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1118 lines
29 KiB
ArmAsm
1118 lines
29 KiB
ArmAsm
.file "sinhl.s"
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// Copyright (c) 2000 - 2002, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 02/02/00 Initial version
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// 04/04/00 Unwind support added
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// 08/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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// 10/12/00 Update to set denormal operand and underflow flags
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// 01/22/01 Fixed to set inexact flag for small args. Fixed incorrect
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// call to __libm_error_support for 710.476 < x < 11357.2166.
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// 05/02/01 Reworked to improve speed of all paths
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 12/04/02 Improved performance
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//
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// API
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//==============================================================
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// long double = sinhl(long double)
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// input floating point f8
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// output floating point f8
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//
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// Registers used
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//==============================================================
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// general registers:
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// r14 -> r40
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// predicate registers used:
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// p6 -> p11
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// floating-point registers used:
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// f9 -> f15; f32 -> f90;
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// f8 has input, then output
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//
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// Overview of operation
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//==============================================================
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// There are seven paths
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// 1. 0 < |x| < 0.25 SINH_BY_POLY
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// 2. 0.25 <=|x| < 32 SINH_BY_TBL
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// 3. 32 <= |x| < 11357.21655 SINH_BY_EXP (merged path with SINH_BY_TBL)
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// 4. |x| >= 11357.21655 SINH_HUGE
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// 5. x=0 Done with early exit
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// 6. x=inf,nan Done with early exit
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// 7. x=denormal SINH_DENORM
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//
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// For double extended we get overflow for x >= 400c b174 ddc0 31ae c0ea
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// >= 11357.21655
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//
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//
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// 1. SINH_BY_POLY 0 < |x| < 0.25
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// ===============
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// Evaluate sinh(x) by a 13th order polynomial
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// Care is take for the order of multiplication; and P_1 is not exactly 1/3!,
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// P_2 is not exactly 1/5!, etc.
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// sinh(x) = sign * (series(e^x) - series(e^-x))/2
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// = sign * (ax + ax^3/3! + ax^5/5! + ax^7/7! + ax^9/9! + ax^11/11!
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// + ax^13/13!)
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// = sign * (ax + ax * ( ax^2 * (1/3! + ax^4 * (1/7! + ax^4*1/11!)) )
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// + ax * ( ax^4 * (1/5! + ax^4 * (1/9! + ax^4*1/13!)) ))
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// = sign * (ax + ax*p_odd + (ax*p_even))
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// = sign * (ax + Y_lo)
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// sinh(x) = sign * (Y_hi + Y_lo)
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// Note that ax = |x|
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//
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// 2. SINH_BY_TBL 0.25 <= |x| < 32.0
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// =============
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// sinh(x) = sinh(B+R)
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// = sinh(B)cosh(R) + cosh(B)sinh(R)
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//
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// ax = |x| = M*log2/64 + R
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// B = M*log2/64
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// M = 64*N + j
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// We will calculate M and get N as (M-j)/64
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// The division is a shift.
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// exp(B) = exp(N*log2 + j*log2/64)
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// = 2^N * 2^(j*log2/64)
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// sinh(B) = 1/2(e^B -e^-B)
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// = 1/2(2^N * 2^(j*log2/64) - 2^-N * 2^(-j*log2/64))
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// sinh(B) = (2^(N-1) * 2^(j*log2/64) - 2^(-N-1) * 2^(-j*log2/64))
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// cosh(B) = (2^(N-1) * 2^(j*log2/64) + 2^(-N-1) * 2^(-j*log2/64))
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// 2^(j*log2/64) is stored as Tjhi + Tjlo , j= -32,....,32
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// Tjhi is double-extended (80-bit) and Tjlo is single(32-bit)
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//
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// R = ax - M*log2/64
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// R = ax - M*log2_by_64_hi - M*log2_by_64_lo
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// exp(R) = 1 + R +R^2(1/2! + R(1/3! + R(1/4! + ... + R(1/n!)...)
