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-rw-r--r--sysdeps/ia64/fpu/e_cosh.S1477
1 files changed, 593 insertions, 884 deletions
diff --git a/sysdeps/ia64/fpu/e_cosh.S b/sysdeps/ia64/fpu/e_cosh.S
index 205653d4bf..0c6c5b451e 100644
--- a/sysdeps/ia64/fpu/e_cosh.S
+++ b/sysdeps/ia64/fpu/e_cosh.S
@@ -1,10 +1,10 @@
.file "cosh.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2002, 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.
+//
+// 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
@@ -20,1081 +20,799 @@
// * 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
+
+// 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
+// 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
+// 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.
-//
+// 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.
+// problem reports or change requests be submitted to it directly at
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// 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
+// 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.
-//
+// 05/07/01 Reworked to improve speed of all paths
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 11/15/02 Improved speed with new algorithm
+
// API
//==============================================================
-// double = cosh(double)
-// input floating point f8
-// output floating point f8
-
+// double cosh(double)
// Overview of operation
//==============================================================
-// There are four paths
+// Case 1: 0 < |x| < 0.25
+// Evaluate cosh(x) by a 12th order polynomial
+// Care is take for the order of multiplication; and A2 is not exactly 1/4!,
+// A3 is not exactly 1/6!, etc.
+// cosh(x) = 1 + (A1*x^2 + A2*x^4 + A3*x^6 + A4*x^8 + A5*x^10 + A6*x^12)
+//
+// Case 2: 0.25 < |x| < 710.47586
+// Algorithm is based on the identity cosh(x) = ( exp(x) + exp(-x) ) / 2.
+// The algorithm for exp is described as below. There are a number of
+// economies from evaluating both exp(x) and exp(-x). Although we
+// are evaluating both quantities, only where the quantities diverge do we
+// duplicate the computations. The basic algorithm for exp(x) is described
+// below.
+//
+// Take the input x. w is "how many log2/128 in x?"
+// w = x * 128/log2
+// n = int(w)
+// x = n log2/128 + r + delta
-// 1. |x| < 0.25 COSH_BY_POLY
-// 2. |x| < 32 COSH_BY_TBL
-// 3. |x| < 2^14 COSH_BY_EXP
-// 4. |x_ >= 2^14 COSH_HUGE
+// n = 128M + index_1 + 2^4 index_2
+// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
-// For paths 1, and 2 SAFE is always 1.
-// For path 4, Safe is always 0.
-// SAFE = 1 means we cannot overflow.
+// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
+// Construct 2^M
+// Get 2^(index_1/128) from table_1;
+// Get 2^(index_2/8) from table_2;
+// Calculate exp(r) by 5th order polynomial
+// r = x - n (log2/128)_high
+// delta = - n (log2/128)_low
+// Calculate exp(delta) as 1 + delta
-#include "libm_support.h"
-// Assembly macros
+// Special values
//==============================================================
-cosh_FR_X = f44
-cosh_FR_SGNX = f40
-
-cosh_FR_Inv_log2by64 = f9
-cosh_FR_log2by64_lo = f11
-cosh_FR_log2by64_hi = f10
-
-cosh_FR_A1 = f9
-cosh_FR_A2 = f10
-cosh_FR_A3 = f11
-
-cosh_FR_Rcub = f12
-cosh_FR_M_temp = f13
-cosh_FR_R_temp = f13
-cosh_FR_Rsq = f13
-cosh_FR_R = f14
-
-cosh_FR_M = f38
-
-cosh_FR_B1 = f15
-cosh_FR_B2 = f32
-cosh_FR_B3 = f33
-
-cosh_FR_peven_temp1 = f34
-cosh_FR_peven_temp2 = f35
-cosh_FR_peven = f36
-
-cosh_FR_podd_temp1 = f34
-cosh_FR_podd_temp2 = f35
-cosh_FR_podd = f37
-
-cosh_FR_J_temp = f9
-cosh_FR_J = f10
+// cosh(+0) = 1.0
+// cosh(-0) = 1.0
-cosh_FR_Mmj = f39
+// cosh(+qnan) = +qnan
+// cosh(-qnan) = -qnan
+// cosh(+snan) = +qnan
+// cosh(-snan) = -qnan
-cosh_FR_N_temp1 = f11
-cosh_FR_N_temp2 = f12
-cosh_FR_N = f13
+// cosh(-inf) = +inf
+// cosh(+inf) = +inf
-cosh_FR_spos = f14
-cosh_FR_sneg = f15
-
-cosh_FR_Tjhi = f32
-cosh_FR_Tjlo = f33
-cosh_FR_Tmjhi = f34
-cosh_FR_Tmjlo = f35
-
-GR_mJ = r35
-GR_J = r36
-
-AD_mJ = r38
-AD_J = r39
-
-cosh_FR_C_hi = f9
-cosh_FR_C_hi_temp = f10
-cosh_FR_C_lo_temp1 = f11
-cosh_FR_C_lo_temp2 = f12
-cosh_FR_C_lo_temp3 = f13
-
-cosh_FR_C_lo = f38
-cosh_FR_S_hi = f39
-
-cosh_FR_S_hi_temp1 = f10
-cosh_FR_Y_hi = f11
-cosh_FR_Y_lo_temp = f12
-cosh_FR_Y_lo = f13
-cosh_FR_COSH = f9
-
-cosh_FR_X2 = f9
-cosh_FR_X4 = f10
-
-cosh_FR_P1 = f14
-cosh_FR_P2 = f15
-cosh_FR_P3 = f32
-cosh_FR_P4 = f33
-cosh_FR_P5 = f34
-cosh_FR_P6 = f35
-
-cosh_FR_TINY_THRESH = f9
-
-cosh_FR_COSH_temp = f10
-cosh_FR_SCALE = f11
+// Overflow and Underflow
+//=======================
+// cosh(x) = largest double normal when
+// x = 710.47586 = 0x408633ce8fb9f87d
+//
+// There is no underflow.
