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503 lines
14 KiB
ArmAsm
503 lines
14 KiB
ArmAsm
.file "nextafterl.s"
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// Copyright (c) 2000 - 2004, 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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// 03/03/00 Modified to conform to C9X, and improve speed of main path
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// 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed
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// 04/04/00 Unwind support added
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// 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3
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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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// 09/09/00 Updated fcmp so that qnans do not raise invalid.
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// 12/15/00 Fixed case of smallest long double normal to largest denormal,
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// now adhere to C99 for two zero args, and fixed flag settings
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// for several cases
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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// 12/14/04 Added error handling on underflow.
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//
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// API
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//==============================================================
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// long double nextafterl( long double x, long double y );
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// input floating point f8, f9
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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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GR_max_pexp = r14
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GR_min_pexp = r15
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GR_exp = r16
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GR_sig = r17
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GR_lnorm_sig = r18
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GR_sign_mask = r19
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GR_exp_mask = r20
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GR_sden_sig = r21
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GR_new_sig = r22
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GR_new_exp = r23
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GR_lden_sig = r24
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GR_snorm_sig = r25
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GR_exp1 = r26
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GR_x_exp = r27
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// r36-39 parameters for libm_error_support
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GR_SAVE_B0 = r34
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GR_SAVE_GP = r35
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GR_SAVE_PFS = r32
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GR_Parameter_X = r36
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GR_Parameter_Y = r37
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GR_Parameter_RESULT = r38
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GR_Parameter_TAG = r39
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FR_lnorm_sig = f10
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FR_lnorm_exp = f11
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FR_lnorm = f12
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FR_sden_sig = f13
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FR_den_exp = f14
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FR_sden = f15
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FR_snorm_exp = f32
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FR_save_f8 = f33
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FR_new_exp = f34
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FR_new_sig = f35
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FR_lden_sig = f36
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FR_snorm_sig = f37
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FR_exp1 = f38
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FR_tmp = f39
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//
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// Overview of operation
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//==============================================================
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// nextafterl determines the next representable value
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// after x in the direction of y.
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.section .text
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GLOBAL_LIBM_ENTRY(nextafterl)
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// Extract signexp from x
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// Is x < y ? p10 if yes, p11 if no
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// Form smallest denormal significand = ulp size
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{ .mfi
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getf.exp GR_exp = f8
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fcmp.lt.s1 p10,p11 = f8, f9
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addl GR_sden_sig = 0x1, r0
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}
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// Form largest normal significand 0xffffffffffffffff
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// Form smallest normal exponent
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{ .mfi
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addl GR_lnorm_sig = -0x1,r0
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nop.f 999
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addl GR_min_pexp = 0x0c001, r0 ;;
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}
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// Extract significand from x
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// Is x=y? This fcmp also sets Invalid and Denormal if required
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// Form largest normal exponent
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{ .mfi
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getf.sig GR_sig = f8
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fcmp.eq.s0 p6,p0 = f8, f9
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addl GR_max_pexp = 0x13ffe, r0
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}
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// Move largest normal significand to fp reg for special cases
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{ .mfi
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setf.sig FR_lnorm_sig = GR_lnorm_sig
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nop.f 999
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addl GR_sign_mask = 0x20000, r0 ;;
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}
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// Move smallest denormal significand and exp to fp regs
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// Is x=nan?
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// Set p12 and p13 based on whether significand increases or decreases
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// It increases (p12 set) if x<y and x>=0 or if x>y and x<0
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// It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
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{ .mfi
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setf.sig FR_sden_sig = GR_sden_sig
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fclass.m p8,p0 = f8, 0xc3
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(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
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}
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// Move smallest normal exp to fp regs
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{ .mfi
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setf.exp FR_snorm_exp = GR_min_pexp
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nop.f 999
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(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
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}
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.pred.rel "mutex",p12,p13
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// Form expected new significand, adding or subtracting 1 ulp increment
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// If x=y set result to y
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// Form smallest normal significand and largest denormal significand
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{ .mfi
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(p12) add GR_new_sig = GR_sig, GR_sden_sig
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(p6) fmerge.s f8=f9,f9
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dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
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}
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{ .mlx
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(p13) sub GR_new_sig = GR_sig, GR_sden_sig
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movl GR_lden_sig = 0x7fffffffffffffff ;;
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}
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// Move expected result significand and signexp to fp regs
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// Is y=nan?