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// = 1 + p_odd + p_even
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// where the p_even uses the A coefficients and the p_even uses
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// the B coefficients
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//
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// So sinh(R) = 1 + p_odd + p_even -(1 -p_odd -p_even)/2 = p_odd
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// cosh(R) = 1 + p_even
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// sinh(B) = S_hi + S_lo
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// cosh(B) = C_hi
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// sinh(x) = sinh(B)cosh(R) + cosh(B)sinh(R)
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//
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// 3. SINH_BY_EXP 32.0 <= |x| < 11357.21655 ( 400c b174 ddc0 31ae c0ea )
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// ==============
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// Can approximate result by exp(x)/2 in this region.
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// Y_hi = Tjhi
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// Y_lo = Tjhi * (p_odd + p_even) + Tjlo
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// sinh(x) = Y_hi + Y_lo
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//
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// 4. SINH_HUGE |x| >= 11357.21655 ( 400c b174 ddc0 31ae c0ea )
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// ============
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// Set error tag and call error support
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//
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//
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// Assembly macros
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//==============================================================
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r_ad5 = r14
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r_rshf_2to57 = r15
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r_exp_denorm = r15
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r_ad_mJ_lo = r15
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r_ad_J_lo = r16
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r_2Nm1 = r17
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r_2mNm1 = r18
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r_exp_x = r18
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r_ad_J_hi = r19
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r_ad2o = r19
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r_ad_mJ_hi = r20
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r_mj = r21
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r_ad2e = r22
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r_ad3 = r23
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r_ad1 = r24
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r_Mmj = r24
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r_rshf = r25
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r_M = r25
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r_N = r25
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r_jshf = r26
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r_exp_2tom57 = r26
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r_j = r26
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r_exp_mask = r27
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r_signexp_x = r28
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r_signexp_sgnx_0_5 = r28
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r_exp_0_25 = r29
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r_sig_inv_ln2 = r30
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r_exp_32 = r30
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r_exp_huge = r30
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r_ad4 = r31
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GR_SAVE_PFS = r34
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GR_SAVE_B0 = r35
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GR_SAVE_GP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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f_ABS_X = f9
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f_X2 = f10
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f_X4 = f11
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f_tmp = f14
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f_RSHF = f15
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f_Inv_log2by64 = f32
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f_log2by64_lo = f33
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f_log2by64_hi = f34
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f_A1 = f35
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f_A2 = f36
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f_A3 = f37
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f_Rcub = f38
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f_M_temp = f39
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f_R_temp = f40
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f_Rsq = f41
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f_R = f42
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f_M = f43
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f_B1 = f44
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f_B2 = f45
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f_B3 = f46
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f_peven_temp1 = f47
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f_peven_temp2 = f48
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f_peven = f49
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f_podd_temp1 = f50
