summaryrefslogtreecommitdiff
path: root/sysdeps/ia64/fpu/e_cosh.S
diff options
context:
space:
mode:
Diffstat (limited to 'sysdeps/ia64/fpu/e_cosh.S')
-rw-r--r--sysdeps/ia64/fpu/e_cosh.S1477
1 files changed, 883 insertions, 594 deletions
diff --git a/sysdeps/ia64/fpu/e_cosh.S b/sysdeps/ia64/fpu/e_cosh.S
index 885456b389..205653d4bf 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 - 2005, Intel Corporation
+// Copyright (C) 2000, 2001, Intel Corporation
// All rights reserved.
-//
-// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// 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.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
@@ -20,801 +20,1081 @@
// * 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://www.intel.com/software/products/opensource/libraries/num.htm.
+// problem reports or change requests be submitted to it directly at
+// http://developer.intel.com/opensource.
//
// 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
+// 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.
-// 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
-// 03/31/05 Reformatted delimiters between data tables
-
+//
// API
//==============================================================
-// double cosh(double)
+// double = cosh(double)
+// input floating point f8
+// output floating point f8
+
// Overview of operation
//==============================================================
-// 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
+// There are four paths
-// n = 128M + index_1 + 2^4 index_2
-// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + 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
-// 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
+// For paths 1, and 2 SAFE is always 1.
+// For path 4, Safe is always 0.
+// SAFE = 1 means we cannot overflow.
+#include "libm_support.h"
-// Special values
+// Assembly macros
//==============================================================
-// cosh(+0) = 1.0
-// cosh(-0) = 1.0
+cosh_FR_X = f44
+cosh_FR_SGNX = f40
-// cosh(+qnan) = +qnan
-// cosh(-qnan) = -qnan
-// cosh(+snan) = +qnan
-// cosh(-snan) = -qnan
+cosh_FR_Inv_log2by64 = f9
+cosh_FR_log2by64_lo = f11
+cosh_FR_log2by64_hi = f10
-// cosh(-inf) = +inf
-// cosh(+inf) = +inf
+cosh_FR_A1 = f9
+cosh_FR_A2 = f10
+cosh_FR_A3 = f11
-// Overflow and Underflow
-//=======================
-// cosh(x) = largest double normal when
-// x = 710.47586 = 0x408633ce8fb9f87d
-//
-// There is no underflow.
+cosh_FR_Rcub = f12
+cosh_FR_M_temp = f13
+cosh_FR_R_temp = f13
+cosh_FR_Rsq = f13
+cosh_FR_R = f14
-// Registers used
-//==============================================================
-// Floating Point registers used:
-// f8, input, output
-// f6 -> f15, f32 -> f61
+cosh_FR_M = f38
-// General registers used:
-// r14 -> r40
+cosh_FR_B1 = f15
+cosh_FR_B2 = f32
+cosh_FR_B3 = f33
-// Predicate registers used:
-// p6 -> p15
+cosh_FR_peven_temp1 = f34
+cosh_FR_peven_temp2 = f35
+cosh_FR_peven = f36
-// Assembly macros
-//==============================================================
+cosh_FR_podd_temp1 = f34
+cosh_FR_podd_temp2 = f35
+cosh_FR_podd = f37
+
+cosh_FR_J_temp = f9
+cosh_FR_J = f10
+
+cosh_FR_Mmj = f39
+
+cosh_FR_N_temp1 = f11
+cosh_FR_N_temp2 = f12
+cosh_FR_N = f13
+
+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
+
+cosh_FR_hi_lo = f10
+
+cosh_FR_poly_podd_temp1 = f11
+cosh_FR_poly_podd_temp2 = f13
+cosh_FR_poly_peven_temp1 = f11
+cosh_FR_poly_peven_temp2 = f13
+
+GR_SAVE_PFS = r41
+GR_SAVE_B0 = r42
+GR_SAVE_GP = r43
+
+GR_Parameter_X = r44
+GR_Parameter_Y = r45
+GR_Parameter_RESULT = r46
-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
//==============================================================
-RODATA
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
+
.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#
-// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
+.section .text
+.proc cosh#
+.align 32
-// 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)
+cosh:
+#ifdef _LIBC
+.global __ieee754_cosh#
+.proc __ieee754_cosh#
+__ieee754_cosh:
+#endif
-.section .text
-GLOBAL_IEEE754_ENTRY(cosh)
+// X NAN?
