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-rw-r--r--sysdeps/ia64/fpu/e_coshf.S1447
1 files changed, 941 insertions, 506 deletions
diff --git a/sysdeps/ia64/fpu/e_coshf.S b/sysdeps/ia64/fpu/e_coshf.S
index 97cb4e1771..969abc4ff6 100644
--- a/sysdeps/ia64/fpu/e_coshf.S
+++ b/sysdeps/ia64/fpu/e_coshf.S
@@ -1,10 +1,10 @@
.file "coshf.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
@@ -20,692 +20,1127 @@
// * 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
-// 02/16/00 The error tag for coshf overflow changed to 65 (from 64).
-// 04/04/00 Unwind support added
-// 08/15/00 Bundle added after call to __libm_error_support to properly
+//==============================================================
+// 2/02/00 Initial version
+// 2/16/00 The error tag for coshf overflow changed to 65 (from 64).
+// 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 algorithm based on expf
-// 03/31/05 Reformatted delimiters between data tables
//
// API
-//*********************************************************************
-// float coshf(float)
-//
+//==============================================================
+// float = coshf(float)
+// input floating point f8
+// output floating point f8
+
+
// Overview of operation
-//*********************************************************************
-// Case 1: 0 < |x| < 0.25
-// Evaluate cosh(x) by a 8th 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)
-//
-// Case 2: 0.25 < |x| < 89.41598
-// 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 * 64/log2
-// NJ = int(w)
-// x = NJ*log2/64 + R
+//==============================================================
+// There are four paths
-// NJ = 64*n + j
-// x = n*log2 + (log2/64)*j + R
-//
-// So, exp(x) = 2^n * 2^(j/64)* exp(R)
-//
-// T = 2^n * 2^(j/64)
-// Construct 2^n
-// Get 2^(j/64) table
-// actually all the entries of 2^(j/64) table are stored in DP and
-// with exponent bits set to 0 -> multiplication on 2^n can be
-// performed by doing logical "or" operation with bits presenting 2^n
-
-// exp(R) = 1 + (exp(R) - 1)
-// P = exp(R) - 1 approximated by Taylor series of 3rd degree
-// P = A3*R^3 + A2*R^2 + R, A3 = 1/6, A2 = 1/2
-//
+// 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
-// The final result is reconstructed as follows
-// exp(x) = T + T*P
+// For paths 1, and 2 SAFE is always 1.
+// For path 4, Safe is always 0.
+// SAFE = 1 means we cannot overflow.
-// Special values
-//*********************************************************************
-// coshf(+0) = 1.0
-// coshf(-0) = 1.0
+#include "libm_support.h"
-// coshf(+qnan) = +qnan
-// coshf(-qnan) = -qnan
-// coshf(+snan) = +qnan
-// coshf(-snan) = -qnan
+// Assembly macros
+//==============================================================
+coshf_FR_X = f44
+coshf_FR_SGNX = f40
-// coshf(-inf) = +inf
-// coshf(+inf) = +inf
+coshf_FR_Inv_log2by64 = f9
+coshf_FR_log2by64_lo = f11
+coshf_FR_log2by64_hi = f10
-// Overflow and Underflow
-//*********************************************************************
-// coshf(x) = largest single normal when
-// x = 89.41598 = 0x42b2d4fc
-//
-// There is no underflow.
+coshf_FR_A1 = f9
+coshf_FR_A2 = f10
+coshf_FR_A3 = f11
-// Registers used
-//*********************************************************************
-// Floating Point registers used:
-// f8 input, output
-// f6,f7, f9 -> f15, f32 -> f45
+coshf_FR_Rcub = f12
+coshf_FR_M_temp = f13
+coshf_FR_R_temp = f13
+coshf_FR_Rsq = f13
+coshf_FR_R = f14
-// General registers used:
-// r2, r3, r16 -> r38
+coshf_FR_M = f38
-// Predicate registers used:
