.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 = r14 r_rshf_2to57 = r15 r_exp_denorm = r15 r_ad_mJ_lo = r15 r_ad_J_lo = r16 r_2Nm1 = r17 r_2mNm1 = r18 r_exp_x = r18 r_ad_J_hi = r19 r_ad2o = r19 r_ad_mJ_hi = r20 r_mj = r21 r_ad2e = r22 r_ad3 = r23 r_ad1 = r24 r_Mmj = r24 r_rshf = r25 r_M = r25 r_N = r25 r_jshf = r26 r_exp_2tom57 = r26 r_j = r26 r_exp_mask = r27 r_signexp_x = r28 r_signexp_0_5 = r28 r_exp_0_25 = r29 r_sig_inv_ln2 = r30 r_exp_32 = r30 r_exp_huge = r30 r_ad4 = r31 GR_SAVE_PFS = r34 GR_SAVE_B0 = r35 GR_SAVE_GP = r36 GR_Parameter_X = r37 GR_Parameter_Y = r38 GR_Parameter_RESULT = r39 GR_Parameter_TAG = r40 f_ABS_X = f9 f_X2 = f10 f_X4 = f11 f_tmp = f14 f_RSHF = f15 f_Inv_log2by64 = f32 f_log2by64_lo = f33 f_log2by64_hi = f34 f_A1 = f35 f_A2 = f36 f_A3 = f37 f_Rcub = f38 f_M_temp = f39 f_R_temp = f40 f_Rsq = f41 f_R = f42 f_M = f43 f_B1 = f44 f_B2 = f45 f_B3 = f46 f_peven_temp1 = f47 f_peven_temp2 = f48 f_peven = f49 f_podd_temp1 = f50 f_podd_temp2 = f51 f_podd = f52 f_poly65 = f53 f_poly6543 = f53 f_poly6to1 = f53 f_poly43 = f54 f_poly21 = f55 f_X3 = f56 f_INV_LN2_2TO63 = f57 f_RSHF_2TO57 = f58 f_2TOM57 = f59 f_smlst_oflow_input = f60 f_pre_result = f61 f_huge = f62 f_spos = f63 f_sneg = f64 f_Tjhi = f65 f_Tjlo = f66 f_Tmjhi = f67 f_Tmjlo = f68 f_S_hi = f69 f_SC_hi_temp = f70 f_C_lo_temp1 = f71 f_C_lo_temp2 = f72 f_C_lo_temp3 = f73 f_C_lo_temp4 = f73 f_C_lo = f74 f_C_hi = f75 f_Y_hi = f77 f_Y_lo_temp = f78 f_Y_lo = f79 f_NORM_X = f80 f_P1 = f81 f_P2 = f82 f_P3 = f83 f_P4 = f84 f_P5 = f85 f_P6 = f86 f_Tjhi_spos = f87 f_Tjlo_spos = f88 f_huge = f89 f_signed_hi_lo = f90 // Data tables //============================================================== // DO NOT CHANGE ORDER OF THESE TABLES RODATA .align 16 LOCAL_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 // P1 LOCAL_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 // B3 LOCAL_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, 0x00003FFF LOCAL_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 0x1F32FB13 LOCAL_OBJECT_END(cosh_j_lo_table) .section .text GLOBAL_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 unnorm COSH_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| >= 0.25 COSH_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 // Get the remaining A,B coefficients { .mmi ldfe f_A3 = [r_ad3],16 nop.m 0 nop.i 0 } ;; // Use constant (1.100*2^(63-6)) to get rounded M into rightmost significand // |x| * 64 * 1/ln2 * 2^(63-6) + 1.1000 * 2^(63+(63-6)) { .mfi nop.m 0 fma.s1 f_M_temp = f_ABS_X, f_INV_LN2_2TO63, f_RSHF_2TO57 mov r_signexp_0_5 = 0x0fffe // signexp of +0.5 } ;; // Test for |x| >= overflow limit { .mfi ldfe f_B1 = [r_ad3],16 fcmp.ge.s1 p6,p0 = f_ABS_X, f_smlst_oflow_input nop.i 0 } ;; { .mfi ldfe f_B2 = [r_ad3],16 nop.f 0 mov r_exp_32 = 0x10004 } ;; // Subtract RSHF constant to get rounded M as a floating point value // M_temp * 2^(63-6) - 2^63 { .mfb ldfe f_B3 = [r_ad3],16 fms.s1 f_M = f_M_temp, f_2TOM57, f_RSHF (p6) br.cond.spnt COSH_HUGE // Branch if result will overflow } ;; { .mfi getf.sig r_M = f_M_temp nop.f 0 cmp.ge p7,p6 = r_exp_x, r_exp_32 // Test if x >= 32 } ;; // Calculate j. j is the signed extension of the six lsb of M. It // has a range of -32 thru 31. // Calculate R // ax - M*log2by64_hi // R = (ax - M*log2by64_hi) - M*log2by64_lo { .mfi nop.m 0 fnma.s1 f_R_temp = f_M, f_log2by64_hi, f_ABS_X and r_j = 0x3f, r_M } ;; { .mii nop.m 0 shl r_jshf = r_j, 0x2 // Shift j so can sign extend it ;; sxt1 r_jshf = r_jshf } ;; { .mii nop.m 0 shr r_j = r_jshf, 0x2 // Now j has range -32 to 31 nop.i 0 } ;; { .mmi shladd r_ad_J_hi = r_j, 4, r_ad4 // pointer to Tjhi sub r_Mmj = r_M, r_j // M-j sub r_mj = r0, r_j // Form -j } ;; // The TBL and EXP branches are merged and predicated // If TBL, p6 true, 0.25 <= |x| < 32 // If EXP, p7 true, 32 <= |x| < overflow_limit // // N = (M-j)/64 { .mfi ldfe f_Tjhi = [r_ad_J_hi] fnma.s1 f_R = f_M, f_log2by64_lo, f_R_temp shr r_N = r_Mmj, 0x6 // N = (M-j)/64 } { .mfi shladd r_ad_mJ_hi = r_mj, 4, r_ad4 // pointer to Tmjhi nop.f 0 shladd r_ad_mJ_lo = r_mj, 2, r_ad5 // pointer to Tmjlo } ;; { .mfi sub r_2mNm1 = r_signexp_0_5, r_N // signexp 2^(-N-1) nop.f 0 shladd r_ad_J_lo = r_j, 2, r_ad5 // pointer to Tjlo } { .mfi ldfe f_Tmjhi = [r_ad_mJ_hi] nop.f 0 add r_2Nm1 = r_signexp_0_5, r_N // signexp 2^(N-1) } ;; { .mmf ldfs f_Tmjlo = [r_ad_mJ_lo] setf.exp f_sneg = r_2mNm1 // Form 2^(-N-1) nop.f 0 } ;; { .mmf ldfs f_Tjlo = [r_ad_J_lo] setf.exp f_spos = r_2Nm1 // Form 2^(N-1) nop.f 0 } ;; // ****************************************************** // STEP 2 (TBL and EXP) // ****************************************************** // Calculate Rsquared and Rcubed in preparation for p_even and p_odd { .mmf nop.m 0 nop.m 0 fma.s1 f_Rsq = f_R, f_R, f0 } ;; // Calculate p_even // B_2 + Rsq *B_3 // B_1 + Rsq * (B_2 + Rsq *B_3) // p_even = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3)) { .mfi nop.m 0 fma.s1 f_peven_temp1 = f_Rsq, f_B3, f_B2 nop.i 0 } // Calculate p_odd // A_2 + Rsq *A_3 // A_1 + Rsq * (A_2 + Rsq *A_3) // podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3)) { .mfi nop.m 0 fma.s1 f_podd_temp1 = f_Rsq, f_A3, f_A2 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_Rcub = f_Rsq, f_R, f0 nop.i 0 } ;; // // If TBL, // Calculate S_hi and S_lo, and C_hi // SC_hi_temp = sneg * Tmjhi // S_hi = spos * Tjhi - SC_hi_temp // S_hi = spos * Tjhi - (sneg * Tmjhi) // C_hi = spos * Tjhi + SC_hi_temp // C_hi = spos * Tjhi + (sneg * Tmjhi) { .mfi nop.m 0 (p6) fma.s1 f_SC_hi_temp = f_sneg, f_Tmjhi, f0 nop.i 0 } ;; // If TBL, // C_lo_temp3 = sneg * Tmjlo // C_lo_temp4 = spos * Tjlo + C_lo_temp3 // C_lo_temp4 = spos * Tjlo + (sneg * Tmjlo) { .mfi nop.m 0 (p6) fma.s1 f_C_lo_temp3 = f_sneg, f_Tmjlo, f0 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_peven_temp2 = f_Rsq, f_peven_temp1, f_B1 nop.i 0 } { .mfi nop.m 0 fma.s1 f_podd_temp2 = f_Rsq, f_podd_temp1, f_A1 nop.i 0 } ;; // If EXP, // Compute 2^(N-1) * Tjhi and 2^(N-1) * Tjlo { .mfi nop.m 0 (p7) fma.s1 f_Tjhi_spos = f_Tjhi, f_spos, f0 nop.i 0 } { .mfi nop.m 0 (p7) fma.s1 f_Tjlo_spos = f_Tjlo, f_spos, f0 nop.i 0 } ;; { .mfi nop.m 0 (p6) fma.s1 f_C_hi = f_spos, f_Tjhi, f_SC_hi_temp nop.i 0 } ;; { .mfi nop.m 0 (p6) fms.s1 f_S_hi = f_spos, f_Tjhi, f_SC_hi_temp nop.i 0 } { .mfi nop.m 0 (p6) fma.s1 f_C_lo_temp4 = f_spos, f_Tjlo, f_C_lo_temp3 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_peven = f_Rsq, f_peven_temp2, f0 nop.i 0 } { .mfi nop.m 0 fma.s1 f_podd = f_podd_temp2, f_Rcub, f_R nop.i 0 } ;; // If TBL, // C_lo_temp1 = spos * Tjhi - C_hi // C_lo_temp2 = sneg * Tmjlo + C_lo_temp1 // C_lo_temp2 = sneg * Tmjlo + (spos * Tjhi - C_hi) { .mfi nop.m 0 (p6) fms.s1 f_C_lo_temp1 = f_spos, f_Tjhi, f_C_hi nop.i 0 } ;; { .mfi nop.m 0 (p6) fma.s1 f_C_lo_temp2 = f_sneg, f_Tmjhi, f_C_lo_temp1 nop.i 0 } ;; // If EXP, // Y_hi = 2^(N-1) * Tjhi // Y_lo = 2^(N-1) * Tjhi * (p_odd + p_even) + 2^(N-1) * Tjlo { .mfi nop.m 0 (p7) fma.s1 f_Y_lo_temp = f_peven, f1, f_podd nop.i 0 } ;; // If TBL, // C_lo = C_lo_temp4 + C_lo_temp2 { .mfi nop.m 0 (p6) fma.s1 f_C_lo = f_C_lo_temp4, f1, f_C_lo_temp2 nop.i 0 } ;; // If TBL, // Y_hi = C_hi // Y_lo = S_hi*p_odd + (C_hi*p_even + C_lo) { .mfi nop.m 0 (p6) fma.s1 f_Y_lo_temp = f_C_hi, f_peven, f_C_lo nop.i 0 } ;; { .mfi nop.m 0 (p7) fma.s1 f_Y_lo = f_Tjhi_spos, f_Y_lo_temp, f_Tjlo_spos nop.i 0 } ;; // Dummy multiply to generate inexact { .mfi nop.m 0 fmpy.s0 f_tmp = f_B2, f_B2 nop.i 0 } { .mfi nop.m 0 (p6) fma.s1 f_Y_lo = f_S_hi, f_podd, f_Y_lo_temp nop.i 0 } ;; // f8 = answer = Y_hi + Y_lo { .mfi nop.m 0 (p7) fma.s0 f8 = f_Y_lo, f1, f_Tjhi_spos nop.i 0 } ;; // f8 = answer = Y_hi + Y_lo { .mfb nop.m 0 (p6) fma.s0 f8 = f_Y_lo, f1, f_C_hi br.ret.sptk b0 // Exit for COSH_BY_TBL and COSH_BY_EXP } ;; // Here if 0 < |x| < 0.25 COSH_BY_POLY: { .mmf ldfe f_P6 = [r_ad2e],16 ldfe f_P5 = [r_ad2o],16 nop.f 0 } ;; { .mmi ldfe f_P4 = [r_ad2e],16 ldfe f_P3 = [r_ad2o],16 nop.i 0 } ;; { .mmi ldfe f_P2 = [r_ad2e],16 ldfe f_P1 = [r_ad2o],16 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_X3 = f_NORM_X, f_X2, f0 nop.i 0 } { .mfi nop.m 0 fma.s1 f_X4 = f_X2, f_X2, f0 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_poly65 = f_X2, f_P6, f_P5 nop.i 0 } { .mfi nop.m 0 fma.s1 f_poly43 = f_X2, f_P4, f_P3 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_poly21 = f_X2, f_P2, f_P1 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_poly6543 = f_X4, f_poly65, f_poly43 nop.i 0 } ;; { .mfi nop.m 0 fma.s1 f_poly6to1 = f_X4, f_poly6543, f_poly21 nop.i 0 } ;; // Dummy multiply to generate inexact { .mfi nop.m 0 fmpy.s0 f_tmp = f_P6, f_P6 nop.i 0 } { .mfb nop.m 0 fma.s0 f8 = f_poly6to1, f_X2, f1 br.ret.sptk b0 // Exit COSH_BY_POLY } ;; // Here if x denorm or unorm COSH_DENORM: // Determine if x really a denorm and not a unorm { .mmf getf.exp r_signexp_x = f_NORM_X mov r_exp_denorm = 0x0c001 // Real denorms have exp < this fmerge.s f_ABS_X = f0, f_NORM_X } ;; { .mfi nop.m 0 fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag nop.i 0 } ;; // Set p8 if really a denorm { .mmi and r_exp_x = r_exp_mask, r_signexp_x ;; cmp.lt p8,p9 = r_exp_x, r_exp_denorm nop.i 0 } ;; // Identify denormal operands. { .mfb nop.m 0 (p8) fma.s0 f8 = f8,f8,f1 // If x denorm, result=1+x^2 (p9) br.cond.sptk COSH_COMMON // Return to main path if x unorm } ;; { .mfb nop.m 0 nop.f 0 br.ret.sptk b0 // Exit if x denorm } ;; // Here if |x| >= overflow limit COSH_HUGE: // for COSH_HUGE, put 24000 in exponent; take sign from input { .mmi mov r_exp_huge = 0x15dbf ;; setf.exp f_huge = r_exp_huge nop.i 0 } ;; { .mfi alloc r32 = ar.pfs,0,5,4,0 fma.s1 f_signed_hi_lo = f_huge, f1, f1 nop.i 0 } ;; { .mfi nop.m 0 fma.s0 f_pre_result = f_signed_hi_lo, f_huge, f0 mov GR_Parameter_TAG = 63 } ;; GLOBAL_IEEE754_END(coshl) 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] = f0,16 // STORE 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] = f8 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 } { .mib stfe [GR_Parameter_Y] = f_pre_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 add GR_Parameter_RESULT = 48,sp nop.m 0 nop.i 0 };; { .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#