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-rw-r--r--sysdeps/ia64/fpu/e_sinhl.S1778
1 files changed, 785 insertions, 993 deletions
diff --git a/sysdeps/ia64/fpu/e_sinhl.S b/sysdeps/ia64/fpu/e_sinhl.S
index b880b95b64..ccc996a8cc 100644
--- a/sysdeps/ia64/fpu/e_sinhl.S
+++ b/sysdeps/ia64/fpu/e_sinhl.S
@@ -1,10 +1,10 @@
.file "sinhl.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
@@ -20,7 +20,7 @@
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
-//
+
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
@@ -35,17 +35,20 @@
//
// 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.
+// 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.
// 10/12/00 Update to set denormal operand and underflow flags
-// 1/22/01 Fixed to set inexact flag for small args. Fixed incorrect
+// 01/22/01 Fixed to set inexact flag for small args. Fixed incorrect
// call to __libm_error_support for 710.476 < x < 11357.2166.
+// 05/02/01 Reworked to improve speed of all paths
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 12/04/02 Improved performance
//
// API
//==============================================================
@@ -56,1269 +59,1058 @@
// Registers used
//==============================================================
// general registers:
-// r32 -> r47
+// r14 -> r40
// predicate registers used:
-// p6 p7 p8 p9
+// p6 -> p11
// floating-point registers used:
-// f9 -> f15; f32 -> f45;
+// f9 -> f15; f32 -> f90;
// f8 has input, then output
//
// Overview of operation
//==============================================================
-// There are four paths
-// 1. |x| < 0.25 SINH_BY_POLY
-// 2. |x| < 32 SINH_BY_TBL
-// 3. |x| < 2^14 SINH_BY_EXP
-// 4. |x_ >= 2^14 SINH_HUGE
-//
-// For double extended we get infinity for x >= 400c b174 ddc0 31ae c0ea
-// >= 1.0110001.... x 2^13
-// >= 11357.2166
+// There are seven paths
+// 1. 0 < |x| < 0.25 SINH_BY_POLY
+// 2. 0.25 <=|x| < 32 SINH_BY_TBL
+// 3. 32 <= |x| < 11357.21655 SINH_BY_EXP (merged path with SINH_BY_TBL)
+// 4. |x| >= 11357.21655 SINH_HUGE
+// 5. x=0 Done with early exit
+// 6. x=inf,nan Done with early exit
+// 7. x=denormal SINH_DENORM
//
-// But for double we get infinity for x >= 408633ce8fb9f87e
-// >= 1.0110...x 2^9
-// >= +7.10476e+002
+// For double extended we get overflow for x >= 400c b174 ddc0 31ae c0ea
+// >= 11357.21655
//
-// And for single we get infinity for x >= 42b3a496
-// >= 1.0110... 2^6
-// >= 89.8215
//
-// SAFE: If there is danger of overflow set SAFE to 0
-// NOT implemented: if there is danger of underflow, set SAFE to 0
-// SAFE for all paths listed below
-//
-// 1. SINH_BY_POLY
+// 1. SINH_BY_POLY 0 < |x| < 0.25
// ===============
-// If |x| is less than the tiny threshold, then clear SAFE
-// For double, the tiny threshold is -1022 = -0x3fe => -3fe + ffff = fc01
-// register-biased, this is fc01
-// For single, the tiny threshold is -126 = -7e => -7e + ffff = ff81
-// If |x| < tiny threshold, set SAFE = 0
+// Evaluate sinh(x) by a 13th order polynomial
+// Care is take for the order of multiplication; and P_1 is not exactly 1/3!,
+// P_2 is not exactly 1/5!, etc.
+// sinh(x) = sign * (series(e^x) - series(e^-x))/2
+// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11!
+// + ax^13/13!)
+// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) )
+// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ))
+// = sign * (ax + ax*p_odd + (ax*p_even))
+// = sign * (ax + Y_lo)
+// sinh(x) = sign * (Y_hi + Y_lo)
+// Note that ax = |x|
//
-// 2. SINH_BY_TBL
+// 2. SINH_BY_TBL 0.25 <= |x| < 32.0
// =============
-// SAFE: SAFE is always 1 for TBL;
+// sinh(x) = sinh(B+R)
+// = sinh(B)cosh(R) + cosh(B)sinh(R)
+//
+// ax = |x| = M*log2/64 + R
+// B = M*log2/64
+// M = 64*N + j
+// We will calculate M and get N as (M-j)/64
+// The division is a shift.
+// exp(B) = exp(N*log2 + j*log2/64)
+// = 2^N * 2^(j*log2/64)
+// sinh(B) = 1/2(e^B -e^-B)
+// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64))
+// sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64))
+// cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64))
+// 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32
+// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)
+//
+// R = ax - M*log2/64
+// R = ax - M*log2_by_64_hi - M*log2_by_64_lo
+// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)
+// = 1 + p_odd + p_even
+// where the p_even uses the A coefficients and the p_even uses
+// the B coefficients
+//
+// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd
+// cosh(R) = 1 + p_even
+// sinh(B) = S_hi + S_lo
+// cosh(B) = C_hi
+// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R)
//
-// 3. SINH_BY_EXP
+// 3. SINH_BY_EXP 32.0 <= |x| < 11357.21655 ( 400c b174 ddc0 31ae c0ea )
// ==============
-// There is a danger of double-extended overflow if N-1 > 16382 = 0x3ffe
-// r34 has N-1; 16382 is in register biased form, 0x13ffd
-// There is danger of double overflow if N-1 > 0x3fe
-// in register biased form, 0x103fd
-// Analagously, there is danger of single overflow if N-1 > 0x7e
-// in register biased form, 0x1007d
-// SAFE: If there is danger of overflow set SAFE to 0
+// Can approximate result by exp(x)/2 in this region.