-// p6 -> p15
+coshf_FR_B1 = f15
+coshf_FR_B2 = f32
+coshf_FR_B3 = f33
-// Assembly macros
-//*********************************************************************
-// integer registers used
-// scratch
-rNJ = r2
-rNJ_neg = r3
-
-rJ_neg = r16
-rN_neg = r17
-rSignexp_x = r18
-rExp_x = r18
-rExp_mask = r19
-rExp_bias = r20
-rAd1 = r21
-rAd2 = r22
-rJ = r23
-rN = r24
-rTblAddr = r25
-rA3 = r26
-rExpHalf = r27
-rLn2Div64 = r28
-rGt_ln = r29
-r17ones_m1 = r29
-rRightShifter = r30
-rJ_mask = r30
-r64DivLn2 = r31
-rN_mask = r31
-// stacked
-GR_SAVE_PFS = r32
-GR_SAVE_B0 = r33
-GR_SAVE_GP = r34
-GR_Parameter_X = r35
-GR_Parameter_Y = r36
-GR_Parameter_RESULT = r37
-GR_Parameter_TAG = r38
-
-// floating point registers used
-FR_X = f10
-FR_Y = f1
-FR_RESULT = f8
-// scratch
-fRightShifter = f6
-f64DivLn2 = f7
-fNormX = f9
-fNint = f10
-fN = f11
-fR = f12
-fLn2Div64 = f13
-fA2 = f14
-fA3 = f15
-// stacked
-fP = f32
-fT = f33
-fMIN_SGL_OFLOW_ARG = f34
-fMAX_SGL_NORM_ARG = f35
-fRSqr = f36
-fA1 = f37
-fA21 = f37
-fA4 = f38
-fA43 = f38
-fA4321 = f38
-fX4 = f39
-fTmp = f39
-fGt_pln = f39
-fWre_urm_f8 = f40
-fXsq = f40
-fP_neg = f41
-fT_neg = f42
-fExp = f43
-fExp_neg = f44
-fAbsX = f45
-
-
-RODATA
-.align 16
+coshf_FR_peven_temp1 = f34
+coshf_FR_peven_temp2 = f35
+coshf_FR_peven = f36
-LOCAL_OBJECT_START(_coshf_table)
-data4 0x42b2d4fd // Smallest single arg to overflow single result
-data4 0x42b2d4fc // Largest single arg to give normal single result
-data4 0x00000000 // pad
-data4 0x00000000 // pad
-//
-// 2^(j/64) table, j goes from 0 to 63
-data8 0x0000000000000000 // 2^(0/64)
-data8 0x00002C9A3E778061 // 2^(1/64)
-data8 0x000059B0D3158574 // 2^(2/64)
-data8 0x0000874518759BC8 // 2^(3/64)
-data8 0x0000B5586CF9890F // 2^(4/64)
-data8 0x0000E3EC32D3D1A2 // 2^(5/64)
-data8 0x00011301D0125B51 // 2^(6/64)
-data8 0x0001429AAEA92DE0 // 2^(7/64)
-data8 0x000172B83C7D517B // 2^(8/64)
-data8 0x0001A35BEB6FCB75 // 2^(9/64)
-data8 0x0001D4873168B9AA // 2^(10/64)
-data8 0x0002063B88628CD6 // 2^(11/64)
-data8 0x0002387A6E756238 // 2^(12/64)
-data8 0x00026B4565E27CDD // 2^(13/64)
-data8 0x00029E9DF51FDEE1 // 2^(14/64)
-data8 0x0002D285A6E4030B // 2^(15/64)
-data8 0x000306FE0A31B715 // 2^(16/64)
-data8 0x00033C08B26416FF // 2^(17/64)
-data8 0x000371A7373AA9CB // 2^(18/64)
-data8 0x0003A7DB34E59FF7 // 2^(19/64)
-data8 0x0003DEA64C123422 // 2^(20/64)
-data8 0x0004160A21F72E2A // 2^(21/64)
-data8 0x00044E086061892D // 2^(22/64)
-data8 0x000486A2B5C13CD0 // 2^(23/64)
-data8 0x0004BFDAD5362A27 // 2^(24/64)
-data8 0x0004F9B2769D2CA7 // 2^(25/64)
-data8 0x0005342B569D4F82 // 2^(26/64)
-data8 0x00056F4736B527DA // 2^(27/64)
-data8 0x0005AB07DD485429 // 2^(28/64)
-data8 0x0005E76F15AD2148 // 2^(29/64)
-data8 0x0006247EB03A5585 // 2^(30/64)
-data8 0x0006623882552225 // 2^(31/64)
-data8 0x0006A09E667F3BCD // 2^(32/64)
-data8 0x0006DFB23C651A2F // 2^(33/64)
-data8 0x00071F75E8EC5F74 // 2^(34/64)
-data8 0x00075FEB564267C9 // 2^(35/64)
-data8 0x0007A11473EB0187 // 2^(36/64)
-data8 0x0007E2F336CF4E62 // 2^(37/64)
-data8 0x00082589994CCE13 // 2^(38/64)
-data8 0x000868D99B4492ED // 2^(39/64)
-data8 0x0008ACE5422AA0DB // 2^(40/64)
-data8 0x0008F1AE99157736 // 2^(41/64)
-data8 0x00093737B0CDC5E5 // 2^(42/64)
-data8 0x00097D829FDE4E50 // 2^(43/64)
-data8 0x0009C49182A3F090 // 2^(44/64)
-data8 0x000A0C667B5DE565 // 2^(45/64)
-data8 0x000A5503B23E255D // 2^(46/64)
-data8 0x000A9E6B5579FDBF // 2^(47/64)
-data8 0x000AE89F995AD3AD // 2^(48/64)
-data8 0x000B33A2B84F15FB // 2^(49/64)
-data8 0x000B7F76F2FB5E47 // 2^(50/64)
