mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-12 22:30:12 +00:00
30891f35fa
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>
1331 lines
35 KiB
ArmAsm
1331 lines
35 KiB
ArmAsm
.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#
|