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glibc/sysdeps/ia64/fpu/w_tgammaf_compat.S
Siddhesh Poyarekar 30891f35fa Remove "Contributed by" lines 
We stopped adding "Contributed by" or similar lines in sources in 2012
in favour of git logs and keeping the Contributors section of the
glibc manual up to date.  Removing these lines makes the license
header a bit more consistent across files and also removes the
possibility of error in attribution when license blocks or files are
copied across since the contributed-by lines don't actually reflect
reality in those cases.

Move all "Contributed by" and similar lines (Written by, Test by,
etc.) into a new file CONTRIBUTED-BY to retain record of these
contributions.  These contributors are also mentioned in
manual/contrib.texi, so we just maintain this additional record as a
courtesy to the earlier developers.

The following scripts were used to filter a list of files to edit in
place and to clean up the CONTRIBUTED-BY file respectively.  These
were not added to the glibc sources because they're not expected to be
of any use in future given that this is a one time task:

https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc
https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02

Reviewed-by: Carlos O'Donell <carlos@redhat.com>
2021-09-03 22:06:44 +05:30

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.file "tgammaf.s"
// Copyright (c) 2001 - 2005, Intel Corporation
// All rights reserved.
//
//
// 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:
// 11/30/01 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 04/04/03 Changed error codes for overflow and negative integers
// 04/10/03 Changed code for overflow near zero handling
// 12/16/03 Fixed parameter passing to/from error handling routine
// 03/31/05 Reformatted delimiters between data tables
//
//*********************************************************************
//
//*********************************************************************
//
// Function: tgammaf(x) computes the principle value of the GAMMA
// function of x.
//
//*********************************************************************
//
// Resources Used:
//
// Floating-Point Registers: f8-f15
// f33-f75
//
// General Purpose Registers:
// r8-r11
// r14-r29
// r32-r36
// r37-r40 (Used to pass arguments to error handling routine)
//
// Predicate Registers: p6-p15
//
//*********************************************************************
//
// IEEE Special Conditions:
//
// tgammaf(+inf) = +inf
// tgammaf(-inf) = QNaN
// tgammaf(+/-0) = +/-inf
// tgammaf(x<0, x - integer) = QNaN
// tgammaf(SNaN) = QNaN
// tgammaf(QNaN) = QNaN
//
//*********************************************************************
//
// Overview
//
// The method consists of three cases.
//
// If 2 <= x < OVERFLOW_BOUNDARY use case tgamma_regular;
// else if 0 < x < 2 use case tgamma_from_0_to_2;
// else if -(i+1) < x < -i, i = 0...43 use case tgamma_negatives;
//
// Case 2 <= x < OVERFLOW_BOUNDARY
// -------------------------------
// Here we use algorithm based on the recursive formula
// GAMMA(x+1) = x*GAMMA(x). For that we subdivide interval
// [2; OVERFLOW_BOUNDARY] into intervals [8*n; 8*(n+1)] and
// approximate GAMMA(x) by polynomial of 22th degree on each
// [8*n; 8*n+1], recursive formula is used to expand GAMMA(x)
// to [8*n; 8*n+1]. In other words we need to find n, i and r
// such that x = 8 * n + i + r where n and i are integer numbers
// and r is fractional part of x. So GAMMA(x) = GAMMA(8*n+i+r) =
// = (x-1)*(x-2)*...*(x-i)*GAMMA(x-i) =
// = (x-1)*(x-2)*...*(x-i)*GAMMA(8*n+r) ~
// ~ (x-1)*(x-2)*...*(x-i)*P12n(r).
//
// Step 1: Reduction
// -----------------
// N = [x] with truncate
// r = x - N, note 0 <= r < 1
//
// n = N & ~0xF - index of table that contains coefficient of
// polynomial approximation
// i = N & 0xF - is used in recursive formula
//
//
// Step 2: Approximation
// ---------------------
// We use factorized minimax approximation polynomials
// P12n(r) = A12*(r^2+C01(n)*r+C00(n))*
// *(r^2+C11(n)*r+C10(n))*...*(r^2+C51(n)*r+C50(n))
//
// Step 3: Recursion
// -----------------
// In case when i > 0 we need to multiply P12n(r) by product
// R(i,x)=(x-1)*(x-2)*...*(x-i). To reduce number of fp-instructions
// we can calculate R as follow:
// R(i,x) = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-1))*(x-i)) if i is
// even or R = ((x-1)*(x-2))*((x-3)*(x-4))*...*((x-(i-2))*(x-(i-1)))*
// *(i-1) if i is odd. In both cases we need to calculate
// R2(i,x) = (x^2-3*x+2)*(x^2-7*x+12)*...*(x^2+x+2*j*(2*j-1)) =
// = ((x^2-x)+2*(1-x))*((x^2-x)+6*(2-x))*...*((x^2-x)+2*(2*j-1)*(j-x)) =
// = (RA+2*RB)*(RA+6*(1-RB))*...*(RA+2*(2*j-1)*(j-1+RB))
// where j = 1..[i/2], RA = x^2-x, RB = 1-x.
//
// Step 4: Reconstruction
// ----------------------
// Reconstruction is just simple multiplication i.e.
// GAMMA(x) = P12n(r)*R(i,x)
//
// Case 0 < x < 2
// --------------
// To calculate GAMMA(x) on this interval we do following
// if 1.0 <= x < 1.25 than GAMMA(x) = P7(x-1)
// if 1.25 <= x < 1.5 than GAMMA(x) = P7(x-x_min) where
// x_min is point of local minimum on [1; 2] interval.