-data8 0x000BCC1E904BC1D2 // 2^(51/64)
-data8 0x000C199BDD85529C // 2^(52/64)
-data8 0x000C67F12E57D14B // 2^(53/64)
-data8 0x000CB720DCEF9069 // 2^(54/64)
-data8 0x000D072D4A07897C // 2^(55/64)
-data8 0x000D5818DCFBA487 // 2^(56/64)
-data8 0x000DA9E603DB3285 // 2^(57/64)
-data8 0x000DFC97337B9B5F // 2^(58/64)
-data8 0x000E502EE78B3FF6 // 2^(59/64)
-data8 0x000EA4AFA2A490DA // 2^(60/64)
-data8 0x000EFA1BEE615A27 // 2^(61/64)
-data8 0x000F50765B6E4540 // 2^(62/64)
-data8 0x000FA7C1819E90D8 // 2^(63/64)
-LOCAL_OBJECT_END(_coshf_table)
-
-LOCAL_OBJECT_START(cosh_p_table)
-data8 0x3efa3001dcf5905b // A4
-data8 0x3f56c1437543543e // A3
-data8 0x3fa5555572601504 // A2
-data8 0x3fdfffffffe2f097 // A1
-LOCAL_OBJECT_END(cosh_p_table)
+coshf_FR_podd_temp1 = f34
+coshf_FR_podd_temp2 = f35
+coshf_FR_podd = f37
+
+coshf_FR_J_temp = f9
+coshf_FR_J = f10
+
+coshf_FR_Mmj = f39
+
+coshf_FR_N_temp1 = f11
+coshf_FR_N_temp2 = f12
+coshf_FR_N = f13
+
+coshf_FR_spos = f14
+coshf_FR_sneg = f15
+
+coshf_FR_Tjhi = f32
+coshf_FR_Tjlo = f33
+coshf_FR_Tmjhi = f34
+coshf_FR_Tmjlo = f35
+
+GR_mJ = r35
+GR_J = r36
+
+AD_mJ = r38
+AD_J = r39
+
+
+GR_SAVE_B0 = r42
+GR_SAVE_PFS = r41
+GR_SAVE_GP = r43
+
+GR_Parameter_X = r44
+GR_Parameter_Y = r45
+GR_Parameter_RESULT = r46
+GR_Parameter_TAG = r47
+
+FR_X = f8
+FR_Y = f0
+FR_RESULT = f44
+
+
+coshf_FR_C_hi = f9
+coshf_FR_C_hi_temp = f10
+coshf_FR_C_lo_temp1 = f11
+coshf_FR_C_lo_temp2 = f12
+coshf_FR_C_lo_temp3 = f13
+
+coshf_FR_C_lo = f38
+coshf_FR_S_hi = f39
+
+coshf_FR_S_hi_temp1 = f10
+coshf_FR_Y_hi = f11
+coshf_FR_Y_lo_temp = f12
+coshf_FR_Y_lo = f13
+coshf_FR_COSH = f9
+
+coshf_FR_X2 = f9
+coshf_FR_X4 = f10
+
+coshf_FR_P1 = f14
+coshf_FR_P2 = f15
+coshf_FR_P3 = f32
+coshf_FR_P4 = f33
+coshf_FR_P5 = f34
+coshf_FR_P6 = f35
+coshf_FR_TINY_THRESH = f9
+
+coshf_FR_COSH_temp = f10
+coshf_FR_SCALE = f11
+
+coshf_FR_hi_lo = f10
+
+coshf_FR_poly_podd_temp1 = f11
+coshf_FR_poly_podd_temp2 = f13
+coshf_FR_poly_peven_temp1 = f11
+coshf_FR_poly_peven_temp2 = f13
+
+// Data tables
+//==============================================================
+
+#ifdef _LIBC
+.rodata
+#else
+.data
+#endif
+
+.align 16
+single_coshf_arg_reduction:
+ASM_TYPE_DIRECTIVE(single_coshf_arg_reduction,@object)
+ data8 0xB8AA3B295C17F0BC, 0x00004005
+ data8 0xB17217F7D1000000, 0x00003FF8
+ data8 0xCF79ABC9E3B39804, 0x00003FD0
+ASM_SIZE_DIRECTIVE(single_coshf_arg_reduction)
+
+single_coshf_p_table:
+ASM_TYPE_DIRECTIVE(single_coshf_p_table,@object)
+ data8 0x8000000000000000, 0x00003FFE
+ data8 0xAAAAAAAAAAAAAB80, 0x00003FFA
+ data8 0xB60B60B60B4FE884, 0x00003FF5
+ data8 0xD00D00D1021D7370, 0x00003FEF
+ data8 0x93F27740C0C2F1CC, 0x00003FE9
+ data8 0x8FA02AC65BCBD5BC, 0x00003FE2
+ASM_SIZE_DIRECTIVE(single_coshf_p_table)
+
+single_coshf_ab_table:
+ASM_TYPE_DIRECTIVE(single_coshf_ab_table,@object)
+ data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC
+ data8 0x88888888884ECDD5, 0x00003FF8
+ data8 0xD00D0C6DCC26A86B, 0x00003FF2
+ data8 0x8000000000000002, 0x00003FFE
+ data8 0xAAAAAAAAAA402C77, 0x00003FFA
+ data8 0xB60B6CC96BDB144D, 0x00003FF5
+ASM_SIZE_DIRECTIVE(single_coshf_ab_table)
+
+single_coshf_j_table:
+ASM_TYPE_DIRECTIVE(single_coshf_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(single_coshf_j_table)
+
+.align 32
+.global coshf#
.section .text
-GLOBAL_IEEE754_ENTRY(coshf)
+.proc coshf#
+.align 32
-{ .mlx
- getf.exp rSignexp_x = f8 // Must recompute if x unorm
- movl r64DivLn2 = 0x40571547652B82FE // 64/ln(2)
+coshf:
+
+#ifdef _LIBC
+.global __ieee754_coshf#
+.proc __ieee754_coshf#
+__ieee754_coshf:
+#endif
+
+// X NAN?