+// Y_hi = Tjhi
+// Y_lo = Tjhi * (p_odd + p_even) + Tjlo
+// sinh(x) = Y_hi + Y_lo
//
-// 4. SINH_HUGE
+// 4. SINH_HUGE |x| >= 11357.21655 ( 400c b174 ddc0 31ae c0ea )
// ============
-// SAFE: SAFE is always 0 for HUGE
+// Set error tag and call error support
+//
//
-
-#include "libm_support.h"
-
// Assembly macros
//==============================================================
-sinh_FR_X = f44
-sinh_FR_X2 = f9
-sinh_FR_X4 = f10
-sinh_FR_SGNX = f40
-sinh_FR_all_ones = f45
-sinh_FR_tmp = f42
-
-sinh_FR_Inv_log2by64 = f9
-sinh_FR_log2by64_lo = f11
-sinh_FR_log2by64_hi = f10
-
-sinh_FR_A1 = f9
-sinh_FR_A2 = f10
-sinh_FR_A3 = f11
-
-sinh_FR_Rcub = f12
-sinh_FR_M_temp = f13
-sinh_FR_R_temp = f13
-sinh_FR_Rsq = f13
-sinh_FR_R = f14
-
-sinh_FR_M = f38
-
-sinh_FR_B1 = f15
-sinh_FR_B2 = f32
-sinh_FR_B3 = f33
+r_ad5 = r14
+r_rshf_2to57 = r15
+r_exp_denorm = r15
+r_ad_mJ_lo = r15
+r_ad_J_lo = r16
+r_2Nm1 = r17
+r_2mNm1 = r18
+r_exp_x = r18
+r_ad_J_hi = r19
+r_ad2o = r19
+r_ad_mJ_hi = r20
+r_mj = r21
+r_ad2e = r22
+r_ad3 = r23
+r_ad1 = r24
+r_Mmj = r24
+r_rshf = r25
+r_M = r25
+r_N = r25
+r_jshf = r26
+r_exp_2tom57 = r26
+r_j = r26
+r_exp_mask = r27
+r_signexp_x = r28
+r_signexp_sgnx_0_5 = r28
+r_exp_0_25 = r29
+r_sig_inv_ln2 = r30
+r_exp_32 = r30
+r_exp_huge = r30
+r_ad4 = r31
+
+GR_SAVE_PFS = r34
+GR_SAVE_B0 = r35
+GR_SAVE_GP = r36
+
+GR_Parameter_X = r37
+GR_Parameter_Y = r38
+GR_Parameter_RESULT = r39
+GR_Parameter_TAG = r40
+
+
+f_ABS_X = f9
+f_X2 = f10
+f_X4 = f11
+f_tmp = f14
+f_RSHF = f15
+
+f_Inv_log2by64 = f32
+f_log2by64_lo = f33
+f_log2by64_hi = f34
+f_A1 = f35
+
+f_A2 = f36
+f_A3 = f37
+f_Rcub = f38
+f_M_temp = f39
+f_R_temp = f40
+
+f_Rsq = f41
+f_R = f42
+f_M = f43
+f_B1 = f44
+f_B2 = f45
+
+f_B3 = f46
+f_peven_temp1 = f47
+f_peven_temp2 = f48
+f_peven = f49
+f_podd_temp1 = f50
+
+f_podd_temp2 = f51
+f_podd = f52
+f_poly65 = f53
+f_poly6543 = f53
+f_poly6to1 = f53
+f_poly43 = f54
+f_poly21 = f55
+
+f_X3 = f56
+f_INV_LN2_2TO63 = f57
+f_RSHF_2TO57 = f58
+f_2TOM57 = f59
+f_smlst_oflow_input = f60
+
+f_pre_result = f61
+f_huge = f62
+f_spos = f63
+f_sneg = f64
+f_Tjhi = f65
+
+f_Tjlo = f66
+f_Tmjhi = f67
+f_Tmjlo = f68
+f_S_hi = f69
+f_SC_hi_temp = f70
+
+f_S_lo_temp1 = f71
+f_S_lo_temp2 = f72
+f_S_lo_temp3 = f73
+f_S_lo_temp4 = f73
+f_S_lo = f74
+f_C_hi = f75
+
+f_Y_hi = f77
+f_Y_lo_temp = f78
+f_Y_lo = f79
+f_NORM_X = f80
+
+f_P1 = f81
+f_P2 = f82
+f_P3 = f83
+f_P4 = f84
+f_P5 = f85
+
+f_P6 = f86
+f_Tjhi_spos = f87
+f_Tjlo_spos = f88
+f_huge = f89
+f_signed_hi_lo = f90
-sinh_FR_peven_temp1 = f34
-sinh_FR_peven_temp2 = f35
-sinh_FR_peven = f36
-
-sinh_FR_podd_temp1 = f34
-sinh_FR_podd_temp2 = f35
-sinh_FR_podd = f37
-
-sinh_FR_poly_podd_temp1 = f11
-sinh_FR_poly_podd_temp2 = f13
-sinh_FR_poly_peven_temp1 = f11
-sinh_FR_poly_peven_temp2 = f13
-
-sinh_FR_J_temp = f9
-sinh_FR_J = f10
-
-sinh_FR_Mmj = f39
-
-sinh_FR_N_temp1 = f11
-sinh_FR_N_temp2 = f12
-sinh_FR_N = f13
-
-sinh_FR_spos = f14
-sinh_FR_sneg = f15
-
-sinh_FR_Tjhi = f32
-sinh_FR_Tjlo = f33
-sinh_FR_Tmjhi = f34
-sinh_FR_Tmjlo = f35
-
-sinh_GR_mJ = r35
-sinh_GR_J = r36
-
-sinh_AD_mJ = r38
-sinh_AD_J = r39
-sinh_GR_all_ones = r40
-
-sinh_FR_S_hi = f9
-sinh_FR_S_hi_temp = f10
-sinh_FR_S_lo_temp1 = f11
-sinh_FR_S_lo_temp2 = f12
-sinh_FR_S_lo_temp3 = f13
-
-sinh_FR_S_lo = f38
-sinh_FR_C_hi = f39
-
-sinh_FR_C_hi_temp1 = f10
-sinh_FR_Y_hi = f11
-sinh_FR_Y_lo_temp = f12
-sinh_FR_Y_lo = f13
-sinh_FR_SINH = f9
-
-sinh_FR_P1 = f14
-sinh_FR_P2 = f15
-sinh_FR_P3 = f32
-sinh_FR_P4 = f33
-sinh_FR_P5 = f34
-sinh_FR_P6 = f35
-
-sinh_FR_TINY_THRESH = f9
-
-sinh_FR_SINH_temp = f10
-sinh_FR_SCALE = f11
-
-sinh_FR_signed_hi_lo = f10
-
-
-GR_SAVE_PFS = r41
-GR_SAVE_B0 = r42
-GR_SAVE_GP = r43
-
-GR_Parameter_X = r44
-GR_Parameter_Y = r45
-GR_Parameter_RESULT = r46
// Data tables
//==============================================================
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+// DO NOT CHANGE ORDER OF THESE TABLES
+RODATA
.align 16
-double_sinh_arg_reduction:
-ASM_TYPE_DIRECTIVE(double_sinh_arg_reduction,@object)
- data8 0xB8AA3B295C17F0BC, 0x00004005
- data8 0xB17217F7D1000000, 0x00003FF8
- data8 0xCF79ABC9E3B39804, 0x00003FD0
-ASM_SIZE_DIRECTIVE(double_sinh_arg_reduction)
-
-double_sinh_p_table:
-ASM_TYPE_DIRECTIVE(double_sinh_p_table,@object)
- data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC
- data8 0x8888888888888412, 0x00003FF8
- data8 0xD00D00D00D4D39F2, 0x00003FF2
- data8 0xB8EF1D28926D8891, 0x00003FEC
- data8 0xD732377688025BE9, 0x00003FE5
- data8 0xB08AF9AE78C1239F, 0x00003FDE
-ASM_SIZE_DIRECTIVE(double_sinh_p_table)
-
-double_sinh_ab_table:
-ASM_TYPE_DIRECTIVE(double_sinh_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_sinh_ab_table)
-
-double_sinh_j_table:
-ASM_TYPE_DIRECTIVE(double_sinh_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_sinh_j_table)
-
-.align 32
-.global sinhl#
-
-.section .text
-.proc sinhl#
-.align 32
-
-sinhl:
-#ifdef _LIBC
-.global __ieee754_sinhl
-.type __ieee754_sinhl,@function
-__ieee754_sinhl:
-#endif
-
-// X infinity or NAN?
