TAG = 139 + frcpa.s0 FR_Output_X_tmp, p8 = f0, f0 + br.cond.sptk __libm_error_region +} +;; + + +GLOBAL_IEEE754_END(log1pl) + +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# |