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f_podd_temp2 = f51
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f_podd = f52
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f_poly65 = f53
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f_poly6543 = f53
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f_poly6to1 = f53
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f_poly43 = f54
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f_poly21 = f55
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f_X3 = f56
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f_INV_LN2_2TO63 = f57
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f_RSHF_2TO57 = f58
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f_2TOM57 = f59
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f_smlst_oflow_input = f60
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f_pre_result = f61
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f_huge = f62
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f_spos = f63
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f_sneg = f64
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f_Tjhi = f65
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f_Tjlo = f66
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f_Tmjhi = f67
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f_Tmjlo = f68
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f_S_hi = f69
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f_SC_hi_temp = f70
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f_S_lo_temp1 = f71
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f_S_lo_temp2 = f72
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f_S_lo_temp3 = f73
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f_S_lo_temp4 = f73
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f_S_lo = f74
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f_C_hi = f75
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f_Y_hi = f77
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f_Y_lo_temp = f78
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f_Y_lo = f79
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f_NORM_X = f80
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f_P1 = f81
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f_P2 = f82
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f_P3 = f83
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f_P4 = f84
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f_P5 = f85
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f_P6 = f86
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f_Tjhi_spos = f87
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f_Tjlo_spos = f88
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f_huge = f89
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f_signed_hi_lo = f90
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// Data tables
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//==============================================================
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// DO NOT CHANGE ORDER OF THESE TABLES
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RODATA
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.align 16
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LOCAL_OBJECT_START(sinh_arg_reduction)
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// data8 0xB8AA3B295C17F0BC, 0x00004005 // 64/log2 -- signif loaded with setf
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data8 0xB17217F7D1000000, 0x00003FF8 // log2/64 high part
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data8 0xCF79ABC9E3B39804, 0x00003FD0 // log2/64 low part
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data8 0xb174ddc031aec0ea, 0x0000400c // Smallest x to overflow (11357.21655)
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LOCAL_OBJECT_END(sinh_arg_reduction)
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LOCAL_OBJECT_START(sinh_p_table)
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data8 0xB08AF9AE78C1239F, 0x00003FDE // P6
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data8 0xB8EF1D28926D8891, 0x00003FEC // P4
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data8 0x8888888888888412, 0x00003FF8 // P2
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data8 0xD732377688025BE9, 0x00003FE5 // P5
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data8 0xD00D00D00D4D39F2, 0x00003FF2 // P3
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data8 0xAAAAAAAAAAAAAAAB, 0x00003FFC // P1
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LOCAL_OBJECT_END(sinh_p_table)
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LOCAL_OBJECT_START(sinh_ab_table)
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data8 0xAAAAAAAAAAAAAAAC, 0x00003FFC // A1
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data8 0x88888888884ECDD5, 0x00003FF8 // A2
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data8 0xD00D0C6DCC26A86B, 0x00003FF2 // A3
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data8 0x8000000000000002, 0x00003FFE // B1
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data8 0xAAAAAAAAAA402C77, 0x00003FFA // B2
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data8 0xB60B6CC96BDB144D, 0x00003FF5 // B3
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LOCAL_OBJECT_END(sinh_ab_table)
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LOCAL_OBJECT_START(sinh_j_hi_table)
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data8 0xB504F333F9DE6484, 0x00003FFE
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data8 0xB6FD91E328D17791, 0x00003FFE
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data8 0xB8FBAF4762FB9EE9, 0x00003FFE
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data8 0xBAFF5AB2133E45FB, 0x00003FFE