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// Form new exponent in case result exponent needs incrementing or decrementing
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{ .mfi
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setf.exp FR_new_exp = GR_exp
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fclass.m p9,p0 = f9, 0xc3
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(p12) add GR_exp1 = 1, GR_exp
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}
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{ .mib
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setf.sig FR_new_sig = GR_new_sig
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(p13) add GR_exp1 = -1, GR_exp
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(p6) br.ret.spnt b0 ;; // Exit if x=y
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}
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// Move largest normal signexp to fp reg for special cases
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// Is x=zero?
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{ .mfi
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setf.exp FR_lnorm_exp = GR_max_pexp
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fclass.m p7,p0 = f8, 0x7
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nop.i 999
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}
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{ .mfb
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setf.exp FR_den_exp = GR_min_pexp
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(p8) fma.s0 f8 = f8,f1,f9
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(p8) br.ret.spnt b0 ;; // Exit if x=nan
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}
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// Move exp+-1 and smallest normal significand to fp regs for special cases
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// Is x=inf?
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{ .mfi
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setf.exp FR_exp1 = GR_exp1
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fclass.m p6,p0 = f8, 0x23
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addl GR_exp_mask = 0x1ffff, r0
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}
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{ .mfb
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setf.sig FR_snorm_sig = GR_snorm_sig
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(p9) fma.s0 f8 = f8,f1,f9
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(p9) br.ret.spnt b0 ;; // Exit if y=nan
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}
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// Move largest denormal significand to fp regs for special cases
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// Save x
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{ .mfb
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setf.sig FR_lden_sig = GR_lden_sig
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mov FR_save_f8 = f8
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(p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
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}
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// Mask off the sign to get x_exp
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{ .mfb
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and GR_x_exp = GR_exp_mask, GR_exp
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nop.f 999
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(p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
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}
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// Check 5 special cases when significand rolls over:
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// 1 sig size incr, x_sig=max_sig, x_exp < max_exp
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// Set p6, result is sig=min_sig, exp++
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// 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
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// Set p7, result is inf, signal overflow
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// 3 sig size decr, x_sig=min_sig, x_exp > min_exp
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// Set p8, result is sig=max_sig, exp--
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// 4 sig size decr, x_sig=min_sig, x_exp = min_exp
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// Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
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// 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
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// Set p10, result is zero, sign of x, signal underflow and inexact
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//
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{ .mmi
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(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
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(p13) cmp.eq.unc p9,p10 = GR_new_sig, GR_lden_sig
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nop.i 999
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;;
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}
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{ .mmi
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(p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
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(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0
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(p9) cmp.le.unc p9,p8 = GR_x_exp, GR_min_pexp
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;;
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}
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// Create small normal in case need to generate underflow flag
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{ .mfi
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nop.m 999
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fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
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nop.i 999
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}
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// Branch if cases 1, 2, 3
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{ .bbb
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(p6) br.cond.spnt NEXT_EXPUP
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(p7) br.cond.spnt NEXT_OVERFLOW
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(p8) br.cond.spnt NEXT_EXPDOWN ;;
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}
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// Branch if cases 4, 5
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{ .mbb
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nop.m 999
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(p9) br.cond.spnt NEXT_NORM_TO_DENORM
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(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
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;;
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}
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// Here if no special cases
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// Set p6 if result will be a denormal, so can force underflow flag
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// Case 1: x_exp=min_exp, x_sig=unnormalized
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// Case 2: x_exp<min_exp
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{ .mfi
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cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
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fmerge.se f8 = FR_new_exp, FR_new_sig
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nop.i 999 ;;
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}
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{ .mfi
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nop.m 999
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nop.f 999
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(p6) tbit.z p6,p0 = GR_new_sig, 63 ;;
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}
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NEXT_COMMON_FINISH:
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// Force underflow and inexact if denormal result
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{ .mfi
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nop.m 999
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(p6) fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
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nop.i 999
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}
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{ .mfb
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nop.m 999
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fnorm.s0 f8 = f8 // Final normalization to result precision
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(p6) br.cond.spnt NEXT_UNDERFLOW ;;
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}
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{ .mfb
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nop.m 999
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nop.f 999
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br.ret.sptk b0;;
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}
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//Special cases
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NEXT_EXPUP:
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{ .mfb
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cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
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fmerge.se f8 = FR_exp1, FR_snorm_sig
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br.cond.sptk NEXT_COMMON_FINISH ;;
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}
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NEXT_EXPDOWN:
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{ .mfb
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cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
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fmerge.se f8 = FR_exp1, FR_lnorm_sig
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br.cond.sptk NEXT_COMMON_FINISH ;;
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}
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NEXT_NORM_TO_DENORM:
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{ .mfi
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nop.m 999
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fmerge.se f8 = FR_exp1, FR_lden_sig
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nop.i 999
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}
