|
|
.file "cosh.s"
// Copyright (c) 2000, 2001, Intel Corporation// All rights reserved.// // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.// // WARRANTY DISCLAIMER// // 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://developer.intel.com/opensource.//// History//==============================================================// 2/02/00 Initial version // 4/04/00 Unwind support added// 8/15/00 Bundle added after call to __libm_error_support to properly// set [the previously overwritten] GR_Parameter_RESULT.// 5/07/01 Reworked to improve speed of all paths//// API//==============================================================// double = cosh(double)// input floating point f8// output floating point f8//// Registers used//==============================================================// general registers: // r32 -> r47// 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| < 710.47586 COSH_BY_EXP (merged path with COSH_BY_TBL)// 4. |x| >= 710.47586 COSH_HUGE// 5. x=0 Done with early exit// 6. x=inf,nan Done with early exit// 7. x=denormal COSH_DENORM//// For double we get overflow for x >= 4008 b19e 747d cfc3 ed8b// >= 710.475860073////// 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| < 710.47586 ( 4008 b19e 747d cfc3 ed8b )// ==============// 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| >= 710.47586 ( 4008 b19e 747d cfc3 ed8b )// ============// Set error tag and call error support////// Assembly macros//==============================================================cosh_GR_ad1 = r34cosh_GR_Mmj = r34cosh_GR_jshf = r36cosh_GR_M = r35cosh_GR_N = r35cosh_GR_exp_2tom57 = r36cosh_GR_j = r36cosh_GR_joff = r36cosh_GR_exp_mask = r37cosh_GR_mJ = r38cosh_AD_mJ = r38cosh_GR_signexp_x = r38cosh_GR_signexp_0_5 = r38cosh_GR_exp_0_25 = r39cosh_GR_J = r39cosh_AD_J = r39cosh_GR_sig_inv_ln2 = r40cosh_GR_exp_32 = r40cosh_GR_exp_huge = r40cosh_GR_all_ones = r40
cosh_GR_ad2e = r41cosh_GR_ad3 = r42cosh_GR_ad4 = r43cosh_GR_rshf = r44cosh_GR_ad2o = r45cosh_GR_rshf_2to57 = r46cosh_GR_exp_denorm = r46cosh_GR_exp_x = r47
GR_SAVE_PFS = r41GR_SAVE_B0 = r42GR_SAVE_GP = r43
GR_Parameter_X = r44GR_Parameter_Y = r45GR_Parameter_RESULT = r46GR_Parameter_TAG = r47
cosh_FR_ABS_X = f9 cosh_FR_X2 = f10cosh_FR_X4 = f11cosh_FR_all_ones = f13cosh_FR_tmp = f14cosh_FR_RSHF = f15
cosh_FR_Inv_log2by64 = f32cosh_FR_log2by64_lo = f33cosh_FR_log2by64_hi = f34cosh_FR_A1 = f35
cosh_FR_A2 = f36cosh_FR_A3 = f37cosh_FR_Rcub = f38cosh_FR_M_temp = f39cosh_FR_R_temp = f40
cosh_FR_Rsq = f41cosh_FR_R = f42cosh_FR_M = f43cosh_FR_B1 = f44cosh_FR_B2 = f45
cosh_FR_B3 = f46cosh_FR_peven_temp1 = f47cosh_FR_peven_temp2 = f48cosh_FR_peven = f49cosh_FR_podd_temp1 = f50
cosh_FR_podd_temp2 = f51cosh_FR_podd = f52cosh_FR_poly65 = f53cosh_FR_poly6543 = f53cosh_FR_poly6to1 = f53cosh_FR_poly43 = f54cosh_FR_poly21 = f55