-// Take invalid fault if enabled
-
+LOCAL_OBJECT_START(sinh_arg_reduction)
+// data8 0xB8AA3B295C17F0BC, 0x00004005 // 64/log2 -- signif loaded with setf
+ data8 0xB17217F7D1000000, 0x00003FF8 // log2/64 high part
+ data8 0xCF79ABC9E3B39804, 0x00003FD0 // log2/64 low part
+ data8 0xb174ddc031aec0ea, 0x0000400c // Smallest x to overflow (11357.21655)
+LOCAL_OBJECT_END(sinh_arg_reduction)
+
+LOCAL_OBJECT_START(sinh_p_table)
+ data8 0xB08AF9AE78C1239F, 0x00003FDE // P6
+ data8 0xB8EF1D28926D8891, 0x00003FEC // P4
+ data8 0x8888888888888412, 0x00003FF8 // P2
+ data8 0xD732377688025BE9, 0x00003FE5 // P5
+ data8 0xD00D00D00D4D39F2, 0x00003FF2 // P3
+ data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // P1
+LOCAL_OBJECT_END(sinh_p_table)
+
+LOCAL_OBJECT_START(sinh_ab_table)
+ data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC // A1
+ data8 0x88888888884ECDD5, 0x00003FF8 // A2
+ data8 0xD00D0C6DCC26A86B, 0x00003FF2 // A3
+ data8 0x8000000000000002, 0x00003FFE // B1
+ data8 0xAAAAAAAAAA402C77, 0x00003FFA // B2
+ data8 0xB60B6CC96BDB144D, 0x00003FF5 // B3
+LOCAL_OBJECT_END(sinh_ab_table)
+
+LOCAL_OBJECT_START(sinh_j_hi_table)
+ data8 0xB504F333F9DE6484, 0x00003FFE
+ data8 0xB6FD91E328D17791, 0x00003FFE
+ data8 0xB8FBAF4762FB9EE9, 0x00003FFE
+ data8 0xBAFF5AB2133E45FB, 0x00003FFE
+ data8 0xBD08A39F580C36BF, 0x00003FFE
+ data8 0xBF1799B67A731083, 0x00003FFE
+ data8 0xC12C4CCA66709456, 0x00003FFE
+ data8 0xC346CCDA24976407, 0x00003FFE
+ data8 0xC5672A115506DADD, 0x00003FFE
+ data8 0xC78D74C8ABB9B15D, 0x00003FFE
+ data8 0xC9B9BD866E2F27A3, 0x00003FFE
+ data8 0xCBEC14FEF2727C5D, 0x00003FFE
+ data8 0xCE248C151F8480E4, 0x00003FFE
+ data8 0xD06333DAEF2B2595, 0x00003FFE
+ data8 0xD2A81D91F12AE45A, 0x00003FFE
+ data8 0xD4F35AABCFEDFA1F, 0x00003FFE
+ data8 0xD744FCCAD69D6AF4, 0x00003FFE
+ data8 0xD99D15C278AFD7B6, 0x00003FFE
+ data8 0xDBFBB797DAF23755, 0x00003FFE
+ data8 0xDE60F4825E0E9124, 0x00003FFE
+ data8 0xE0CCDEEC2A94E111, 0x00003FFE
+ data8 0xE33F8972BE8A5A51, 0x00003FFE
+ data8 0xE5B906E77C8348A8, 0x00003FFE
+ data8 0xE8396A503C4BDC68, 0x00003FFE
+ data8 0xEAC0C6E7DD24392F, 0x00003FFE
+ data8 0xED4F301ED9942B84, 0x00003FFE
+ data8 0xEFE4B99BDCDAF5CB, 0x00003FFE
+ data8 0xF281773C59FFB13A, 0x00003FFE
+ data8 0xF5257D152486CC2C, 0x00003FFE
+ data8 0xF7D0DF730AD13BB9, 0x00003FFE
+ data8 0xFA83B2DB722A033A, 0x00003FFE
+ data8 0xFD3E0C0CF486C175, 0x00003FFE
+ data8 0x8000000000000000, 0x00003FFF // Center of table
+ data8 0x8164D1F3BC030773, 0x00003FFF
+ data8 0x82CD8698AC2BA1D7, 0x00003FFF
+ data8 0x843A28C3ACDE4046, 0x00003FFF
+ data8 0x85AAC367CC487B15, 0x00003FFF
+ data8 0x871F61969E8D1010, 0x00003FFF
+ data8 0x88980E8092DA8527, 0x00003FFF
+ data8 0x8A14D575496EFD9A, 0x00003FFF
+ data8 0x8B95C1E3EA8BD6E7, 0x00003FFF
+ data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF
+ data8 0x8EA4398B45CD53C0, 0x00003FFF
+ data8 0x9031DC431466B1DC, 0x00003FFF
+ data8 0x91C3D373AB11C336, 0x00003FFF
+ data8 0x935A2B2F13E6E92C, 0x00003FFF
+ data8 0x94F4EFA8FEF70961, 0x00003FFF
+ data8 0x96942D3720185A00, 0x00003FFF
+ data8 0x9837F0518DB8A96F, 0x00003FFF
+ data8 0x99E0459320B7FA65, 0x00003FFF
+ data8 0x9B8D39B9D54E5539, 0x00003FFF
+ data8 0x9D3ED9A72CFFB751, 0x00003FFF
+ data8 0x9EF5326091A111AE, 0x00003FFF
+ data8 0xA0B0510FB9714FC2, 0x00003FFF
+ data8 0xA27043030C496819, 0x00003FFF
+ data8 0xA43515AE09E6809E, 0x00003FFF
+ data8 0xA5FED6A9B15138EA, 0x00003FFF
+ data8 0xA7CD93B4E965356A, 0x00003FFF
+ data8 0xA9A15AB4EA7C0EF8, 0x00003FFF
+ data8 0xAB7A39B5A93ED337, 0x00003FFF
+ data8 0xAD583EEA42A14AC6, 0x00003FFF
+ data8 0xAF3B78AD690A4375, 0x00003FFF
+ data8 0xB123F581D2AC2590, 0x00003FFF
+ data8 0xB311C412A9112489, 0x00003FFF
+ data8 0xB504F333F9DE6484, 0x00003FFF
+LOCAL_OBJECT_END(sinh_j_hi_table)
+
+LOCAL_OBJECT_START(sinh_j_lo_table)
+ data4 0x1EB2FB13
+ data4 0x1CE2CBE2
+ data4 0x1DDC3CBC
+ data4 0x1EE9AA34
+ data4 0x9EAEFDC1
+ data4 0x9DBF517B
+ data4 0x1EF88AFB
+ data4 0x1E03B216
+ data4 0x1E78AB43
+ data4 0x9E7B1747
+ data4 0x9EFE3C0E
+ data4 0x9D36F837
+ data4 0x9DEE53E4
+ data4 0x9E24AE8E
+ data4 0x1D912473
+ data4 0x1EB243BE
+ data4 0x1E669A2F
+ data4 0x9BBC610A
+ data4 0x1E761035
+ data4 0x9E0BE175
+ data4 0x1CCB12A1
+ data4 0x1D1BFE90
+ data4 0x1DF2F47A
+ data4 0x1EF22F22
+ data4 0x9E3F4A29
+ data4 0x1EC01A5B
+ data4 0x1E8CAC3A
+ data4 0x9DBB3FAB
+ data4 0x1EF73A19
+ data4 0x9BB795B5
+ data4 0x1EF84B76
+ data4 0x9EF5818B
+ data4 0x00000000 // Center of table
+ data4 0x1F77CACA
+ data4 0x1EF8A91D
+ data4 0x1E57C976
+ data4 0x9EE8DA92
+ data4 0x1EE85C9F
+ data4 0x1F3BF1AF
+ data4 0x1D80CA1E
+ data4 0x9D0373AF
+ data4 0x9F167097
+ data4 0x1EB70051
+ data4 0x1F6EB029
+ data4 0x1DFD6D8E
+ data4 0x9EB319B0
+ data4 0x1EBA2BEB
+ data4 0x1F11D537
+ data4 0x1F0D5A46
+ data4 0x9E5E7BCA
+ data4 0x9F3AAFD1
+ data4 0x9E86DACC
+ data4 0x9F3EDDC2
+ data4 0x1E496E3D
+ data4 0x9F490BF6
+ data4 0x1DD1DB48
+ data4 0x1E65EBFB
+ data4 0x9F427496
+ data4 0x1F283C4A
+ data4 0x1F4B0047
+ data4 0x1F130152
+ data4 0x9E8367C0
+ data4 0x9F705F90
+ data4 0x1EFB3C53
+ data4 0x1F32FB13
+LOCAL_OBJECT_END(sinh_j_lo_table)
-{ .mfi
- alloc r32 = ar.pfs,0,12,4,0
-(p0) fclass.m.unc p6,p0 = f8, 0xe3 //@qnan | @snan | @inf
- mov sinh_GR_all_ones = -1
-}
-;;
+.section .text
+GLOBAL_IEEE754_ENTRY(sinhl)
-{ .mfb
- nop.m 999
-(p6) fma.s0 f8 = f8,f1,f8
-(p6) br.ret.spnt b0 ;;
-}
-
-// Put 0.25 in f9; p6 true if x < 0.25
-// Make constant that will generate inexact when squared
{ .mlx
- setf.sig sinh_FR_all_ones = sinh_GR_all_ones
-(p0) movl r32 = 0x000000000000fffd ;;
-}
-
-{ .mfi
-(p0) setf.exp f9 = r32
-(p0) fclass.m.unc p7,p0 = f8, 0x07 //@zero
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p0) fmerge.s sinh_FR_X = f0,f8
-(p7) br.ret.spnt b0 ;;
+ getf.exp r_signexp_x = f8 // Get signexp of x, must redo if unorm
+ movl r_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
}
-
-// Identify denormal operands.