// if 1.5 <= x < 1.75 than GAMMA(x) = P7(x-1.5)
// if 1.75 <= x < 2.0 than GAMMA(x) = P7(x-1.5)
// and
// if 0 < x < 1 than GAMMA(x) = GAMMA(x+1)/x
//
// Case -(i+1) < x < -i, i = 0...43
// ----------------------------------
// Here we use the fact that GAMMA(-x) = PI/(x*GAMMA(x)*sin(PI*x)) and
// so we need to calculate GAMMA(x), sin(PI*x)/PI. Calculation of
// GAMMA(x) is described above.
//
// Step 1: Reduction
// -----------------
// Note that period of sin(PI*x) is 2 and range reduction for
// sin(PI*x) is like to range reduction for GAMMA(x)
// i.e rs = x - round(x) and |rs| <= 0.5.
//
// Step 2: Approximation
// ---------------------
// To approximate sin(PI*x)/PI = sin(PI*(2*n+rs))/PI =
// = (-1)^n*sin(PI*rs)/PI Taylor series is used.
// sin(PI*rs)/PI ~ S17(rs).
//
// Step 3: Division
// ----------------
// To calculate 1/x and 1/(GAMMA(x)*S12(rs)) we use frcpa
// instruction with following Newton-Raphson interations.
//
//
//*********************************************************************
GR_ad_Data = r8
GR_TAG = r8
GR_SignExp = r9
GR_Sig = r10
GR_ArgNz = r10
GR_RqDeg = r11
GR_NanBound = r14
GR_ExpOf025 = r15
GR_ExpOf05 = r16
GR_ad_Co = r17
GR_ad_Ce = r18
GR_TblOffs = r19
GR_Arg = r20
GR_Exp2Ind = r21
GR_TblOffsMask = r21
GR_Offs = r22
GR_OvfNzBound = r23
GR_ZeroResBound = r24
GR_ad_SinO = r25
GR_ad_SinE = r26
GR_Correction = r27
GR_Tbl12Offs = r28
GR_NzBound = r28
GR_ExpOf1 = r29
GR_fpsr = r29
GR_SAVE_B0 = r33
GR_SAVE_PFS = r34
GR_SAVE_GP = r35
GR_SAVE_SP = r36
GR_Parameter_X = r37
GR_Parameter_Y = r38
GR_Parameter_RESULT = r39
GR_Parameter_TAG = r40
FR_X = f10
FR_Y = f1
FR_RESULT = f8
FR_iXt = f11
FR_Xt = f12
FR_r = f13
FR_r2 = f14
FR_r4 = f15
FR_C01 = f33
FR_A7 = f33
FR_C11 = f34
FR_A6 = f34
FR_C21 = f35
FR_A5 = f35
FR_C31 = f36
FR_A4 = f36
FR_C41 = f37
FR_A3 = f37
FR_C51 = f38
FR_A2 = f38
FR_C00 = f39
FR_A1 = f39
FR_C10 = f40
FR_A0 = f40
FR_C20 = f41
FR_C30 = f42
FR_C40 = f43
FR_C50 = f44
FR_An = f45
FR_OvfBound = f46
FR_InvAn = f47
FR_Multplr = f48
FR_NormX = f49
FR_X2mX = f50
FR_1mX = f51
FR_Rq0 = f51
FR_Rq1 = f52
FR_Rq2 = f53
FR_Rq3 = f54
FR_Rcp0 = f55
FR_Rcp1 = f56
FR_Rcp2 = f57
FR_InvNormX1 = f58
FR_InvNormX2 = f59
FR_rs = f60
FR_rs2 = f61
FR_LocalMin = f62
FR_10 = f63
FR_05 = f64
FR_S32 = f65
FR_S31 = f66
FR_S01 = f67
FR_S11 = f68
FR_S21 = f69
FR_S00 = f70
FR_S10 = f71
FR_S20 = f72
FR_GAMMA = f73
FR_2 = f74
FR_6 = f75
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(tgammaf_data)
data8 0x3FDD8B618D5AF8FE // local minimum (0.461632144968362356785)
data8 0x4024000000000000 // 10.0
data8 0x3E90FC992FF39E13 // S32
data8 0xBEC144B2760626E2 // S31
//
//[2; 8)
data8 0x4009EFD1BA0CB3B4 // C01
data8 0x3FFFB35378FF4822 // C11
data8 0xC01032270413B896 // C41
data8 0xC01F171A4C0D6827 // C51
data8 0x40148F8E197396AC // C20
data8 0x401C601959F1249C // C30
data8 0x3EE21AD881741977 // An
data8 0x4041852200000000 // overflow boundary (35.04010009765625)
data8 0x3FD9CE68F695B198 // C21
data8 0xBFF8C30AC900DA03 // C31
data8 0x400E17D2F0535C02 // C00
data8 0x4010689240F7FAC8 // C10
data8 0x402563147DDCCF8D // C40
data8 0x4033406D0480A21C // C50
//
//[8; 16)
data8 0x4006222BAE0B793B // C01
data8 0x4002452733473EDA // C11
data8 0xC0010EF3326FDDB3 // C41
data8 0xC01492B817F99C0F // C51
data8 0x40099C905A249B75 // C20
data8 0x4012B972AE0E533D // C30
data8 0x3FE6F6DB91D0D4CC // An
data8 0x4041852200000000 // overflow boundary
data8 0x3FF545828F7B73C5 // C21
data8 0xBFBBD210578764DF // C31
data8 0x4000542098F53CFC // C00
data8 0x40032C1309AD6C81 // C10
data8 0x401D7331E19BD2E1 // C40
data8 0x402A06807295EF57 // C50
//
//[16; 24)
data8 0x4000131002867596 // C01
data8 0x3FFAA362D5D1B6F2 // C11
data8 0xBFFCB6985697DB6D // C41
data8 0xC0115BEE3BFC3B3B // C51
data8 0x3FFE62FF83456F73 // C20