-{ .mlx
- getf.exp rSignexp_x = f8 // Must recompute if x unorm
- movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
-}
-{ .mlx
- addl rAD_TB1 = @ltoff(exp_table_1), gp
- movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56)
+{ .mfi
+ alloc r32 = ar.pfs,0,12,4,0
+(p0) fclass.m.unc p6,p7 = f8, 0xc3 //@snan | @qnan
+ nop.i 999
}
;;
-{ .mfi
- ld8 rAD_TB1 = [rAD_TB1]
- fclass.m p6,p0 = f8,0x0b // Test for x=unorm
- mov rExp_mask = 0x1ffff
-}
-{ .mfi
- mov rExp_bias = 0xffff
- fnorm.s1 fNormX = f8
- mov rExp_2tom56 = 0xffff-56
+
+{ .mfb
+ nop.m 999
+(p6) fma.d.s0 f8 = f8,f1,f8
+(p6) br.ret.spnt b0 ;;
}
-;;
-// 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
+// X infinity
{ .mfi
- 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
+ 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 ;;
+}
+
+
+
+// Put 0.25 in f9; p6 true if x < 0.25
{ .mlx
- setf.d fRSHF_2TO56 = rRshf_2to56 // Form const 1.100 * 2^(63+56)
- movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for right shift
+ nop.m 999
+(p0) movl r32 = 0x000000000000fffd ;;
}
-;;
{ .mfi
- 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
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
}
-{ .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_COMMON:
{ .mfi
- ldfe fLn2_by_128_hi = [rAD_TB1],16
- nop.f 0
- nop.i 0
+ nop.m 999
+(p0) fmerge.s cosh_FR_X = f0,f8
+ 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
+
+{ .mfi
+ nop.m 999
+(p0) fmerge.s cosh_FR_SGNX = f8,f1
+ nop.i 999 ;;
}
-;;
{ .mfi
- ldfe fLn2_by_128_lo = [rAD_TB1],16
- nop.f 0
- nop.i 0
+ nop.m 999
+(p0) fcmp.lt.unc p0,p7 = cosh_FR_X,f9
+ 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
+
+{ .mib
+ nop.m 999
+ nop.i 999
+(p7) br.cond.sptk L(COSH_BY_TBL)
}
;;
-// After that last load rAD_TB1 points to the beginning of table 1
-{ .mfi
- 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
+
+// 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
}
;;
-{ .mfi
- nop.m 0
- fmerge.s fAbsX = f0, fNormX // Form |x|
- nop.i 0
-}
-{ .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
+{ .mmi
+ ld8 r34 = [r34]
+ nop.m 999
+ 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
- add rAD_P = 0x180, rAD_TB1
- fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56
- add rAD_TB2 = 0x100, rAD_TB1
+// 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 ;;
}
-;;
-// 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.
-//
+{ .mmi
+(p0) ldfe cosh_FR_P2 = [r34],16 ;;
+(p0) ldfe cosh_FR_P3 = [r34],16
+ nop.i 999 ;;
+}
+
+{ .mmi
+(p0) ldfe cosh_FR_P4 = [r34],16 ;;
+(p0) ldfe cosh_FR_P5 = [r34],16
+ nop.i 999 ;;
+}
{ .mfi
- ldfpd fP5, fP4 = [rAD_P] ,16
- fcmp.ge.s1 p15,p14 = fAbsX,fMIN_DBL_OFLOW_ARG
- nop.i 0
+(p0) ldfe cosh_FR_P6 = [r34],16
+(p0) fma.s1 cosh_FR_X4 = cosh_FR_X2, cosh_FR_X2, f0
+ nop.i 999 ;;
}
-;;
-// 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.