+
+
+{ .mfi
+ alloc r32 = ar.pfs,0,12,4,0
+(p0) fclass.m.unc p6,p7 = f8, 0xc3
+ nop.i 999 ;;
+}
+{ .mfb
+ nop.m 999
+(p6) fma.s.s0 f8 = f8,f1,f8
+(p6) br.ret.spnt b0 ;;
}
+
+{ .mfi
+ nop.m 999
+ nop.f 999
+ nop.i 999 ;;
+}
+
+// X infinity
+{ .mfi
+ nop.m 999
+(p0) fclass.m.unc p6,p0 = f8, 0x23
+ 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
- addl rTblAddr = @ltoff(_coshf_table),gp
- movl rRightShifter = 0x43E8000000000000 // DP Right Shifter
+ nop.m 999
+(p0) movl r32 = 0x000000000000fffd ;;
}
-;;
{ .mfi
- // point to the beginning of the table
- ld8 rTblAddr = [rTblAddr]
- fclass.m p6, p0 = f8, 0x0b // Test for x=unorm
- addl rA3 = 0x3E2AA, r0 // high bits of 1.0/6.0 rounded to SP
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
}
+
{ .mfi
- nop.m 0
- fnorm.s1 fNormX = f8 // normalized x
- addl rExpHalf = 0xFFFE, r0 // exponent of 1/2
+ nop.m 999
+(p0) fmerge.s coshf_FR_X = f0,f8
+ nop.i 999
}
-;;
{ .mfi
- setf.d f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg
- fclass.m p15, p0 = f8, 0x1e3 // test for NaT,NaN,Inf
- nop.i 0
+ nop.m 999
+(p0) fmerge.s coshf_FR_SGNX = f8,f1
+ nop.i 999 ;;
}
-{ .mlx
- // load Right Shifter to FP reg
- setf.d fRightShifter = rRightShifter
- movl rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR
+
+{ .mfi
+ nop.m 999
+(p0) fcmp.lt.unc p0,p7 = coshf_FR_X,f9
+ nop.i 999 ;;
+}
+
+{ .mib
+ nop.m 999
+ nop.i 999
+(p7) br.cond.sptk L(COSH_BY_TBL) ;;
+}
+
+
+// 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(single_coshf_p_table), gp
+ nop.i 999
+}
+;;
+
+{ .mmi
+ ld8 r34 = [r34]
+ nop.m 999
+ nop.i 999
}
;;
+// Calculate coshf_FR_X2 = ax*ax and coshf_FR_X4 = ax*ax*ax*ax
+{ .mmf
+ nop.m 999
+(p0) ldfe coshf_FR_P1 = [r34],16
+(p0) fma.s1 coshf_FR_X2 = coshf_FR_X, coshf_FR_X, f0 ;;
+}
+
+{ .mmi
+(p0) ldfe coshf_FR_P2 = [r34],16 ;;
+(p0) ldfe coshf_FR_P3 = [r34],16
+ nop.i 999 ;;
+}
+
+{ .mmi
+(p0) ldfe coshf_FR_P4 = [r34],16 ;;
+(p0) ldfe coshf_FR_P5 = [r34],16
+ nop.i 999 ;;
+}
+
{ .mfi
- mov rExp_mask = 0x1ffff
- fcmp.eq.s1 p13, p0 = f0, f8 // test for x = 0.0
- shl rA3 = rA3, 12 // 0x3E2AA000, approx to 1.0/6.0 in SP
+(p0) ldfe coshf_FR_P6 = [r34],16
+(p0) fma.s1 coshf_FR_X4 = coshf_FR_X2, coshf_FR_X2, f0
+ nop.i 999 ;;
}
-{ .mfb
- nop.m 0
- nop.f 0
-(p6) br.cond.spnt COSH_UNORM // Branch if x=unorm
+
+// Calculate coshf_FR_podd = x4 *(x4 * P_5 + P_3) + P_1
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_poly_podd_temp1 = coshf_FR_X4, coshf_FR_P5, coshf_FR_P3
+ nop.i 999 ;;
}
-;;
-COSH_COMMON:
{ .mfi
- setf.exp fA2 = rExpHalf // load A2 to FP reg
- nop.f 0
- mov rExp_bias = 0xffff
+ nop.m 999
+(p0) fma.s1 coshf_FR_podd = coshf_FR_X4, coshf_FR_poly_podd_temp1, coshf_FR_P1
+ nop.i 999
}
-{ .mfb
- setf.d fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg
-(p15) fma.s.s0 f8 = f8, f8, f0 // result if x = NaT,NaN,Inf
-(p15) br.ret.spnt b0 // exit here if x = NaT,NaN,Inf
+
+// Calculate coshf_FR_peven = p_even = x4 *(x4 * (x4 * P_6 + P_4) + P_2)
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_poly_peven_temp1 = coshf_FR_X4, coshf_FR_P6, coshf_FR_P4
+ nop.i 999 ;;
}
-;;
{ .mfi
- // min overflow and max normal threshold
- ldfps fMIN_SGL_OFLOW_ARG, fMAX_SGL_NORM_ARG = [rTblAddr], 8
- nop.f 0
- and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x
+ nop.m 999
+(p0) fma.s1 coshf_FR_poly_peven_temp2 = coshf_FR_X4, coshf_FR_poly_peven_temp1, coshf_FR_P2