-{ .mfi
- nop.m 999
- fclass.m.unc p10,p0 = f8, 0x09 // + denorm
- nop.i 999
-};;
-{ .mfi
- nop.m 999
- fclass.m.unc p11,p0 = f8, 0x0a // - denorm
- nop.i 999
+{ .mlx
+ addl r_ad1 = @ltoff(sinh_arg_reduction), gp
+ movl r_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57)
}
+;;
{ .mfi
- nop.m 999
-(p0) fmerge.s sinh_FR_SGNX = f8,f1
- nop.i 999 ;;
+ ld8 r_ad1 = [r_ad1]
+ fmerge.s f_ABS_X = f0,f8
+ mov r_exp_0_25 = 0x0fffd // Form exponent for 0.25
}
-
{ .mfi
- nop.m 999
-(p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9
- nop.i 999 ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p7) br.cond.sptk L(SINH_BY_TBL) ;;
-}
-
-
-L(SINH_BY_POLY):
-
-// POLY cannot overflow so there is no need to call __libm_error_support
-// Set tiny_SAFE (p7) to 1(0) if answer is not tiny
-// Currently we do not use tiny_SAFE. So the setting of tiny_SAFE is
-// commented out.
-//(p0) movl r32 = 0x000000000000fc01
-//(p0) setf.exp f10 = r32
-//(p0) fcmp.lt.unc.s1 p6,p7 = f8,f10
-// Here is essentially the algorithm for SINH_BY_POLY. Care is take for the order
-// of multiplication; and P_1 is not exactly 1/3!, P_2 is not exactly 1/5!, etc.
-// Note that ax = |x|
-// sinh(x) = sign * (series(e^x) - series(e^-x))/2
-// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11! + ax^13/13!)
-// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) )
-// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ) )
-// = sign * (ax + ax*p_odd + (ax*p_even))
-// = sign * (ax + Y_lo)
-// sinh(x) = sign * (Y_hi + Y_lo)
-// Get the values of P_x from the table
-{ .mfb
-(p0) addl r34 = @ltoff(double_sinh_p_table), gp
-(p10) fma.s0 f8 = f8,f8,f8
-(p10) br.ret.spnt b0
-}
-;;
-
-{ .mfb
- ld8 r34 = [r34]
-(p11) fnma.s0 f8 = f8,f8,f8
-(p11) br.ret.spnt b0
+ nop.m 0
+ fnorm.s1 f_NORM_X = f8
+ mov r_exp_2tom57 = 0xffff-57
}
;;
-// Calculate sinh_FR_X2 = ax*ax and sinh_FR_X4 = ax*ax*ax*ax
-{ .mmf
- nop.m 999
-(p0) ldfe sinh_FR_P1 = [r34],16
-(p0) fma.s1 sinh_FR_X2 = sinh_FR_X, sinh_FR_X, f0 ;;
-}
-
-{ .mmi
-(p0) ldfe sinh_FR_P2 = [r34],16 ;;
-(p0) ldfe sinh_FR_P3 = [r34],16
- nop.i 999 ;;
-}
-
-{ .mmi
-(p0) ldfe sinh_FR_P4 = [r34],16 ;;
-(p0) ldfe sinh_FR_P5 = [r34],16
- nop.i 999 ;;
-}
-
{ .mfi
-(p0) ldfe sinh_FR_P6 = [r34],16
-(p0) fma.s1 sinh_FR_X4 = sinh_FR_X2, sinh_FR_X2, f0
- nop.i 999 ;;
+ setf.d f_RSHF_2TO57 = r_rshf_2to57 // Form const 1.100 * 2^120
+ fclass.m p10,p0 = f8, 0x0b // Test for denorm
+ mov r_exp_mask = 0x1ffff
}
-
-// Calculate sinh_FR_podd = p_odd and sinh_FR_peven = p_even
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_poly_podd_temp1 = sinh_FR_X4, sinh_FR_P5, sinh_FR_P3
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_poly_podd_temp2 = sinh_FR_X4, sinh_FR_poly_podd_temp1, sinh_FR_P1
- nop.i 999
+{ .mlx
+ setf.sig f_INV_LN2_2TO63 = r_sig_inv_ln2 // Form 1/ln2 * 2^63
+ movl r_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_poly_peven_temp1 = sinh_FR_X4, sinh_FR_P6, sinh_FR_P4
- nop.i 999 ;;
+ nop.m 0
+ fclass.m p7,p0 = f8, 0x07 // Test if x=0
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_podd = sinh_FR_X2, sinh_FR_poly_podd_temp2, f0
- nop.i 999
+ setf.exp f_2TOM57 = r_exp_2tom57 // Form 2^-57 for scaling
+ nop.f 0
+ add r_ad3 = 0x90, r_ad1 // Point to ab_table
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_poly_peven_temp2 = sinh_FR_X4, sinh_FR_poly_peven_temp1, sinh_FR_P2
- nop.i 999 ;;
+ setf.d f_RSHF = r_rshf // Form right shift const 1.100 * 2^63
+ fclass.m p6,p0 = f8, 0xe3 // Test if x nan, inf
+ add r_ad4 = 0x2f0, r_ad1 // Point to j_hi_table midpoint
}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_peven = sinh_FR_X4, sinh_FR_poly_peven_temp2, f0
- nop.i 999 ;;
+{ .mib
+ add r_ad2e = 0x20, r_ad1 // Point to p_table
+ nop.i 0
+(p10) br.cond.spnt SINH_DENORM // Branch if x denorm
}
+;;
-// Calculate sinh_FR_Y_lo = ax*p_odd + (ax*p_even)
+// Common path -- return here from SINH_DENORM if x is unnorm
+SINH_COMMON:
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_X, sinh_FR_peven, f0
- nop.i 999 ;;
+ ldfe f_smlst_oflow_input = [r_ad2e],16
+ nop.f 0
+ add r_ad5 = 0x580, r_ad1 // Point to j_lo_table midpoint
}
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_X, sinh_FR_podd, sinh_FR_Y_lo_temp
- nop.i 999 ;;
+{ .mib
+ ldfe f_log2by64_hi = [r_ad1],16
+ and r_exp_x = r_exp_mask, r_signexp_x
+(p7) br.ret.spnt b0 // Exit if x=0
}
+;;
-// Calculate sinh_FR_SINH = Y_hi + Y_lo. Note that ax = Y_hi
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_SINH = sinh_FR_X, f1, sinh_FR_Y_lo
- nop.i 999 ;;
-}
-// Dummy multiply to generate inexact
+// Get the A coefficients for SINH_BY_TBL
{ .mfi
- nop.m 999
-(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones
- nop.i 999
+ ldfe f_A1 = [r_ad3],16
+ fcmp.lt.s1 p8,p9 = f8,f0 // Test for x<0
+ cmp.lt p7,p0 = r_exp_x, r_exp_0_25 // Test x < 0.25
}
-
-// Calculate f8 = sign * (Y_hi + Y_lo)
-// Go to return
{ .mfb
- nop.m 999
-(p0) fma.s0 f8 = sinh_FR_SGNX,sinh_FR_SINH,f0
-(p0) br.ret.sptk b0 ;;
-}
-
-
-L(SINH_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
-// we want to leave now.