+// 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 ;;
+}
-// 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
+{ .mfi
+ nop.m 999
+(p0) fma.s1 cosh_FR_podd = cosh_FR_X4, cosh_FR_poly_podd_temp1, cosh_FR_P1
+ nop.i 999
+}
+// Calculate cosh_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2)
{ .mfi
- ldfpd fP3, fP2 = [rAD_P]
-(p14) fcmp.gt.unc.s1 p14,p0 = fAbsX,fMAX_DBL_NORM_ARG
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_poly_peven_temp1 = cosh_FR_X4, cosh_FR_P6, cosh_FR_P4
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 0
- fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
-(p15) br.cond.spnt COSH_CERTAIN_OVERFLOW
+
+{ .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 ;;
}
-;;
{ .mfi
- getf.sig rN = fW_2TO56_RSH
- nop.f 0
- mov rExp_bias_minus_1 = 0xfffe
+ nop.m 999
+(p0) fma.s1 cosh_FR_peven = cosh_FR_X4, cosh_FR_poly_peven_temp2, f0
+ nop.i 999 ;;
}
-;;
-// rIndex_1 has index_1
-// rIndex_2_16 has index_2 * 16
-// rBiased_M has M
+// 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 ;;
+}
+
+{ .mfb
+ nop.m 999
+(p0) fma.d.s0 f8 = f1, f1, cosh_FR_Y_lo
+(p0) br.ret.sptk b0 ;;
+}
+
+
+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 ;;
+}
-// rM has true M
-// r = x - Nfloat * ln2_by_128_hi
-// f = 1 - Nfloat * ln2_by_128_lo
{ .mfi
- and rIndex_1 = 0x0f, rN
- fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX
- shr rM = rN, 0x7
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
}
+
{ .mfi
- and rIndex_2_16 = 0x70, rN
- fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1
- sub rN_neg = r0, rN
+ nop.m 999
+(p0) fcmp.ge.unc p6,p7 = cosh_FR_X,f9
+ nop.i 999 ;;
}
-;;
-{ .mmi
- and rIndex_1_neg = 0x0f, rN_neg
- add rBiased_M = rExp_bias_minus_1, rM
- shr rM_neg = rN_neg, 0x7
+{ .mib
+ nop.m 999
+ nop.i 999
+(p6) br.cond.spnt L(COSH_HUGE) ;;
}
+
+// 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
- and rIndex_2_16_neg = 0x70, rN_neg
- add rAD_T2 = rAD_TB2, rIndex_2_16
- shladd rAD_T1 = rIndex_1, 4, rAD_TB1
+(p0) adds r32 = 0x1,r0
+(p0) addl r34 = @ltoff(double_cosh_arg_reduction), gp
+ nop.i 999
}
;;
-// rAD_T1 has address of T1
-// rAD_T2 has address if T2
+// 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 ;;
+}
{ .mmi
- setf.exp f2M = rBiased_M
- ldfe fT2 = [rAD_T2]
- nop.i 0
+(p0) ldfe cosh_FR_Inv_log2by64 = [r34],16 ;;
+(p0) ldfe cosh_FR_log2by64_hi = [r34],16
+ nop.i 999 ;;
+}
+
+{ .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
- 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
+ nop.m 999
+(p0) addl r34 = @ltoff(double_cosh_ab_table), gp
+ nop.i 999
}
;;
-// Create Scale = 2^M
-// Load T1 and T2
{ .mmi
- 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
+ ld8 r34 = [r34]
+ nop.m 999
+ nop.i 999
}
;;
+
+// 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 0
- fma.s1 fRsq = fR, fR, f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_M = cosh_FR_X, cosh_FR_Inv_log2by64, f0
+ nop.i 999
}
+
{ .mfi
- ldfe fT1_neg = [rAD_T1_neg]
- fma.s1 fP54 = fR, fP5, fP4
- nop.i 0
+(p0) ldfe cosh_FR_A1 = [r34],16
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fP32 = fR, fP3, fP2
- nop.i 0
+ nop.m 999
+(p0) fcvt.fx.s1 cosh_FR_M_temp = cosh_FR_M
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 0
- fnma.s1 fP54_neg = fR, fP5, fP4
- nop.i 0
+ nop.m 999
+(p0) fnorm.s1 cosh_FR_M = cosh_FR_M_temp
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fnma.s1 fP32_neg = fR, fP3, fP2
- nop.i 0
+(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 ;;
}
-;;
+
+// 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 0
- fma.s1 fP5432 = fRsq, fP54, fP32
- nop.i 0
+ nop.m 999
+(p0) fnma.s1 cosh_FR_R_temp = cosh_FR_M, cosh_FR_log2by64_hi, cosh_FR_X
+ nop.i 999
}
+
{ .mfi
- nop.m 0
- fma.s1 fS2 = fF,fT2,f0
- nop.i 0
+(p0) ldfe cosh_FR_A2 = [r34],16
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fS1 = f2M,fT1,f0
- nop.i 0
+ nop.m 999
+(p0) fnma.s1 cosh_FR_R = cosh_FR_M, cosh_FR_log2by64_lo, cosh_FR_R_temp
+ nop.i 999
+}
+
+// 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 0
- fma.s1 fP5432_neg = fRsq, fP54_neg, fP32_neg
- nop.i 0
+ 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