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_peven = coshf_FR_X4, coshf_FR_poly_peven_temp2, f0
+ nop.i 999 ;;
+}
+
+// Y_lo = x2*p_odd + p_even
+// Calculate f8 = Y_hi + Y_lo
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_Y_lo = coshf_FR_X2, coshf_FR_podd, coshf_FR_peven
+ nop.i 999 ;;
}
+
{ .mfb
- setf.s fA3 = rA3 // load A3 to FP reg
-(p13) fma.s.s0 f8 = f1, f1, f0 // result if x = 0.0
-(p13) br.ret.spnt b0 // exit here if x =0.0
+ nop.m 999
+(p0) fma.s.s0 f8 = f1, f1, coshf_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 = 0x0000000000010006 ;;
}
-;;
{ .mfi
- sub rExp_x = rExp_x, rExp_bias // True exponent of x
- fmerge.s fAbsX = f0, fNormX // Form |x|
- nop.i 0
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- // x*(64/ln(2)) + Right Shifter
- fma.s1 fNint = fNormX, f64DivLn2, fRightShifter
- add rTblAddr = 8, rTblAddr
+ nop.m 999
+(p0) fcmp.ge.unc p6,p7 = coshf_FR_X,f9
+ 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
+
+{ .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
+// coshf(x) = coshf(B+R)
+// = coshf(B) coshf(R) + sinh(B) sinh(R)
+// coshf(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(single_coshf_arg_reduction), gp
+ nop.i 999
}
;;
-{ .mfi
- nop.m 0
- // check for overflow
- fcmp.ge.s1 p12, p13 = fAbsX, fMIN_SGL_OFLOW_ARG
- mov rJ_mask = 0x3f // 6-bit mask for J
+
+// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and
+// put them in an exponent.
+// coshf_FR_spos = 2^(N-1) and coshf_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
+(p0) ldfe coshf_FR_Inv_log2by64 = [r34],16 ;;
+(p0) ldfe coshf_FR_log2by64_hi = [r34],16
+ nop.i 999 ;;
+}
+
+{ .mbb
+(p0) ldfe coshf_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(single_coshf_ab_table), gp
+ nop.i 999
}
;;
-{ .mfb
- nop.m 0
- fms.s1 fN = fNint, f1, fRightShifter // n in FP register
- // branch out if overflow
-(p12) br.cond.spnt COSH_CERTAIN_OVERFLOW
+{ .mmi
+ 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)
+// coshf_FR_M = M = truncate(ax/(log2/64))
+// Put the significand of M in r35
+// and the floating point representation of M in coshf_FR_M
+
{ .mfi
- getf.sig rNJ = fNint // bits of n, j
- // check for possible overflow
- fcmp.gt.s1 p13, p0 = fAbsX, fMAX_SGL_NORM_ARG
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_M = coshf_FR_X, coshf_FR_Inv_log2by64, f0
+ nop.i 999
}
-;;
{ .mfi
- addl rN = 0xFFBF - 63, rNJ // biased and shifted n-1,j
- fnma.s1 fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64
- and rJ = rJ_mask, rNJ // bits of j
+(p0) ldfe coshf_FR_A1 = [r34],16
+ nop.f 999
+ nop.i 999 ;;
}
+
{ .mfi
- sub rNJ_neg = r0, rNJ // bits of n, j for -x
- nop.f 0
- andcm rN_mask = -1, rJ_mask // 0xff...fc0 to mask N
+ nop.m 999
+(p0) fcvt.fx.s1 coshf_FR_M_temp = coshf_FR_M
+ nop.i 999 ;;
}
-;;
{ .mfi
- shladd rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table
- nop.f 0
- and rN = rN_mask, rN // biased, shifted n-1
+ nop.m 999
+(p0) fnorm.s1 coshf_FR_M = coshf_FR_M_temp
+ nop.i 999 ;;
}
+
{ .mfi
- addl rN_neg = 0xFFBF - 63, rNJ_neg // -x biased, shifted n-1,j
- nop.f 0
- and rJ_neg = rJ_mask, rNJ_neg // bits of j for -x
+(p0) getf.sig r35 = coshf_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
- ld8 rJ = [rJ] // Table value
- nop.f 0
- shl rN = rN, 46 // 2^(n-1) bits in DP format
+ nop.m 999
+(p0) fnma.s1 coshf_FR_R_temp = coshf_FR_M, coshf_FR_log2by64_hi, coshf_FR_X
+ nop.i 999
}
+
{ .mfi
- shladd rJ_neg = rJ_neg, 3, rTblAddr // addr in 2^(j/64) table -x