cosh_FR_INV_LN2_2TO63= f57cosh_FR_RSHF_2TO57 = f58cosh_FR_2TOM57 = f59cosh_FR_smlst_oflow_input = f60
cosh_FR_pre_result = f61cosh_FR_huge = f62cosh_FR_spos = f63cosh_FR_sneg = f64cosh_FR_Tjhi = f65
cosh_FR_Tjlo = f66cosh_FR_Tmjhi = f67cosh_FR_Tmjlo = f68cosh_FR_S_hi = f69cosh_FR_SC_hi_temp = f70
cosh_FR_C_lo_temp1 = f71 cosh_FR_C_lo_temp2 = f72 cosh_FR_C_lo_temp3 = f73 cosh_FR_C_lo_temp4 = f73 cosh_FR_C_lo = f74cosh_FR_C_hi = f75
cosh_FR_C_hi_temp1 = f76cosh_FR_Y_hi = f77 cosh_FR_Y_lo_temp = f78 cosh_FR_Y_lo = f79 cosh_FR_NORM_X = f80
cosh_FR_P1 = f81cosh_FR_P2 = f82cosh_FR_P3 = f83cosh_FR_P4 = f84cosh_FR_P5 = f85
cosh_FR_P6 = f86cosh_FR_Tjhi_spos = f87cosh_FR_Tjlo_spos = f88cosh_FR_huge = f89cosh_FR_signed_hi_lo = f90
// Data tables//==============================================================
// DO NOT CHANGE ORDER OF THESE TABLES.data
.align 16double_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
double_cosh_p_table: data8 0xb19e747dcfc3ed8b, 0x00004008 // Smallest x to overflow (710.47586) data8 0x8FA02AC65BCBD5BC, 0x00003FE2 // P6 data8 0xD00D00D1021D7370, 0x00003FEF // P4 data8 0xAAAAAAAAAAAAAB80, 0x00003FFA // P2 data8 0x93F27740C0C2F1CC, 0x00003FE9 // P5 data8 0xB60B60B60B4FE884, 0x00003FF5 // P3 data8 0x8000000000000000, 0x00003FFE // P1
double_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
double_cosh_j_table: data8 0xB504F333F9DE6484, 0x00003FFE, 0x1EB2FB13, 0x00000000 data8 0xB6FD91E328D17791, 0x00003FFE, 0x1CE2CBE2, 0x00000000 data8 0xB8FBAF4762FB9EE9, 0x00003FFE, 0x1DDC3CBC, 0x00000000 data8 0xBAFF5AB2133E45FB, 0x00003FFE, 0x1EE9AA34, 0x00000000 data8 0xBD08A39F580C36BF, 0x00003FFE, 0x9EAEFDC1, 0x00000000 data8 0xBF1799B67A731083, 0x00003FFE, 0x9DBF517B, 0x00000000 data8 0xC12C4CCA66709456, 0x00003FFE, 0x1EF88AFB, 0x00000000 data8 0xC346CCDA24976407, 0x00003FFE, 0x1E03B216, 0x00000000 data8 0xC5672A115506DADD, 0x00003FFE, 0x1E78AB43, 0x00000000 data8 0xC78D74C8ABB9B15D, 0x00003FFE, 0x9E7B1747, 0x00000000 data8 0xC9B9BD866E2F27A3, 0x00003FFE, 0x9EFE3C0E, 0x00000000 data8 0xCBEC14FEF2727C5D, 0x00003FFE, 0x9D36F837, 0x00000000 data8 0xCE248C151F8480E4, 0x00003FFE, 0x9DEE53E4, 0x00000000 data8 0xD06333DAEF2B2595, 0x00003FFE, 0x9E24AE8E, 0x00000000 data8 0xD2A81D91F12AE45A, 0x00003FFE, 0x1D912473, 0x00000000 data8 0xD4F35AABCFEDFA1F, 0x00003FFE, 0x1EB243BE, 0x00000000 data8 0xD744FCCAD69D6AF4, 0x00003FFE, 0x1E669A2F, 0x00000000 data8 0xD99D15C278AFD7B6, 0x00003FFE, 0x9BBC610A, 0x00000000 data8 0xDBFBB797DAF23755, 0x00003FFE, 0x1E761035, 0x00000000 data8 0xDE60F4825E0E9124, 0x00003FFE, 0x9E0BE175, 0x00000000 data8 0xE0CCDEEC2A94E111, 0x00003FFE, 0x1CCB12A1, 0x00000000 data8 0xE33F8972BE8A5A51, 0x00003FFE, 0x1D1BFE90, 0x00000000 data8 0xE5B906E77C8348A8, 0x00003FFE, 0x1DF2F47A, 0x00000000 data8 0xE8396A503C4BDC68, 