.file "exp10.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//==============================================================// 08/25/00 Initial version// 05/20/02 Cleaned up namespace and sf0 syntax// 09/06/02 Improved performance; no inexact flags on exact cases// 01/29/03 Added missing } to bundle templates// 12/16/04 Call error handling on underflow.// 03/31/05 Reformatted delimiters between data tables//// API//==============================================================// double exp10(double)//// Overview of operation//==============================================================// Background//// Implementation//// Let x= (K + fh + fl + r)/log2(10), where// K is an integer, fh= 0.b1 b2 b3 b4 b5,// fl= 2^{-5}* 0.b6 b7 b8 b8 b10 (fh, fl >= 0),// and |r|<2^{-11}// Th is a table that stores 2^fh (32 entries) rounded to// double extended precision (only mantissa is stored)// Tl is a table that stores 2^fl (32 entries) rounded to// double extended precision (only mantissa is stored)//// 10^x is approximated as// 2^K * Th [ f ] * Tl [ f ] * (1+c1*e+c1*r+c2*r^2+c3*r^3+c4*r^4),// where e= (x*log2(10)_hi-RN(x*log2(10)_hi))+log2(10)_lo*x// Note there are only 22 non-zero values that produce an exact result://  1.0, 2.0, ... 22.0.// We test for these cases and use s1 to avoid setting the inexact flag.// Special values//==============================================================// exp10(0)= 1// exp10(+inf)= inf// exp10(-inf)= 0//// Registers used//==============================================================// r2-r3, r14-r40// f6-f15, f32-f52// p6-p12//GR_TBL_START        = r2GR_LOG_TBL          = r3GR_OF_LIMIT         = r14GR_UF_LIMIT         = r15GR_EXP_CORR         = r16GR_F_low            = r17GR_F_high           = r18GR_K                = r19GR_Flow_ADDR        = r20GR_BIAS             = r21GR_Fh               = r22GR_Fh_ADDR          = r23GR_EXPMAX           = r24GR_BIAS53           = r25GR_ROUNDVAL         = r26GR_SNORM_LIMIT      = r26GR_MASK             = r27GR_KF0              = r28GR_MASK_low         = r29GR_COEFF_START      = r30GR_exact_limit      = r31GR_SAVE_B0          = r33GR_SAVE_PFS         = r34GR_SAVE_GP          = r35GR_SAVE_SP          = r36GR_Parameter_X      = r37GR_Parameter_Y      = r38GR_Parameter_RESULT = r39GR_Parameter_TAG    = r40FR_X                = f10FR_Y                = f1FR_RESULT           = f8FR_COEFF1           = f6FR_COEFF2           = f7FR_R                = f9FR_LOG2_10          = f10FR_2P53             = f11FR_KF0              = f12FR_COEFF3           = f13FR_COEFF4           = f14FR_UF_LIMIT         = f15FR_OF_LIMIT         = f32FR_DX_L210          = f33FR_ROUNDVAL         = f34FR_KF               = f35FR_2_TO_K           = f36FR_T_low            = f37FR_T_high           = f38FR_P34              = f39FR_R2               = f40FR_P12              = f41FR_T_low_K          = f42FR_P14              = f43FR_T                = f44FR_P                = f45FR_L2_10_low        = f46FR_L2_10_high       = f47FR_E0               = f48FR_E                = f49FR_exact_limit      = f50FR_int_x            = f51FR_SNORM_LIMIT      = f52// Data tables//==============================================================RODATA.align 16LOCAL_OBJECT_START(poly_coeffs)data8 0xd49a784bcd1b8afe, 0x00003fcb // log2(10)*2^(10-63)data8 0x9257edfe9b5fb698, 0x3fbf // log2(10)_low (bits 64...127)data8 0x3fac6b08d704a0c0, 0x3f83b2ab6fba4e77 // C_3 and C_4data8 0xb17217f7d1cf79ab, 0x00003ffe // C_1data8 0xf5fdeffc162c7541, 0x00003ffc // C_2LOCAL_OBJECT_END(poly_coeffs)LOCAL_OBJECT_START(T_table)// 