data8 0x4007E33478A114C4 // C30
data8 0x41E9B2B73795ED57 // An
data8 0x4041852200000000 // overflow boundary
data8 0x3FEEB1F345BC2769 // C21
data8 0xBFC3BBE6E7F3316F // C31
data8 0x3FF14E07DA5E9983 // C00
data8 0x3FF53B76BF81E2C0 // C10
data8 0x4014051E0269A3DC // C40
data8 0x40229D4227468EDB // C50
//
//[24; 32)
data8 0x3FFAF7BD498384DE // C01
data8 0x3FF62AD8B4D1C3D2 // C11
data8 0xBFFABCADCD004C32 // C41
data8 0xC00FADE97C097EC9 // C51
data8 0x3FF6DA9ED737707E // C20
data8 0x4002A29E9E0C782C // C30
data8 0x44329D5B5167C6C3 // An
data8 0x4041852200000000 // overflow boundary
data8 0x3FE8943CBBB4B727 // C21
data8 0xBFCB39D466E11756 // C31
data8 0x3FE879AF3243D8C1 // C00
data8 0x3FEEC7DEBB14CE1E // C10
data8 0x401017B79BA80BCB // C40
data8 0x401E941DC3C4DE80 // C50
//
//[32; 40)
data8 0x3FF7ECB3A0E8FE5C // C01
data8 0x3FF3815A8516316B // C11
data8 0xBFF9ABD8FCC000C3 // C41
data8 0xC00DD89969A4195B // C51
data8 0x3FF2E43139CBF563 // C20
data8 0x3FFF96DC3474A606 // C30
data8 0x46AFF4CA9B0DDDF0 // An
data8 0x4041852200000000 // overflow boundary
data8 0x3FE4CE76DA1B5783 // C21
data8 0xBFD0524DB460BC4E // C31
data8 0x3FE35852DF14E200 // C00
data8 0x3FE8C7610359F642 // C10
data8 0x400BCF750EC16173 // C40
data8 0x401AC14E02EA701C // C50
//
//[40; 48)
data8 0x3FF5DCE4D8193097 // C01
data8 0x3FF1B0D8C4974FFA // C11
data8 0xBFF8FB450194CAEA // C41
data8 0xC00C9658E030A6C4 // C51
data8 0x3FF068851118AB46 // C20
data8 0x3FFBF7C7BB46BF7D // C30
data8 0x3FF0000000000000 // An
data8 0x4041852200000000 // overflow boundary
data8 0x3FE231DEB11D847A // C21
data8 0xBFD251ECAFD7E935 // C31
data8 0x3FE0368AE288F6BF // C00
data8 0x3FE513AE4215A70C // C10
data8 0x4008F960F7141B8B // C40
data8 0x40183BA08134397B // C50
//
//[1.0; 1.25)
data8 0xBFD9909648921868 // A7
data8 0x3FE96FFEEEA8520F // A6
data8 0xBFED0800D93449B8 // A3
data8 0x3FEFA648D144911C // A2
data8 0xBFEE3720F7720B4D // A5
data8 0x3FEF4857A010CA3B // A4
data8 0xBFE2788CCD545AA4 // A1
data8 0x3FEFFFFFFFE9209E // A0
//
//[1.25; 1.5)
data8 0xBFB421236426936C // A7
data8 0x3FAF237514F36691 // A6
data8 0xBFC0BADE710A10B9 // A3
data8 0x3FDB6C5465BBEF1F // A2
data8 0xBFB7E7F83A546EBE // A5
data8 0x3FC496A01A545163 // A4
data8 0xBDEE86A39D8452EB // A1
data8 0x3FEC56DC82A39AA2 // A0
//
//[1.5; 1.75)
data8 0xBF94730B51795867 // A7
data8 0x3FBF4203E3816C7B // A6
data8 0xBFE85B427DBD23E4 // A3
data8 0x3FEE65557AB26771 // A2
data8 0xBFD59D31BE3AB42A // A5
data8 0x3FE3C90CC8F09147 // A4
data8 0xBFE245971DF735B8 // A1
data8 0x3FEFFC613AE7FBC8 // A0
//
//[1.75; 2.0)
data8 0xBF7746A85137617E // A7
data8 0x3FA96E37D09735F3 // A6
data8 0xBFE3C24AC40AC0BB // A3
data8 0x3FEC56A80A977CA5 // A2
data8 0xBFC6F0E707560916 // A5
data8 0x3FDB262D949175BE // A4
data8 0xBFE1C1AEDFB25495 // A1
data8 0x3FEFEE1E644B2022 // A0
//
// sin(pi*x)/pi
data8 0xC026FB0D377656CC // S01
data8 0x3FFFB15F95A22324 // S11
data8 0x406CE58F4A41C6E7 // S10
data8 0x404453786302C61E // S20
data8 0xC023D59A47DBFCD3 // S21
data8 0x405541D7ABECEFCA // S00
//
// 1/An for [40; 48)
data8 0xCAA7576DE621FCD5, 0x3F68
LOCAL_OBJECT_END(tgammaf_data)
//==============================================================
// Code
//==============================================================
.section .text
GLOBAL_LIBM_ENTRY(tgammaf)
{ .mfi
getf.exp GR_SignExp = f8
fma.s1 FR_NormX = f8,f1,f0
addl GR_ad_Data = @ltoff(tgammaf_data), gp
}
{ .mfi
mov GR_ExpOf05 = 0xFFFE
fcvt.fx.trunc.s1 FR_iXt = f8 // [x]
mov GR_Offs = 0 // 2 <= x < 8
};;
{ .mfi
getf.d GR_Arg = f8
fcmp.lt.s1 p14,p15 = f8,f0
mov GR_Tbl12Offs = 0
}
{ .mfi
setf.exp FR_05 = GR_ExpOf05
fma.s1 FR_2 = f1,f1,f1 // 2
mov GR_Correction = 0
};;
{ .mfi
ld8 GR_ad_Data = [GR_ad_Data]
fclass.m p10,p0 = f8,0x1E7 // is x NaTVal, NaN, +/-0 or +/-INF?