0x00003FFE, 0x1EF22F22, 0x00000000 data8 0xEAC0C6E7DD24392F, 0x00003FFE, 0x9E3F4A29, 0x00000000 data8 0xED4F301ED9942B84, 0x00003FFE, 0x1EC01A5B, 0x00000000 data8 0xEFE4B99BDCDAF5CB, 0x00003FFE, 0x1E8CAC3A, 0x00000000 data8 0xF281773C59FFB13A, 0x00003FFE, 0x9DBB3FAB, 0x00000000 data8 0xF5257D152486CC2C, 0x00003FFE, 0x1EF73A19, 0x00000000 data8 0xF7D0DF730AD13BB9, 0x00003FFE, 0x9BB795B5, 0x00000000 data8 0xFA83B2DB722A033A, 0x00003FFE, 0x1EF84B76, 0x00000000 data8 0xFD3E0C0CF486C175, 0x00003FFE, 0x9EF5818B, 0x00000000 data8 0x8000000000000000, 0x00003FFF, 0x00000000, 0x00000000 data8 0x8164D1F3BC030773, 0x00003FFF, 0x1F77CACA, 0x00000000 data8 0x82CD8698AC2BA1D7, 0x00003FFF, 0x1EF8A91D, 0x00000000 data8 0x843A28C3ACDE4046, 0x00003FFF, 0x1E57C976, 0x00000000 data8 0x85AAC367CC487B15, 0x00003FFF, 0x9EE8DA92, 0x00000000 data8 0x871F61969E8D1010, 0x00003FFF, 0x1EE85C9F, 0x00000000 data8 0x88980E8092DA8527, 0x00003FFF, 0x1F3BF1AF, 0x00000000 data8 0x8A14D575496EFD9A, 0x00003FFF, 0x1D80CA1E, 0x00000000 data8 0x8B95C1E3EA8BD6E7, 0x00003FFF, 0x9D0373AF, 0x00000000 data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF, 0x9F167097, 0x00000000 data8 0x8EA4398B45CD53C0, 0x00003FFF, 0x1EB70051, 0x00000000 data8 0x9031DC431466B1DC, 0x00003FFF, 0x1F6EB029, 0x00000000 data8 0x91C3D373AB11C336, 0x00003FFF, 0x1DFD6D8E, 0x00000000 data8 0x935A2B2F13E6E92C, 0x00003FFF, 0x9EB319B0, 0x00000000 data8 0x94F4EFA8FEF70961, 0x00003FFF, 0x1EBA2BEB, 0x00000000 data8 0x96942D3720185A00, 0x00003FFF, 0x1F11D537, 0x00000000 data8 0x9837F0518DB8A96F, 0x00003FFF, 0x1F0D5A46, 0x00000000 data8 0x99E0459320B7FA65, 0x00003FFF, 0x9E5E7BCA, 0x00000000 data8 0x9B8D39B9D54E5539, 0x00003FFF, 0x9F3AAFD1, 0x00000000 data8 0x9D3ED9A72CFFB751, 0x00003FFF, 0x9E86DACC, 0x00000000 data8 0x9EF5326091A111AE, 0x00003FFF, 0x9F3EDDC2, 0x00000000 data8 0xA0B0510FB9714FC2, 0x00003FFF, 0x1E496E3D, 0x00000000 data8 0xA27043030C496819, 0x00003FFF, 0x9F490BF6, 0x00000000 data8 0xA43515AE09E6809E, 0x00003FFF, 0x1DD1DB48, 0x00000000 data8 0xA5FED6A9B15138EA, 0x00003FFF, 0x1E65EBFB, 0x00000000 data8 0xA7CD93B4E965356A, 0x00003FFF, 0x9F427496, 0x00000000 data8 0xA9A15AB4EA7C0EF8, 0x00003FFF, 0x1F283C4A, 0x00000000 data8 0xAB7A39B5A93ED337, 0x00003FFF, 0x1F4B0047, 0x00000000 data8 0xAD583EEA42A14AC6, 0x00003FFF, 0x1F130152, 0x00000000 data8 0xAF3B78AD690A4375, 0x00003FFF, 0x9E8367C0, 0x00000000 data8 0xB123F581D2AC2590, 0x00003FFF, 0x9F705F90, 0x00000000 data8 0xB311C412A9112489, 0x00003FFF, 0x1EFB3C53, 0x00000000 data8 0xB504F333F9DE6484, 0x00003FFF, 0x1F32FB13, 0x00000000
.align 32.global cosh#
.section .text.proc cosh#
.align 32
cosh:
{ .mlx alloc r32 = ar.pfs,0,12,4,0 movl cosh_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2}{ .mlx addl cosh_GR_ad1 = @ltoff(double_cosh_arg_reduction), gp movl cosh_GR_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57)};;