- nop.f 0
- and rN_neg = rN_mask, rN_neg // biased, shifted n-1 for -x
+(p0) ldfe coshf_FR_A2 = [r34],16
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- ld8 rJ_neg = [rJ_neg] // Table value for -x
- nop.f 0
- shl rN_neg = rN_neg, 46 // 2^(n-1) bits in DP format for -x
+ nop.m 999
+(p0) fnma.s1 coshf_FR_R = coshf_FR_M, coshf_FR_log2by64_lo, coshf_FR_R_temp
+ nop.i 999
+}
+
+// Get the B coefficients
+// f15 = B_1
+// f32 = B_2
+// f33 = B_3
+
+{ .mmi
+(p0) ldfe coshf_FR_A3 = [r34],16 ;;
+(p0) ldfe coshf_FR_B1 = [r34],16
+ nop.i 999 ;;
}
-;;
+
+{ .mmi
+(p0) ldfe coshf_FR_B2 = [r34],16 ;;
+(p0) ldfe coshf_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
- or rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format
- nop.f 0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_Rsq = coshf_FR_R, coshf_FR_R, f0
+(p0) shr r36 = r37, 0x2 ;;
}
-;;
-{ .mmf
- setf.d fT = rN // 2^(n-1) * 2^(j/64)
- or rN_neg = rN_neg, rJ_neg // -x bits of 2^n * 2^(j/64) in DP
- fma.s1 fRSqr = fR, fR, f0 // R^2
+// 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(single_coshf_j_table), gp
+ nop.i 999
}
;;
{ .mfi
- setf.d fT_neg = rN_neg // 2^(n-1) * 2^(j/64) for -x
- fma.s1 fP = fA3, fR, fA2 // A3*R + A2
- nop.i 0
+ ld8 r37 = [r37]
+(p0) fma.s1 coshf_FR_Rcub = coshf_FR_Rsq, coshf_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
- fnma.s1 fP_neg = fA3, fR, fA2 // A3*R + A2 for -x
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_peven_temp1 = coshf_FR_Rsq, coshf_FR_B3, coshf_FR_B2
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fP = fP, fRSqr, fR // P = (A3*R + A2)*R^2 + R
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_peven_temp2 = coshf_FR_Rsq, coshf_FR_peven_temp1, coshf_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
- fms.s1 fP_neg = fP_neg, fRSqr, fR // P = (A3*R + A2)*R^2 + R, -x
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_podd_temp1 = coshf_FR_Rsq, coshf_FR_A3, coshf_FR_A2
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fmpy.s0 fTmp = fLn2Div64, fLn2Div64 // Force inexact
- nop.i 0
+(p0) setf.exp coshf_FR_N_temp1 = r39
+ nop.f 999
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fExp = fP, fT, fT // exp(x)/2
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_peven = coshf_FR_Rsq, coshf_FR_peven_temp2, f0
+ nop.i 999
}
-{ .mfb
- nop.m 0
- fma.s1 fExp_neg = fP_neg, fT_neg, fT_neg // exp(-x)/2
- // branch out if possible overflow result
-(p13) br.cond.spnt COSH_POSSIBLE_OVERFLOW
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_podd_temp2 = coshf_FR_Rsq, coshf_FR_podd_temp1, coshf_FR_A1
+ nop.i 999 ;;
}
-;;
-{ .mfb
- nop.m 0
- // final result in the absence of overflow
- fma.s.s0 f8 = fExp, f1, fExp_neg // result = (exp(x)+exp(-x))/2
- // exit here in the absence of overflow
- br.ret.sptk b0 // Exit main path, 0.25 <= |x| < 89.41598
+{ .mfi
+(p0) setf.exp f9 = r32
+ nop.f 999
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_podd = coshf_FR_podd_temp2, coshf_FR_Rcub, coshf_FR_R
+ nop.i 999
+}
+
+// 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 coshf_FR_N_temp2 = r40
+(p0) movl r40 = 0x0000000000000020 ;;
+}
+
+{ .mfi
+(p0) sub GR_mJ = r40, r36
+(p0) fmerge.se coshf_FR_spos = coshf_FR_N_temp1, f1
+(p0) adds GR_J = 0x20, r36 ;;
+}
+
+{ .mii
+ nop.m 999
+(p0) shl GR_mJ = GR_mJ, 5 ;;
+(p0) add AD_mJ = r37, GR_mJ ;;
}
-;;
-// Here if 0 < |x| < 0.25. Evaluate 8th order polynomial.