-// Double-extended:
-// Go to HUGE if |x| >= 2^14, 1000d (register-biased) is e = 14 (true)
-// 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)
-
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x000000000001000d ;;
-}
-
-{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ add r_ad2o = 0x30, r_ad2e // Point to p_table odd coeffs
+(p6) fma.s0 f8 = f8,f1,f0 // Result for x nan, inf
+(p6) br.ret.spnt b0 // Exit for x nan, inf
}
+;;
+// Calculate X2 = ax*ax for SINH_BY_POLY
{ .mfi
- nop.m 999
-(p0) fcmp.ge.unc.s1 p6,p7 = sinh_FR_X,f9
- nop.i 999 ;;
+ ldfe f_log2by64_lo = [r_ad1],16
+ nop.f 0
+ nop.i 0
}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p6) br.cond.spnt L(SINH_HUGE) ;;
+{ .mfb
+ ldfe f_A2 = [r_ad3],16
+ fma.s1 f_X2 = f_NORM_X, f_NORM_X, f0
+(p7) br.cond.spnt SINH_BY_POLY
}
+;;
-// r32 = 1
-// r34 = N-1
-// r35 = N
-// r36 = j
-// r37 = N+1
-
-// TBL can never overflow
-// sinh(x) = sinh(B+R)
-// = sinh(B)cosh(R) + cosh(B)sinh(R)
-//
-// ax = |x| = M*log2/64 + R
-// B = M*log2/64
-// M = 64*N + j
-// We will calcualte M and get N as (M-j)/64
-// The division is a shift.
-// exp(B) = exp(N*log2 + j*log2/64)
-// = 2^N * 2^(j*log2/64)
-// sinh(B) = 1/2(e^B -e^-B)
-// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64))
-// sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64))
-// cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64))
-// 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32
-// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)
-// R = ax - M*log2/64
-// R = ax - M*log2_by_64_hi - M*log2_by_64_lo
-// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)
-// = 1 + p_odd + p_even
-// where the p_even uses the A coefficients and the p_even uses the B coefficients
-// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd
-// cosh(R) = 1 + p_even
-// sinh(B) = S_hi + S_lo
-// cosh(B) = C_hi
-// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R)
+// Here if |x| >= 0.25
+SINH_BY_TBL:
// ******************************************************
-// STEP 1 (TBL and EXP)
+// STEP 1 (TBL and EXP) - Argument reduction
// ******************************************************
// Get the following constants.
-// f9 = Inv_log2by64
-// f10 = log2by64_hi
-// f11 = log2by64_lo
-
-{ .mmi
-(p0) adds r32 = 0x1,r0
-(p0) addl r34 = @ltoff(double_sinh_arg_reduction), gp
- nop.i 999
-}
-;;
-
-{ .mmi
- ld8 r34 = [r34]
- nop.m 999
- nop.i 999
-}
-;;
+// Inv_log2by64
+// log2by64_hi
+// log2by64_lo
// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and
// put them in an exponent.
-// sinh_FR_spos = 2^(N-1) and sinh_FR_sneg = 2^(-N-1)
-// r39 = 0xffff + (N-1) = 0xffff +N -1
-// r40 = 0xffff - (N +1) = 0xffff -N -1
-
-{ .mlx
- nop.m 999
-(p0) movl r38 = 0x000000000000fffe ;;
-}
-
-{ .mmi
-(p0) ldfe sinh_FR_Inv_log2by64 = [r34],16 ;;
-(p0) ldfe sinh_FR_log2by64_hi = [r34],16
- nop.i 999 ;;
-}
-
-{ .mbb
-(p0) ldfe sinh_FR_log2by64_lo = [r34],16
- nop.b 999
- nop.b 999 ;;
-}
+// f_spos = 2^(N-1) and f_sneg = 2^(-N-1)
+// 0xffff + (N-1) = 0xffff +N -1
+// 0xffff - (N +1) = 0xffff -N -1
-// Get the A coefficients
-// f9 = A_1
-// f10 = A_2
-// f11 = A_3
-{ .mmi
- nop.m 999
-(p0) addl r34 = @ltoff(double_sinh_ab_table), gp
- nop.i 999
-}
-;;
+// Calculate M and keep it as integer and floating point.
+// M = round-to-integer(x*Inv_log2by64)
+// f_M = M = truncate(ax/(log2/64))
+// Put the integer representation of M in r_M
+// and the floating point representation of M in f_M
+// Get the remaining A,B coefficients
{ .mmi
- ld8 r34 = [r34]
- nop.m 999
- nop.i 999
+ ldfe f_A3 = [r_ad3],16
+ nop.m 0
+ nop.i 0
}
;;
-
-// Calculate M and keep it as integer and floating point.
-// f38 = M = round-to-integer(x*Inv_log2by64)
-// sinh_FR_M = M = truncate(ax/(log2/64))
-// Put the significand of M in r35
-// and the floating point representation of M in sinh_FR_M
-
+.pred.rel "mutex",p8,p9
+// Use constant (1.100*2^(63-6)) to get rounded M into rightmost significand
+// |x| * 64 * 1/ln2 * 2^(63-6) + 1.1000 * 2^(63+(63-6))
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_M = sinh_FR_X, sinh_FR_Inv_log2by64, f0
- nop.i 999
+(p8) mov r_signexp_sgnx_0_5 = 0x2fffe // signexp of -0.5
+ fma.s1 f_M_temp = f_ABS_X, f_INV_LN2_2TO63, f_RSHF_2TO57
+(p9) mov r_signexp_sgnx_0_5 = 0x0fffe // signexp of +0.5
}
+;;
+// Test for |x| >= overflow limit
{ .mfi
-(p0) ldfe sinh_FR_A1 = [r34],16
- nop.f 999
- nop.i 999 ;;
+ ldfe f_B1 = [r_ad3],16
+ fcmp.ge.s1 p6,p0 = f_ABS_X, f_smlst_oflow_input
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fcvt.fx.s1 sinh_FR_M_temp = sinh_FR_M
- nop.i 999 ;;
+ ldfe f_B2 = [r_ad3],16
+ nop.f 0
+ mov r_exp_32 = 0x10004
}
+;;
-{ .mfi
- nop.m 999
-(p0) fnorm.s1 sinh_FR_M = sinh_FR_M_temp
- nop.i 999 ;;
+// Subtract RSHF constant to get rounded M as a floating point value
+// M_temp * 2^(63-6) - 2^63
+{ .mfb
+ ldfe f_B3 = [r_ad3],16
+ fms.s1 f_M = f_M_temp, f_2TOM57, f_RSHF
+(p6) br.cond.spnt SINH_HUGE // Branch if result will overflow
}
+;;
{ .mfi
-(p0) getf.sig r35 = sinh_FR_M_temp
- nop.f 999
- nop.i 999 ;;
+ getf.sig r_M = f_M_temp
+ nop.f 0
+ cmp.ge p7,p6 = r_exp_x, r_exp_32 // Test if x >= 32
}
+;;
-// M is still in r35. Calculate j. j is the signed extension of the six lsb of M. It
+// 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 = ax - M*log2by64_hi
-// f14 = f13 - f8*f11 = R = (ax - M*log2by64_hi) - M*log2by64_lo
-
-{ .mfi
- nop.m 999
-(p0) fnma.s1 sinh_FR_R_temp = sinh_FR_M, sinh_FR_log2by64_hi, sinh_FR_X
- nop.i 999
-}
+// ax - M*log2by64_hi
+// R = (ax - M*log2by64_hi) - M*log2by64_lo
{ .mfi
-(p0) ldfe sinh_FR_A2 = [r34],16
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+ fnma.s1 f_R_temp = f_M, f_log2by64_hi, f_ABS_X