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// Force underflow and inexact
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{ .mfb
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nop.m 999
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fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
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br.cond.sptk NEXT_UNDERFLOW ;;
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}
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NEXT_UNDERFLOW_TO_ZERO:
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{ .mfb
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cmp.eq p6,p0 = r0,r0
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fmerge.s f8 = FR_save_f8,f0
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br.cond.sptk NEXT_COMMON_FINISH ;;
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}
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NEXT_INF:
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// Here if f8 is +- infinity
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// INF
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// if f8 is +inf, no matter what y is return largest long double
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// if f8 is -inf, no matter what y is return -largest long double
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// Create largest long double
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{ .mfi
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nop.m 999
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fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
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nop.i 999 ;;
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}
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{ .mfb
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nop.m 999
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fmerge.s f8 = f8,FR_lnorm
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br.ret.sptk b0 ;;
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}
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NEXT_ZERO:
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// Here if f8 is +- zero
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// ZERO
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// if f8 is zero and y is +, return + smallest long double denormal
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// if f8 is zero and y is -, return - smallest long double denormal
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{ .mfi
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nop.m 999
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fmerge.se FR_sden = f0,FR_sden_sig
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nop.i 999 ;;
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}
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// Create small normal to generate underflow flag
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{ .mfi
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nop.m 999
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fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
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nop.i 999 ;;
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}
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// Add correct sign from direction arg
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{ .mfi
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nop.m 999
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fmerge.s f8 = f9,FR_sden
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nop.i 999 ;;
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}
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// Force underflow and inexact flags
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{ .mfb
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nop.m 999
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fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
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br.cond.sptk NEXT_UNDERFLOW ;;
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}
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NEXT_UNDERFLOW:
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// Here if result is a denorm, or input is finite and result is zero
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// Call error support to report possible range error
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{ .mib
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alloc r32=ar.pfs,2,2,4,0
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mov GR_Parameter_TAG = 267 // Error code
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br.cond.sptk __libm_error_region // Branch to error call
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}
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;;
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NEXT_OVERFLOW:
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// Here if input is finite, but result will be infinite
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// Use frcpa to generate infinity of correct sign
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// Call error support to report possible range error
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{ .mfi
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alloc r32=ar.pfs,2,2,4,0
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frcpa.s1 f8,p6 = FR_save_f8, f0
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nop.i 999 ;;
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}
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// Create largest double
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{ .mfi
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nop.m 999
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fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
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nop.i 999 ;;
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}
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// Force overflow and inexact flags to be set
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{ .mfb
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mov GR_Parameter_TAG = 153 // Error code
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fma.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
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br.cond.sptk __libm_error_region // Branch to error call
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}
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;;
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GLOBAL_LIBM_END(nextafterl)
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LOCAL_LIBM_ENTRY(__libm_error_region)
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.prologue
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// (1)
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{ .mfi
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add GR_Parameter_Y=-32,sp // Parameter 2 value
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nop.f 0
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.save ar.pfs,GR_SAVE_PFS
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mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
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}
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{ .mfi
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.fframe 64
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add sp=-64,sp // Create new stack
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nop.f 0
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mov GR_SAVE_GP=gp // Save gp
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};;
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// (2)
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{ .mmi
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stfe [GR_Parameter_Y] = f9,16 // STORE Parameter 2 on stack
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add GR_Parameter_X = 16,sp // Parameter 1 address
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.save b0, GR_SAVE_B0
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mov GR_SAVE_B0=b0 // Save b0
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};;
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.body
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// (3)
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{ .mib
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stfe [GR_Parameter_X] = FR_save_f8 // STORE Parameter 1 on stack
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add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
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nop.b 0
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}
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{ .mib
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stfe [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack
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add GR_Parameter_Y = -16,GR_Parameter_Y
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br.call.sptk b0=__libm_error_support# // Call error handling function
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};;
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{ .mmi
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nop.m 0
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nop.m 0
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add GR_Parameter_RESULT = 48,sp
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};;
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// (4)
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{ .mmi
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ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
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.restore sp
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add sp = 64,sp // Restore stack pointer
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mov b0 = GR_SAVE_B0 // Restore return address
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};;
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{ .mib
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mov gp = GR_SAVE_GP // Restore gp
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mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
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br.ret.sptk b0 // Return
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};;
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LOCAL_LIBM_END(__libm_error_region)
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.type __libm_error_support#,@function
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.global __libm_error_support#
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