.file "coshl.s"// Copyright (c) 2000 - 2002, 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.// 01/23/01 Set inexact flag for large args.// 05/07/01 Reworked to improve speed of all paths// 05/20/02 Cleaned up namespace and sf0 syntax// 12/06/02 Improved performance//// API//==============================================================// long double = coshl(long double)// input  floating point f8// output floating point f8//// Registers used//==============================================================// general registers: // r14 -> r40// predicate registers used:// p6 -> p11// floating-point registers used:// f9 -> f15; f32 -> f90; // f8 has input, then output//// Overview of operation//==============================================================// There are seven paths// 1. 0 < |x| < 0.25          COSH_BY_POLY// 2. 0.25 <=|x| < 32         COSH_BY_TBL// 3. 32 <= |x| < 11357.21655 COSH_BY_EXP (merged path with COSH_BY_TBL)// 4. |x| >= 11357.21655      COSH_HUGE// 5. x=0                     Done with early exit// 6. x=inf,nan               Done with early exit// 7. x=denormal              COSH_DENORM//// For double extended we get overflow for x >= 400c b174 ddc0 31ae c0ea//                                           >= 11357.21655////// 1. COSH_BY_POLY   0 < |x| < 0.25// ===============// Evaluate cosh(x) by a 12th order polynomial// Care is take for the order of multiplication; and P2 is not exactly 1/4!, // P3 is not exactly 1/6!, etc.// cosh(x) = 1 + (P1*x^2 + P2*x^4 + P3*x^6 + P4*x^8 + P5*x^10 + P6*x^12)//// 2. COSH_BY_TBL   0.25 <= |x| < 32.0// =============// cosh(x) = cosh(B+R)//         = cosh(B)cosh(R) + sinh(B)sinh(R)// // ax = |x| = M*log2/64 + R// B = M*log2/64// M = 64*N + j //   We will calculate M and get N as (M-j)/64//   The division is a shift.// exp(B)  = exp(N*log2 + j*log2/64)//         = 2^N * 2^(j*log2/64)// cosh(B) = 1/2(e^B + e^-B)//         = 1/2(2^N * 2^(j*log2/64) + 2^-N * 2^(-j*log2/64)) // cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64)) // sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64)) // 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)//// R = ax - M*log2/64// R = ax - M*log2_by_64_hi - M*log2_by_64_lo// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)//        = 1 + p_odd + p_even//        where the p_even uses the A coefficients and the p_even uses //        the B coefficients//// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd//    cosh(R) = 1 + p_even//    cosh(B) = C_hi + C_lo//    sinh(B) = S_hi// cosh(x) = cosh(B)cosh(R) + sinh(B)sinh(R)//// 3. COSH_BY_EXP   32.0 <= |x| < 11357.21655  ( 400c b174 ddc0 31ae c0ea )// ==============// Can approximate result by exp(x)/2 in this region.// Y_hi = Tjhi// Y_lo = Tjhi * (p_odd + p_even) + Tjlo// cosh(x) = Y_hi + Y_lo//// 4. COSH_HUGE     |x| >= 11357.21655  ( 400c b174 ddc0 31ae c0ea )// ============// Set error tag and call error support////// Assembly macros//==============================================================r_ad5                 = r14r_rshf_2to57          = r15r_exp_denorm          = r15r_ad_mJ_lo            = r15r_ad_J_lo             = r16r_2Nm1                = r17r_2mNm1               = r18r_exp_x               = r18r_ad_J_hi             = r19r_ad2o                = r19r_ad_mJ_hi            = r20r_mj                  = r21r_ad2e                = r22r_ad3                 = r23r_ad1                 = r24r_Mmj                 = r24r_rshf                = r25r_M                   = r25r_N                   = r25r_jshf                = r26r_exp_2tom57          = r26r_j                   = r26r_exp_mask            = r27r_signexp_x           = r28r_signexp_0_5         = r28r_exp_0_25            = r29r_sig_inv_ln2         = r30r_exp_32              = r30r_exp_huge            = r30r_ad4                 = r31GR_SAVE_PFS           = r34GR_SAVE_B0            = r35GR_SAVE_GP            = r36GR_Parameter_X        = r37GR_Parameter_Y        = r38GR_Parameter_RESULT   = r39GR_Parameter_TAG      = r40f_ABS_X               = f9 f_X2                  = f10f_X4                  = f11f_tmp                 = f14f_RSHF                = f15f_Inv_log2by64        = f32f_log2by64_lo         = f33f_log2by64_hi         = f34f_A1                  = f35f_A2                  = f36f_A3                  = f37f_Rcub                = f38f_M_temp              = f39f_R_temp              = f40f_Rsq                 = f41f_R                   = f42f_M                   = f43f_B1                  = f44f_B2                  = f45f_B3                  = f46f_peven_temp1         = f47f_peven_temp2         = f48f_peven               = f49f_podd_temp1          = f50f_podd_temp2          = f51f_podd                = f52f_poly65              = f53f_poly6543            = f53f_poly6to1            = f53f_poly43              = f54f_poly21              = f55f_X3                  = f56f_INV_LN2_2TO63       = f57f_RSHF_2TO57          = f58f_2TOM57              = f59f_smlst_oflow_input   = f60f_pre_result          = f61f_huge                = f62f_spos                = f63f_sneg                = f64f_Tjhi                = f65f_Tjlo                = f66f_Tmjhi               = f67f_Tmjlo               = f68f_S_hi                = f69f_SC_hi_temp          = f70f_C_lo_temp1          = f71 f_C_lo_temp2          = f72 f_C_lo_temp3          = f73 f_C_lo_temp4          = f73 f_C_lo                = f74f_C_hi                = f75f_Y_hi                = f77 f_Y_lo_temp           = f78 f_Y_lo                = f79 f_NORM_X              = f80f_P1                  = f81f_P2                  = f82f_P3                  = f83f_P4                  = f84f_P5                  = f85f_P6                  = f86f_Tjhi_spos           = f87f_Tjlo_spos           = f88f_huge                = f89f_signed_hi_lo        = f90// Data tables//==============================================================// DO NOT CHANGE ORDER OF THESE TABLESRODATA.align 16LOCAL_OBJECT_START(cosh_arg_reduction)//   data8 0xB8AA3B295C17F0BC, 0x00004005  // 64/log2 -- signif loaded with setf   data8 0xB17217F7D1000000, 0x00003FF8  // log2/64 high part   data8 0xCF79ABC9E3B39804, 0x00003FD0  // log2/64 low part   data8 0xb174ddc031aec0ea, 0x0000400c  // Smallest x to overflow (11357.21655)LOCAL_OBJECT_END(cosh_arg_reduction)LOCAL_OBJECT_START(cosh_p_table)   data8 0x8FA02AC65BCBD5BC, 0x00003FE2  // P6   data8 0xD00D00D1021D7370, 0x00003FEF  // P4   data8 0xAAAAAAAAAAAAAB80, 0x00003FFA  // P2   data8 0x93F27740C0C2F1CC, 0x00003FE9  // P5   data8 0xB60B60B60B4FE884, 0x00003FF5  // P3   data8 0x8000000000000000, 0x00003FFE  // P1LOCAL_OBJECT_END(cosh_p_table)LOCAL_OBJECT_START(cosh_ab_table)   data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC  // A1   data8 0x88888888884ECDD5, 0x00003FF8  // A2   data8 0xD00D0C6DCC26A86B, 0x00003FF2  // A3   data8 0x8000000000000002, 0x00003FFE  // B1   data8 0xAAAAAAAAAA402C77, 0x00003FFA  // B2   data8 0xB60B6CC96BDB144D, 0x00003FF5  // B3LOCAL_OBJECT_END(cosh_ab_table)LOCAL_OBJECT_START(cosh_j_hi_table)   data8 0xB504F333F9DE6484, 0x00003FFE   data8 0xB6FD91E328D17791, 0x00003FFE   data8 0xB8FBAF4762FB9EE9, 0x00003FFE   data8 0xBAFF5AB2133E45FB, 0x00003FFE   data8 0xBD08A39F580C36BF, 0x00003FFE   data8 0xBF1799B67A731083, 