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Diffstat (limited to 'sysdeps/ia64/fpu/e_coshl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_coshl.S | 1095 |
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diff --git a/sysdeps/ia64/fpu/e_coshl.S b/sysdeps/ia64/fpu/e_coshl.S new file mode 100644 index 0000000..43da1ab --- /dev/null +++ b/sysdeps/ia64/fpu/e_coshl.S @@ -0,0 +1,1095 @@ +.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# |