.file "coshf.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//*********************************************************************// 02/02/00 Initial version// 02/16/00 The error tag for coshf overflow changed to 65 (from 64).// 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.// 05/07/01 Reworked to improve speed of all paths// 05/20/02 Cleaned up namespace and sf0 syntax// 11/15/02 Improved algorithm based on expf// 03/31/05 Reformatted delimiters between data tables//// API//*********************************************************************// float coshf(float)//// Overview of operation//*********************************************************************// Case 1:  0 < |x| < 0.25//  Evaluate cosh(x) by a 8th order polynomial//  Care is take for the order of multiplication; and A2 is not exactly 1/4!,//  A3 is not exactly 1/6!, etc.//  cosh(x) = 1 + (A1*x^2 + A2*x^4 + A3*x^6 + A4*x^8)//// Case 2:  0.25 < |x| < 89.41598//  Algorithm is based on the identity cosh(x) = ( exp(x) + exp(-x) ) / 2.//  The algorithm for exp is described as below.  There are a number of//  economies from evaluating both exp(x) and exp(-x).  Although we//  are evaluating both quantities, only where the quantities diverge do we//  duplicate the computations.  The basic algorithm for exp(x) is described//  below.//// Take the input x. w is "how many log2/128 in x?"//  w = x * 64/log2//  NJ = int(w)//  x = NJ*log2/64 + R//  NJ = 64*n + j//  x = n*log2 + (log2/64)*j + R////  So, exp(x) = 2^n * 2^(j/64)* exp(R)////  T =  2^n * 2^(j/64)//       Construct 2^n//       Get 2^(j/64) table//           actually all the entries of 2^(j/64) table are stored in DP and//           with exponent bits set to 0 -> multiplication on 2^n can be//           performed by doing logical "or" operation with bits presenting 2^n//  exp(R) = 1 + (exp(R) - 1)//  P = exp(R) - 1 approximated by Taylor series of 3rd degree//      P = A3*R^3 + A2*R^2 + R, A3 = 1/6, A2 = 1/2////  The final result is reconstructed as follows//  exp(x) = T + T*P// Special values//*********************************************************************// coshf(+0)    = 1.0// coshf(-0)    = 1.0// coshf(+qnan) = +qnan// coshf(-qnan) = -qnan// coshf(+snan) = +qnan// coshf(-snan) = -qnan// coshf(-inf)  = +inf// coshf(+inf)  = +inf// Overflow and Underflow//*********************************************************************// coshf(x) = largest single normal when//     x = 89.41598 = 0x42b2d4fc//// There is no underflow.// Registers used//*********************************************************************// Floating Point registers used:// f8 input, output// f6,f7, f9 -> f15,  f32 -> f45// General registers used:// r2, r3, r16 -> r38// Predicate registers used:// p6 -> p15// Assembly macros//*********************************************************************// integer registers used// scratchrNJ                   = r2rNJ_neg               = r3rJ_neg                = r16rN_neg                = r17rSignexp_x            = r18rExp_x                = r18rExp_mask             = r19rExp_bias             = r20rAd1                  = r21rAd2                  = r22rJ                    = r23rN                    = r24rTblAddr              = r25rA3                   = r26rExpHalf              = r27rLn2Div64             = r28rGt_ln                = r29r17ones_m1            = r29rRightShifter         = r30rJ_mask               = r30r64DivLn2             = r31rN_mask               = r31// stackedGR_SAVE_PFS           = r32GR_SAVE_B0            = r33GR_SAVE_GP            = r34GR_Parameter_X        = r35GR_Parameter_Y        = r36GR_Parameter_RESULT   = r37GR_Parameter_TAG      = r38// floating point registers usedFR_X                  = f10FR_Y                  = f1FR_RESULT             = f8// scratchfRightShifter         = f6f64DivLn2             = f7fNormX                = f9fNint                 = f10fN                    = f11fR                    = f12fLn2Div64             = f13fA2                   = f14fA3                   = f15// stackedfP                    = f32fT                    = f33fMIN_SGL_OFLOW_ARG    = f34fMAX_SGL_NORM_ARG     = f35fRSqr                 = f36fA1                   = f37fA21                  = f37fA4                   = f38fA43                  = f38fA4321                = f38fX4                   = f39fTmp                  = f39fGt_pln               = f39fWre_urm_f8           = f40fXsq                  = f40fP_neg                = f41fT_neg                = f42fExp                  = f43fExp_neg              = f44fAbsX                 = f45RODATA.align 16LOCAL_OBJECT_START(_coshf_table)data4 0x42b2d4fd         // Smallest single arg to overflow single resultdata4 0x42b2d4fc         // Largest