{ .mfi ld8 cosh_GR_ad1 = [cosh_GR_ad1] fmerge.s cosh_FR_ABS_X = f0,f8 mov cosh_GR_exp_0_25 = 0x0fffd // Form exponent for 0.25}{ .mfi nop.m 999 fnorm.s1 cosh_FR_NORM_X = f8 mov cosh_GR_exp_2tom57 = 0xffff-57};;
{ .mfi setf.d cosh_FR_RSHF_2TO57 = cosh_GR_rshf_2to57 // Form const 1.100 * 2^120 fclass.m p10,p0 = f8, 0x0b // Test for denorm mov cosh_GR_exp_mask = 0x1ffff }{ .mlx setf.sig cosh_FR_INV_LN2_2TO63 = cosh_GR_sig_inv_ln2 // Form 1/ln2 * 2^63 movl cosh_GR_rshf = 0x43e8000000000000 // 1.10000 2^63 for right shift};;
{ .mfi getf.exp cosh_GR_signexp_x = f8 // Extract signexp of x fclass.m p7,p0 = f8, 0x07 // Test if x=0 nop.i 999}{ .mfi setf.exp cosh_FR_2TOM57 = cosh_GR_exp_2tom57 // Form 2^-57 for scaling nop.f 999 add cosh_GR_ad3 = 0x90, cosh_GR_ad1 // Point to ab_table};;
{ .mfi setf.d cosh_FR_RSHF = cosh_GR_rshf // Form right shift const 1.100 * 2^63 fclass.m p6,p0 = f8, 0xc3 // Test if x nan add cosh_GR_ad4 = 0x4f0, cosh_GR_ad1 // Point to j_table midpoint}{ .mib add cosh_GR_ad2e = 0x20, cosh_GR_ad1 // Point to p_table mov cosh_GR_all_ones = -1(p10) br.cond.spnt COSH_DENORM // Branch if x denorm};;
// Common path -- return here from COSH_DENORM if x is unnormCOSH_COMMON:{ .mfi ldfe cosh_FR_smlst_oflow_input = [cosh_GR_ad2e],16 fclass.m p10,p0 = f8, 0x23 // Test if x inf and cosh_GR_exp_x = cosh_GR_exp_mask, cosh_GR_signexp_x}{ .mfb ldfe cosh_FR_log2by64_hi = [cosh_GR_ad1],16 (p7) fma.d.s0 f8 = f1,f1,f0 // If x=0, result is 1.0(p7) br.ret.spnt b0 // Exit if x=0};;
{ .mfi// Make constant that will generate inexact when squared setf.sig cosh_FR_all_ones = cosh_GR_all_ones nop.f 999 cmp.ge p7,p0 = cosh_GR_exp_x, cosh_GR_exp_0_25 // Test x < 0.25}{ .mfb add cosh_GR_ad2o = 0x30, cosh_GR_ad2e // Point to p_table odd coeffs(p6) fma.d.s0 f8 = f8,f1,f8 // If x nan, return quietized nan(p6) br.ret.spnt b0 // Exit for x nan};;
// Get the A coefficients for COSH_BY_TBL// Calculate X2 = ax*ax for COSH_BY_POLY{ .mfi ldfe cosh_FR_log2by64_lo = [cosh_GR_ad1],16 (p10) fmerge.s f8 = f0, f8 // If x inf, result is +inf nop.i 999}{ .mfb ldfe cosh_FR_A1 = [cosh_GR_ad3],16 fma.s1 cosh_FR_X2 = cosh_FR_ABS_X, cosh_FR_ABS_X, f0(p7) br.cond.sptk COSH_BY_TBL};;
// Here if 0 < |x| < 0.25COSH_BY_POLY: { .mmf ldfe cosh_FR_P6 = [cosh_GR_ad2e],16 ldfe cosh_FR_P5 = [cosh_GR_ad2o],16 nop.f 999};;
{ .mmi ldfe cosh_FR_P4 = [cosh_GR_ad2e],16 ldfe cosh_FR_P3 = [cosh_GR_ad2o],16 nop.i 999};;
{ .mmi ldfe cosh_FR_P2 = [cosh_GR_ad2e],16 ldfe cosh_FR_P1 = [cosh_GR_ad2o],16 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_X4 = cosh_FR_X2, cosh_FR_X2, f0 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_poly65 = cosh_FR_X2, cosh_FR_P6, cosh_FR_P5 nop.i 999}{ .mfi nop.m 999 fma.s1 cosh_FR_poly43 = cosh_FR_X2, cosh_FR_P4, cosh_FR_P3 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_poly21 = cosh_FR_X2, cosh_FR_P2, cosh_FR_P1 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_poly6543 = cosh_FR_X4, cosh_FR_poly65, cosh_FR_poly43 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_poly6to1 = cosh_FR_X4, cosh_FR_poly6543, cosh_FR_poly21 nop.i 999};;