-cosh_FR_hi_lo = f10
+// Registers used
+//==============================================================
+// Floating Point registers used:
+// f8, input, output
+// f6 -> f15, f32 -> f61
-cosh_FR_poly_podd_temp1 = f11
-cosh_FR_poly_podd_temp2 = f13
-cosh_FR_poly_peven_temp1 = f11
-cosh_FR_poly_peven_temp2 = f13
+// General registers used:
+// r14 -> r40
-GR_SAVE_PFS = r41
-GR_SAVE_B0 = r42
-GR_SAVE_GP = r43
+// Predicate registers used:
+// p6 -> p15
-GR_Parameter_X = r44
-GR_Parameter_Y = r45
-GR_Parameter_RESULT = r46
+// Assembly macros
+//==============================================================
+rRshf = r14
+rN_neg = r14
+rAD_TB1 = r15
+rAD_TB2 = r16
+rAD_P = r17
+rN = r18
+rIndex_1 = r19
+rIndex_2_16 = r20
+rM = r21
+rBiased_M = r21
+rSig_inv_ln2 = r22
+rIndex_1_neg = r22
+rExp_bias = r23
+rExp_bias_minus_1 = r23
+rExp_mask = r24
+rTmp = r24
+rGt_ln = r24
+rIndex_2_16_neg = r24
+rM_neg = r25
+rBiased_M_neg = r25
+rRshf_2to56 = r26
+rAD_T1_neg = r26
+rExp_2tom56 = r28
+rAD_T2_neg = r28
+rAD_T1 = r29
+rAD_T2 = r30
+rSignexp_x = r31
+rExp_x = r31
+
+GR_SAVE_B0 = r33
+GR_SAVE_PFS = r34
+GR_SAVE_GP = r35
+GR_SAVE_SP = r36
+
+GR_Parameter_X = r37
+GR_Parameter_Y = r38
+GR_Parameter_RESULT = r39
+GR_Parameter_TAG = r40
+
+
+FR_X = f10
+FR_Y = f1
+FR_RESULT = f8
+
+fRSHF_2TO56 = f6
+fINV_LN2_2TO63 = f7
+fW_2TO56_RSH = f9
+f2TOM56 = f11
+fP5 = f12
+fP4 = f13
+fP3 = f14
+fP2 = f15
+
+fLn2_by_128_hi = f33
+fLn2_by_128_lo = f34
+
+fRSHF = f35
+fNfloat = f36
+fNormX = f37
+fR = f38
+fF = f39
+
+fRsq = f40
+f2M = f41
+fS1 = f42
+fT1 = f42
+fS2 = f43
+fT2 = f43
+fS = f43
+fWre_urm_f8 = f44
+fAbsX = f44
+
+fMIN_DBL_OFLOW_ARG = f45
+fMAX_DBL_NORM_ARG = f46
+fXsq = f47
+fX4 = f48
+fGt_pln = f49
+fTmp = f49
+
+fP54 = f50
+fP5432 = f50
+fP32 = f51
+fP = f52
+fP54_neg = f53
+fP5432_neg = f53
+fP32_neg = f54
+fP_neg = f55
+fF_neg = f56
+
+f2M_neg = f57
+fS1_neg = f58
+fT1_neg = f58
+fS2_neg = f59
+fT2_neg = f59
+fS_neg = f59
+fExp = f60
+fExp_neg = f61
+
+fA6 = f50
+fA65 = f50
+fA6543 = f50
+fA654321 = f50
+fA5 = f51
+fA4 = f52
+fA43 = f52
+fA3 = f53
+fA2 = f54
+fA21 = f54
+fA1 = f55
// Data tables
//==============================================================
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
+RODATA
.align 16
-double_cosh_arg_reduction:
-ASM_TYPE_DIRECTIVE(double_cosh_arg_reduction,@object)
- data8 0xB8AA3B295C17F0BC, 0x00004005
- data8 0xB17217F7D1000000, 0x00003FF8
- data8 0xCF79ABC9E3B39804, 0x00003FD0
-ASM_SIZE_DIRECTIVE(double_cosh_arg_reduction)
-
-double_cosh_p_table:
-ASM_TYPE_DIRECTIVE(double_cosh_p_table,@object)
- data8 0x8000000000000000, 0x00003FFE
- data8 0xAAAAAAAAAAAAAB80, 0x00003FFA
- data8 0xB60B60B60B4FE884, 0x00003FF5
- data8 0xD00D00D1021D7370, 0x00003FEF
- data8 0x93F27740C0C2F1CC, 0x00003FE9
- data8 0x8FA02AC65BCBD5BC, 0x00003FE2
-ASM_SIZE_DIRECTIVE(double_cosh_p_table)
-
-double_cosh_ab_table:
-ASM_TYPE_DIRECTIVE(double_cosh_ab_table,@object)
- data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC
- data8 0x88888888884ECDD5, 0x00003FF8
- data8 0xD00D0C6DCC26A86B, 0x00003FF2
- data8 0x8000000000000002, 0x00003FFE
- data8 0xAAAAAAAAAA402C77, 0x00003FFA
- data8 0xB60B6CC96BDB144D, 0x00003FF5
-ASM_SIZE_DIRECTIVE(double_cosh_ab_table)
-
-double_cosh_j_table:
-ASM_TYPE_DIRECTIVE(double_cosh_j_table,@object)
- 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
-ASM_SIZE_DIRECTIVE(double_cosh_j_table)
-
-.align 32
-.global cosh#
-.section .text
-.proc cosh#
-.align 32
+// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
-cosh:
+// double-extended 1/ln(2)
+// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
+// 3fff b8aa 3b29 5c17 f0bc
+// For speed the significand will be loaded directly with a movl and setf.sig
+// and the exponent will be bias+63 instead of bias+0. Thus subsequent
+// computations need to scale appropriately.