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data8 0xBD08A39F580C36BF, 0x00003FFE
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data8 0xBF1799B67A731083, 0x00003FFE
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data8 0xC12C4CCA66709456, 0x00003FFE
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data8 0xC346CCDA24976407, 0x00003FFE
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data8 0xC5672A115506DADD, 0x00003FFE
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data8 0xC78D74C8ABB9B15D, 0x00003FFE
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data8 0xC9B9BD866E2F27A3, 0x00003FFE
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data8 0xCBEC14FEF2727C5D, 0x00003FFE
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data8 0xCE248C151F8480E4, 0x00003FFE
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data8 0xD06333DAEF2B2595, 0x00003FFE
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data8 0xD2A81D91F12AE45A, 0x00003FFE
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data8 0xD4F35AABCFEDFA1F, 0x00003FFE
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data8 0xD744FCCAD69D6AF4, 0x00003FFE
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data8 0xD99D15C278AFD7B6, 0x00003FFE
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data8 0xDBFBB797DAF23755, 0x00003FFE
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data8 0xDE60F4825E0E9124, 0x00003FFE
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data8 0xE0CCDEEC2A94E111, 0x00003FFE
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data8 0xE33F8972BE8A5A51, 0x00003FFE
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data8 0xE5B906E77C8348A8, 0x00003FFE
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data8 0xE8396A503C4BDC68, 0x00003FFE
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data8 0xEAC0C6E7DD24392F, 0x00003FFE
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data8 0xED4F301ED9942B84, 0x00003FFE
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data8 0xEFE4B99BDCDAF5CB, 0x00003FFE
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data8 0xF281773C59FFB13A, 0x00003FFE
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data8 0xF5257D152486CC2C, 0x00003FFE
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data8 0xF7D0DF730AD13BB9, 0x00003FFE
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data8 0xFA83B2DB722A033A, 0x00003FFE
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data8 0xFD3E0C0CF486C175, 0x00003FFE
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data8 0x8000000000000000, 0x00003FFF // Center of table
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data8 0x8164D1F3BC030773, 0x00003FFF
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data8 0x82CD8698AC2BA1D7, 0x00003FFF
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data8 0x843A28C3ACDE4046, 0x00003FFF
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data8 0x85AAC367CC487B15, 0x00003FFF
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data8 0x871F61969E8D1010, 0x00003FFF
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data8 0x88980E8092DA8527, 0x00003FFF
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data8 0x8A14D575496EFD9A, 0x00003FFF
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data8 0x8B95C1E3EA8BD6E7, 0x00003FFF
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data8 0x8D1ADF5B7E5BA9E6, 0x00003FFF
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data8 0x8EA4398B45CD53C0, 0x00003FFF
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data8 0x9031DC431466B1DC, 0x00003FFF
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data8 0x91C3D373AB11C336, 0x00003FFF
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data8 0x935A2B2F13E6E92C, 0x00003FFF
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data8 0x94F4EFA8FEF70961, 0x00003FFF
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data8 0x96942D3720185A00, 0x00003FFF
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data8 0x9837F0518DB8A96F, 0x00003FFF
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data8 0x99E0459320B7FA65, 0x00003FFF
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data8 0x9B8D39B9D54E5539, 0x00003FFF
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data8 0x9D3ED9A72CFFB751, 0x00003FFF
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data8 0x9EF5326091A111AE, 0x00003FFF
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data8 0xA0B0510FB9714FC2, 0x00003FFF
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data8 0xA27043030C496819, 0x00003FFF
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data8 0xA43515AE09E6809E, 0x00003FFF
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data8 0xA5FED6A9B15138EA, 0x00003FFF
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data8 0xA7CD93B4E965356A, 0x00003FFF
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data8 0xA9A15AB4EA7C0EF8, 0x00003FFF
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data8 0xAB7A39B5A93ED337, 0x00003FFF
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data8 0xAD583EEA42A14AC6, 0x00003FFF
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data8 0xAF3B78AD690A4375, 0x00003FFF
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data8 0xB123F581D2AC2590, 0x00003FFF
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data8 0xB311C412A9112489, 0x00003FFF
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data8 0xB504F333F9DE6484, 0x00003FFF
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LOCAL_OBJECT_END(sinh_j_hi_table)
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LOCAL_OBJECT_START(sinh_j_lo_table)
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data4 0x1EB2FB13
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data4 0x1CE2CBE2
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data4 0x1DDC3CBC