+ and r_j = 0x3f, r_M
}
+;;
-{ .mfi
- nop.m 999
-(p0) fnma.s1 sinh_FR_R = sinh_FR_M, sinh_FR_log2by64_lo, sinh_FR_R_temp
- nop.i 999
+{ .mii
+ nop.m 0
+ shl r_jshf = r_j, 0x2 // Shift j so can sign extend it
+;;
+ sxt1 r_jshf = r_jshf
}
+;;
-// Get the B coefficients
-// f15 = B_1
-// f32 = B_2
-// f33 = B_3
-
-{ .mmi
-(p0) ldfe sinh_FR_A3 = [r34],16 ;;
-(p0) ldfe sinh_FR_B1 = [r34],16
- nop.i 999 ;;
+{ .mii
+ nop.m 0
+ shr r_j = r_jshf, 0x2 // Now j has range -32 to 31
+ nop.i 0
}
+;;
{ .mmi
-(p0) ldfe sinh_FR_B2 = [r34],16 ;;
-(p0) ldfe sinh_FR_B3 = [r34],16
- nop.i 999 ;;
-}
-
-{ .mii
- nop.m 999
-(p0) shl r34 = r36, 0x2 ;;
-(p0) sxt1 r37 = r34 ;;
+ shladd r_ad_J_hi = r_j, 4, r_ad4 // pointer to Tjhi
+ sub r_Mmj = r_M, r_j // M-j
+ sub r_mj = r0, r_j // Form -j
}
+;;
-// ******************************************************
-// 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
-
+// The TBL and EXP branches are merged and predicated
+// If TBL, p6 true, 0.25 <= |x| < 32
+// If EXP, p7 true, 32 <= |x| < overflow_limit
+//
+// N = (M-j)/64
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Rsq = sinh_FR_R, sinh_FR_R, f0
-(p0) shr r36 = r37, 0x2 ;;
+ ldfe f_Tjhi = [r_ad_J_hi]
+ fnma.s1 f_R = f_M, f_log2by64_lo, f_R_temp
+ shr r_N = r_Mmj, 0x6 // N = (M-j)/64
}
-
-// r34 = M-j = r35 - r36
-// r35 = N = (M-j)/64
-
-{ .mii
-(p0) sub r34 = r35, r36
- nop.i 999 ;;
-(p0) shr r35 = r34, 0x6 ;;
+{ .mfi
+ shladd r_ad_mJ_hi = r_mj, 4, r_ad4 // pointer to Tmjhi
+ nop.f 0
+ shladd r_ad_mJ_lo = r_mj, 2, r_ad5 // pointer to Tmjlo
}
+;;
-{ .mii
-(p0) sub r40 = r38, r35
-(p0) adds r37 = 0x1, r35
-(p0) add r39 = r38, r35 ;;
+{ .mfi
+ sub r_2mNm1 = r_signexp_sgnx_0_5, r_N // signexp sgnx*2^(-N-1)
+ nop.f 0
+ shladd r_ad_J_lo = r_j, 2, r_ad5 // pointer to Tjlo
}
-
-// 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_sinh_j_table), gp
- nop.i 999
+{ .mfi
+ ldfe f_Tmjhi = [r_ad_mJ_hi]
+ nop.f 0
+ add r_2Nm1 = r_signexp_sgnx_0_5, r_N // signexp sgnx*2^(N-1)
}
;;
-{ .mmi
- ld8 r37 = [r37]
- nop.m 999
- nop.i 999
+{ .mmf
+ ldfs f_Tmjlo = [r_ad_mJ_lo]
+ setf.exp f_sneg = r_2mNm1 // Form sgnx * 2^(-N-1)
+ nop.f 0
}
;;
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Rcub = sinh_FR_Rsq, sinh_FR_R, f0
- nop.i 999
+{ .mmf
+ ldfs f_Tjlo = [r_ad_J_lo]
+ setf.exp f_spos = r_2Nm1 // Form sgnx * 2^(N-1)
+ nop.f 0
}
+;;
// ******************************************************
-// STEP 3 Now decide if we need to branch to EXP
+// STEP 2 (TBL and EXP)
// ******************************************************
-// Put 32 in f9; p6 true if x < 32
-// Go to EXP if |x| >= 32
+// Calculate Rsquared and Rcubed in preparation for p_even and p_odd
-{ .mlx
- nop.m 999
-(p0) movl r32 = 0x0000000000010004 ;;
+{ .mmf
+ nop.m 0
+ nop.m 0
+ fma.s1 f_Rsq = f_R, f_R, f0
}
+;;
-// Calculate p_even
-// f34 = B_2 + Rsq *B_3
-// f35 = B_1 + Rsq*f34 = B_1 + Rsq * (B_2 + Rsq *B_3)
-// f36 = p_even = Rsq * f35 = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3))
-
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_peven_temp1 = sinh_FR_Rsq, sinh_FR_B3, sinh_FR_B2
- nop.i 999 ;;
-}
+// Calculate p_even
+// B_2 + Rsq *B_3
+// B_1 + Rsq * (B_2 + Rsq *B_3)
+// p_even = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3))
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_peven_temp2 = sinh_FR_Rsq, sinh_FR_peven_temp1, sinh_FR_B1
- nop.i 999
+ nop.m 0
+ fma.s1 f_peven_temp1 = f_Rsq, f_B3, f_B2
+ 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))
-
+// A_2 + Rsq *A_3
+// A_1 + Rsq * (A_2 + Rsq *A_3)
+// podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3))
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_podd_temp1 = sinh_FR_Rsq, sinh_FR_A3, sinh_FR_A2
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_podd_temp1 = f_Rsq, f_A3, f_A2
+ nop.i 0
}
+;;
{ .mfi
-(p0) setf.exp sinh_FR_N_temp1 = r39
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_Rcub = f_Rsq, f_R, f0
+ nop.i 0
}
+;;
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_peven = sinh_FR_Rsq, sinh_FR_peven_temp2, f0
- nop.i 999
-}
+//
+// If TBL,
+// Calculate S_hi and S_lo, and C_hi
+// SC_hi_temp = sneg * Tmjhi
+// S_hi = spos * Tjhi - SC_hi_temp
+// S_hi = spos * Tjhi - (sneg * Tmjhi)
+// C_hi = spos * Tjhi + SC_hi_temp
+// C_hi = spos * Tjhi + (sneg * Tmjhi)
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_podd_temp2 = sinh_FR_Rsq, sinh_FR_podd_temp1, sinh_FR_A1
- nop.i 999 ;;
+ nop.m 0
+(p6) fma.s1 f_SC_hi_temp = f_sneg, f_Tmjhi, f0
+ nop.i 0
}
+;;
+// If TBL,
+// S_lo_temp3 = sneg * Tmjlo
+// S_lo_temp4 = spos * Tjlo - S_lo_temp3
+// S_lo_temp4 = spos * Tjlo -(sneg * Tmjlo)
{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+(p6) fma.s1 f_S_lo_temp3 = f_sneg, f_Tmjlo, f0
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_podd = sinh_FR_podd_temp2, sinh_FR_Rcub, sinh_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 sinh_FR_N_temp2 = r40
-(p0) movl r40 = 0x0000000000000020 ;;
+ nop.m 0
+ fma.s1 f_peven_temp2 = f_Rsq, f_peven_temp1, f_B1
+ nop.i 0
}
-
{ .mfi
-(p0) sub sinh_GR_mJ = r40, r36
-(p0) fmerge.se sinh_FR_spos = sinh_FR_N_temp1, f1
-(p0) adds sinh_GR_J = 0x20, r36 ;;
-}
-
-{ .mii
- nop.m 999
-(p0) shl sinh_GR_mJ = sinh_GR_mJ, 5 ;;
-(p0) add sinh_AD_mJ = r37, sinh_GR_mJ ;;
-}
-
-{ .mmi
- nop.m 999
-(p0) ldfe sinh_FR_Tmjhi = [sinh_AD_mJ],16
-(p0) shl sinh_GR_J = sinh_GR_J, 5 ;;
+ nop.m 0
+ fma.s1 f_podd_temp2 = f_Rsq, f_podd_temp1, f_A1
+ nop.i 0
}
+;;
+// If EXP,
+// Compute sgnx * 2^(N-1) * Tjhi and sgnx * 2^(N-1) * Tjlo
{ .mfi
-(p0) ldfs sinh_FR_Tmjlo = [sinh_AD_mJ],16
-(p0) fcmp.lt.unc.s1 p0,p7 = sinh_FR_X,f9
-(p0) add sinh_AD_J = r37, sinh_GR_J ;;
-}
-
-{ .mmi
-(p0) ldfe sinh_FR_Tjhi = [sinh_AD_J],16 ;;