+// The constant 128/ln(2) is needed for the computation of w. This is also
+// obtained by scaling the computations.
+//
+// Two shifting constants are loaded directly with movl and setf.d.
+// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7)
+// This constant is added to x*1/ln2 to shift the integer part of
+// x*128/ln2 into the rightmost bits of the significand.
+// The result of this fma is fW_2TO56_RSH.
+// 2. fRSHF = 1.1000..00 * 2^(63)
+// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give
+// the integer part of w, n, as a floating-point number.
+// The result of this fms is fNfloat.
+
+
+LOCAL_OBJECT_START(exp_table_1)
+data8 0x408633ce8fb9f87e // smallest dbl overflow arg
+data8 0x408633ce8fb9f87d // largest dbl arg to give normal dbl result
+data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
+data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
+//
+// Table 1 is 2^(index_1/128) where
+// index_1 goes from 0 to 15
+//
+data8 0x8000000000000000 , 0x00003FFF
+data8 0x80B1ED4FD999AB6C , 0x00003FFF
+data8 0x8164D1F3BC030773 , 0x00003FFF
+data8 0x8218AF4373FC25EC , 0x00003FFF
+data8 0x82CD8698AC2BA1D7 , 0x00003FFF
+data8 0x8383594EEFB6EE37 , 0x00003FFF
+data8 0x843A28C3ACDE4046 , 0x00003FFF
+data8 0x84F1F656379C1A29 , 0x00003FFF
+data8 0x85AAC367CC487B15 , 0x00003FFF
+data8 0x8664915B923FBA04 , 0x00003FFF
+data8 0x871F61969E8D1010 , 0x00003FFF
+data8 0x87DB357FF698D792 , 0x00003FFF
+data8 0x88980E8092DA8527 , 0x00003FFF
+data8 0x8955EE03618E5FDD , 0x00003FFF
+data8 0x8A14D575496EFD9A , 0x00003FFF
+data8 0x8AD4C6452C728924 , 0x00003FFF
+LOCAL_OBJECT_END(exp_table_1)
+
+// Table 2 is 2^(index_1/8) where
+// index_2 goes from 0 to 7
+LOCAL_OBJECT_START(exp_table_2)
+data8 0x8000000000000000 , 0x00003FFF
+data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
+data8 0x9837F0518DB8A96F , 0x00003FFF
+data8 0xA5FED6A9B15138EA , 0x00003FFF
+data8 0xB504F333F9DE6484 , 0x00003FFF
+data8 0xC5672A115506DADD , 0x00003FFF
+data8 0xD744FCCAD69D6AF4 , 0x00003FFF
+data8 0xEAC0C6E7DD24392F , 0x00003FFF
+LOCAL_OBJECT_END(exp_table_2)
+
+LOCAL_OBJECT_START(exp_p_table)
+data8 0x3f8111116da21757 //P5
+data8 0x3fa55555d787761c //P4
+data8 0x3fc5555555555414 //P3
+data8 0x3fdffffffffffd6a //P2
+LOCAL_OBJECT_END(exp_p_table)
+
+LOCAL_OBJECT_START(cosh_p_table)
+data8 0x8FA02AC65BCBD5BC, 0x00003FE2 // A6
+data8 0xD00D00D1021D7370, 0x00003FEF // A4
+data8 0xAAAAAAAAAAAAAB80, 0x00003FFA // A2
+data8 0x93F27740C0C2F1CC, 0x00003FE9 // A5
+data8 0xB60B60B60B4FE884, 0x00003FF5 // A3
+data8 0x8000000000000000, 0x00003FFE // A1
+LOCAL_OBJECT_END(cosh_p_table)
-#ifdef _LIBC
-.global __ieee754_cosh#
-.proc __ieee754_cosh#
-__ieee754_cosh:
-#endif
-// X NAN?
+.section .text
+GLOBAL_IEEE754_ENTRY(cosh)
-{ .mfi
- alloc r32 = ar.pfs,0,12,4,0
-(p0) fclass.m.unc p6,p7 = f8, 0xc3 //@snan | @qnan
- nop.i 999
+{ .mlx
+ getf.exp rSignexp_x = f8 // Must recompute if x unorm
+ movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
}
-;;
-
-
-{ .mfb
- nop.m 999
-(p6) fma.d.s0 f8 = f8,f1,f8
-(p6) br.ret.spnt b0 ;;
+{ .mlx
+ addl rAD_TB1 = @ltoff(exp_table_1), gp
+ movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
}
+;;
-
-// X infinity
{ .mfi
- nop.m 999
-(p0) fclass.m.unc p6,p0 = f8, 0x23 //@inf
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p6) fmerge.s f8 = f0,f8
-(p6) br.ret.spnt b0 ;;
+ ld8 rAD_TB1 = [rAD_TB1]
+ fclass.m p6,p0 = f8,0x0b // Test for x=unorm
+ mov rExp_mask = 0x1ffff
}
-
-
-
-// Put 0.25 in f9; p6 true if x < 0.25
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x000000000000fffd ;;
-}
-
{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ mov rExp_bias = 0xffff
+ fnorm.s1 fNormX = f8
+ mov rExp_2tom56 = 0xffff-56
}
+;;
+
+// Form two constants we need
+// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
+// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
{ .mfi
- nop.m 999
-(p0) fmerge.s cosh_FR_X = f0,f8
+ setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63
+ fclass.m p8,p0 = f8,0x07 // Test for x=0
nop.i 999
}
-
-{ .mfi
- nop.m 999
-(p0) fmerge.s cosh_FR_SGNX = f8,f1
- nop.i 999 ;;
+{ .mlx
+ setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56)
+ movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
}
+;;
{ .mfi
- nop.m 999
-(p0) fcmp.lt.unc p0,p7 = cosh_FR_X,f9
- nop.i 999 ;;
+ ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_NORM_ARG = [rAD_TB1],16
+ fclass.m p10,p0 = f8,0x1e3 // Test for x=inf, nan, NaT
+ nop.i 0
}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p7) br.cond.sptk L(COSH_BY_TBL)
+{ .mfb
+ setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat
+ nop.f 0
+(p6) br.cond.spnt COSH_UNORM // Branch if x=unorm
}
;;
-
-// COSH_BY_POLY:
-// POLY cannot overflow so there is no need to call __libm_error_support
-// Get the values of P_x from the table
-
-{ .mmi
- nop.m 999
-(p0) addl r34 = @ltoff(double_cosh_p_table), gp
- nop.i 999
+COSH_COMMON:
+{ .mfi
+ ldfe fLn2_by_128_hi = [rAD_TB1],16
+ nop.f 0
+ nop.i 0
}
-;;
-
-{ .mmi
- ld8 r34 = [r34]
- nop.m 999
- nop.i 999
+{ .mfb
+ setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63
+(p8) fma.d.s0 f8 = f1,f1,f0 // quick exit for x=0
+(p8) br.ret.spnt b0
}
;;
-
-// Calculate cosh_FR_X2 = ax*ax and cosh_FR_X4 = ax*ax*ax*ax
-{ .mmf
- nop.m 999
-(p0) ldfe cosh_FR_P1 = [r34],16
-(p0) fma.s1 cosh_FR_X2 = cosh_FR_X, cosh_FR_X, f0 ;;
-}
-
-{ .mmi
-(p0) ldfe cosh_FR_P2 = [r34],16 ;;
-(p0) ldfe cosh_FR_P3 = [r34],16
- nop.i 999 ;;
+{ .mfi
+ ldfe fLn2_by_128_lo = [rAD_TB1],16
+ nop.f 0
+ nop.i 0
}
-
-{ .mmi
-(p0) ldfe cosh_FR_P4 = [r34],16 ;;
-(p0) ldfe cosh_FR_P5 = [r34],16
- nop.i 999 ;;
+{ .mfb
+ and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
+(p10) fma.d.s0 f8 = f8,f8,f0 // Result if x=inf, nan, NaT
+(p10) br.ret.spnt b0 // quick exit for x=inf, nan, NaT
}
+;;
+// After that last load rAD_TB1 points to the beginning of table 1
{ .mfi
-(p0) ldfe cosh_FR_P6 = [r34],16
-(p0) fma.s1 cosh_FR_X4 = cosh_FR_X2, cosh_FR_X2, f0
- nop.i 999 ;;
+ nop.m 0
+ fcmp.eq.s0 p6,p0 = f8, f0 // Dummy to set D
+ sub rExp_x = rExp_x, rExp_bias // True exponent of x
}
+;;
-// Calculate cosh_FR_podd = x4 *(x4 * P_5 + P_3) + P_1
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_poly_podd_temp1 = cosh_FR_X4, cosh_FR_P5, cosh_FR_P3
- nop.i 999 ;;
+ nop.m 0
+ fmerge.s fAbsX = f0, fNormX // Form |x|
+ nop.i 0
}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_podd = cosh_FR_X4, cosh_FR_poly_podd_temp1, cosh_FR_P1
- nop.i 999
+{ .mfb
+ cmp.gt p7, p0 = -2, rExp_x // Test |x| < 2^(-2)
+ fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path
+(p7) br.cond.spnt COSH_SMALL // Branch if 0 < |x| < 2^-2
}
+;;
-// Calculate cosh_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2)
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_poly_peven_temp1 = cosh_FR_X4, cosh_FR_P6, cosh_FR_P4
- nop.i 999 ;;
-}
+// W = X * Inv_log2_by_128
+// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
+// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_poly_peven_temp2 = cosh_FR_X4, cosh_FR_poly_peven_temp1, cosh_FR_P2
- nop.i 999 ;;
+ add rAD_P = 0x180, rAD_TB1
+ fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
+ add rAD_TB2 = 0x100, rAD_TB1
}
+;;
+
+// Divide arguments into the following categories:
+// Certain Safe - 0.25 <= |x| <= MAX_DBL_NORM_ARG
+// Possible Overflow p14 - MAX_DBL_NORM_ARG < |x| < MIN_DBL_OFLOW_ARG
+// Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= |x| < +inf
+//
+// If the input is really a double arg, then there will never be
+// "Possible Overflow" arguments.
+//
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_peven = cosh_FR_X4, cosh_FR_poly_peven_temp2, f0
- nop.i 999 ;;
+ ldfpd fP5, fP4 = [rAD_P] ,16
+ fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG
+ nop.i 0
}
+;;
+
+// Nfloat = round_int(W)
+// The signficand of fW_2TO56_RSH contains the rounded integer part of W,
+// as a twos complement number in the lower bits (that is, it may be negative).
+// That twos complement number (called N) is put into rN.
+
+// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
+// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
+// Thus, fNfloat contains the floating point version of N
-// Y_lo = x2*p_odd + p_even
-// Calculate f8 = Y_hi + Y_lo
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_X2, cosh_FR_podd, cosh_FR_peven
- nop.i 999 ;;
+ ldfpd fP3, fP2 = [rAD_P]
+(p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-(p0) fma.d.s0 f8 = f1, f1, cosh_FR_Y_lo
-(p0) br.ret.sptk b0 ;;
+ nop.m 0
+ fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
+(p15) br.cond.spnt COSH_CERTAIN_OVERFLOW
}
+;;
-
-L(COSH_BY_TBL):
-
-// Now that we are at TBL; so far all we know is that |x| >= 0.25.