0x00003FFE   data8 0xC12C4CCA66709456, 0x00003FFE   data8 0xC346CCDA24976407, 0x00003FFE   data8 0xC5672A115506DADD, 0x00003FFE   data8 0xC78D74C8ABB9B15D, 0x00003FFE   data8 0xC9B9BD866E2F27A3, 0x00003FFE   data8 0xCBEC14FEF2727C5D, 0x00003FFE   data8 0xCE248C151F8480E4, 0x00003FFE   data8 0xD06333DAEF2B2595, 0x00003FFE   data8 0xD2A81D91F12AE45A, 0x00003FFE   data8 0xD4F35AABCFEDFA1F, 0x00003FFE   data8 0xD744FCCAD69D6AF4, 0x00003FFE   data8 0xD99D15C278AFD7B6, 0x00003FFE   data8 0xDBFBB797DAF23755, 0x00003FFE   data8 0xDE60F4825E0E9124, 0x00003FFE   data8 0xE0CCDEEC2A94E111, 0x00003FFE   data8 0xE33F8972BE8A5A51, 0x00003FFE   data8 0xE5B906E77C8348A8, 0x00003FFE   data8 0xE8396A503C4BDC68, 0x00003FFE   data8 0xEAC0C6E7DD24392F, 0x00003FFE   data8 0xED4F301ED9942B84, 0x00003FFE   data8 0xEFE4B99BDCDAF5CB, 0x00003FFE   data8 0xF281773C59FFB13A, 0x00003FFE   data8 0xF5257D152486CC2C, 0x00003FFE   data8 0xF7D0DF730AD13BB9, 0x00003FFE   data8 0xFA83B2DB722A033A, 0x00003FFE   data8 0xFD3E0C0CF486C175, 0x00003FFE   data8 0x8000000000000000, 0x00003FFF // Center of table   data8 0x8164D1F3BC030773, 0x00003FFF   data8 0x82CD8698AC2BA1D7, 0x00003FFF   data8 0x843A28C3ACDE4046, 0x00003FFF   data8 0x85AAC367CC487B15, 0x00003FFF   data8 0x871F61969E8D1010, 0x00003FFF   data8 0x88980E8092DA8527, 0x00003FFF   data8 0x8A14D575496EFD9A, 0x00003FFF   data8 0x8B95C1E3EA8BD6E7, 0x00003FFF   data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF   data8 0x8EA4398B45CD53C0, 0x00003FFF   data8 0x9031DC431466B1DC, 0x00003FFF   data8 0x91C3D373AB11C336, 0x00003FFF   data8 0x935A2B2F13E6E92C, 0x00003FFF   data8 0x94F4EFA8FEF70961, 0x00003FFF   data8 0x96942D3720185A00, 0x00003FFF   data8 0x9837F0518DB8A96F, 0x00003FFF   data8 0x99E0459320B7FA65, 0x00003FFF   data8 0x9B8D39B9D54E5539, 0x00003FFF   data8 0x9D3ED9A72CFFB751, 0x00003FFF   data8 0x9EF5326091A111AE, 0x00003FFF   data8 0xA0B0510FB9714FC2, 0x00003FFF   data8 0xA27043030C496819, 0x00003FFF   data8 0xA43515AE09E6809E, 0x00003FFF   data8 0xA5FED6A9B15138EA, 0x00003FFF   data8 0xA7CD93B4E965356A, 0x00003FFF   data8 0xA9A15AB4EA7C0EF8, 0x00003FFF   data8 0xAB7A39B5A93ED337, 0x00003FFF   data8 0xAD583EEA42A14AC6, 0x00003FFF   data8 0xAF3B78AD690A4375, 0x00003FFF   data8 0xB123F581D2AC2590, 0x00003FFF   data8 0xB311C412A9112489, 0x00003FFF   data8 0xB504F333F9DE6484, 0x00003FFFLOCAL_OBJECT_END(cosh_j_hi_table)LOCAL_OBJECT_START(cosh_j_lo_table)   data4 0x1EB2FB13   data4 0x1CE2CBE2   data4 0x1DDC3CBC   data4 0x1EE9AA34   data4 0x9EAEFDC1   data4 0x9DBF517B   data4 0x1EF88AFB   data4 0x1E03B216   data4 0x1E78AB43   data4 0x9E7B1747   data4 0x9EFE3C0E   data4 0x9D36F837   data4 0x9DEE53E4   data4 0x9E24AE8E   data4 0x1D912473   data4 0x1EB243BE   data4 0x1E669A2F   data4 0x9BBC610A   data4 0x1E761035   data4 0x9E0BE175   data4 0x1CCB12A1   data4 0x1D1BFE90   data4 0x1DF2F47A   data4 0x1EF22F22   data4 0x9E3F4A29   data4 0x1EC01A5B   data4 0x1E8CAC3A   data4 0x9DBB3FAB   data4 0x1EF73A19   data4 0x9BB795B5   data4 0x1EF84B76   data4 0x9EF5818B   data4 0x00000000 // Center of table   data4 0x1F77CACA   data4 0x1EF8A91D   data4 0x1E57C976   data4 0x9EE8DA92   data4 0x1EE85C9F   data4 0x1F3BF1AF   data4 0x1D80CA1E   data4 0x9D0373AF   data4 0x9F167097   data4 0x1EB70051   data4 0x1F6EB029   data4 0x1DFD6D8E   data4 0x9EB319B0   data4 0x1EBA2BEB   data4 0x1F11D537   data4 0x1F0D5A46   data4 0x9E5E7BCA   data4 0x9F3AAFD1   data4 0x9E86DACC   data4 0x9F3EDDC2   data4 0x1E496E3D   data4 0x9F490BF6   data4 0x1DD1DB48   data4 0x1E65EBFB   data4 0x9F427496   data4 0x1F283C4A   data4 0x1F4B0047   data4 0x1F130152   data4 0x9E8367C0   