tbit.z p12,p13 = GR_SignExp,16 // p13 if |x| >= 2
}
{ .mfi
mov GR_ExpOf1 = 0xFFFF
fcvt.fx.s1 FR_rs = f8 // round(x)
and GR_Exp2Ind = 7,GR_SignExp
};;
.pred.rel "mutex",p14,p15
{ .mfi
(p15) cmp.eq.unc p11,p0 = GR_ExpOf1,GR_SignExp // p11 if 1 <= x < 2
(p14) fma.s1 FR_1mX = f1,f1,f8 // 1 - |x|
mov GR_Sig = 0 // if |x| < 2
}
{ .mfi
(p13) cmp.eq.unc p7,p0 = 2,GR_Exp2Ind
(p15) fms.s1 FR_1mX = f1,f1,f8 // 1 - |x|
(p13) cmp.eq.unc p8,p0 = 3,GR_Exp2Ind
};;
.pred.rel "mutex",p7,p8
{ .mfi
(p7) mov GR_Offs = 0x7 // 8 <= |x| < 16
nop.f 0
(p8) tbit.z.unc p0,p6 = GR_Arg,51
}
{ .mib
(p13) cmp.lt.unc p9,p0 = 3,GR_Exp2Ind
(p8) mov GR_Offs = 0xE // 16 <= |x| < 32
// jump if x is NaTVal, NaN, +/-0 or +/-INF?
(p10) br.cond.spnt tgammaf_spec_args
};;
.pred.rel "mutex",p14,p15
.pred.rel "mutex",p6,p9
{ .mfi
(p9) mov GR_Offs = 0x1C // 32 <= |x|
(p14) fma.s1 FR_X2mX = FR_NormX,FR_NormX,FR_NormX // x^2-|x|
(p9) tbit.z.unc p0,p8 = GR_Arg,50
}
{ .mfi
ldfpd FR_LocalMin,FR_10 = [GR_ad_Data],16
(p15) fms.s1 FR_X2mX = FR_NormX,FR_NormX,FR_NormX // x^2-|x|
(p6) add GR_Offs = 0x7,GR_Offs // 24 <= x < 32
};;
.pred.rel "mutex",p8,p12
{ .mfi
add GR_ad_Ce = 0x50,GR_ad_Data
(p15) fcmp.lt.unc.s1 p10,p0 = f8,f1 // p10 if 0 <= x < 1
mov GR_OvfNzBound = 2
}
{ .mib
ldfpd FR_S32,FR_S31 = [GR_ad_Data],16
(p8) add GR_Offs = 0x7,GR_Offs // 40 <= |x|
// jump if 1 <= x < 2
(p11) br.cond.spnt tgammaf_from_1_to_2
};;
{ .mfi
shladd GR_ad_Ce = GR_Offs,4,GR_ad_Ce
fcvt.xf FR_Xt = FR_iXt // [x]
(p13) cmp.eq.unc p7,p0 = r0,GR_Offs // p7 if 2 <= |x| < 8
}
{ .mfi
shladd GR_ad_Co = GR_Offs,4,GR_ad_Data
fma.s1 FR_6 = FR_2,FR_2,FR_2
mov GR_ExpOf05 = 0x7FC
};;
{ .mfi
(p13) getf.sig GR_Sig = FR_iXt // if |x| >= 2
frcpa.s1 FR_Rcp0,p0 = f1,FR_NormX
(p10) shr GR_Arg = GR_Arg,51
}
{ .mib
ldfpd FR_C01,FR_C11 = [GR_ad_Co],16
(p7) mov GR_Correction = 2
// jump if 0 < x < 1
(p10) br.cond.spnt tgammaf_from_0_to_1
};;
{ .mfi
ldfpd FR_C21,FR_C31 = [GR_ad_Ce],16
fma.s1 FR_Rq2 = f1,f1,FR_1mX // 2 - |x|
(p14) sub GR_Correction = r0,GR_Correction
}
{ .mfi
ldfpd FR_C41,FR_C51 = [GR_ad_Co],16
(p14) fcvt.xf FR_rs = FR_rs
(p14) add GR_ad_SinO = 0x3A0,GR_ad_Data
};;
.pred.rel "mutex",p14,p15
{ .mfi
ldfpd FR_C00,FR_C10 = [GR_ad_Ce],16
nop.f 0
(p14) sub GR_Sig = GR_Correction,GR_Sig
}
{ .mfi
ldfpd FR_C20,FR_C30 = [GR_ad_Co],16
fma.s1 FR_Rq1 = FR_1mX,FR_2,FR_X2mX // (x-1)*(x-2)
(p15) sub GR_Sig = GR_Sig,GR_Correction
};;
{ .mfi
(p14) ldfpd FR_S01,FR_S11 = [GR_ad_SinO],16
fma.s1 FR_Rq3 = FR_2,f1,FR_1mX // 3 - |x|
and GR_RqDeg = 0x6,GR_Sig
}
{ .mfi
ldfpd FR_C40,FR_C50 = [GR_ad_Ce],16
(p14) fma.d.s0 FR_X = f0,f0,f8 // set deno flag
mov GR_NanBound = 0x30016 // -2^23
};;
.pred.rel "mutex",p14,p15
{ .mfi
(p14) add GR_ad_SinE = 0x3C0,GR_ad_Data
(p15) fms.s1 FR_r = FR_NormX,f1,FR_Xt // r = x - [x]
cmp.eq p8,p0 = 2,GR_RqDeg
}
{ .mfi
ldfpd FR_An,FR_OvfBound = [GR_ad_Co]
(p14) fms.s1 FR_r = FR_Xt,f1,FR_NormX // r = |x - [x]|
cmp.eq p9,p0 = 4,GR_RqDeg
};;
.pred.rel "mutex",p8,p9
{ .mfi
(p14) ldfpd FR_S21,FR_S00 = [GR_ad_SinE],16
(p8) fma.s1 FR_Rq0 = FR_2,f1,FR_1mX // (3-x)
tbit.z p0,p6 = GR_Sig,0
}
{ .mfi
(p14) ldfpd FR_S10,FR_S20 = [GR_ad_SinO],16
(p9) fma.s1 FR_Rq0 = FR_2,FR_2,FR_1mX // (5-x)
cmp.eq p10,p0 = 6,GR_RqDeg