-// The first two steps are the same for TBL and EXP, but if we are HUGE
-// Double
-// Go to HUGE if |x| >= 2^10, 10009 (register-biased) is e = 10 (true)
-// Single
-// Go to HUGE if |x| >= 2^7, 10006 (register-biased) is e = 7 (true)
-// we want to leave now. Go to HUGE if |x| >= 2^14
-// 1000d (register-biased) is e = 14 (true)
-
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x0000000000010009 ;;
+{ .mfi
+ getf.sig rN = fW_2TO56_RSH
+ nop.f 0
+ mov rExp_bias_minus_1 = 0xfffe
}
+;;
+
+// rIndex_1 has index_1
+// rIndex_2_16 has index_2 * 16
+// rBiased_M has M
+// rM has true M
+// r = x - Nfloat * ln2_by_128_hi
+// f = 1 - Nfloat * ln2_by_128_lo
{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ and rIndex_1 = 0x0f, rN
+ fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
+ shr rM = rN, 0x7
}
-
{ .mfi
- nop.m 999
-(p0) fcmp.ge.unc p6,p7 = cosh_FR_X,f9
- nop.i 999 ;;
+ and rIndex_2_16 = 0x70, rN
+ fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
+ sub rN_neg = r0, rN
}
+;;
-{ .mib
- nop.m 999
- nop.i 999
-(p6) br.cond.spnt L(COSH_HUGE) ;;
+{ .mmi
+ and rIndex_1_neg = 0x0f, rN_neg
+ add rBiased_M = rExp_bias_minus_1, rM
+ shr rM_neg = rN_neg, 0x7
}
-
-// r32 = 1
-// r34 = N-1
-// r35 = N
-// r36 = j
-// r37 = N+1
-
-// TBL can never overflow
-// cosh(x) = cosh(B+R)
-// = cosh(B) cosh(R) + sinh(B) sinh(R)
-// cosh(R) can be approximated by 1 + p_even
-// sinh(R) can be approximated by p_odd
-
-// ******************************************************
-// STEP 1 (TBL and EXP)
-// ******************************************************
-// Get the following constants.
-// f9 = Inv_log2by64
-// f10 = log2by64_hi
-// f11 = log2by64_lo
-
{ .mmi
-(p0) adds r32 = 0x1,r0
-(p0) addl r34 = @ltoff(double_cosh_arg_reduction), gp
- nop.i 999
+ and rIndex_2_16_neg = 0x70, rN_neg
+ add rAD_T2 = rAD_TB2, rIndex_2_16
+ shladd rAD_T1 = rIndex_1, 4, rAD_TB1
}
;;
-// 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)
-// r39 = 0xffff + (N-1) = 0xffff +N -1
-// r40 = 0xffff - (N +1) = 0xffff -N -1
-
-{ .mlx
- ld8 r34 = [r34]
-(p0) movl r38 = 0x000000000000fffe ;;
-}
+// rAD_T1 has address of T1
+// rAD_T2 has address if T2
{ .mmi
-(p0) ldfe cosh_FR_Inv_log2by64 = [r34],16 ;;
-(p0) ldfe cosh_FR_log2by64_hi = [r34],16
- nop.i 999 ;;
+ setf.exp f2M = rBiased_M
+ ldfe fT2 = [rAD_T2]
+ nop.i 0
}
-
-{ .mbb
-(p0) ldfe cosh_FR_log2by64_lo = [r34],16
- nop.b 999
- nop.b 999 ;;
-}
-
-// Get the A coefficients
-// f9 = A_1
-// f10 = A_2
-// f11 = A_3
-
{ .mmi
- nop.m 999
-(p0) addl r34 = @ltoff(double_cosh_ab_table), gp
- nop.i 999
+ add rBiased_M_neg = rExp_bias_minus_1, rM_neg
+ add rAD_T2_neg = rAD_TB2, rIndex_2_16_neg
+ shladd rAD_T1_neg = rIndex_1_neg, 4, rAD_TB1
}
;;
+// Create Scale = 2^M
+// Load T1 and T2
{ .mmi
- ld8 r34 = [r34]
- nop.m 999
- nop.i 999
+ ldfe fT1 = [rAD_T1]
+ nop.m 0
+ nop.i 0
+}
+{ .mmf
+ setf.exp f2M_neg = rBiased_M_neg
+ ldfe fT2_neg = [rAD_T2_neg]
+ fma.s1 fF_neg = fNfloat, fLn2_by_128_lo, f1
}
;;
-
-// 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 significand of M in r35
-// and the floating point representation of M in cosh_FR_M
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_M = cosh_FR_X, cosh_FR_Inv_log2by64, f0
- nop.i 999
+ nop.m 0
+ fma.s1 fRsq = fR, fR, f0
+ nop.i 0
}
-
{ .mfi
-(p0) ldfe cosh_FR_A1 = [r34],16
- nop.f 999
- nop.i 999 ;;
+ ldfe fT1_neg = [rAD_T1_neg]
+ fma.s1 fP54 = fR, fP5, fP4
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fcvt.fx.s1 cosh_FR_M_temp = cosh_FR_M
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fP32 = fR, fP3, fP2
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fnorm.s1 cosh_FR_M = cosh_FR_M_temp
- nop.i 999 ;;
+ nop.m 0
+ fnma.s1 fP54_neg = fR, fP5, fP4
+ nop.i 0
}
+;;
{ .mfi
-(p0) getf.sig r35 = cosh_FR_M_temp
- nop.f 999
- nop.i 999 ;;
-}
-
-// M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It
-// has a range of -32 thru 31.