-COSH_SMALL:
{ .mmi
- add rAd1 = 0x200, rTblAddr
- add rAd2 = 0x210, rTblAddr
- nop.i 0
+ nop.m 999
+(p0) ldfe coshf_FR_Tmjhi = [AD_mJ],16
+(p0) shl GR_J = GR_J, 5 ;;
+}
+
+{ .mfi
+(p0) ldfs coshf_FR_Tmjlo = [AD_mJ],16
+(p0) fcmp.lt.unc.s1 p6,p7 = coshf_FR_X,f9
+(p0) add AD_J = r37, GR_J ;;
}
-;;
{ .mmi
- ldfpd fA4, fA3 = [rAd1]
- ldfpd fA2, fA1 = [rAd2]
- nop.i 0
+(p0) ldfe coshf_FR_Tjhi = [AD_J],16 ;;
+(p0) ldfs coshf_FR_Tjlo = [AD_J],16
+ nop.i 999 ;;
}
-;;
+
+{ .mfb
+ nop.m 999
+(p0) fmerge.se coshf_FR_sneg = coshf_FR_N_temp2, f1
+(p7) br.cond.spnt L(COSH_BY_EXP) ;;
+}
+
+// ******************************************************
+// If NOT branch to EXP
+// ******************************************************
+// Calculate C_hi
+// ******************************************************
+// coshf_FR_C_hi_temp = coshf_FR_sneg * coshf_FR_Tmjhi
+// coshf_FR_C_hi = coshf_FR_spos * coshf_FR_Tjhi + (coshf_FR_sneg * coshf_FR_Tmjhi)
{ .mfi
- nop.m 0
- fma.s1 fX4 = fXsq, fXsq, f0
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_hi_temp = coshf_FR_sneg, coshf_FR_Tmjhi, f0
+ nop.i 999 ;;
}
-;;
{ .mfi
- nop.m 0
- fma.s1 fA43 = fXsq, fA4, fA3
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_hi = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_C_hi_temp
+ nop.i 999
}
+
+// ******************************************************
+// Calculate S_hi
+// ******************************************************
+// coshf_FR_S_hi_temp1 = coshf_FR_sneg * coshf_FR_Tmjhi
+// coshf_FR_S_hi = coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi_temp1
+
{ .mfi
- nop.m 0
- fma.s1 fA21 = fXsq, fA2, fA1
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_S_hi_temp1 = coshf_FR_sneg, coshf_FR_Tmjhi, f0
+ nop.i 999 ;;
}
-;;
+
+// ******************************************************
+// Calculate C_lo
+// ******************************************************
+// coshf_FR_C_lo_temp1 = coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi
+// coshf_FR_C_lo_temp2 = coshf_FR_sneg * coshf_FR_Tmjlo + (coshf_FR_spos * coshf_FR_Tjhi - coshf_FR_C_hi)
+// coshf_FR_C_lo_temp1 = coshf_FR_sneg * coshf_FR_Tmjlo
+// coshf_FR_C_lo_temp3 = coshf_FR_spos * coshf_FR_Tjlo + (coshf_FR_sneg * coshf_FR_Tmjlo)
+// coshf_FR_C_lo = coshf_FR_C_lo_temp3 + coshf_FR_C_lo_temp2
{ .mfi
- nop.m 0
- fma.s1 fA4321 = fX4, fA43, fA21
- nop.i 0
+ nop.m 999
+(p0) fms.s1 coshf_FR_C_lo_temp1 = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_C_hi
+ nop.i 999
}
-;;
-// Dummy multiply to generate inexact
{ .mfi
- nop.m 0
- fmpy.s0 fTmp = fA4, fA4
- nop.i 0
+ nop.m 999
+(p0) fms.s1 coshf_FR_S_hi = coshf_FR_spos, coshf_FR_Tjhi, coshf_FR_S_hi_temp1
+ nop.i 999 ;;
}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_lo_temp2 = coshf_FR_sneg, coshf_FR_Tmjhi, coshf_FR_C_lo_temp1
+ nop.i 999
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_lo_temp1 = coshf_FR_sneg, coshf_FR_Tmjlo, f0
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_lo_temp3 = coshf_FR_spos, coshf_FR_Tjlo, coshf_FR_C_lo_temp1
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_C_lo = coshf_FR_C_lo_temp3, f1, coshf_FR_C_lo_temp2
+ nop.i 999 ;;
+}
+
+// ******************************************************
+// coshf_FR_Y_lo_temp = coshf_FR_C_hi * coshf_FR_peven + coshf_FR_C_lo
+// coshf_FR_Y_lo = coshf_FR_S_hi * coshf_FR_podd + coshf_FR_Y_lo_temp
+// coshf_FR_COSH = Y_hi + Y_lo
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_Y_lo_temp = coshf_FR_C_hi, coshf_FR_peven, coshf_FR_C_lo
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s1 coshf_FR_Y_lo = coshf_FR_S_hi, coshf_FR_podd, coshf_FR_Y_lo_temp
+ nop.i 999 ;;
+}
+
{ .mfb
- nop.m 0
- fma.s.s0 f8 = fA4321, fXsq, f1
- br.ret.sptk b0 // Exit if 0 < |x| < 0.25
+ nop.m 999
+(p0) fma.s.s0 f8 = coshf_FR_C_hi, f1, coshf_FR_Y_lo
+(p0) br.ret.sptk b0 ;;
}
-;;
-COSH_POSSIBLE_OVERFLOW:
-// Here if fMAX_SGL_NORM_ARG < x < fMIN_SGL_OFLOW_ARG
-// This cannot happen if input is a single, only if input higher precision.
-// Overflow is a possibility, not a certainty.