}
;;
{ .mfi
- nop.m 0
- fma.s1 fS1_neg = f2M_neg,fT1_neg,f0
- nop.i 0
+ ld8 r37 = [r37]
+(p0) fma.s1 cosh_FR_Rcub = cosh_FR_Rsq, cosh_FR_R, f0
+ nop.i 999
+}
+
+// ******************************************************
+// 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 0
- fma.s1 fS2_neg = fF_neg,fT2_neg,f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_peven_temp1 = cosh_FR_Rsq, cosh_FR_B3, cosh_FR_B2
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fP = fRsq, fP5432, fR
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_peven_temp2 = cosh_FR_Rsq, cosh_FR_peven_temp1, cosh_FR_B1
+ nop.i 999
}
+
+// 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 0
- fma.s1 fS = fS1,fS2,f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_podd_temp1 = cosh_FR_Rsq, cosh_FR_A3, cosh_FR_A2
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fms.s1 fP_neg = fRsq, fP5432_neg, fR
- nop.i 0
+(p0) setf.exp cosh_FR_N_temp1 = r39
+ nop.f 999
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 0
- fma.s1 fS_neg = fS1_neg,fS2_neg,f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_peven = cosh_FR_Rsq, cosh_FR_peven_temp2, f0
+ 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
+ nop.m 999
+(p0) fma.s1 cosh_FR_podd_temp2 = cosh_FR_Rsq, cosh_FR_podd_temp1, cosh_FR_A1
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fExp = fS, fP, fS
- nop.i 0
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 0
- fma.s1 fExp_neg = fS_neg, fP_neg, fS_neg
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_podd = cosh_FR_podd_temp2, cosh_FR_Rcub, cosh_FR_R
+ nop.i 999
}
-;;
-{ .mfb
- nop.m 0
- fma.d.s0 f8 = fExp, f1, fExp_neg
- br.ret.sptk b0 // Normal path exit
+// 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 ;;
}
-;;
-// Here if 0 < |x| < 0.25
-COSH_SMALL:
-{ .mmf
- add rAD_T1 = 0x1a0, rAD_TB1
- add rAD_T2 = 0x1d0, rAD_TB1
+{ .mfi
+(p0) sub GR_mJ = r40, r36
+(p0) fmerge.se cosh_FR_spos = cosh_FR_N_temp1, f1
+(p0) adds GR_J = 0x20, r36 ;;
}
-;;
-{ .mmf
- ldfe fA6 = [rAD_T1],16
- ldfe fA5 = [rAD_T2],16
- nop.f 0
+{ .mii
+ nop.m 999
+(p0) shl GR_mJ = GR_mJ, 5 ;;
+(p0) add AD_mJ = r37, GR_mJ ;;
}
-;;
{ .mmi
- ldfe fA4 = [rAD_T1],16
- ldfe fA3 = [rAD_T2],16
- nop.i 0
+ 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 ;;
}
-;;
{ .mmi
- ldfe fA2 = [rAD_T1],16
- ldfe fA1 = [rAD_T2],16
- nop.i 0
+(p0) ldfe cosh_FR_Tjhi = [AD_J],16 ;;
+(p0) ldfs cosh_FR_Tjlo = [AD_J],16
+ nop.i 999 ;;
}
-;;
+
+{ .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 0
- fma.s1 fX4 = fXsq, fXsq, f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_C_hi_temp = cosh_FR_sneg, cosh_FR_Tmjhi, f0
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fA65 = fXsq, fA6, fA5
- nop.i 0
+ 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 0
- fma.s1 fA43 = fXsq, fA4, fA3
- nop.i 0
+ 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
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fA21 = fXsq, fA2, fA1
- nop.i 0
+ nop.m 999
+(p0) fms.s1 cosh_FR_S_hi = cosh_FR_spos, cosh_FR_Tjhi, cosh_FR_S_hi_temp1
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fA6543 = fX4, fA65, fA43
- nop.i 0
+ 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 0
- fma.s1 fA654321 = fX4, fA6543, fA21
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_C_lo_temp1 = cosh_FR_sneg, cosh_FR_Tmjlo, f0
+ nop.i 999 ;;
}
-;;
-// Dummy multiply to generate inexact
{ .mfi
- nop.m 0
- fmpy.s0 fTmp = fA6, fA6
- nop.i 0
+ 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 ;;
}
+
+{ .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 ;;
+}
+
+// ******************************************************
+// 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 ;;
+}
+
+{ .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 ;;
+}
+
{ .mfb
- nop.m 0
- fma.d.s0 f8 = fA654321, fXsq, f1
- br.ret.sptk b0 // Exit if 0 < |x| < 0.25
+ nop.m 999
+(p0) fma.d.s0 f8 = cosh_FR_C_hi, f1, cosh_FR_Y_lo
+(p0) br.ret.sptk b0 ;;
}
-;;
+L(COSH_BY_EXP):
-COSH_POSSIBLE_OVERFLOW:
+// 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)
-// 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.
