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Diffstat (limited to 'sysdeps/ia64/fpu/e_atanhl.S')
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diff --git a/sysdeps/ia64/fpu/e_atanhl.S b/sysdeps/ia64/fpu/e_atanhl.S new file mode 100644 index 0000000000..8266bd56fb --- /dev/null +++ b/sysdeps/ia64/fpu/e_atanhl.S @@ -0,0 +1,1155 @@ +.file "atanhl.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: +// 09/10/01 Initial version +// 12/11/01 Corrected .restore syntax +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/10/03 Reordered header: .section, .global, .proc, .align; +// used data8 for long double table values +// +//********************************************************************* +// +//********************************************************************* +// +// Function: atanhl(x) computes the principle value of the inverse +// hyperbolic tangent of x. +// +//********************************************************************* +// +// Resources Used: +// +// Floating-Point Registers: f8 (Input and Return Value) +// f33-f73 +// +// General Purpose Registers: +// r32-r52 +// r49-r52 (Used to pass arguments to error handling routine) +// +// Predicate Registers: p6-p15 +// +//********************************************************************* +// +// IEEE Special Conditions: +// +// atanhl(inf) = QNaN +// atanhl(-inf) = QNaN +// atanhl(+/-0) = +/-0 +// atanhl(1) = +inf +// atanhl(-1) = -inf +// atanhl(|x|>1) = QNaN +// atanhl(SNaN) = QNaN +// atanhl(QNaN) = QNaN +// +//********************************************************************* +// +// Overview +// +// The method consists of two cases. +// +// If |x| < 1/32 use case atanhl_near_zero; +// else use case atanhl_regular; +// +// Case atanhl_near_zero: +// +// atanhl(x) can be approximated by the Taylor series expansion +// up to order 17. +// +// Case atanhl_regular: +// +// Here we use formula atanhl(x) = sign(x)*log1pl(2*|x|/(1-|x|))/2 and +// calculation is subdivided into two stages. The first stage is +// calculating of X = 2*|x|/(1-|x|). The second one is calculating of +// sign(x)*log1pl(X)/2. To obtain required accuracy we use precise division +// algorythm output of which is a pair of two extended precision values those +// approximate result of division with accuracy higher than working +// precision. This pair is passed to modified log1pl function. +// +// +// 1. calculating of X = 2*|x|/(1-|x|) +// ( based on Peter Markstein's "IA-64 and Elementary Functions" book ) +// ******************************************************************** +// +// a = 2*|x| +// b = 1 - |x| +// b_lo = |x| - (1 - b) +// +// y = frcpa(b) initial approximation of 1/b +// q = a*y initial approximation of a/b +// +// e = 1 - b*y +// e2 = e + e^2 +// e1 = e^2 +// y1 = y + y*e2 = y + y*(e+e^2) +// +// e3 = e + e1^2 +// y2 = y + y1*e3 = y + y*(e+e^2+..