2^{0.00000 b6 b7 b8 b9 b10}data8 0x8000000000000000, 0x8016302f17467628data8 0x802c6436d0e04f50, 0x80429c17d77c18eddata8 0x8058d7d2d5e5f6b0, 0x806f17687707a7afdata8 0x80855ad965e88b83, 0x809ba2264dada76adata8 0x80b1ed4fd999ab6c, 0x80c83c56b50cf77fdata8 0x80de8f3b8b85a0af, 0x80f4e5ff089f763edata8 0x810b40a1d81406d4, 0x81219f24a5baa59ddata8 0x813801881d886f7b, 0x814e67cceb90502cdata8 0x8164d1f3bc030773, 0x817b3ffd3b2f2e47data8 0x8191b1ea15813bfd, 0x81a827baf7838b78data8 0x81bea1708dde6055, 0x81d51f0b8557ec1cdata8 0x81eba08c8ad4536f, 0x820225f44b55b33bdata8 0x8218af4373fc25eb, 0x822f3c7ab205c89adata8 0x8245cd9ab2cec048, 0x825c62a423d13f0cdata8 0x8272fb97b2a5894c, 0x828998760d01faf3data8 0x82a0393fe0bb0ca8, 0x82b6ddf5dbc35906//// 2^{0.b1 b2 b3 b4 b5}data8 0x8000000000000000, 0x82cd8698ac2ba1d7data8 0x85aac367cc487b14, 0x88980e8092da8527data8 0x8b95c1e3ea8bd6e6, 0x8ea4398b45cd53c0data8 0x91c3d373ab11c336, 0x94f4efa8fef70961data8 0x9837f0518db8a96f, 0x9b8d39b9d54e5538data8 0x9ef5326091a111ad, 0xa27043030c496818data8 0xa5fed6a9b15138ea, 0xa9a15ab4ea7c0ef8data8 0xad583eea42a14ac6, 0xb123f581d2ac258fdata8 0xb504f333f9de6484, 0xb8fbaf4762fb9ee9data8 0xbd08a39f580c36be, 0xc12c4cca66709456data8 0xc5672a115506dadd, 0xc9b9bd866e2f27a2data8 0xce248c151f8480e3, 0xd2a81d91f12ae45adata8 0xd744fccad69d6af4, 0xdbfbb797daf23755data8 0xe0ccdeec2a94e111, 0xe5b906e77c8348a8data8 0xeac0c6e7dd24392e, 0xefe4b99bdcdaf5cbdata8 0xf5257d152486cc2c, 0xfa83b2db722a033aLOCAL_OBJECT_END(T_table).section .textGLOBAL_IEEE754_ENTRY(exp10){.mfi       alloc r32= ar.pfs, 1, 4, 4, 0       // will continue only for non-zero normal/denormal numbers       fclass.nm.unc p12, p7= f8, 0x1b       mov GR_BIAS53= 0xffff+63-10}{.mlx       // GR_TBL_START= pointer to log2(10), C_1...C_4 followed by T_table       addl GR_TBL_START= @ltoff(poly_coeffs), gp       movl GR_ROUNDVAL= 0x3fc00000             // 1.5 (SP)};;{.mfi       ld8 GR_COEFF_START= [ GR_TBL_START ]     // Load pointer to coeff table       fcmp.lt.s1 p6, p8= f8, f0                // X<0 ?       nop.i 0};;{.mlx       setf.exp FR_2P53= GR_BIAS53              // 2^{63-10}       movl GR_UF_LIMIT= 0xc07439b746e36b52     // (-2^10-51) / log2(10)}{.mlx       setf.s FR_ROUNDVAL= GR_ROUNDVAL       movl GR_OF_LIMIT= 0x40734413509f79fe     // Overflow threshold};;{.mlx       ldfe FR_LOG2_10= [ GR_COEFF_START ], 16  // load log2(10)*2^(10-63)       movl GR_SNORM_LIMIT= 0xc0733a7146f72a41  // Smallest normal threshold}{.mib       nop.m 0       nop.i 0 (p12) br.cond.spnt SPECIAL_exp10               // Branch if nan, inf, zero};;{.mmf       ldfe FR_L2_10_low= [ GR_COEFF_START ], 16 // load log2(10)_low       setf.d FR_OF_LIMIT= GR_OF_LIMIT           // Set overflow limit       fma.s0 f8= f8, f1, f0                     // normalize x};;{.mfi       ldfpd FR_COEFF3, FR_COEFF4= [ GR_COEFF_START ], 16 // load C_3, C_4 (p8)  fcvt.fx.s1 FR_int_x = f8                   // Convert x to integer       nop.i 0}{.mfi       setf.d FR_UF_LIMIT= GR_UF_LIMIT            // Set underflow limit       fma.s1 FR_KF0= f8, FR_LOG2_10, FR_ROUNDVAL // y= (x*log2(10)*2^10 +                                                  //    1.5*2^63) * 2^(-63)       mov GR_EXP_CORR= 0xffff-126};;{.mfi       setf.d FR_SNORM_LIMIT= GR_SNORM_LIMIT      // Set smallest normal limit       fma.s1 FR_L2_10_high= FR_LOG2_10, FR_2P53, f0 // FR_LOG2_10= log2(10)_hi       nop.i 0};;{.mfi       ldfe FR_COEFF1= [ GR_COEFF_START ], 16    // load C_1       fms.s1 FR_KF= FR_KF0, f1, FR_ROUNDVAL     // (K+f)*2^(10-63)       mov GR_MASK= 1023