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data4 0x1EE9AA34
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data4 0x9EAEFDC1
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data4 0x9DBF517B
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data4 0x1EF88AFB
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data4 0x1E03B216
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data4 0x1E78AB43
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data4 0x9E7B1747
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data4 0x9EFE3C0E
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data4 0x9D36F837
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data4 0x9DEE53E4
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data4 0x9E24AE8E
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data4 0x1D912473
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data4 0x1EB243BE
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data4 0x1E669A2F
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data4 0x9BBC610A
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data4 0x1E761035
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data4 0x9E0BE175
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data4 0x1CCB12A1
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data4 0x1D1BFE90
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data4 0x1DF2F47A
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data4 0x1EF22F22
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data4 0x9E3F4A29
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data4 0x1EC01A5B
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data4 0x1E8CAC3A
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data4 0x9DBB3FAB
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data4 0x1EF73A19
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data4 0x9BB795B5
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data4 0x1EF84B76
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data4 0x9EF5818B
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data4 0x00000000 // Center of table
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data4 0x1F77CACA
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data4 0x1EF8A91D
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data4 0x1E57C976
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data4 0x9EE8DA92
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data4 0x1EE85C9F
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data4 0x1F3BF1AF
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data4 0x1D80CA1E
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data4 0x9D0373AF
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data4 0x9F167097
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data4 0x1EB70051
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data4 0x1F6EB029
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data4 0x1DFD6D8E
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data4 0x9EB319B0
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|
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)
|
|
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(sinhl)
|
|
|
|
{ .mlx
|
|
getf.exp r_signexp_x = f8 // Get signexp of x, must redo if unorm
|
|
movl r_sig_inv_ln2 = 0xb8aa3b295c17f0bc // significand of 1/ln2
|
|
}
|
|
{ .mlx
|
|
addl r_ad1 = @ltoff(sinh_arg_reduction), gp
|
|
movl r_rshf_2to57 = 0x4778000000000000 // 1.10000 2^(63+57)
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ld8 r_ad1 = [r_ad1]
|
|
fmerge.s f_ABS_X = f0,f8
|
|
mov r_exp_0_25 = 0x0fffd // Form exponent for 0.25
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnorm.s1 f_NORM_X = f8
|
|
mov r_exp_2tom57 = 0xffff-57
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.d f_RSHF_2TO57 = r_rshf_2to57 // Form const 1.100 * 2^120
|
|
fclass.m p10,p0 = f8, 0x0b // Test for denorm
|
|
mov r_exp_mask = 0x1ffff
|
|
}
|
|
{ .mlx
|
|
setf.sig f_INV_LN2_2TO63 = r_sig_inv_ln2 // Form 1/ln2 * 2^63
|
|
movl r_rshf = 0x43e8000000000000 // 1.1000 2^63 for right shift
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m p7,p0 = f8, 0x07 // Test if x=0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
setf.exp f_2TOM57 = r_exp_2tom57 // Form 2^-57 for scaling
|
|
nop.f 0
|
|
add r_ad3 = 0x90, r_ad1 // Point to ab_table
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.d f_RSHF = r_rshf // Form right shift const 1.100 * 2^63
|
|
fclass.m p6,p0 = f8, 0xe3 // Test if x nan, inf
|
|
add r_ad4 = 0x2f0, r_ad1 // Point to j_hi_table midpoint
|
|
}
|
|
{ .mib
|
|
add r_ad2e = 0x20, r_ad1 // Point to p_table
|
|
nop.i 0
|
|
(p10) br.cond.spnt SINH_DENORM // Branch if x denorm
|
|
}
|
|
;;
|
|
|
|
// Common path -- return here from SINH_DENORM if x is unnorm
|
|
SINH_COMMON:
|
|
{ .mfi
|
|
ldfe f_smlst_oflow_input = [r_ad2e],16
|
|
nop.f 0
|
|
add r_ad5 = 0x580, r_ad1 // Point to j_lo_table midpoint
|
|
}
|
|
{ .mib
|
|
ldfe f_log2by64_hi = [r_ad1],16
|
|
and r_exp_x = r_exp_mask, r_signexp_x
|
|
(p7) br.ret.spnt b0 // Exit if x=0
|
|
}
|
|
;;
|
|
|
|
// Get the A coefficients for SINH_BY_TBL
|
|
{ .mfi
|
|
ldfe f_A1 = [r_ad3],16
|
|
fcmp.lt.s1 p8,p9 = f8,f0 // Test for x<0
|
|
cmp.lt p7,p0 = r_exp_x, r_exp_0_25 // Test x < 0.25
|
|
}
|
|
{ .mfb
|
|
add r_ad2o = 0x30, r_ad2e // Point to p_table odd coeffs
|
|
(p6) fma.s0 f8 = f8,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
|
|
ldfe f_log2by64_lo = [r_ad1],16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
ldfe f_A2 = [r_ad3],16
|
|
fma.s1 f_X2 = f_NORM_X, f_NORM_X, f0
|
|
(p7) br.cond.spnt SINH_BY_POLY
|
|
}
|
|
;;
|
|
|
|
// Here if |x| >= 0.25
|
|
SINH_BY_TBL:
|
|
// ******************************************************
|
|
// STEP 1 (TBL and EXP) - Argument reduction
|
|
// ******************************************************
|
|
// Get the following constants.