};;
{ .mfi
(p14) getf.s GR_Arg = f8
(p14) fcmp.eq.unc.s1 p13,p0 = FR_NormX,FR_Xt
(p14) mov GR_ZeroResBound = 0xC22C // -43
}
{ .mfi
(p14) ldfe FR_InvAn = [GR_ad_SinE]
(p10) fma.s1 FR_Rq0 = FR_6,f1,FR_1mX // (7-x)
cmp.eq p7,p0 = r0,GR_RqDeg
};;
{ .mfi
(p14) cmp.ge.unc p11,p0 = GR_SignExp,GR_NanBound
fma.s1 FR_Rq2 = FR_Rq2,FR_6,FR_X2mX // (x-3)*(x-4)
(p14) shl GR_ZeroResBound = GR_ZeroResBound,16
}
{ .mfb
(p14) mov GR_OvfNzBound = 0x802
(p14) fms.s1 FR_rs = FR_rs,f1,FR_NormX // rs = round(x) - x
// jump if x < -2^23 i.e. x is negative integer
(p11) br.cond.spnt tgammaf_singularity
};;
{ .mfi
nop.m 0
(p7) fma.s1 FR_Rq1 = f0,f0,f1
(p14) shl GR_OvfNzBound = GR_OvfNzBound,20
}
{ .mfb
nop.m 0
fma.s1 FR_Rq3 = FR_Rq3,FR_10,FR_X2mX // (x-5)*(x-6)
// jump if x is negative integer such that -2^23 < x < 0
(p13) br.cond.spnt tgammaf_singularity
};;
{ .mfi
nop.m 0
fma.s1 FR_C01 = FR_C01,f1,FR_r
(p14) mov GR_ExpOf05 = 0xFFFE
}
{ .mfi
(p14) cmp.eq.unc p7,p0 = GR_Arg,GR_OvfNzBound
fma.s1 FR_C11 = FR_C11,f1,FR_r
(p14) cmp.ltu.unc p11,p0 = GR_Arg,GR_OvfNzBound
};;
{ .mfi
nop.m 0
fma.s1 FR_C21 = FR_C21,f1,FR_r
(p14) cmp.ltu.unc p9,p0 = GR_ZeroResBound,GR_Arg
}
{ .mfb
nop.m 0
fma.s1 FR_C31 = FR_C31,f1,FR_r
// jump if argument is close to 0 negative
(p11) br.cond.spnt tgammaf_overflow
};;
{ .mfi
nop.m 0
fma.s1 FR_C41 = FR_C41,f1,FR_r
nop.i 0
}
{ .mfb
nop.m 0
fma.s1 FR_C51 = FR_C51,f1,FR_r
// jump if x is negative noninteger such that -2^23 < x < -43
(p9) br.cond.spnt tgammaf_underflow
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_rs2 = FR_rs,FR_rs,f0
nop.i 0
}
{ .mfb
nop.m 0
(p14) fma.s1 FR_S01 = FR_rs,FR_rs,FR_S01
// jump if argument is 0x80200000
(p7) br.cond.spnt tgammaf_overflow_near0_bound
};;
{ .mfi
nop.m 0
(p6) fnma.s1 FR_Rq1 = FR_Rq1,FR_Rq0,f0
nop.i 0
}
{ .mfi
nop.m 0
(p10) fma.s1 FR_Rq2 = FR_Rq2,FR_Rq3,f0
and GR_Sig = 0x7,GR_Sig
};;
{ .mfi
nop.m 0
fma.s1 FR_C01 = FR_C01,FR_r,FR_C00
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C11 = FR_C11,FR_r,FR_C10
cmp.eq p6,p7 = r0,GR_Sig // p6 if |x| from one of base intervals
};;
{ .mfi
nop.m 0
fma.s1 FR_C21 = FR_C21,FR_r,FR_C20
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C31 = FR_C31,FR_r,FR_C30
(p7) cmp.lt.unc p9,p0 = 2,GR_RqDeg
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_S11 = FR_rs,FR_rs,FR_S11
nop.i 0
}
{ .mfi
nop.m 0
(p14) fma.s1 FR_S21 = FR_rs,FR_rs,FR_S21
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C41 = FR_C41,FR_r,FR_C40
nop.i 0
}
{ .mfi
nop.m 0
(p14) fma.s1 FR_S32 = FR_rs2,FR_S32,FR_S31
nop.i 0
};;
{ .mfi
nop.m 0
(p9) fma.s1 FR_Rq1 = FR_Rq1,FR_Rq2,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C51 = FR_C51,FR_r,FR_C50
nop.i 0
};;
{ .mfi
(p14) getf.exp GR_SignExp = FR_rs
fma.s1 FR_C01 = FR_C01,FR_C11,f0
nop.i 0
}
{ .mfi
nop.m 0
(p14) fma.s1 FR_S01 = FR_S01,FR_rs2,FR_S00
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C21 = FR_C21,FR_C31,f0
nop.i 0
}
{ .mfi
nop.m 0
// NR-iteration
(p14) fnma.s1 FR_InvNormX1 = FR_Rcp0,FR_NormX,f1
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_S11 = FR_S11,FR_rs2,FR_S10
(p14) tbit.z.unc p11,p12 = GR_SignExp,17
}
{ .mfi
nop.m 0
(p14) fma.s1 FR_S21 = FR_S21,FR_rs2,FR_S20
nop.i 0
