about summary refs log tree commit diff
path: root/sysdeps/ia64/fpu/e_coshl.S
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/ia64/fpu/e_coshl.S')
-rw-r--r--sysdeps/ia64/fpu/e_coshl.S1095
1 files changed, 1095 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_coshl.S b/sysdeps/ia64/fpu/e_coshl.S
new file mode 100644
index 0000000000..43da1ab04d
--- /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#