|
|
// Inv_log2by64
|
|
// log2by64_hi
|
|
// log2by64_lo
|
|
|
|
|
|
// We want 2^(N-1) and 2^(-N-1). So bias N-1 and -N-1 and
|
|
// put them in an exponent.
|
|
// f_spos = 2^(N-1) and f_sneg = 2^(-N-1)
|
|
// 0xffff + (N-1) = 0xffff +N -1
|
|
// 0xffff - (N +1) = 0xffff -N -1
|
|
|
|
|
|
// Calculate M and keep it as integer and floating point.
|
|
// M = round-to-integer(x*Inv_log2by64)
|
|
// f_M = M = truncate(ax/(log2/64))
|
|
// Put the integer representation of M in r_M
|
|
// and the floating point representation of M in f_M
|
|
|
|
// Get the remaining A,B coefficients
|
|
{ .mmi
|
|
ldfe f_A3 = [r_ad3],16
|
|
nop.m 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.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
|
|
(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
|
|
ldfe f_B1 = [r_ad3],16
|
|
fcmp.ge.s1 p6,p0 = f_ABS_X, f_smlst_oflow_input
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe f_B2 = [r_ad3],16
|
|
nop.f 0
|
|
mov r_exp_32 = 0x10004
|
|
}
|
|
;;
|
|
|
|
// Subtract RSHF constant to get rounded M as a floating point value
|
|
// M_temp * 2^(63-6) - 2^63
|
|
{ .mfb
|
|
ldfe f_B3 = [r_ad3],16
|
|
fms.s1 f_M = f_M_temp, f_2TOM57, f_RSHF
|
|
(p6) br.cond.spnt SINH_HUGE // Branch if result will overflow
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig r_M = f_M_temp
|
|
nop.f 0
|
|
cmp.ge p7,p6 = r_exp_x, r_exp_32 // Test if x >= 32
|
|
}
|
|
;;
|
|
|
|
// Calculate j. j is the signed extension of the six lsb of M. It
|
|
// has a range of -32 thru 31.
|
|
|
|
// Calculate R
|
|
// ax - M*log2by64_hi
|
|
// R = (ax - M*log2by64_hi) - M*log2by64_lo
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 f_R_temp = f_M, f_log2by64_hi, f_ABS_X
|
|
and r_j = 0x3f, r_M
|
|
}
|
|
;;
|
|
|
|
{ .mii
|
|
nop.m 0
|
|
shl r_jshf = r_j, 0x2 // Shift j so can sign extend it
|
|
;;
|
|
sxt1 r_jshf = r_jshf
|
|
}
|
|
;;
|
|
|
|
{ .mii
|
|
nop.m 0
|
|
shr r_j = r_jshf, 0x2 // Now j has range -32 to 31
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
shladd r_ad_J_hi = r_j, 4, r_ad4 // pointer to Tjhi
|
|
sub r_Mmj = r_M, r_j // M-j
|
|
sub r_mj = r0, r_j // Form -j
|
|
}
|
|
;;
|
|
|
|
// The TBL and EXP branches are merged and predicated
|
|
// If TBL, p6 true, 0.25 <= |x| < 32
|
|
// If EXP, p7 true, 32 <= |x| < overflow_limit
|
|
//
|
|
// N = (M-j)/64
|
|
{ .mfi
|
|
ldfe f_Tjhi = [r_ad_J_hi]
|
|
fnma.s1 f_R = f_M, f_log2by64_lo, f_R_temp
|
|
shr r_N = r_Mmj, 0x6 // N = (M-j)/64
|
|
}
|
|
{ .mfi
|
|
shladd r_ad_mJ_hi = r_mj, 4, r_ad4 // pointer to Tmjhi
|
|
nop.f 0
|
|
shladd r_ad_mJ_lo = r_mj, 2, r_ad5 // pointer to Tmjlo
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
sub r_2mNm1 = r_signexp_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
|
|
}
|
|
{ .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)
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
ldfs f_Tmjlo = [r_ad_mJ_lo]
|
|
setf.exp f_sneg = r_2mNm1 // Form sgnx * 2^(-N-1)
|
|
nop.f 0
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
ldfs f_Tjlo = [r_ad_J_lo]
|
|
setf.exp f_spos = r_2Nm1 // Form sgnx * 2^(N-1)
|
|
nop.f 0
|
|
}
|
|
;;
|
|
|
|
// ******************************************************
|
|
// STEP 2 (TBL and EXP)
|
|
// ******************************************************
|
|
// Calculate Rsquared and Rcubed in preparation for p_even and p_odd
|
|
|
|
{ .mmf
|
|
nop.m 0
|
|
nop.m 0
|