};;
{ .mfi
nop.m 0
(p15) fcmp.lt.unc.s1 p0,p13 = FR_NormX,FR_OvfBound
nop.i 0
}
{ .mfi
nop.m 0
(p14) fma.s1 FR_S32 = FR_rs2,FR_S32,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_C41 = FR_C41,FR_C51,f0
nop.i 0
}
{ .mfi
nop.m 0
(p7) fma.s1 FR_An = FR_Rq1,FR_An,f0
nop.i 0
};;
{ .mfb
nop.m 0
nop.f 0
// jump if x > 35.04010009765625
(p13) br.cond.spnt tgammaf_overflow
};;
{ .mfi
nop.m 0
// NR-iteration
(p14) fma.s1 FR_InvNormX1 = FR_Rcp0,FR_InvNormX1,FR_Rcp0
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_S01 = FR_S01,FR_S11,f0
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_S21 = FR_S21,FR_S32,f0
nop.i 0
};;
{ .mfi
(p14) getf.exp GR_SignExp = FR_NormX
fma.s1 FR_C01 = FR_C01,FR_C21,f0
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_C41 = FR_C41,FR_An,f0
(p14) mov GR_ExpOf1 = 0x2FFFF
};;
{ .mfi
nop.m 0
// NR-iteration
(p14) fnma.s1 FR_InvNormX2 = FR_InvNormX1,FR_NormX,f1
nop.i 0
};;
.pred.rel "mutex",p11,p12
{ .mfi
nop.m 0
(p12) fnma.s1 FR_S01 = FR_S01,FR_S21,f0
nop.i 0
}
{ .mfi
nop.m 0
(p11) fma.s1 FR_S01 = FR_S01,FR_S21,f0
nop.i 0
};;
{ .mfi
nop.m 0
(p14) fma.s1 FR_GAMMA = FR_C01,FR_C41,f0
(p14) tbit.z.unc p6,p7 = GR_Sig,0
}
{ .mfb
nop.m 0
(p15) fma.s.s0 f8 = FR_C01,FR_C41,f0
(p15) br.ret.spnt b0 // exit for positives
};;
.pred.rel "mutex",p11,p12
{ .mfi
nop.m 0
(p12) fms.s1 FR_S01 = FR_rs,FR_S01,FR_rs
nop.i 0
}
{ .mfi
nop.m 0
(p11) fma.s1 FR_S01 = FR_rs,FR_S01,FR_rs
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
fma.s1 FR_InvNormX2 = FR_InvNormX1,FR_InvNormX2,FR_InvNormX1
cmp.eq p10,p0 = 0x23,GR_Offs
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fma.s1 FR_GAMMA = FR_S01,FR_GAMMA,f0
cmp.gtu p8,p0 = GR_SignExp,GR_ExpOf1
}
{ .mfi
nop.m 0
(p7) fnma.s1 FR_GAMMA = FR_S01,FR_GAMMA,f0
cmp.eq p9,p0 = GR_SignExp,GR_ExpOf1
};;
{ .mfi
nop.m 0
// NR-iteration
fnma.s1 FR_InvNormX1 = FR_InvNormX2,FR_NormX,f1
nop.i 0
}
{ .mfi
nop.m 0
(p10) fma.s1 FR_InvNormX2 = FR_InvNormX2,FR_InvAn,f0
nop.i 0
};;
{ .mfi
nop.m 0
frcpa.s1 FR_Rcp0,p0 = f1,FR_GAMMA
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_Multplr = FR_NormX,f1,f1 // x - 1
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
fnma.s1 FR_Rcp1 = FR_Rcp0,FR_GAMMA,f1
nop.i 0
};;
.pred.rel "mutex",p8,p9
{ .mfi
nop.m 0
// 1/x or 1/(An*x)
(p8) fma.s1 FR_Multplr = FR_InvNormX2,FR_InvNormX1,FR_InvNormX2
nop.i 0
}
{ .mfi
nop.m 0
(p9) fma.s1 FR_Multplr = f1,f1,f0
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
fnma.s1 FR_Rcp2 = FR_Rcp1,FR_GAMMA,f1
nop.i 0
}
{ .mfi
nop.m 0
// NR-iteration
fma.s1 FR_Rcp1 = FR_Rcp1,FR_Multplr,f0
nop.i 0
};;
{ .mfb
nop.m 0
fma.s.s0 f8 = FR_Rcp1,FR_Rcp2,FR_Rcp1
br.ret.sptk b0
};;
// here if 0 < x < 1
//--------------------------------------------------------------------
.align 32
tgammaf_from_0_to_1:
{ .mfi
cmp.lt p7,p0 = GR_Arg,GR_ExpOf05
// NR-iteration
fnma.s1 FR_Rcp1 = FR_Rcp0,FR_NormX,f1
cmp.eq p8,p0 = GR_Arg,GR_ExpOf05
}
{ .mfi
cmp.gt p9,p0 = GR_Arg,GR_ExpOf05
fma.s1 FR_r = f0,f0,FR_NormX // reduced arg for (0;1)
mov GR_ExpOf025 = 0x7FA
};;
{ .mfi
getf.s GR_ArgNz = f8
fma.d.s0 FR_X = f0,f0,f8 // set deno flag
shl GR_OvfNzBound = GR_OvfNzBound,20
}
{ .mfi
(p8) mov GR_Tbl12Offs = 0x80 // 0.5 <= x < 0.75
nop.f 0