// Dummy multiply to generate inexact{ .mfi nop.m 999 fmpy.s0 cosh_FR_tmp = cosh_FR_all_ones, cosh_FR_all_ones nop.i 999}{ .mfb nop.m 999 fma.d.s0 f8 = cosh_FR_poly6to1, cosh_FR_X2, f1 br.ret.sptk b0 // Exit 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.// cosh_FR_spos = 2^(N-1) and cosh_FR_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)// cosh_FR_M = M = truncate(ax/(log2/64))// Put the integer representation of M in cosh_GR_M// and the floating point representation of M in cosh_FR_M
// Get the remaining A,B coefficients{ .mfb ldfe cosh_FR_A2 = [cosh_GR_ad3],16 nop.f 999(p10) br.ret.spnt b0 // Exit if x inf};;
{ .mmi ldfe cosh_FR_A3 = [cosh_GR_ad3],16 ;;
ldfe cosh_FR_B1 = [cosh_GR_ad3],16 nop.i 999};;
// 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 999 fma.s1 cosh_FR_M_temp = cosh_FR_ABS_X, cosh_FR_INV_LN2_2TO63, cosh_FR_RSHF_2TO57 mov cosh_GR_signexp_0_5 = 0x0fffe // signexp of +0.5};;
// Test for |x| >= overflow limit{ .mfi nop.m 999 fcmp.ge.s1 p6,p0 = cosh_FR_ABS_X, cosh_FR_smlst_oflow_input nop.i 999};;
{ .mfi ldfe cosh_FR_B2 = [cosh_GR_ad3],16 nop.f 999 nop.i 999};;
// Subtract RSHF constant to get rounded M as a floating point value// M_temp * 2^(63-6) - 2^63{ .mfb ldfe cosh_FR_B3 = [cosh_GR_ad3],16 fms.s1 cosh_FR_M = cosh_FR_M_temp, cosh_FR_2TOM57, cosh_FR_RSHF(p6) br.cond.spnt COSH_HUGE // Branch if result will overflow};;
{ .mfi getf.sig cosh_GR_M = cosh_FR_M_temp nop.f 999 nop.i 999};;
// 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 999 fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_ABS_X and cosh_GR_j = 0x3f, cosh_GR_M};;
{ .mii nop.m 999 shl cosh_GR_jshf = cosh_GR_j, 0x2 ;; // Shift j so can sign extend it
sxt1 cosh_GR_jshf = cosh_GR_jshf};;
// N = (M-j)/64{ .mii mov cosh_GR_exp_32 = 0x10004 shr cosh_GR_j = cosh_GR_jshf, 0x2 ;; // Now j has range -32 to 31
sub cosh_GR_Mmj = cosh_GR_M, cosh_GR_j ;; // M-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//{ .mfi cmp.ge p7,p6 = cosh_GR_exp_x, cosh_GR_exp_32 // Test if x >= 32 fnma.s1 cosh_FR_R = cosh_FR_M, cosh_FR_log2by64_lo, cosh_FR_R_temp shr cosh_GR_N = cosh_GR_Mmj, 0x6 // N = (M-j)/64 };;
{ .mmi sub r40 = cosh_GR_signexp_0_5, cosh_GR_N // signexp of 2^(-N-1) add r39 = cosh_GR_signexp_0_5, cosh_GR_N // signexp of 2^(N-1) shl cosh_GR_joff = cosh_GR_j,5 // Make j offset to j_table};;
{ .mfi setf.exp cosh_FR_spos = r39 // Form 2^(N-1) nop.f 999 sub cosh_GR_mJ = r0, cosh_GR_joff // Table offset for -j}{ .mfi setf.exp cosh_FR_sneg = r40 // Form 2^(-N-1) nop.f 999 add cosh_GR_J = r0, cosh_GR_joff // Table offset for +j};;