|
fma.s1 f_Rsq = f_R, f_R, f0
|
|
}
|
|
;;
|
|
|
|
|
|
// Calculate p_even
|
|
// B_2 + Rsq *B_3
|
|
// B_1 + Rsq * (B_2 + Rsq *B_3)
|
|
// p_even = Rsq * (B_1 + Rsq * (B_2 + Rsq *B_3))
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_peven_temp1 = f_Rsq, f_B3, f_B2
|
|
nop.i 0
|
|
}
|
|
// Calculate p_odd
|
|
// A_2 + Rsq *A_3
|
|
// A_1 + Rsq * (A_2 + Rsq *A_3)
|
|
// podd = R + Rcub * (A_1 + Rsq * (A_2 + Rsq *A_3))
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_podd_temp1 = f_Rsq, f_A3, f_A2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_Rcub = f_Rsq, f_R, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
//
|
|
// If TBL,
|
|
// Calculate S_hi and S_lo, and C_hi
|
|
// SC_hi_temp = sneg * Tmjhi
|
|
// S_hi = spos * Tjhi - SC_hi_temp
|
|
// S_hi = spos * Tjhi - (sneg * Tmjhi)
|
|
// C_hi = spos * Tjhi + SC_hi_temp
|
|
// C_hi = spos * Tjhi + (sneg * Tmjhi)
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 f_SC_hi_temp = f_sneg, f_Tmjhi, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// If TBL,
|
|
// S_lo_temp3 = sneg * Tmjlo
|
|
// S_lo_temp4 = spos * Tjlo - S_lo_temp3
|
|
// S_lo_temp4 = spos * Tjlo -(sneg * Tmjlo)
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 f_S_lo_temp3 = f_sneg, f_Tmjlo, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_peven_temp2 = f_Rsq, f_peven_temp1, f_B1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_podd_temp2 = f_Rsq, f_podd_temp1, f_A1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// If EXP,
|
|
// Compute sgnx * 2^(N-1) * Tjhi and sgnx * 2^(N-1) * Tjlo
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s1 f_Tjhi_spos = f_Tjhi, f_spos, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s1 f_Tjlo_spos = f_Tjlo, f_spos, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fms.s1 f_S_hi = f_spos, f_Tjhi, f_SC_hi_temp
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 f_C_hi = f_spos, f_Tjhi, f_SC_hi_temp
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fms.s1 f_S_lo_temp4 = f_spos, f_Tjlo, f_S_lo_temp3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_peven = f_Rsq, f_peven_temp2, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_podd = f_podd_temp2, f_Rcub, f_R
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// If TBL,
|
|
// 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 0
|
|
(p6) fms.s1 f_S_lo_temp1 = f_spos, f_Tjhi, f_S_hi
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fnma.s1 f_S_lo_temp2 = f_sneg, f_Tmjhi, f_S_lo_temp1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// 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 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 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)
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 f_Y_lo_temp = f_S_hi, f_peven, f_S_lo
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s1 f_Y_lo = f_Tjhi_spos, f_Y_lo_temp, f_Tjlo_spos
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Dummy multiply to generate inexact
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s0 f_tmp = f_B2, f_B2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s1 f_Y_lo = f_C_hi, f_podd, f_Y_lo_temp
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// f8 = answer = Y_hi + Y_lo
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.s0 f8 = f_Y_lo, f1, f_Tjhi_spos
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// f8 = answer = Y_hi + Y_lo
