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Diffstat (limited to 'sysdeps/ia64/fpu/w_tgammaf.S')
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diff --git a/sysdeps/ia64/fpu/w_tgammaf.S b/sysdeps/ia64/fpu/w_tgammaf.S new file mode 100644 index 0000000..4363ca2 --- /dev/null +++ b/sysdeps/ia64/fpu/w_tgammaf.S @@ -0,0 +1,1328 @@ +.file "tgammaf.s" + + +// Copyright (c) 2001 - 2003, 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 +// +//********************************************************************* +// +//********************************************************************* +// +// 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 + stfd [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 + stfd [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 + stfd [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 + ldfd 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# + |