+e^6) +// +// r = a - b*q +// e = 1 - b*y2 +// X = q + r*y2 high part of a/b +// +// y3 = y2 + y2*e4 +// r1 = a - b*X +// r1 = r1 - b_lo*X +// X_lo = r1*y3 low part of a/b +// +// 2. special log1p algorithm overview +// *********************************** +// +// Here we use a table lookup method. The basic idea is that in +// order to compute logl(Arg) = log1pl (Arg-1) for an argument Arg in [1,2), +// we construct a value G such that G*Arg is close to 1 and that +// logl(1/G) is obtainable easily from a table of values calculated +// beforehand. Thus +// +// logl(Arg) = logl(1/G) + logl(G*Arg) +// = logl(1/G) + logl(1 + (G*Arg - 1)) +// +// Because |G*Arg - 1| is small, the second term on the right hand +// side can be approximated by a short polynomial. We elaborate +// this method in several steps. +// +// Step 0: Initialization +// ------ +// We need to calculate logl(X + X_lo + 1). Obtain N, S_hi such that +// +// X + X_lo + 1 = 2^N * ( S_hi + S_lo ) exactly +// +// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense +// that |S_lo| <= ulp(S_hi). +// +// For the special version of log1p we add X_lo to S_lo (S_lo = S_lo + X_lo) +// !-----------------------------------------------------------------------! +// +// Step 1: Argument Reduction +// ------ +// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate +// +// G := G_1 * G_2 * G_3 +// r := (G * S_hi - 1) + G * S_lo +// +// These G_j's have the property that the product is exactly +// representable and that |r| < 2^(-12) as a result. +// +// Step 2: Approximation +// ------ +// logl(1 + r) is approximated by a short polynomial poly(r). +// +// Step 3: Reconstruction +// ------ +// Finally, log1pl(X + X_lo) = logl(X + X_lo + 1) is given by +// +// logl(X + X_lo + 1) = logl(2^N * (S_hi + S_lo)) +// ~=~ N*logl(2) + logl(1/G) + logl(1 + r) +// ~=~ N*logl(2) + logl(1/G) + poly(r). +// +// For detailed description see log1p1 function, regular path. +// +//********************************************************************* + +RODATA +.align 64 + +// ************* DO NOT CHANGE THE ORDER OF THESE TABLES ************* + +LOCAL_OBJECT_START(Constants_TaylorSeries) +data8 0xF0F0F0F0F0F0F0F1,0x00003FFA // C17 +data8 0x8888888888888889,0x00003FFB // C15 +data8 0x9D89D89D89D89D8A,0x00003FFB // C13 +data8 0xBA2E8BA2E8BA2E8C,0x00003FFB // C11 +data8 0xE38E38E38E38E38E,0x00003FFB // C9 +data8 0x9249249249249249,0x00003FFC // C7 +data8 0xCCCCCCCCCCCCCCCD,0x00003FFC // C5 +data8 0xAAAAAAAAAAAAAAAA,0x00003FFD // C3 +data4 0x3f000000 // 1/2 +data4 0x00000000 // pad +data4 0x00000000 +data4 0x00000000 +LOCAL_OBJECT_END(Constants_TaylorSeries) + +LOCAL_OBJECT_START(Constants_Q) +data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 // log2_hi +data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 // log2_lo +data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 // Q4 +data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 // Q3 +data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 // Q2 +data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 // Q1 +LOCAL_OBJECT_END(Constants_Q) + + +// Z1 - 16 bit fixed +LOCAL_OBJECT_START(Constants_Z_1) +data4 0x00008000 +data4 0x00007879 +data4 0x000071C8 +data4 0x00006BCB +data4 0x00006667 +data4 0x00006187 +data4 0x00005D18 +data4 0x0000590C +data4 0x00005556 +data4 0x000051EC +data4 0x00004EC5 +data4 0x00004BDB +data4 0x00004925 +data4 0x0000469F +data4 0x00004445 +data4 0x00004211 +LOCAL_OBJECT_END(Constants_Z_1) + +// G1 and H1 - IEEE single and h1 - IEEE double +LOCAL_OBJECT_START(Constants_G_H_h1) +data4 0x3F800000,0x00000000 +data8 0x0000000000000000 +data4 0x3F70F0F0,0x3D785196 +data8 0x3DA163A6617D741C +data4 0x3F638E38,0x3DF13843 +data8 0x3E2C55E6CBD3D5BB +data4 0x3F579430,0x3E2FF9A0 +data8 0xBE3EB0BFD86EA5E7 +data4 0x3F4CCCC8,0x3E647FD6 +data8 0x3E2E6A8C86B12760 +data4 0x3F430C30,0x3E8B3AE7 +data8 0x3E47574C5C0739BA +data4 0x3F3A2E88,0x3EA30C68 +data8 0x3E20E30F13E8AF2F +data4 0x3F321640,0x3EB9CEC8 +data8 0xBE42885BF2C630BD +data4 0x3F2AAAA8,0x3ECF9927 +data8 0x3E497F3497E577C6 +data4 0x3F23D708,0x3EE47FC5 +data8 0x3E3E6A6EA6B0A5AB +data4 0x3F1D89D8,0x3EF8947D +data8 0xBDF43E3CD328D9BE +data4 0x3F17B420,0x3F05F3A1 +data8 0x3E4094C30ADB090A +data4 0x3F124920,0x3F0F4303 +data8 0xBE28FBB2FC1FE510 +data4 0x3F0D3DC8,0x3F183EBF +data8 0x3E3A789510FDE3FA +data4 0x3F088888,0x3F20EC80 +data8 0x3E508CE57CC8C98F +data4 0x3F042108,0x3F29516A +data8 0xBE534874A223106C +LOCAL_OBJECT_END(Constants_G_H_h1) + +// Z2 - 16 bit fixed +LOCAL_OBJECT_START(Constants_Z_2) +data4 0x00008000 +data4 0x00007F81 +data4 0x00007F02 +data4 0x00007E85 +data4 0x00007E08 +data4 0x00007D8D +data4 0x00007D12 +data4 0x00007C98 +data4 0x00007C20 +data4 0x00007BA8 +data4 0x00007B31 +data4 0x00007ABB +data4 0x00007A45 +data4 0x000079D1 +data4 0x0000795D +data4 0x000078EB +LOCAL_OBJECT_END(Constants_Z_2) + +// G2 and H2 - IEEE single and h2 - IEEE double +LOCAL_OBJECT_START(Constants_G_H_h2) +data4 0x3F800000,0x00000000 +data8 0x0000000000000000 +data4 0x3F7F00F8,0x3B7F875D +data8 0x3DB5A11622C42273 +data4 0x3F7E03F8,0x3BFF015B +data8 0x3DE620CF21F86ED3 +data4 0x3F7D08E0,0x3C3EE393 +data8 0xBDAFA07E484F34ED +data4 0x3F7C0FC0,0x3C7E0586 +data8 0xBDFE07F03860BCF6 +data4 0x3F7B1880,0x3C9E75D2 +data8 0x3DEA370FA78093D6 +data4 0x3F7A2328,0x3CBDC97A +data8 