single arg to give normal single resultdata4 0x00000000         // paddata4 0x00000000         // pad//// 2^(j/64) table, j goes from 0 to 63data8 0x0000000000000000 // 2^(0/64)data8 0x00002C9A3E778061 // 2^(1/64)data8 0x000059B0D3158574 // 2^(2/64)data8 0x0000874518759BC8 // 2^(3/64)data8 0x0000B5586CF9890F // 2^(4/64)data8 0x0000E3EC32D3D1A2 // 2^(5/64)data8 0x00011301D0125B51 // 2^(6/64)data8 0x0001429AAEA92DE0 // 2^(7/64)data8 0x000172B83C7D517B // 2^(8/64)data8 0x0001A35BEB6FCB75 // 2^(9/64)data8 0x0001D4873168B9AA // 2^(10/64)data8 0x0002063B88628CD6 // 2^(11/64)data8 0x0002387A6E756238 // 2^(12/64)data8 0x00026B4565E27CDD // 2^(13/64)data8 0x00029E9DF51FDEE1 // 2^(14/64)data8 0x0002D285A6E4030B // 2^(15/64)data8 0x000306FE0A31B715 // 2^(16/64)data8 0x00033C08B26416FF // 2^(17/64)data8 0x000371A7373AA9CB // 2^(18/64)data8 0x0003A7DB34E59FF7 // 2^(19/64)data8 0x0003DEA64C123422 // 2^(20/64)data8 0x0004160A21F72E2A // 2^(21/64)data8 0x00044E086061892D // 2^(22/64)data8 0x000486A2B5C13CD0 // 2^(23/64)data8 0x0004BFDAD5362A27 // 2^(24/64)data8 0x0004F9B2769D2CA7 // 2^(25/64)data8 0x0005342B569D4F82 // 2^(26/64)data8 0x00056F4736B527DA // 2^(27/64)data8 0x0005AB07DD485429 // 2^(28/64)data8 0x0005E76F15AD2148 // 2^(29/64)data8 0x0006247EB03A5585 // 2^(30/64)data8 0x0006623882552225 // 2^(31/64)data8 0x0006A09E667F3BCD // 2^(32/64)data8 0x0006DFB23C651A2F // 2^(33/64)data8 0x00071F75E8EC5F74 // 2^(34/64)data8 0x00075FEB564267C9 // 2^(35/64)data8 0x0007A11473EB0187 // 2^(36/64)data8 0x0007E2F336CF4E62 // 2^(37/64)data8 0x00082589994CCE13 // 2^(38/64)data8 0x000868D99B4492ED // 2^(39/64)data8 0x0008ACE5422AA0DB // 2^(40/64)data8 0x0008F1AE99157736 // 2^(41/64)data8 0x00093737B0CDC5E5 // 2^(42/64)data8 0x00097D829FDE4E50 // 2^(43/64)data8 0x0009C49182A3F090 // 2^(44/64)data8 0x000A0C667B5DE565 // 2^(45/64)data8 0x000A5503B23E255D // 2^(46/64)data8 0x000A9E6B5579FDBF // 2^(47/64)data8 0x000AE89F995AD3AD // 2^(48/64)data8 0x000B33A2B84F15FB // 2^(49/64)data8 0x000B7F76F2FB5E47 // 2^(50/64)data8 0x000BCC1E904BC1D2 // 2^(51/64)data8 0x000C199BDD85529C // 2^(52/64)data8 0x000C67F12E57D14B // 2^(53/64)data8 0x000CB720DCEF9069 // 2^(54/64)data8 0x000D072D4A07897C // 2^(55/64)data8 0x000D5818DCFBA487 // 2^(56/64)data8 0x000DA9E603DB3285 // 2^(57/64)data8 0x000DFC97337B9B5F // 2^(58/64)data8 0x000E502EE78B3FF6 // 2^(59/64)data8 0x000EA4AFA2A490DA // 2^(60/64)data8 0x000EFA1BEE615A27 // 2^(61/64)data8 0x000F50765B6E4540 // 2^(62/64)data8 0x000FA7C1819E90D8 // 2^(63/64)LOCAL_OBJECT_END(_coshf_table)LOCAL_OBJECT_START(cosh_p_table)data8 0x3efa3001dcf5905b // A4data8 0x3f56c1437543543e // A3data8 0x3fa5555572601504 // A2data8 0x3fdfffffffe2f097 // A1LOCAL_OBJECT_END(cosh_p_table).section .textGLOBAL_IEEE754_ENTRY(coshf){ .mlx      getf.exp        rSignexp_x = f8  // Must recompute if x unorm      movl            r64DivLn2 = 0x40571547652B82FE // 64/ln(2)}{ .mlx      addl            rTblAddr = @ltoff(_coshf_table),gp      movl            rRightShifter = 0x43E8000000000000 // DP Right Shifter};;{ .mfi      // point to the beginning of the table      ld8             rTblAddr = [rTblAddr]      fclass.m        p6, p0 = f8, 0x0b   // Test for x=unorm      addl            rA3 = 0x3E2AA, r0   // high bits of 1.0/6.0 rounded to SP}{ .mfi      nop.m           0      fnorm.s1        fNormX = f8 // normalized x      addl            rExpHalf = 0xFFFE, r0 // exponent of 1/2};;{ .mfi      setf.d          f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg      fclass.m        p15, p0 = f8, 0x1e3   // test for NaT,NaN,Inf      nop.i           0}{ .mlx      // load Right Shifter to FP reg      setf.d          fRightShifter = rRightShifter      movl            rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR};;{ .mfi      mov             rExp_mask = 0x1ffff      fcmp.eq.s1      p13, p0 = f0, f8 // test for x = 0.0      shl             rA3 = rA3, 12    // 0x3E2AA000, approx to 1.0/6.0 in SP}{ .mfb      nop.m           0      nop.f           0(p6)  br.cond.spnt    COSH_UNORM            // Branch if x=unorm};;COSH_COMMON:{ .mfi      setf.exp        fA2 = rExpHalf        // load A2 to FP reg      nop.f           0      mov             rExp_bias = 0xffff}{ .mfb      setf.d          fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg(p15) fma.s.s0        f8 = f8, f8, f0       // result if x = NaT,NaN,Inf(p15) br.ret.spnt     b0                    // exit here if x = NaT,NaN,Inf};;{ .mfi      // min overflow and max normal threshold      ldfps           fMIN_SGL_OFLOW_ARG, fMAX_SGL_NORM_ARG = [rTblAddr], 8      nop.f           0      and             rExp_x = rExp_mask, rSignexp_x // Biased exponent of x}{ .mfb      setf.s          fA3 = rA3                  // load A3 to FP reg