-// r35 = M
-// r36 = j
-{ .mii
- nop.m 999
- nop.i 999 ;;
-(p0) and r36 = 0x3f, r35 ;;
+ nop.m 0
+ fnma.s1 fP32_neg = fR, fP3, fP2
+ nop.i 0
}
-
-// Calculate R
-// f13 = f44 - f12*f10 = x - M*log2by64_hi
-// f14 = f13 - f8*f11 = R = (x - M*log2by64_hi) - M*log2by64_lo
+;;
{ .mfi
- nop.m 999
-(p0) fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_X
- nop.i 999
+ nop.m 0
+ fma.s1 fP5432 = fRsq, fP54, fP32
+ nop.i 0
}
-
{ .mfi
-(p0) ldfe cosh_FR_A2 = [r34],16
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fS2 = fF,fT2,f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fnma.s1 cosh_FR_R = cosh_FR_M, cosh_FR_log2by64_lo, cosh_FR_R_temp
- nop.i 999
+ nop.m 0
+ fma.s1 fS1 = f2M,fT1,f0
+ nop.i 0
}
-
-// Get the B coefficients
-// f15 = B_1
-// f32 = B_2
-// f33 = B_3
-
-{ .mmi
-(p0) ldfe cosh_FR_A3 = [r34],16 ;;
-(p0) ldfe cosh_FR_B1 = [r34],16
- nop.i 999 ;;
-}
-
-{ .mmi
-(p0) ldfe cosh_FR_B2 = [r34],16 ;;
-(p0) ldfe cosh_FR_B3 = [r34],16
- nop.i 999 ;;
-}
-
-{ .mii
- nop.m 999
-(p0) shl r34 = r36, 0x2 ;;
-(p0) sxt1 r37 = r34 ;;
-}
-
-// ******************************************************
-// STEP 2 (TBL and EXP)
-// ******************************************************
-// Calculate Rsquared and Rcubed in preparation for p_even and p_odd
-// f12 = R*R*R
-// f13 = R*R
-// f14 = R <== from above
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Rsq = cosh_FR_R, cosh_FR_R, f0
-(p0) shr r36 = r37, 0x2 ;;
-}
-
-// r34 = M-j = r35 - r36
-// r35 = N = (M-j)/64
-
-{ .mii
-(p0) sub r34 = r35, r36
- nop.i 999 ;;
-(p0) shr r35 = r34, 0x6 ;;
-}
-
-{ .mii
-(p0) sub r40 = r38, r35
-(p0) adds r37 = 0x1, r35
-(p0) add r39 = r38, r35 ;;
-}
-
-// Get the address of the J table, add the offset,
-// addresses are sinh_AD_mJ and sinh_AD_J, get the T value
-// f32 = T(j)_hi
-// f33 = T(j)_lo
-// f34 = T(-j)_hi
-// f35 = T(-j)_lo
-
-{ .mmi
-(p0) sub r34 = r35, r32
-(p0) addl r37 = @ltoff(double_cosh_j_table), gp
- nop.i 999
+ nop.m 0
+ fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg
+ nop.i 0
}
;;
{ .mfi
- ld8 r37 = [r37]
-(p0) fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_FR_R, f0
- nop.i 999
+ nop.m 0
+ fma.s1 fS1_neg = f2M_neg,fT1_neg,f0
+ nop.i 0
}
-
-// ******************************************************
-// STEP 3 Now decide if we need to branch to EXP
-// ******************************************************
-// Put 32 in f9; p6 true if x < 32
-
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x0000000000010004 ;;
-}
-
-// Calculate p_even
-// f34 = B_2 + Rsq *B_3
-// f35 = B_1 + Rsq*f34 = B_1 + Rsq * (B_2 + Rsq *B_3)
-// f36 = peven = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3))
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_peven_temp1 = cosh_FR_Rsq, cosh_FR_B3, cosh_FR_B2
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fS2_neg = fF_neg,fT2_neg,f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_peven_temp2 = cosh_FR_Rsq, cosh_FR_peven_temp1, cosh_FR_B1
- nop.i 999
+ nop.m 0
+ fma.s1 fP = fRsq, fP5432, fR
+ nop.i 0
}
-
-// Calculate p_odd
-// f34 = A_2 + Rsq *A_3
-// f35 = A_1 + Rsq * (A_2 + Rsq *A_3)
-// f37 = podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3))
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_podd_temp1 = cosh_FR_Rsq, cosh_FR_A3, cosh_FR_A2
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fS = fS1,fS2,f0
+ nop.i 0
}
+;;
{ .mfi
-(p0) setf.exp cosh_FR_N_temp1 = r39
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+ fms.s1 fP_neg = fRsq, fP5432_neg, fR
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0
- nop.i 999
+ nop.m 0
+ fma.s1 fS_neg = fS1_neg,fS2_neg,f0
+ nop.i 0
}
+;;
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1
- nop.i 999 ;;
+{ .mfb
+ nop.m 0
+ fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
+(p14) br.cond.spnt COSH_POSSIBLE_OVERFLOW
}
+;;
{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fExp = fS, fP, fS
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_podd = cosh_FR_podd_temp2, cosh_FR_Rcub, cosh_FR_R
- nop.i 999
+ nop.m 0
+ fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg
+ nop.i 0
}
+;;
-// sinh_GR_mj contains the table offset for -j
-// sinh_GR_j contains the table offset for +j
-// p6 is true when j <= 0
-
-{ .mlx
-(p0) setf.exp cosh_FR_N_temp2 = r40
-(p0) movl r40 = 0x0000000000000020 ;;
+{ .mfb
+ nop.m 0
+ fma.d.s0 f8 = fExp, f1, fExp_neg
+ br.ret.sptk b0 // Normal path exit
}
+;;
-{ .mfi
-(p0) sub GR_mJ = r40, r36
-(p0) fmerge.se cosh_FR_spos = cosh_FR_N_temp1, f1
-(p0) adds GR_J = 0x20, r36 ;;
+// Here if 0 < |x| < 0.25
+COSH_SMALL:
+{ .mmf
+ add rAD_T1 = 0x1a0, rAD_TB1
+ add rAD_T2 = 0x1d0, rAD_TB1
}
+;;
-{ .mii
- nop.m 999
-(p0) shl GR_mJ = GR_mJ, 5 ;;
-(p0) add AD_mJ = r37, GR_mJ ;;
+{ .mmf