|
|
{ .mfb
|
|
nop.m 0
|
|
(p6) fma.s0 f8 = f_Y_lo, f1, f_S_hi
|
|
br.ret.sptk b0 // Exit for SINH_BY_TBL and SINH_BY_EXP
|
|
}
|
|
;;
|
|
|
|
|
|
// 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
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ldfe f_P4 = [r_ad2e],16
|
|
ldfe f_P3 = [r_ad2o],16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ldfe f_P2 = [r_ad2e],16
|
|
ldfe f_P1 = [r_ad2o],16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_X3 = f_NORM_X, f_X2, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_X4 = f_X2, f_X2, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_poly65 = f_X2, f_P6, f_P5
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_poly43 = f_X2, f_P4, f_P3
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_poly21 = f_X2, f_P2, f_P1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_poly6543 = f_X4, f_poly65, f_poly43
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 f_poly6to1 = f_X4, f_poly6543, f_poly21
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Dummy multiply to generate inexact
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s0 f_tmp = f_P6, f_P6
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 f8 = f_poly6to1, f_X3, f_NORM_X
|
|
br.ret.sptk b0 // Exit SINH_BY_POLY
|
|
}
|
|
;;
|
|
|
|
|
|
// 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 0
|
|
fcmp.eq.s0 p10,p0 = f8, f0 // Set denorm flag
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Set p8 if really a denorm
|
|
{ .mmi
|
|
and r_exp_x = r_exp_mask, r_signexp_x
|
|
;;
|
|
cmp.lt p8,p9 = r_exp_x, r_exp_denorm
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Identify denormal operands.
|
|
{ .mfb
|
|
nop.m 0
|
|
(p8) 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
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s0 f8 = f8,f8,f8 // If x +denorm, result=x+x^2
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
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
|
|
}
|
|
;;
|
|
|
|
|
|
// 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
|
|
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 0
|
|
(p9) fma.s1 f_signed_hi_lo = f_huge, f1, f1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s0 f_pre_result = f_signed_hi_lo, f_huge, f0
|
|
mov GR_Parameter_TAG = 126
|
|
}
|
|
;;
|
|
|
|
GLOBAL_IEEE754_END(sinhl)
|
|
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
|
|
{ .mfi
|
|
add GR_Parameter_Y=-32,sp // Parameter 2 value
|
|
nop.f 0
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
|
|
{ .mmi
|
|
stfe [GR_Parameter_Y] = f0,16 // STORE Parameter 2 on stack
|
|
add GR_Parameter_X = 16,sp // Parameter 1 address
|
|
.save b0, GR_SAVE_B0
|
|
mov GR_SAVE_B0=b0 // Save b0
|
|
};;
|
|
|
|
.body
|
|
{ .mib
|
|
stfe [GR_Parameter_X] = f8 // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfe [GR_Parameter_Y] = f_pre_result // STORE Parameter 3 on stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
};;
|
|
|
|
{ .mmi
|
|
add GR_Parameter_RESULT = 48,sp
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.restore sp
|
|
add sp = 64,sp // Restore stack pointer
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
};;
|
|
|
|
{ .mib
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
br.ret.sptk b0 // Return
|
|
};;
|
|
|
|
LOCAL_LIBM_END(__libm_error_region)
|
|
|
|
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|