-(p0) ldfs sinh_FR_Tjlo = [sinh_AD_J],16
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-(p0) fmerge.se sinh_FR_sneg = sinh_FR_N_temp2, f1
-(p7) br.cond.spnt L(SINH_BY_EXP) ;;
+ nop.m 0
+(p7) fma.s1 f_Tjhi_spos = f_Tjhi, f_spos, f0
+ nop.i 0
}
-
{ .mfi
- nop.m 999
- nop.f 999
- nop.i 999 ;;
+ nop.m 0
+(p7) fma.s1 f_Tjlo_spos = f_Tjlo, f_spos, f0
+ nop.i 0
}
-
-// ******************************************************
-// If NOT branch to EXP
-// ******************************************************
-// Calculate S_hi and S_lo
-// sinh_FR_S_hi_temp = sinh_FR_sneg * sinh_FR_Tmjhi
-// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi_temp
-// sinh_FR_S_hi = sinh_FR_spos * sinh_FR_Tjhi - (sinh_FR_sneg * sinh_FR_Tmjlo)
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_S_hi_temp = sinh_FR_sneg, sinh_FR_Tmjhi, f0
- nop.i 999 ;;
+ nop.m 0
+(p6) fms.s1 f_S_hi = f_spos, f_Tjhi, f_SC_hi_temp
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fms.s1 sinh_FR_S_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi_temp
- nop.i 999
+ nop.m 0
+(p6) fma.s1 f_C_hi = f_spos, f_Tjhi, f_SC_hi_temp
+ nop.i 0
}
-
-// Calculate C_hi
-// sinh_FR_C_hi_temp1 = sinh_FR_sneg * sinh_FR_Tmjhi
-// sinh_FR_C_hi = sinh_FR_spos * sinh_FR_Tjhi + sinh_FR_C_hi_temp1
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_C_hi_temp1 = sinh_FR_sneg, sinh_FR_Tmjhi, f0
- nop.i 999 ;;
+ nop.m 0
+(p6) fms.s1 f_S_lo_temp4 = f_spos, f_Tjlo, f_S_lo_temp3
+ nop.i 0
}
-
-// sinh_FR_S_lo_temp1 = sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi
-// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_spos * sinh_FR_Tjhi - sinh_FR_S_hi)
-// sinh_FR_S_lo_temp2 = -sinh_FR_sneg * sinh_FR_Tmjlo + (sinh_FR_S_lo_temp1 )
+;;
{ .mfi
- nop.m 999
-(p0) fms.s1 sinh_FR_S_lo_temp1 = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_S_hi
- nop.i 999
+ nop.m 0
+ fma.s1 f_peven = f_Rsq, f_peven_temp2, f0
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_C_hi = sinh_FR_spos, sinh_FR_Tjhi, sinh_FR_C_hi_temp1
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_podd = f_podd_temp2, f_Rcub, f_R
+ nop.i 0
}
+;;
+
+// If TBL,
+// S_lo_temp1 = spos * Tjhi - S_hi
+// S_lo_temp2 = -sneg * Tmjlo + S_lo_temp1
+// S_lo_temp2 = -sneg * Tmjlo + (spos * Tjhi - S_hi)
{ .mfi
- nop.m 999
-(p0) fnma.s1 sinh_FR_S_lo_temp2 = sinh_FR_sneg, sinh_FR_Tmjhi, sinh_FR_S_lo_temp1
- nop.i 999
+ nop.m 0
+(p6) fms.s1 f_S_lo_temp1 = f_spos, f_Tjhi, f_S_hi
+ nop.i 0
}
-
-// sinh_FR_S_lo_temp1 = sinh_FR_sneg * sinh_FR_Tmjlo
-// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo - sinh_FR_S_lo_temp1
-// sinh_FR_S_lo_temp3 = sinh_FR_spos * sinh_FR_Tjlo -(sinh_FR_sneg * sinh_FR_Tmjlo)
-// sinh_FR_S_lo = sinh_FR_S_lo_temp3 + sinh_FR_S_lo_temp2
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_S_lo_temp1 = sinh_FR_sneg, sinh_FR_Tmjlo, f0
- nop.i 999 ;;
+ nop.m 0
+(p6) fnma.s1 f_S_lo_temp2 = f_sneg, f_Tmjhi, f_S_lo_temp1
+ nop.i 0
}
+;;
-/////////// BUG FIX fma to fms -TK
+// If EXP,
+// Y_hi = sgnx * 2^(N-1) * Tjhi
+// Y_lo = sgnx * 2^(N-1) * Tjhi * (p_odd + p_even) + sgnx * 2^(N-1) * Tjlo
{ .mfi
- nop.m 999
-(p0) fms.s1 sinh_FR_S_lo_temp3 = sinh_FR_spos, sinh_FR_Tjlo, sinh_FR_S_lo_temp1
- nop.i 999 ;;
+ nop.m 0
+(p7) fma.s1 f_Y_lo_temp = f_peven, f1, f_podd
+ nop.i 0
}
+;;
+// If TBL,
+// S_lo = S_lo_temp4 + S_lo_temp2
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_S_lo = sinh_FR_S_lo_temp3, f1, sinh_FR_S_lo_temp2
- nop.i 999 ;;
+ nop.m 0
+(p6) fma.s1 f_S_lo = f_S_lo_temp4, f1, f_S_lo_temp2
+ nop.i 0
}
+;;
+// If TBL,
// Y_hi = S_hi
// Y_lo = C_hi*p_odd + (S_hi*p_even + S_lo)
-// sinh_FR_Y_lo_temp = sinh_FR_S_hi * sinh_FR_peven + sinh_FR_S_lo
-// sinh_FR_Y_lo = sinh_FR_C_hi * sinh_FR_podd + sinh_FR_Y_lo_temp
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_S_hi, sinh_FR_peven, sinh_FR_S_lo
- nop.i 999 ;;
+ nop.m 0
+(p6) fma.s1 f_Y_lo_temp = f_S_hi, f_peven, f_S_lo
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_C_hi, sinh_FR_podd, sinh_FR_Y_lo_temp
- nop.i 999 ;;
+ nop.m 0
+(p7) fma.s1 f_Y_lo = f_Tjhi_spos, f_Y_lo_temp, f_Tjlo_spos
+ nop.i 0
}
-
-// sinh_FR_SINH = Y_hi + Y_lo
-// f8 = answer = sinh_FR_SGNX * sinh_FR_SINH
+;;
// Dummy multiply to generate inexact
{ .mfi
- nop.m 999
-(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones
- nop.i 999
+ nop.m 0
+ fmpy.s0 f_tmp = f_B2, f_B2
+ nop.i 0
+}
+{ .mfi
+ nop.m 0
+(p6) fma.s1 f_Y_lo = f_C_hi, f_podd, f_Y_lo_temp
+ nop.i 0
}
+;;
+
+// f8 = answer = Y_hi + Y_lo
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_SINH = sinh_FR_S_hi, f1, sinh_FR_Y_lo
- nop.i 999 ;;
+ nop.m 0
+(p7) fma.s0 f8 = f_Y_lo, f1, f_Tjhi_spos
+ nop.i 0
}
+;;
+// f8 = answer = Y_hi + Y_lo
{ .mfb
- nop.m 999
-(p0) fma.s0 f8 = sinh_FR_SGNX, sinh_FR_SINH,f0
-(p0) br.ret.sptk b0 ;;
+ nop.m 0
+(p6) fma.s0 f8 = f_Y_lo, f1, f_S_hi
+ br.ret.sptk b0 // Exit for SINH_BY_TBL and SINH_BY_EXP
}
+;;
-L(SINH_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
-// Y_hi = Tjhi
-// Y_lo = Tjhi * (p_odd + p_even) +Tjlo
-// Scale = sign * 2^(N-1)
-// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_peven + sinh_FR_podd)
-// sinh_FR_Y_lo = sinh_FR_Tjhi * (sinh_FR_Y_lo_temp )
+// Here if 0 < |x| < 0.25
+SINH_BY_POLY:
+{ .mmf
+ ldfe f_P6 = [r_ad2e],16
+ ldfe f_P5 = [r_ad2o],16
+ nop.f 0
+}
+;;
-{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo_temp = sinh_FR_peven, f1, sinh_FR_podd
- nop.i 999
+{ .mmi
+ ldfe f_P4 = [r_ad2e],16
+ ldfe f_P3 = [r_ad2o],16
+ nop.i 0
}
+;;
-// 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 = 0x0000000000003ffe ;;
+{ .mmi
+ ldfe f_P2 = [r_ad2e],16
+ ldfe f_P1 = [r_ad2o],16
+ nop.i 0
}
+;;
{ .mfi
-(p0) cmp.gt.unc p0,p7 = r34, r32