+ ldfe fA6 = [rAD_T1],16
+ ldfe fA5 = [rAD_T2],16
+ nop.f 0
}
+;;
{ .mmi
- nop.m 999
-(p0) ldfe cosh_FR_Tmjhi = [AD_mJ],16
-(p0) shl GR_J = GR_J, 5 ;;
-}
-
-{ .mfi
-(p0) ldfs cosh_FR_Tmjlo = [AD_mJ],16
-(p0) fcmp.lt.unc.s1 p6,p7 = cosh_FR_X,f9
-(p0) add AD_J = r37, GR_J ;;
+ ldfe fA4 = [rAD_T1],16
+ ldfe fA3 = [rAD_T2],16
+ nop.i 0
}
+;;
{ .mmi
-(p0) ldfe cosh_FR_Tjhi = [AD_J],16 ;;
-(p0) ldfs cosh_FR_Tjlo = [AD_J],16
- nop.i 999 ;;
+ ldfe fA2 = [rAD_T1],16
+ ldfe fA1 = [rAD_T2],16
+ nop.i 0
}
-
-{ .mfb
- nop.m 999
-(p0) fmerge.se cosh_FR_sneg = cosh_FR_N_temp2, f1
-(p7) br.cond.spnt L(COSH_BY_EXP) ;;
-}
-
-// ******************************************************
-// If NOT branch to EXP
-// ******************************************************
-// Calculate C_hi
-// ******************************************************
-// cosh_FR_C_hi_temp = cosh_FR_sneg * cosh_FR_Tmjhi
-// cosh_FR_C_hi = cosh_FR_spos * cosh_FR_Tjhi + (cosh_FR_sneg * cosh_FR_Tmjhi)
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_hi_temp = cosh_FR_sneg, cosh_FR_Tmjhi, f0
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi_temp
- nop.i 999
-}
-
-// ******************************************************
-// Calculate S_hi
-// ******************************************************
-// cosh_FR_S_hi_temp1 = cosh_FR_sneg * cosh_FR_Tmjhi
-// cosh_FR_S_hi = cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi_temp1
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_S_hi_temp1 = cosh_FR_sneg, cosh_FR_Tmjhi, f0
- nop.i 999 ;;
-}
-
-// ******************************************************
-// Calculate C_lo
-// ******************************************************
-// cosh_FR_C_lo_temp1 = cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi
-// cosh_FR_C_lo_temp2 = cosh_FR_sneg * cosh_FR_Tmjlo + (cosh_FR_spos * cosh_FR_Tjhi - cosh_FR_C_hi)
-// cosh_FR_C_lo_temp1 = cosh_FR_sneg * cosh_FR_Tmjlo
-// cosh_FR_C_lo_temp3 = cosh_FR_spos * cosh_FR_Tjlo + (cosh_FR_sneg * cosh_FR_Tmjlo)
-// cosh_FR_C_lo = cosh_FR_C_lo_temp3 + cosh_FR_C_lo_temp2
+;;
{ .mfi
- nop.m 999
-(p0) fms.s1 cosh_FR_C_lo_temp1 = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_C_hi
- nop.i 999
+ nop.m 0
+ fma.s1 fX4 = fXsq, fXsq, f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fms.s1 cosh_FR_S_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_S_hi_temp1
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fA65 = fXsq, fA6, fA5
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_lo_temp2 = cosh_FR_sneg, cosh_FR_Tmjhi, cosh_FR_C_lo_temp1
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_lo_temp1 = cosh_FR_sneg, cosh_FR_Tmjlo, f0
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fA43 = fXsq, fA4, fA3
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_lo_temp3 = cosh_FR_spos, cosh_FR_Tjlo, cosh_FR_C_lo_temp1
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fA21 = fXsq, fA2, fA1
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_C_lo = cosh_FR_C_lo_temp3, f1, cosh_FR_C_lo_temp2
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fA6543 = fX4, fA65, fA43
+ nop.i 0
}
-
-// ******************************************************
-// cosh_FR_Y_lo_temp = cosh_FR_C_hi * cosh_FR_peven + cosh_FR_C_lo
-// cosh_FR_Y_lo = cosh_FR_S_hi * cosh_FR_podd + cosh_FR_Y_lo_temp
-// cosh_FR_COSH = Y_hi + Y_lo
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_C_hi, cosh_FR_peven, cosh_FR_C_lo
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 fA654321 = fX4, fA6543, fA21
+ nop.i 0
}
+;;
+// Dummy multiply to generate inexact
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_S_hi, cosh_FR_podd, cosh_FR_Y_lo_temp
- nop.i 999 ;;
+ nop.m 0
+ fmpy.s0 fTmp = fA6, fA6
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-(p0) fma.d.s0 f8 = cosh_FR_C_hi, f1, cosh_FR_Y_lo
-(p0) br.ret.sptk b0 ;;
+ nop.m 0
+ fma.d.s0 f8 = fA654321, fXsq, f1
+ br.ret.sptk b0 // Exit if 0 < |x| < 0.25
}
+;;
-L(COSH_BY_EXP):
-// When p7 is true, we know that an overflow is not going to happen
-// When p7 is false, we must check for possible overflow
-// p7 is the over_SAFE flag
-// f44 = Scale * (Y_hi + Y_lo)
-// = cosh_FR_spos * (cosh_FR_Tjhi + cosh_FR_Y_lo)
+COSH_POSSIBLE_OVERFLOW:
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd
- nop.i 999
-}
-
-// Now we are in EXP. This is the only path where an overflow is possible
-// but not for certain. So this is the only path where over_SAFE has any use.
-// r34 still has N-1
-// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe
-// There is a danger of double overflow if N-1 > 0x3fe = 1022
+// Here if fMAX_DBL_NORM_ARG < |x| < fMIN_DBL_OFLOW_ARG
+// This cannot happen if input is a double, only if input higher precision.
+// Overflow is a possibility, not a certainty.