0x3DFF579172A753D0 +data4 0x3F792FB0,0x3CDCFE47 +data8 0x3DFEBE6CA7EF896B +data4 0x3F783E08,0x3CFC15D0 +data8 0x3E0CF156409ECB43 +data4 0x3F774E38,0x3D0D874D +data8 0xBE0B6F97FFEF71DF +data4 0x3F766038,0x3D1CF49B +data8 0xBE0804835D59EEE8 +data4 0x3F757400,0x3D2C531D +data8 0x3E1F91E9A9192A74 +data4 0x3F748988,0x3D3BA322 +data8 0xBE139A06BF72A8CD +data4 0x3F73A0D0,0x3D4AE46F +data8 0x3E1D9202F8FBA6CF +data4 0x3F72B9D0,0x3D5A1756 +data8 0xBE1DCCC4BA796223 +data4 0x3F71D488,0x3D693B9D +data8 0xBE049391B6B7C239 +LOCAL_OBJECT_END(Constants_G_H_h2) + +// G3 and H3 - IEEE single and h3 - IEEE double +LOCAL_OBJECT_START(Constants_G_H_h3) +data4 0x3F7FFC00,0x38800100 +data8 0x3D355595562224CD +data4 0x3F7FF400,0x39400480 +data8 0x3D8200A206136FF6 +data4 0x3F7FEC00,0x39A00640 +data8 0x3DA4D68DE8DE9AF0 +data4 0x3F7FE400,0x39E00C41 +data8 0xBD8B4291B10238DC +data4 0x3F7FDC00,0x3A100A21 +data8 0xBD89CCB83B1952CA +data4 0x3F7FD400,0x3A300F22 +data8 0xBDB107071DC46826 +data4 0x3F7FCC08,0x3A4FF51C +data8 0x3DB6FCB9F43307DB +data4 0x3F7FC408,0x3A6FFC1D +data8 0xBD9B7C4762DC7872 +data4 0x3F7FBC10,0x3A87F20B +data8 0xBDC3725E3F89154A +data4 0x3F7FB410,0x3A97F68B +data8 0xBD93519D62B9D392 +data4 0x3F7FAC18,0x3AA7EB86 +data8 0x3DC184410F21BD9D +data4 0x3F7FA420,0x3AB7E101 +data8 0xBDA64B952245E0A6 +data4 0x3F7F9C20,0x3AC7E701 +data8 0x3DB4B0ECAABB34B8 +data4 0x3F7F9428,0x3AD7DD7B +data8 0x3D9923376DC40A7E +data4 0x3F7F8C30,0x3AE7D474 +data8 0x3DC6E17B4F2083D3 +data4 0x3F7F8438,0x3AF7CBED +data8 0x3DAE314B811D4394 +data4 0x3F7F7C40,0x3B03E1F3 +data8 0xBDD46F21B08F2DB1 +data4 0x3F7F7448,0x3B0BDE2F +data8 0xBDDC30A46D34522B +data4 0x3F7F6C50,0x3B13DAAA +data8 0x3DCB0070B1F473DB +data4 0x3F7F6458,0x3B1BD766 +data8 0xBDD65DDC6AD282FD +data4 0x3F7F5C68,0x3B23CC5C +data8 0xBDCDAB83F153761A +data4 0x3F7F5470,0x3B2BC997 +data8 0xBDDADA40341D0F8F +data4 0x3F7F4C78,0x3B33C711 +data8 0x3DCD1BD7EBC394E8 +data4 0x3F7F4488,0x3B3BBCC6 +data8 0xBDC3532B52E3E695 +data4 0x3F7F3C90,0x3B43BAC0 +data8 0xBDA3961EE846B3DE +data4 0x3F7F34A0,0x3B4BB0F4 +data8 0xBDDADF06785778D4 +data4 0x3F7F2CA8,0x3B53AF6D +data8 0x3DCC3ED1E55CE212 +data4 0x3F7F24B8,0x3B5BA620 +data8 0xBDBA31039E382C15 +data4 0x3F7F1CC8,0x3B639D12 +data8 0x3D635A0B5C5AF197 +data4 0x3F7F14D8,0x3B6B9444 +data8 0xBDDCCB1971D34EFC +data4 0x3F7F0CE0,0x3B7393BC +data8 0x3DC7450252CD7ADA +data4 0x3F7F04F0,0x3B7B8B6D +data8 0xBDB68F177D7F2A42 +LOCAL_OBJECT_END(Constants_G_H_h3) + + + +// Floating Point Registers + +FR_C17 = f50 +FR_C15 = f51 +FR_C13 = f52 +FR_C11 = f53 +FR_C9 = f54 +FR_C7 = f55 +FR_C5 = f56 +FR_C3 = f57 +FR_x2 = f58 +FR_x3 = f59 +FR_x4 = f60 +FR_x8 = f61 + +FR_Rcp = f61 + +FR_A = f33 +FR_R1 = f33 + +FR_E1 = f34 +FR_E3 = f34 +FR_Y2 = f34 +FR_Y3 = f34 + +FR_E2 = f35 +FR_Y1 = f35 + +FR_B = f36 +FR_Y0 = f37 +FR_E0 = f38 +FR_E4 = f39 +FR_Q0 = f40 +FR_R0 = f41 +FR_B_lo = f42 + +FR_abs_x = f43 +FR_Bp = f44 +FR_Bn = f45 +FR_Yp = f46 +FR_Yn = f47 + +FR_X = f48 +FR_BB = f48 +FR_X_lo = f49 + +FR_G = f50 +FR_Y_hi = f51 +FR_H = f51 +FR_h = f52 +FR_G2 = f53 +FR_H2 = f54 +FR_h2 = f55 +FR_G3 = f56 +FR_H3 = f57 +FR_h3 = f58 + +FR_Q4 = f59 +FR_poly_lo = f59 +FR_Y_lo = f59 + +FR_Q3 = f60 +FR_Q2 = f61 + +FR_Q1 = f62 +FR_poly_hi = f62 + +FR_float_N = f63 + +FR_AA = f64 +FR_S_lo = f64 + +FR_S_hi = f65 +FR_r = f65 + +FR_log2_hi = f66 +FR_log2_lo = f67 +FR_Z = f68 +FR_2_to_minus_N = f69 +FR_rcub = f70 +FR_rsq = f71 +FR_05r = f72 +FR_Half = f73 + +FR_Arg_X = f50 +FR_Arg_Y = f0 +FR_RESULT = f8 + + + +// General Purpose Registers + +GR_ad_05 = r33 +GR_Index1 = r34 +GR_ArgExp = r34 +GR_Index2 = r35 +GR_ExpMask = r35 +GR_NearZeroBound = r36 +GR_signif = r36 +GR_X_0 = r37 +GR_X_1 = r37 +GR_X_2 = r38 +GR_Index3 = r38 +GR_minus_N = r39 +GR_Z_1 = r40 +GR_Z_2 = r40 +GR_N = r41 +GR_Bias = r42 +GR_M = r43 +GR_ad_taylor = r44 +GR_ad_taylor_2 = r45 +GR_ad2_tbl_3 = r45 +GR_ad_tbl_1 = r46 +GR_ad_tbl_2 = r47 +GR_ad_tbl_3 = r48 +GR_ad_q = r49 +GR_ad_z_1 = r50 +GR_ad_z_2 = r51 +GR_ad_z_3 = r52 + +// +// Added for unwind support +// +GR_SAVE_PFS = r46 +GR_SAVE_B0 = r47 +GR_SAVE_GP = r48 +GR_Parameter_X = r49 +GR_Parameter_Y = r50 +GR_Parameter_RESULT = r51 +GR_Parameter_TAG = r52 + + + +.section .text +GLOBAL_LIBM_ENTRY(atanhl) + +{ .mfi + alloc r32 = ar.pfs,0,17,4,0 + fnma.s1 FR_Bp = f8,f1,f1 // b = 1 - |arg| (for x>0) + mov GR_ExpMask = 0x1ffff +} +{ .mfi + addl GR_ad_taylor = @ltoff(Constants_TaylorSeries),gp + fma.s1 FR_Bn = f8,f1,f1 // b = 1 - |arg| (for x<0) + mov GR_NearZeroBound = 0xfffa // biased exp of 1/32 +};; +{ .mfi + getf.exp GR_ArgExp = f8 + fcmp.lt.s1 p6,p7 = f8,f0 // is negative? + nop.i 0 +} +{ .mfi + ld8 GR_ad_taylor = [GR_ad_taylor] + fmerge.s FR_abs_x = f1,f8 + nop.i 0 +};; +{ .mfi + nop.m 0 + fclass.m p8,p0 = f8,0x1C7 // is arg NaT,Q/SNaN or +/-0 ? + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x2 = f8,f8,f0 + nop.i 0 +};; +{ .mfi + add GR_ad_z_1 = 0x0F0,GR_ad_taylor + fclass.m p9,p0 = f8,0x0a // is arg -denormal ? + add GR_ad_taylor_2 = 0x010,GR_ad_taylor +} +{ .mfi + add GR_ad_05 = 0x080,GR_ad_taylor + nop.f 0 + nop.i 0 +};; +{ .mfi + ldfe FR_C17 = [GR_ad_taylor],32 + fclass.m p10,p0 = f8,0x09 // is arg +denormal ? + add GR_ad_tbl_1 = 0x040,GR_ad_z_1 // point to Constants_G_H_h1 +} +{ .mfb + add GR_ad_z_2 = 0x140,GR_ad_z_1 // point to Constants_Z_2 + (p8) fma.s0 f8 = f8,f1,f0 // NaN or +/-0 + (p8) br.ret.spnt b0 // exit for Nan or +/-0 +};; +{ .mfi + ldfe FR_C15 = [GR_ad_taylor_2],32 + fclass.m p15,p0 = f8,0x23 // is +/-INF ? + add GR_ad_tbl_2 = 