-(p0) fmerge.s sinh_FR_SCALE = sinh_FR_SGNX, sinh_FR_spos
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_X3 = f_NORM_X, f_X2, f0
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_Y_lo = sinh_FR_Tjhi, sinh_FR_Y_lo_temp, sinh_FR_Tjlo
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_X4 = f_X2, f_X2, f0
+ nop.i 0
}
+;;
-// f8 = answer = scale * (Y_hi + Y_lo)
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_SINH_temp = sinh_FR_Y_lo, f1, sinh_FR_Tjhi
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_poly65 = f_X2, f_P6, f_P5
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s0 f44 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_poly43 = f_X2, f_P4, f_P3
+ nop.i 0
}
+;;
-// Dummy multiply to generate inexact
{ .mfi
- nop.m 999
-(p7) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones
- nop.i 999 ;;
+ nop.m 0
+ fma.s1 f_poly21 = f_X2, f_P2, f_P1
+ nop.i 0
}
+;;
-// If over_SAFE is set, return
-{ .mfb
- nop.m 999
-(p7) fmerge.s f8 = f44,f44
-(p7) br.ret.sptk b0 ;;
+{ .mfi
+ nop.m 0
+ fma.s1 f_poly6543 = f_X4, f_poly65, f_poly43
+ 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;;
+ nop.m 0
+ fma.s1 f_poly6to1 = f_X4, f_poly6543, f_poly21
+ nop.i 0
}
+;;
+// Dummy multiply to generate inexact
{ .mfi
- nop.m 999
-(p0) fma.s2 f43 = sinh_FR_SCALE, sinh_FR_SINH_temp, f0
- nop.i 999 ;;
+ nop.m 0
+ fmpy.s0 f_tmp = f_P6, f_P6
+ nop.i 0
}
-
-// 13FFF => 13FFF -FFFF = 4000(true)
-// 4000 + 3FFF = 7FFF, which is 1 more that the exponent of the largest
-// long double (7FFE). So 0 13FFF 8000000000000000 is one ulp more than
-// largest long 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 = 0x00000000013FFF ;;
+{ .mfb
+ nop.m 0
+ fma.s0 f8 = f_poly6to1, f_X3, f_NORM_X
+ br.ret.sptk b0 // Exit SINH_BY_POLY
}
+;;
-{ .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
+// Here if x denorm or unorm
+SINH_DENORM:
+// Determine if x really a denorm and not a unorm
+{ .mmf
+ getf.exp r_signexp_x = f_NORM_X
+ mov r_exp_denorm = 0x0c001 // Real denorms have exp < this
+ fmerge.s f_ABS_X = f0, f_NORM_X
}
+;;
{ .mfi
- nop.m 999
-(p0) fmerge.ns f42 = f41, f41
- nop.i 999 ;;
+ nop.m 0
+ fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag
+ nop.i 0
}
+;;
-// The error tag for overflow is 126
-{ .mii
- nop.m 999
- nop.i 999 ;;
-(p8) mov r47 = 126 ;;
+// Set p8 if really a denorm
+{ .mmi
+ and r_exp_x = r_exp_mask, r_signexp_x
+;;
+ cmp.lt p8,p9 = r_exp_x, r_exp_denorm
+ nop.i 0
}
+;;
+// Identify denormal operands.
{ .mfb
- nop.m 999
-(p0) fcmp.le.unc.s1 p9, p0 = f43, f42
-(p8) br.cond.spnt L(SINH_ERROR_SUPPORT) ;;
-}
-
-{ .mii
- nop.m 999
- nop.i 999 ;;
-(p9) mov r47 = 126
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p9) br.cond.spnt L(SINH_ERROR_SUPPORT) ;;
+ nop.m 0
+(p8) fcmp.ge.unc.s1 p6,p7 = f8, f0 // Test sign of denorm
+(p9) br.cond.sptk SINH_COMMON // Return to main path if x unorm
}
+;;
-// Dummy multiply to generate inexact
{ .mfi
- nop.m 999
-(p0) fmpy.s0 sinh_FR_tmp = sinh_FR_all_ones, sinh_FR_all_ones
- nop.i 999 ;;
+ nop.m 0
+(p6) fma.s0 f8 = f8,f8,f8 // If x +denorm, result=x+x^2
+ nop.i 0
}
-
{ .mfb
- nop.m 999
-(p0) fmerge.s f8 = f44,f44
-(p0) br.ret.sptk b0 ;;
+ nop.m 0
+(p7) fnma.s0 f8 = f8,f8,f8 // If x -denorm, result=x-x^2
+ br.ret.sptk b0 // Exit if x denorm
}
+;;
-L(SINH_HUGE):
-
-// for SINH_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 ;;
+// Here if |x| >= overflow limit
+SINH_HUGE:
+// for SINH_HUGE, put 24000 in exponent; take sign from input
+{ .mmi
+ mov r_exp_huge = 0x15dbf
+;;
+ setf.exp f_huge = r_exp_huge
+ nop.i 0
}
+;;
+.pred.rel "mutex",p8,p9
{ .mfi
-(p0) setf.exp f9 = r32
- nop.f 999
- nop.i 999 ;;
+ alloc r32 = ar.pfs,0,5,4,0
+(p8) fnma.s1 f_signed_hi_lo = f_huge, f1, f1
+ nop.i 0
}
-
{ .mfi
- nop.m 999
-(p0) fma.s1 sinh_FR_signed_hi_lo = sinh_FR_SGNX, f9, f1
- nop.i 999 ;;
+ nop.m 0
+(p9) fma.s1 f_signed_hi_lo = f_huge, f1, f1
+ nop.i 0
}
+;;
{ .mfi
- nop.m 999
-(p0) fma.s0 f44 = sinh_FR_signed_hi_lo, f9, f0
-(p0) mov r47 = 126
-}
-.endp sinhl
-ASM_SIZE_DIRECTIVE(sinhl)
-#ifdef _LIBC
-ASM_SIZE_DIRECTIVE(__ieee754_sinhl)
-#endif
-
-// 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:
-L(SINH_ERROR_SUPPORT):
+ nop.m 0
+ fma.s0 f_pre_result = f_signed_hi_lo, f_huge, f0
+ mov GR_Parameter_TAG = 126
+}
+;;
+
+GLOBAL_IEEE754_END(sinhl)
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
-// (1)
{ .mfi
- add GR_Parameter_Y=-32,sp // Parameter 2 value
+ 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
+ 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
- stfe [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack
- add GR_Parameter_X = 16,sp // Parameter 1 address
+ stfe [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack
+ add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
- mov GR_SAVE_B0=b0 // Save b0
+ mov GR_SAVE_B0=b0 // Save b0
};;
.body
-// (3)
{ .mib
- stfe [GR_Parameter_X] = f8 // STORE Parameter 1 on stack
+ stfe [GR_Parameter_X] = f8 // STORE Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
nop.b 0
}
{ .mib
- stfe [GR_Parameter_Y] = f44 // STORE Parameter 3 on stack
+ stfe [GR_Parameter_Y] = f_pre_result // STORE Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
- br.call.sptk b0=__libm_error_support# // Call error handling function
+ 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
- ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
+ ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
- add sp = 64,sp // Restore stack pointer
- mov b0 = GR_SAVE_B0 // Restore return address
+ 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
+ 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)
+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 2024-04-27 22:48:12 +0000