.file "nexttowardl.s"
// Copyright (c) 2001 - 2004, Intel Corporation
// All rights reserved.
//
// Contributed 2001 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
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * 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
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 08/15/01 Initial version
// 08/23/01 Corrected error tag number
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 12/14/04 Added error handling on underflow.
//
// API
//==============================================================
// long double nexttowardl( long double x, long double y );
// input floating point f8, f9
// output floating point f8
//
// Registers used
//==============================================================
GR_max_pexp = r14
GR_min_pexp = r15
GR_exp = r16
GR_sig = r17
GR_lnorm_sig = r18
GR_sign_mask = r19
GR_exp_mask = r20
GR_sden_sig = r21
GR_new_sig = r22
GR_new_exp = r23
GR_lden_sig = r24
GR_snorm_sig = r25
GR_exp1 = r26
GR_x_exp = r27
// r36-39 parameters for libm_error_support
GR_SAVE_B0 = r34
GR_SAVE_GP = r35
GR_SAVE_PFS = r32
GR_Parameter_X = r36
GR_Parameter_Y = r37
GR_Parameter_RESULT = r38
GR_Parameter_TAG = r39
FR_lnorm_sig = f10
FR_lnorm_exp = f11
FR_lnorm = f12
FR_sden_sig = f13
FR_den_exp = f14
FR_sden = f15
FR_snorm_exp = f32
FR_save_f8 = f33
FR_new_exp = f34
FR_new_sig = f35
FR_lden_sig = f36
FR_snorm_sig = f37
FR_exp1 = f38
FR_tmp = f39
//
// Overview of operation
//==============================================================
// nexttowardl determines the next representable value
// after x in the direction of y.
.section .text
GLOBAL_LIBM_ENTRY(nexttowardl)
// Extract signexp from x
// Is x < y ? p10 if yes, p11 if no
// Form smallest denormal significand = ulp size
{ .mfi
getf.exp GR_exp = f8
fcmp.lt.s1 p10,p11 = f8, f9
addl GR_sden_sig = 0x1, r0
}
// Form largest normal significand 0xffffffffffffffff
// Form smallest normal exponent
{ .mfi
addl GR_lnorm_sig = -0x1,r0
nop.f 999
addl GR_min_pexp = 0x0c001, r0 ;;
}
// Extract significand from x
// Is x=y? This fcmp also sets Invalid and Denormal if required
// Form largest normal exponent
{ .mfi
getf.sig GR_sig = f8
fcmp.eq.s0 p6,p0 = f8, f9
addl GR_max_pexp = 0x13ffe, r0
}
// Move largest normal significand to fp reg for special cases
{ .mfi
setf.sig FR_lnorm_sig = GR_lnorm_sig
nop.f 999
addl GR_sign_mask = 0x20000, r0 ;;
}
// Move smallest denormal significand and exp to fp regs
// Is x=nan?
// Set p12 and p13 based on whether significand increases or decreases
// It increases (p12 set) if x<y and x>=0 or if x>y and x<0
// It decreases (p13 set) if x<y and x<0 or if x>y and x>=0
{ .mfi
setf.sig FR_sden_sig = GR_sden_sig
fclass.m p8,p0 = f8, 0xc3
(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask
}
// Move smallest normal exp to fp regs
{ .mfi
setf.exp FR_snorm_exp = GR_min_pexp
nop.f 999
(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;
}
.pred.rel "mutex",p12,p13
// Form expected new significand, adding or subtracting 1 ulp increment
// If x=y set result to y
// Form smallest normal significand and largest denormal significand
{ .mfi
(p12) add GR_new_sig = GR_sig, GR_sden_sig
(p6) fmerge.s f8=f9,f9
dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000
}
{ .mlx
(p13) sub GR_new_sig = GR_sig, GR_sden_sig
movl GR_lden_sig = 0x7fffffffffffffff ;;
}
// Move expected result significand and signexp to fp regs
// Is y=nan?