+{ .mfi
+ nop.m 999
+(p0) fma.s1 cosh_FR_Y_lo_temp = cosh_FR_peven, f1, cosh_FR_podd
+ nop.i 999
+}
-// 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
+// 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
+
+{ .mlx
+ nop.m 999
+(p0) movl r32 = 0x00000000000003fe ;;
+}
{ .mfi
- mov rGt_ln = 0x103ff // Exponent for largest dbl + 1 ulp
- fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
- nop.i 0
+(p0) cmp.gt.unc p0,p7 = r34, r32
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- 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
+ nop.m 999
+(p0) fma.s1 cosh_FR_Y_lo = cosh_FR_Tjhi, cosh_FR_Y_lo_temp, cosh_FR_Tjlo
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fsetc.s2 0x7F,0x40 // Turn off wre in sf2
- nop.i 0
+ nop.m 999
+(p0) fma.s1 cosh_FR_COSH_temp = cosh_FR_Y_lo, f1, cosh_FR_Tjhi
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow
- nop.i 0
+ nop.m 999
+(p0) fma.d.s0 f44 = cosh_FR_spos, cosh_FR_COSH_temp, f0
+ nop.i 999 ;;
}
-;;
+// If over_SAFE is set, return
{ .mfb
- nop.m 0
- nop.f 0
-(p6) br.cond.spnt COSH_CERTAIN_OVERFLOW // Branch if overflow
+ nop.m 999
+(p7) fmerge.s f8 = f44,f44
+(p7) br.ret.sptk b0 ;;
}
-;;
-{ .mfb
- nop.m 0
- fma.d.s0 f8 = fS, fP, fS
- br.ret.sptk b0 // Exit if really no overflow
+// 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;;
}
-;;
-COSH_CERTAIN_OVERFLOW:
-{ .mmi
- sub rTmp = rExp_mask, r0, 1
-;;
- setf.exp fTmp = rTmp
- nop.i 0
+{ .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 ;;
+}
+
+{ .mmf
+ nop.m 999
+(p0) setf.exp f41 = r32
+(p0) fsetc.s2 0x7F,0x40 ;;
}
-;;
{ .mfi
- alloc r32=ar.pfs,1,4,4,0
- fmerge.s FR_X = f8,f8
- nop.i 0
+ nop.m 999
+(p0) fcmp.ge.unc.s1 p8, p0 = f43, f41
+ nop.i 999
}
+
+{ .mfi
+ nop.m 999
+(p0) fmerge.ns f42 = f41, f41
+ nop.i 999 ;;
+}
+
+// The error tag for overflow is 64
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+(p8) mov r47 = 64 ;;
+}
+
{ .mfb
- 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
+ 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 ;;
}
-;;
-// Here if x unorm
-COSH_UNORM:
{ .mfb
- 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
+ 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 ;;
}
-;;
-GLOBAL_IEEE754_END(cosh)
+{ .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
+}
+;;
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.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:
.prologue
+// (1)
{ .mfi
add GR_Parameter_Y=-32,sp // Parameter 2 value
nop.f 0
@@ -823,32 +1103,39 @@ LOCAL_LIBM_ENTRY(__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] = FR_Y,16 // STORE Parameter 2 on stack
- add GR_Parameter_X = 16,sp // Parameter 1 address
+ 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
+ mov GR_SAVE_B0=b0 // Save b0
};;
+
.body
+// (3)
{ .mib
- stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
+ stfd [GR_Parameter_X] = f8 // 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] = FR_RESULT // STORE Parameter 3 on stack
+ stfd [GR_Parameter_Y] = f44 // 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
- add GR_Parameter_RESULT = 48,sp
nop.m 0
- nop.i 0
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
};;
+
+// (4)
{ .mmi
ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
@@ -861,6 +1148,8 @@ LOCAL_LIBM_ENTRY(__libm_error_region)
br.ret.sptk b0 // Return
};;
-LOCAL_LIBM_END(__libm_error_region)
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
+
.type __libm_error_support#,@function
.global __libm_error_support#
View Lorry Controller Status