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x00000000000003fe ;;
-}
+// Recompute result using status field 2 with user's rounding mode,
+// and wre set. If result is larger than largest double, then we have
+// overflow
{ .mfi
-(p0) cmp.gt.unc p0,p7 = r34, r32
- nop.f 999
- nop.i 999 ;;
+ mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
+ fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_Tjhi, cosh_FR_Y_lo_temp, cosh_FR_Tjlo
- nop.i 999 ;;
+ setf.exp fGt_pln = rGt_ln // Create largest double + 1 ulp
+ fma.d.s2 fWre_urm_f8 = fS, fP, fS // Result with wre set
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_COSH_temp = cosh_FR_Y_lo, f1, cosh_FR_Tjhi
- nop.i 999 ;;
+ nop.m 0
+ fsetc.s2 0x7F,0x40 // Turn off wre in sf2
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.d.s0 f44 = cosh_FR_spos, cosh_FR_COSH_temp, f0
- nop.i 999 ;;
+ nop.m 0
+ fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
+ nop.i 0
}
+;;
-// If over_SAFE is set, return
{ .mfb
- nop.m 999
-(p7) fmerge.s f8 = f44,f44
-(p7) br.ret.sptk b0 ;;
-}
-
-// Else see if we overflowed
-// S0 user supplied status
-// S2 user supplied status + WRE + TD (Overflows)
-// If WRE is set then an overflow will not occur in EXP.
-// The input value that would cause a register (WRE) value to overflow is about 2^15
-// and this input would go into the HUGE path.
-// Answer with WRE is in f43.
-
-{ .mfi
- nop.m 999
-(p0) fsetc.s2 0x7F,0x42
- nop.i 999;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.d.s2 f43 = cosh_FR_spos, cosh_FR_COSH_temp, f0
- nop.i 999 ;;
-}
-
-// 103FF => 103FF -FFFF = 400(true)
-// 400 + 3FF = 7FF, which is 1 more that the exponent of the largest
-// double (7FE). So 0 103FF 8000000000000000 is one ulp more than
-// largest double in register bias
-// Now set p8 if the answer with WRE is greater than or equal this value
-// Also set p9 if the answer with WRE is less than or equal to negative this value
-
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x00000000000103ff ;;
+ nop.m 0
+ nop.f 0
+(p6) br.cond.spnt COSH_CERTAIN_OVERFLOW // Branch if overflow
}
+;;
-{ .mmf
- nop.m 999
-(p0) setf.exp f41 = r32
-(p0) fsetc.s2 0x7F,0x40 ;;
+{ .mfb
+ nop.m 0
+ fma.d.s0 f8 = fS, fP, fS
+ br.ret.sptk b0 // Exit if really no overflow
}
+;;
-{ .mfi
- nop.m 999
-(p0) fcmp.ge.unc.s1 p8, p0 = f43, f41
- nop.i 999
+COSH_CERTAIN_OVERFLOW:
+{ .mmi
+ sub rTmp = rExp_mask, r0, 1
+;;
+ setf.exp fTmp = rTmp
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fmerge.ns f42 = f41, f41
- nop.i 999 ;;
+ alloc r32=ar.pfs,1,4,4,0
+ fmerge.s FR_X = f8,f8
+ nop.i 0
}
-
-// The error tag for overflow is 64
-{ .mii
- nop.m 999
- nop.i 999 ;;
-(p8) mov r47 = 64 ;;
-}
-
{ .mfb
- nop.m 999
-(p0) fcmp.le.unc.s1 p9, p0 = f43, f42
-(p8) br.cond.spnt __libm_error_region ;;
-}
-
-{ .mii
- nop.m 999
- nop.i 999 ;;
-(p9) mov r47 = 64
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p9) br.cond.spnt __libm_error_region ;;
+ mov GR_Parameter_TAG = 64
+ fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result
+ br.cond.sptk __libm_error_region
}
+;;
+// Here if x unorm
+COSH_UNORM:
{ .mfb
- nop.m 999
-(p0) fmerge.s f8 = f44,f44
-(p0) br.ret.sptk b0 ;;
-}
-
-
-// for COSH_HUGE, put 24000 in exponent; take sign from input; add 1
-// SAFE: SAFE is always 0 for HUGE
-
-L(COSH_HUGE):
-
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x0000000000015dbf ;;
-}
-
-{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 cosh_FR_hi_lo = f1, f9, f1
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.d.s0 f44 = f9, cosh_FR_hi_lo, f0
-(p0) mov r47 = 64
+ getf.exp rSignexp_x = fNormX // Must recompute if x unorm
+ fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag
+ br.cond.sptk COSH_COMMON
}
;;
-.endp cosh#
-ASM_SIZE_DIRECTIVE(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:
+GLOBAL_IEEE754_END(cosh)
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
-// (1)
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
@@ -1103,39 +821,32 @@ __libm_error_region:
}
{ .mfi
.fframe 64
- add sp=-64,sp // Create new stack
+ add sp=-64,sp // Create new stack
nop.f 0
- mov GR_SAVE_GP=gp // Save gp
+ 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
+ stfd [GR_Parameter_Y] = FR_Y,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
+ mov GR_SAVE_B0=b0 // Save b0
};;
-
.body
-// (3)
{ .mib
- stfd [GR_Parameter_X] = f8 // STORE Parameter 1 on stack
+ stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
- nop.b 0
+ nop.b 0
}
{ .mib
- stfd [GR_Parameter_Y] = f44 // STORE Parameter 3 on stack
+ stfd [GR_Parameter_Y] = FR_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
+ br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- nop.m 0
- nop.m 0
add GR_Parameter_RESULT = 48,sp
+ nop.m 0
+ nop.i 0
};;
-
-// (4)
{ .mmi
ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
@@ -1148,8 +859,6 @@ __libm_error_region:
br.ret.sptk b0 // Return
};;
-.endp __libm_error_region
-ASM_SIZE_DIRECTIVE(__libm_error_region)
-
+LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
generated by cgit v1.2.3 (git 2.39.1) at 2024-10-31 23:09:28 +0000