// Form new exponent in case result exponent needs incrementing or decrementing
{ .mfi
setf.exp FR_new_exp = GR_exp
fclass.m p9,p0 = f9, 0xc3
(p12) add GR_exp1 = 1, GR_exp
}
{ .mib
setf.sig FR_new_sig = GR_new_sig
(p13) add GR_exp1 = -1, GR_exp
(p6) br.ret.spnt b0 ;; // Exit if x=y
}
// Move largest normal signexp to fp reg for special cases
// Is x=zero?
{ .mfi
setf.exp FR_lnorm_exp = GR_max_pexp
fclass.m p7,p0 = f8, 0x7
nop.i 999
}
{ .mfb
setf.exp FR_den_exp = GR_min_pexp
(p8) fma.s0 f8 = f8,f1,f9
(p8) br.ret.spnt b0 ;; // Exit if x=nan
}
// Move exp+-1 and smallest normal significand to fp regs for special cases
// Is x=inf?
{ .mfi
setf.exp FR_exp1 = GR_exp1
fclass.m p6,p0 = f8, 0x23
addl GR_exp_mask = 0x1ffff, r0
}
{ .mfb
setf.sig FR_snorm_sig = GR_snorm_sig
(p9) fma.s0 f8 = f8,f1,f9
(p9) br.ret.spnt b0 ;; // Exit if y=nan
}
// Move largest denormal significand to fp regs for special cases
// Save x
{ .mfb
setf.sig FR_lden_sig = GR_lden_sig
mov FR_save_f8 = f8
(p7) br.cond.spnt NEXT_ZERO ;; // Exit if x=0
}
// Mask off the sign to get x_exp
{ .mfb
and GR_x_exp = GR_exp_mask, GR_exp
nop.f 999
(p6) br.cond.spnt NEXT_INF ;; // Exit if x=inf
}
// Check 5 special cases when significand rolls over:
// 1 sig size incr, x_sig=max_sig, x_exp < max_exp
// Set p6, result is sig=min_sig, exp++
// 2 sig size incr, x_sig=max_sig, x_exp >= max_exp
// Set p7, result is inf, signal overflow
// 3 sig size decr, x_sig=min_sig, x_exp > min_exp
// Set p8, result is sig=max_sig, exp--
// 4 sig size decr, x_sig=min_sig, x_exp = min_exp
// Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact
// 5 sig size decr, x_sig=min_den_sig, x_exp = min_exp
// Set p10, result is zero, sign of x, signal underflow and inexact
//
{ .mmi
(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0
(p13) cmp.eq.unc p9,p10 = GR_new_sig, GR_lden_sig
nop.i 999
;;
}
{ .mmi
(p6) cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp
(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0
(p9) cmp.le.unc p9,p8 = GR_x_exp, GR_min_pexp
;;
}
// Create small normal in case need to generate underflow flag
{ .mfi
nop.m 999
fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
nop.i 999
}
// Branch if cases 1, 2, 3
{ .bbb
(p6) br.cond.spnt NEXT_EXPUP
(p7) br.cond.spnt NEXT_OVERFLOW
(p8) br.cond.spnt NEXT_EXPDOWN ;;
}
// Branch if cases 4, 5
{ .mbb
nop.m 999
(p9) br.cond.spnt NEXT_NORM_TO_DENORM
(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO
;;
}
// Here if no special cases
// Set p6 if result will be a denormal, so can force underflow flag
// Case 1: x_exp=min_exp, x_sig=unnormalized
// Case 2: x_exp<min_exp
{ .mfi
cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
fmerge.se f8 = FR_new_exp, FR_new_sig
nop.i 999 ;;
}
{ .mfi
nop.m 999
nop.f 999
(p6) tbit.z p6,p0 = GR_new_sig, 63 ;;
}
NEXT_COMMON_FINISH:
// Force underflow and inexact if denormal result
{ .mfi
nop.m 999
(p6) fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
nop.i 999
}
{ .mfb
nop.m 999
fnorm.s0 f8 = f8 // Final normalization to result precision