data4 0x9F705F90   data4 0x1EFB3C53   data4 0x1F32FB13LOCAL_OBJECT_END(cosh_j_lo_table).section .textGLOBAL_IEEE754_ENTRY(coshl){ .mlx      getf.exp        r_signexp_x = f8   // Get signexp of x, must redo if unorm      movl            r_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2}{ .mlx      addl            r_ad1 = @ltoff(cosh_arg_reduction), gp      movl            r_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57)};;{ .mfi      ld8             r_ad1 = [r_ad1]      fmerge.s        f_ABS_X    = f0,f8      mov             r_exp_0_25 = 0x0fffd    // Form exponent for 0.25}{ .mfi      nop.m           0      fnorm.s1        f_NORM_X = f8            mov             r_exp_2tom57 = 0xffff-57};;{ .mfi      setf.d          f_RSHF_2TO57 = r_rshf_2to57 // Form const 1.100 * 2^120      fclass.m        p10,p0 = f8, 0x0b           // Test for denorm      mov             r_exp_mask = 0x1ffff }{ .mlx      setf.sig        f_INV_LN2_2TO63 = r_sig_inv_ln2 // Form 1/ln2 * 2^63      movl            r_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift};;{ .mfi      nop.m           0      fclass.m        p7,p0 = f8, 0x07  // Test if x=0      nop.i           0}{ .mfi      setf.exp        f_2TOM57 = r_exp_2tom57 // Form 2^-57 for scaling      nop.f           0      add             r_ad3 = 0x90, r_ad1  // Point to ab_table};;{ .mfi      setf.d          f_RSHF = r_rshf     // Form right shift const 1.100 * 2^63      fclass.m        p6,p0 = f8, 0xe3     // Test if x nan, inf      add             r_ad4 = 0x2f0, r_ad1 // Point to j_hi_table midpoint}{ .mib      add             r_ad2e = 0x20, r_ad1 // Point to p_table      nop.i           0(p10) br.cond.spnt    COSH_DENORM          // Branch if x denorm};;// Common path -- return here from COSH_DENORM if x is unnormCOSH_COMMON:{ .mfi      ldfe            f_smlst_oflow_input = [r_ad2e],16(p7)  fma.s0          f8 = f1, f1, f0      // Result = 1.0 if x=0      add             r_ad5 = 0x580, r_ad1 // Point to j_lo_table midpoint}{ .mib      ldfe            f_log2by64_hi  = [r_ad1],16             and             r_exp_x = r_exp_mask, r_signexp_x(p7)  br.ret.spnt     b0                  // Exit if x=0};;// Get the A coefficients for COSH_BY_TBL{ .mfi      ldfe            f_A1 = [r_ad3],16                  fcmp.lt.s1      p8,p9 = f8,f0           // Test for x<0      cmp.lt          p7,p0 = r_exp_x, r_exp_0_25  // Test x < 0.25}{ .mfb      add             r_ad2o = 0x30, r_ad2e  // Point to p_table odd coeffs(p6)  fma.s0          f8 = f8,f8,f0          // Result for x nan, inf          (p6)  br.ret.spnt     b0                     // Exit for x nan, inf};;// Calculate X2 = ax*ax for COSH_BY_POLY{ .mfi      ldfe            f_log2by64_lo  = [r_ad1],16             nop.f           0      nop.i           0}{ .mfb      ldfe            f_A2 = [r_ad3],16                  fma.s1          f_X2 = f_NORM_X, f_NORM_X, f0(p7)  br.cond.spnt    COSH_BY_POLY};;// Here if |x| >= 0.25COSH_BY_TBL: // ******************************************************// STEP 1 (TBL and EXP) - Argument reduction// ******************************************************// Get the following constants. // Inv_log2by64// log2by64_hi// log2by64_lo// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and// put them in an exponent.// f_spos = 2^(N-1) and f_sneg = 2^(-N-1)// 0xffff + (N-1)  = 0xffff +N -1// 0xffff - (N +1) = 0xffff -N -1// Calculate M and keep it as integer and floating point.// M = round-to-integer(x*Inv_log2by64)// f_M = M = truncate(ax/(log2/64))// Put the integer representation of M in r_M//    and the floating point representation of M in f_M