+L(COSH_BY_EXP):
-// Recompute result using status field 2 with user's rounding mode,
-// and wre set. If result is larger than largest single, then we have
-// 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)
+// = coshf_FR_spos * (coshf_FR_Tjhi + coshf_FR_Y_lo)
{ .mfi
- mov rGt_ln = 0x1007f // Exponent for largest single + 1 ulp
- fsetc.s2 0x7F,0x42 // Get user's round mode, set wre
- nop.i 0
+ nop.m 999
+(p0) fma.s1 coshf_FR_Y_lo_temp = coshf_FR_peven, f1, coshf_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
+// There is a danger of single overflow if N-1 > 0x7e = 126
+
+{ .mlx
+ nop.m 999
+(p0) movl r32 = 0x000000000000007e ;;
}
-;;
{ .mfi
- setf.exp fGt_pln = rGt_ln // Create largest single + 1 ulp
- fma.s.s2 fWre_urm_f8 = fP, fT, fT // Result with wre set
- nop.i 0
+(p0) cmp.gt.unc p0,p7 = r34, r32
+ nop.f 999
+ 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 coshf_FR_Y_lo = coshf_FR_Tjhi, coshf_FR_Y_lo_temp, coshf_FR_Tjlo
+ 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.s1 coshf_FR_COSH_temp = coshf_FR_Y_lo, f1, coshf_FR_Tjhi
+ nop.i 999 ;;
}
-;;
-{ .mfb
- nop.m 0
- nop.f 0
-(p6) br.cond.spnt COSH_CERTAIN_OVERFLOW // Branch if overflow
+{ .mfi
+ nop.m 999
+(p0) fma.s.s0 f44 = coshf_FR_spos, coshf_FR_COSH_temp, f0
+ nop.i 999 ;;
}
-;;
+// If over_SAFE is set, return
{ .mfb
- nop.m 0
- fma.s.s0 f8 = fP, fT, fT
- br.ret.sptk b0 // Exit if really no overflow
+ nop.m 999
+(p7) fmerge.s f8 = f44,f44
+(p7) br.ret.sptk b0 ;;
}
-;;
-// here if overflow
-COSH_CERTAIN_OVERFLOW:
-{ .mmi
- addl r17ones_m1 = 0x1FFFE, r0
-;;
- setf.exp fTmp = r17ones_m1
- nop.i 0
+// 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
- alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers
- fmerge.s FR_X = f8,f8
- nop.i 0
+ nop.m 999
+(p0) fma.s.s2 f43 = coshf_FR_spos, coshf_FR_COSH_temp, f0
+ nop.i 999 ;;
+}
+
+// 1 more that the exponent of the largest double (7FE) = 7FF
+// 7FF - 3FF = 400 (true); 400 + FFFF = 103FF (register-biased)
+// So 0 103FF 8000000000000000 is one ulp more than
+// largest double in register bias
+// 1 more that the exponent of the largest single (FE) = FF
+// FF - 7F = 80 (true); 80 + FFFF = 1007F (register-biased)
+// 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 = 0x000000000001007f ;;
+}
+
+{ .mmf
+ nop.m 999
+(p0) setf.exp f41 = r32
+(p0) fsetc.s2 0x7F,0x40 ;;
}
+
+{ .mfi
+ 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 65
+{ .mii
+ nop.m 999
+ nop.i 999 ;;
+(p8) mov GR_Parameter_TAG = 65 ;;
+}
+
{ .mfb
- mov GR_Parameter_TAG = 65
- fma.s.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 GR_Parameter_TAG = 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 // Return to main path
+ nop.m 999
+(p0) fmerge.s f8 = f44,f44
+(p0) br.ret.sptk b0 ;;
}
-;;
-GLOBAL_IEEE754_END(coshf)
+
+L(COSH_HUGE):
+
+// for COSH_HUGE, put 24000 in exponent; take sign from input; add 1
+// SAFE: SAFE is always 0 for 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 coshf_FR_hi_lo = f1, f9, f1
+ nop.i 999 ;;
+}
+
+{ .mfi
+ nop.m 999
+(p0) fma.s.s0 f44 = f9, coshf_FR_hi_lo, f0
+(p0) mov GR_Parameter_TAG = 65
+}
+.endp coshf
+ASM_SIZE_DIRECTIVE(coshf)
-LOCAL_LIBM_ENTRY(__libm_error_region)
+.proc __libm_error_region
+__libm_error_region:
.prologue
{ .mfi
- add GR_Parameter_Y=-32,sp // Parameter 2 value
- nop.f 0
+ 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
+ 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
+.fframe 64
+ add sp=-64,sp // Create new stack
+ nop.f 0
+ mov GR_SAVE_GP=gp // Save gp
};;
{ .mmi
- stfs [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
+ stfs [GR_Parameter_Y] = FR_Y,16 // Save 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
-{ .mfi
- stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
- nop.f 0
- add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
+{ .mib
+ stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack
+ add GR_Parameter_RESULT = 0,GR_Parameter_Y
+ nop.b 0 // Parameter 3 address
}
{ .mib
- stfs [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
+ stfs [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
+ add GR_Parameter_Y = -16,GR_Parameter_Y
+ br.call.sptk.many b0=__libm_error_support# // Call error handling function
};;
-
{ .mmi
- add GR_Parameter_RESULT = 48,sp
- nop.m 0
- nop.i 0
+ nop.m 0
+ nop.m 0
+ add GR_Parameter_RESULT = 48,sp
};;
-
{ .mmi
- ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
+ ldfs 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
+ 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)
+ mov gp = GR_SAVE_GP // Restore gp
+ mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
+ br.ret.sptk b0 // Return
+};;
+.endp __libm_error_region
+ASM_SIZE_DIRECTIVE(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
generated by cgit v1.2.3 (git 2.39.1) at 2024-05-20 17:41:15 +0000