(p6) br.cond.spnt NEXT_UNDERFLOW ;;
}
{ .mfb
nop.m 999
nop.f 999
br.ret.sptk b0;;
}
//Special cases
NEXT_EXPUP:
{ .mfb
cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
fmerge.se f8 = FR_exp1, FR_snorm_sig
br.cond.sptk NEXT_COMMON_FINISH ;;
}
NEXT_EXPDOWN:
{ .mfb
cmp.lt p6,p7 = GR_x_exp, GR_min_pexp
fmerge.se f8 = FR_exp1, FR_lnorm_sig
br.cond.sptk NEXT_COMMON_FINISH ;;
}
NEXT_NORM_TO_DENORM:
{ .mfi
nop.m 999
fmerge.se f8 = FR_exp1, FR_lden_sig
nop.i 999
}
// Force underflow and inexact
{ .mfb
nop.m 999
fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
br.cond.sptk NEXT_UNDERFLOW ;;
}
NEXT_UNDERFLOW_TO_ZERO:
{ .mfb
cmp.eq p6,p0 = r0,r0
fmerge.s f8 = FR_save_f8,f0
br.cond.sptk NEXT_COMMON_FINISH ;;
}
NEXT_INF:
// Here if f8 is +- infinity
// INF
// if f8 is +inf, no matter what y is return largest long double
// if f8 is -inf, no matter what y is return -largest long double
// Create largest long double
{ .mfi
nop.m 999
fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
nop.i 999 ;;
}
{ .mfb
nop.m 999
fmerge.s f8 = f8,FR_lnorm
br.ret.sptk b0 ;;
}
NEXT_ZERO:
// Here if f8 is +- zero
// ZERO
// if f8 is zero and y is +, return + smallest long double denormal
// if f8 is zero and y is -, return - smallest long double denormal
{ .mfi
nop.m 999
fmerge.se FR_sden = f0,FR_sden_sig
nop.i 999 ;;
}
// Create small normal to generate underflow flag
{ .mfi
nop.m 999
fmerge.se FR_tmp = FR_snorm_exp, FR_lnorm_sig
nop.i 999 ;;
}
// Add correct sign from direction arg
{ .mfi
nop.m 999
fmerge.s f8 = f9,FR_sden
nop.i 999 ;;
}
// Force underflow and inexact flags
{ .mfb
nop.m 999
fma.s0 FR_tmp = FR_tmp,FR_tmp,f0
br.cond.sptk NEXT_UNDERFLOW ;;
}
NEXT_UNDERFLOW:
// Here if result is a denorm, or input is finite and result is zero
// Call error support to report possible range error
{ .mib
alloc r32=ar.pfs,2,2,4,0
mov GR_Parameter_TAG = 270 // Error code
br.cond.sptk __libm_error_region // Branch to error call
}
;;
NEXT_OVERFLOW:
// Here if input is finite, but result will be infinite
// Use frcpa to generate infinity of correct sign
// Call error support to report possible range error
{ .mfi
alloc r32=ar.pfs,2,2,4,0
frcpa.s1 f8,p6 = FR_save_f8, f0
nop.i 999 ;;
}
// Create largest double
{ .mfi
nop.m 999
fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig
nop.i 999 ;;
}
// Force overflow and inexact flags to be set
{ .mfb
mov GR_Parameter_TAG = 198 // Error code
fma.s0 FR_tmp = FR_lnorm,FR_lnorm,f0
br.cond.sptk __libm_error_region // Branch to error call
}
;;
GLOBAL_LIBM_END(nexttowardl)
LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
// (1)
{ .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
};;
// (2)
{ .mmi
stfe [GR_Parameter_Y] = f9,16 // 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
// (3)
{ .mib
stfe [GR_Parameter_X] = FR_save_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] = f8 // 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
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
// (4)
{ .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#