(p7) cmp.ge.unc p6,p0 = GR_Arg,GR_ExpOf025
};;
.pred.rel "mutex",p6,p9
{ .mfi
(p9) mov GR_Tbl12Offs = 0xC0 // 0.75 <= x < 1
nop.f 0
(p6) mov GR_Tbl12Offs = 0x40 // 0.25 <= x < 0.5
}
{ .mfi
add GR_ad_Ce = 0x2C0,GR_ad_Data
nop.f 0
add GR_ad_Co = 0x2A0,GR_ad_Data
};;
{ .mfi
add GR_ad_Co = GR_ad_Co,GR_Tbl12Offs
nop.f 0
cmp.lt p12,p0 = GR_ArgNz,GR_OvfNzBound
}
{ .mib
add GR_ad_Ce = GR_ad_Ce,GR_Tbl12Offs
cmp.eq p7,p0 = GR_ArgNz,GR_OvfNzBound
// jump if argument is 0x00200000
(p7) br.cond.spnt tgammaf_overflow_near0_bound
};;
{ .mmb
ldfpd FR_A7,FR_A6 = [GR_ad_Co],16
ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16
// jump if argument is close to 0 positive
(p12) br.cond.spnt tgammaf_overflow
};;
{ .mfi
ldfpd FR_A3,FR_A2 = [GR_ad_Co],16
// NR-iteration
fma.s1 FR_Rcp1 = FR_Rcp0,FR_Rcp1,FR_Rcp0
nop.i 0
}
{ .mfb
ldfpd FR_A1,FR_A0 = [GR_ad_Ce],16
nop.f 0
br.cond.sptk tgamma_from_0_to_2
};;
// here if 1 < x < 2
//--------------------------------------------------------------------
.align 32
tgammaf_from_1_to_2:
{ .mfi
add GR_ad_Co = 0x2A0,GR_ad_Data
fms.s1 FR_r = f0,f0,FR_1mX
shr GR_TblOffs = GR_Arg,47
}
{ .mfi
add GR_ad_Ce = 0x2C0,GR_ad_Data
nop.f 0
mov GR_TblOffsMask = 0x18
};;
{ .mfi
nop.m 0
nop.f 0
and GR_TblOffs = GR_TblOffs,GR_TblOffsMask
};;
{ .mfi
shladd GR_ad_Co = GR_TblOffs,3,GR_ad_Co
nop.f 0
nop.i 0
}
{ .mfi
shladd GR_ad_Ce = GR_TblOffs,3,GR_ad_Ce
nop.f 0
cmp.eq p6,p7 = 8,GR_TblOffs
};;
{ .mmi
ldfpd FR_A7,FR_A6 = [GR_ad_Co],16
ldfpd FR_A5,FR_A4 = [GR_ad_Ce],16
nop.i 0
};;
{ .mmi
ldfpd FR_A3,FR_A2 = [GR_ad_Co],16
ldfpd FR_A1,FR_A0 = [GR_ad_Ce],16
nop.i 0
};;
.align 32
tgamma_from_0_to_2:
{ .mfi
nop.m 0
(p6) fms.s1 FR_r = FR_r,f1,FR_LocalMin
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
(p10) fnma.s1 FR_Rcp2 = FR_Rcp1,FR_NormX,f1
nop.i 0
};;
{ .mfi
nop.m 0
fms.s1 FR_r2 = FR_r,FR_r,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A7 = FR_A7,FR_r,FR_A6
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A5 = FR_A5,FR_r,FR_A4
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A3 = FR_A3,FR_r,FR_A2
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_A1 = FR_A1,FR_r,FR_A0
nop.i 0
};;
{ .mfi
nop.m 0
// NR-iteration
(p10) fma.s1 FR_Rcp2 = FR_Rcp1,FR_Rcp2,FR_Rcp1
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A7 = FR_A7,FR_r2,FR_A5
nop.i 0
}
{ .mfi
nop.m 0
fma.s1 FR_r4 = FR_r2,FR_r2,f0
nop.i 0
};;
{ .mfi
nop.m 0
fma.s1 FR_A3 = FR_A3,FR_r2,FR_A1
nop.i 0
};;
{ .mfi
nop.m 0
(p10) fma.s1 FR_GAMMA = FR_A7,FR_r4,FR_A3
nop.i 0
}
{ .mfi
nop.m 0
(p11) fma.s.s0 f8 = FR_A7,FR_r4,FR_A3
nop.i 0
};;
{ .mfb
nop.m 0
(p10) fma.s.s0 f8 = FR_GAMMA,FR_Rcp2,f0
br.ret.sptk b0
};;
// overflow
//--------------------------------------------------------------------
.align 32
tgammaf_overflow_near0_bound:
.pred.rel "mutex",p14,p15
{ .mfi
mov GR_fpsr = ar.fpsr
nop.f 0
(p15) mov r8 = 0x7f8
}
{ .mfi
nop.m 0
nop.f 0
(p14) mov r8 = 0xff8
};;
{ .mfi
nop.m 0
nop.f 0
shl r8 = r8,20
};;
{ .mfi
sub r8 = r8,r0,1
nop.f 0
extr.u GR_fpsr = GR_fpsr,10,2 // rounding mode
};;
.pred.rel "mutex",p14,p15
{ .mfi
// set p8 to 0 in case of overflow and to 1 otherwise
// for negative arg:
// no overflow if rounding mode either Z or +Inf, i.e.
