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Diffstat (limited to 'sysdeps/ia64/fpu/w_tgammaf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/w_tgammaf.S | 1331 |
1 files changed, 0 insertions, 1331 deletions
diff --git a/sysdeps/ia64/fpu/w_tgammaf.S b/sysdeps/ia64/fpu/w_tgammaf.S deleted file mode 100644 index dda0d0fe9d..0000000000 --- a/sysdeps/ia64/fpu/w_tgammaf.S +++ /dev/null @@ -1,1331 +0,0 @@ -.file "tgammaf.s" - - -// Copyright (c) 2001 - 2005, 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: -// 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) - -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# - |