// Get the address of the J table midpoint, add the offset { .mmf add cosh_AD_mJ = cosh_GR_ad4, cosh_GR_mJ add cosh_AD_J = cosh_GR_ad4, cosh_GR_J nop.f 999};;
{ .mmf ldfe cosh_FR_Tmjhi = [cosh_AD_mJ],16 ldfe cosh_FR_Tjhi = [cosh_AD_J],16 nop.f 999};;
// ******************************************************// STEP 2 (TBL and EXP)// ******************************************************// Calculate Rsquared and Rcubed in preparation for p_even and p_odd
{ .mmf ldfs cosh_FR_Tmjlo = [cosh_AD_mJ],16 ldfs cosh_FR_Tjlo = [cosh_AD_J],16 fma.s1 cosh_FR_Rsq = cosh_FR_R, cosh_FR_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 999 fma.s1 cosh_FR_peven_temp1 = cosh_FR_Rsq, cosh_FR_B3, cosh_FR_B2 nop.i 999}// 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 999 fma.s1 cosh_FR_podd_temp1 = cosh_FR_Rsq, cosh_FR_A3, cosh_FR_A2 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_FR_R, f0 nop.i 999};;
// // If TBL, // Calculate C_hi and C_lo, and S_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 999(p6) fma.s1 cosh_FR_SC_hi_temp = cosh_FR_sneg, cosh_FR_Tmjhi, f0 nop.i 999};;
// 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 999(p6) fma.s1 cosh_FR_C_lo_temp3 = cosh_FR_sneg, cosh_FR_Tmjlo, f0 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_peven_temp2 = cosh_FR_Rsq, cosh_FR_peven_temp1, cosh_FR_B1 nop.i 999}{ .mfi nop.m 999 fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1 nop.i 999};;
// If EXP, // Compute 2^(N-1) * Tjhi and 2^(N-1) * Tjlo{ .mfi nop.m 999(p7) fma.s1 cosh_FR_Tjhi_spos = cosh_FR_Tjhi, cosh_FR_spos, f0 nop.i 999}{ .mfi nop.m 999(p7) fma.s1 cosh_FR_Tjlo_spos = cosh_FR_Tjlo, cosh_FR_spos, f0 nop.i 999};;
{ .mfi nop.m 999(p6) fma.s1 cosh_FR_C_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_SC_hi_temp nop.i 999};;
{ .mfi nop.m 999(p6) fms.s1 cosh_FR_S_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_SC_hi_temp nop.i 999}{ .mfi nop.m 999(p6) fma.s1 cosh_FR_C_lo_temp4 = cosh_FR_spos, cosh_FR_Tjlo, cosh_FR_C_lo_temp3 nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0 nop.i 999}{ .mfi nop.m 999 fma.s1 cosh_FR_podd = cosh_FR_podd_temp2, cosh_FR_Rcub, cosh_FR_R nop.i 999};;
// 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 999(p6) fms.s1 cosh_FR_C_lo_temp1 = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi nop.i 999};;
{ .mfi nop.m 999(p6) fma.s1 cosh_FR_C_lo_temp2 = cosh_FR_sneg, cosh_FR_Tmjhi, cosh_FR_C_lo_temp1 nop.i 999};;
// 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 999(p7) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd nop.i 999};;
// If TBL,// C_lo = C_lo_temp4 + C_lo_temp2{ .mfi nop.m 999(p6) fma.s1 cosh_FR_C_lo = cosh_FR_C_lo_temp4, f1, cosh_FR_C_lo_temp2 nop.i 999};;