// GR_fpsr > 1
(p14) cmp.lt p8,p0 = 1,GR_fpsr
nop.f 0
// for positive arg:
// no overflow if rounding mode either Z or -Inf, i.e.
// (GR_fpsr & 1) == 0
(p15) tbit.z p0,p8 = GR_fpsr,0
};;
{ .mib
(p8) setf.s f8 = r8 // set result to 0x7f7fffff without
// OVERFLOW flag raising
nop.i 0
(p8) br.ret.sptk b0
};;
.align 32
tgammaf_overflow:
{ .mfi
nop.m 0
nop.f 0
mov r8 = 0x1FFFE
};;
{ .mfi
setf.exp f9 = r8
fmerge.s FR_X = f8,f8
nop.i 0
};;
.pred.rel "mutex",p14,p15
{ .mfi
nop.m 0
(p14) fnma.s.s0 f8 = f9,f9,f0 // set I,O and -INF result
mov GR_TAG = 261 // overflow
}
{ .mfb
nop.m 0
(p15) fma.s.s0 f8 = f9,f9,f0 // set I,O and +INF result
br.cond.sptk tgammaf_libm_err
};;
// x is negative integer or +/-0
//--------------------------------------------------------------------
.align 32
tgammaf_singularity:
{ .mfi
nop.m 0
fmerge.s FR_X = f8,f8
mov GR_TAG = 262 // negative
}
{ .mfb
nop.m 0
frcpa.s0 f8,p0 = f0,f0
br.cond.sptk tgammaf_libm_err
};;
// x is negative noninteger with big absolute value
//--------------------------------------------------------------------
.align 32
tgammaf_underflow:
{ .mfi
mov r8 = 0x00001
nop.f 0
tbit.z p6,p7 = GR_Sig,0
};;
{ .mfi
setf.exp f9 = r8
nop.f 0
nop.i 0
};;
.pred.rel "mutex",p6,p7
{ .mfi
nop.m 0
(p6) fms.s.s0 f8 = f9,f9,f9
nop.i 0
}
{ .mfb
nop.m 0
(p7) fma.s.s0 f8 = f9,f9,f9
br.ret.sptk b0
};;
// x for natval, nan, +/-inf or +/-0
//--------------------------------------------------------------------
.align 32
tgammaf_spec_args:
{ .mfi
nop.m 0
fclass.m p6,p0 = f8,0x1E1 // Test x for natval, nan, +inf
nop.i 0
};;
{ .mfi
nop.m 0
fclass.m p7,p8 = f8,0x7 // +/-0
nop.i 0
};;
{ .mfi
nop.m 0
fmerge.s FR_X = f8,f8
nop.i 0
}
{ .mfb
nop.m 0
(p6) fma.s.s0 f8 = f8,f1,f8
(p6) br.ret.spnt b0
};;
.pred.rel "mutex",p7,p8
{ .mfi
(p7) mov GR_TAG = 262 // negative
(p7) frcpa.s0 f8,p0 = f1,f8
nop.i 0
}
{ .mib
nop.m 0
nop.i 0
(p8) br.cond.spnt tgammaf_singularity
};;
.align 32
tgammaf_libm_err:
{ .mfi
alloc r32 = ar.pfs,1,4,4,0
nop.f 0
mov GR_Parameter_TAG = GR_TAG
};;
GLOBAL_LIBM_END(tgammaf)
libm_alias_float_other (tgamma, tgamma)
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
stfs [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack
add GR_Parameter_X = 16,sp // Parameter 1 address
.save b0, GR_SAVE_B0
mov GR_SAVE_B0=b0 // Save b0
};;
.body
{ .mib
stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
nop.b 0
}
{ .mib
stfs [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
add GR_Parameter_Y = -16,GR_Parameter_Y
br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
nop.m 0
nop.m 0
add GR_Parameter_RESULT = 48,sp
};;
{ .mmi
ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack
.restore sp
add sp = 64,sp // Restore stack pointer
mov b0 = GR_SAVE_B0 // Restore return address
};;
{ .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#
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