// If TBL,// Y_hi = C_hi // Y_lo = S_hi*p_odd + (C_hi*p_even + C_lo){ .mfi nop.m 999(p6) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_C_hi, cosh_FR_peven, cosh_FR_C_lo nop.i 999};;
{ .mfi nop.m 999(p7) fma.s1 cosh_FR_Y_lo = cosh_FR_Tjhi_spos, cosh_FR_Y_lo_temp, cosh_FR_Tjlo_spos nop.i 999};;
// Dummy multiply to generate inexact{ .mfi nop.m 999 fmpy.s0 cosh_FR_tmp = cosh_FR_all_ones, cosh_FR_all_ones nop.i 999}{ .mfi nop.m 999(p6) fma.s1 cosh_FR_Y_lo = cosh_FR_S_hi, cosh_FR_podd, cosh_FR_Y_lo_temp nop.i 999};;
// f8 = answer = Y_hi + Y_lo{ .mfi nop.m 999(p7) fma.d.s0 f8 = cosh_FR_Y_lo, f1, cosh_FR_Tjhi_spos nop.i 999};;
// f8 = answer = Y_hi + Y_lo{ .mfb nop.m 999(p6) fma.d.s0 f8 = cosh_FR_Y_lo, f1, cosh_FR_C_hi br.ret.sptk b0 // Exit for COSH_BY_TBL and COSH_BY_EXP};;
// Here if x denorm or unormCOSH_DENORM:// Determine if x really a denorm and not a unorm{ .mmf getf.exp cosh_GR_signexp_x = cosh_FR_NORM_X mov cosh_GR_exp_denorm = 0x0fc01 // Real denorms will have exp < this fmerge.s cosh_FR_ABS_X = f0, cosh_FR_NORM_X};;
{ .mfi nop.m 999 fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag nop.i 999};;
// Set p8 if really a denorm{ .mmi and cosh_GR_exp_x = cosh_GR_exp_mask, cosh_GR_signexp_x ;;
cmp.lt p8,p9 = cosh_GR_exp_x, cosh_GR_exp_denorm nop.i 999};;
{ .mfb nop.m 999(p8) fma.d.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 999 nop.f 999 br.ret.sptk b0 // Exit if x denorm};;
// Here if |x| >= overflow limitCOSH_HUGE: // for COSH_HUGE, put 24000 in exponent{ .mmi mov cosh_GR_exp_huge = 0x15dbf ;;
setf.exp cosh_FR_huge = cosh_GR_exp_huge nop.i 999};;
{ .mfi nop.m 999 fma.s1 cosh_FR_signed_hi_lo = cosh_FR_huge, f1, f1 nop.i 999};;
{ .mfi nop.m 999 fma.d.s0 cosh_FR_pre_result = cosh_FR_signed_hi_lo, cosh_FR_huge, f0 mov GR_Parameter_TAG = 64};;
.endp cosh
// Stack operations when calling error support.// (1) (2) (3) (call) (4)// sp -> + psp -> + psp -> + sp -> +// | | | |// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8// | | | |// | <-GR_Y Y2->| Y2 ->| <- GR_Y |// | | | |// | | <- GR_X X1 ->| |// | | | |// sp-64 -> + sp -> + sp -> + +// save ar.pfs save b0 restore gp// save gp restore ar.pfs
.proc __libm_error_region__libm_error_region:COSH_ERROR_SUPPORT:.prologue
// (1){ .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};;
// (2){ .mmi stfd [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// (3){ .mib stfd [GR_Parameter_X] = f8 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 }{ .mib stfd [GR_Parameter_Y] = cosh_FR_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 nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp};;
// (4){ .mmi ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack.restore 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};;
.endp __libm_error_region
.type __libm_error_support#,@function
.global __libm_error_support#
|