0x180,GR_ad_z_1 // point to Constants_G_H_h2 +} +{ .mfb + ldfe FR_C13 = [GR_ad_taylor],32 + (p9) fnma.s0 f8 = f8,f8,f8 // -denormal + (p9) br.ret.spnt b0 // exit for -denormal +};; +{ .mfi + ldfe FR_C11 = [GR_ad_taylor_2],32 + fcmp.eq.s0 p13,p0 = FR_abs_x,f1 // is |arg| = 1? + nop.i 0 +} +{ .mfb + ldfe FR_C9 = [GR_ad_taylor],32 +(p10) fma.s0 f8 = f8,f8,f8 // +denormal +(p10) br.ret.spnt b0 // exit for +denormal +};; +{ .mfi + ldfe FR_C7 = [GR_ad_taylor_2],32 + (p6) frcpa.s1 FR_Yn,p11 = f1,FR_Bn // y = frcpa(b) + and GR_ArgExp = GR_ArgExp,GR_ExpMask // biased exponent +} +{ .mfb + ldfe FR_C5 = [GR_ad_taylor],32 + fnma.s1 FR_B = FR_abs_x,f1,f1 // b = 1 - |arg| +(p15) br.cond.spnt atanhl_gt_one // |arg| > 1 +};; +{ .mfb + cmp.gt p14,p0 = GR_NearZeroBound,GR_ArgExp + (p7) frcpa.s1 FR_Yp,p12 = f1,FR_Bp // y = frcpa(b) +(p13) br.cond.spnt atanhl_eq_one // |arg| = 1/32 +} +{ .mfb + ldfe FR_C3 = [GR_ad_taylor_2],32 + fma.s1 FR_A = FR_abs_x,f1,FR_abs_x // a = 2 * |arg| +(p14) br.cond.spnt atanhl_near_zero // |arg| < 1/32 +};; +{ .mfi + nop.m 0 + fcmp.gt.s0 p8,p0 = FR_abs_x,f1 // is |arg| > 1 ? + nop.i 0 +};; +.pred.rel "mutex",p6,p7 +{ .mfi + nop.m 0 + (p6) fnma.s1 FR_B_lo = FR_Bn,f1,f1 // argt = 1 - (1 - |arg|) + nop.i 0 +} +{ .mfi + ldfs FR_Half = [GR_ad_05] + (p7) fnma.s1 FR_B_lo = FR_Bp,f1,f1 + nop.i 0 +};; +{ .mfi + nop.m 0 + (p6) fnma.s1 FR_E0 = FR_Yn,FR_Bn,f1 // e = 1-b*y + nop.i 0 +} +{ .mfb + nop.m 0 + (p6) fma.s1 FR_Y0 = FR_Yn,f1,f0 + (p8) br.cond.spnt atanhl_gt_one // |arg| > 1 +};; +{ .mfi + nop.m 0 + (p7) fnma.s1 FR_E0 = FR_Yp,FR_Bp,f1 + nop.i 0 +} +{ .mfi + nop.m 0 + (p6) fma.s1 FR_Q0 = FR_A,FR_Yn,f0 // q = a*y + nop.i 0 +};; +{ .mfi + nop.m 0 + (p7) fma.s1 FR_Q0 = FR_A,FR_Yp,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + (p7) fma.s1 FR_Y0 = FR_Yp,f1,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fclass.nm p10,p0 = f8,0x1FF // test for unsupported + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2 + nop.i 0 +};; +{ .mfb + nop.m 0 +// Return generated NaN or other value for unsupported values. +(p10) fma.s0 f8 = f8, f0, f0 +(p10) br.ret.spnt b0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_B_lo = FR_abs_x,f1,FR_B_lo // b_lo = argt-|arg| + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_R0 = FR_B,FR_Q0,FR_A // r = a-b*q + nop.i 0 +};; +{ .mfi + nop.m 0 + fnma.s1 FR_E4 = FR_B,FR_Y2,f1 // e4 = 1-b*y2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_X = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_Z = FR_X,f1,f1 // x+1 + nop.i 0 +};; +{ .mfi + nop.m 0 + (p6) fnma.s1 FR_Half = FR_Half,f1,f0 // sign(arg)/2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 FR_R1 = FR_B,FR_X,FR_A // r1 = a-b*x + nop.i 0 +};; +{ .mfi + getf.sig GR_signif = FR_Z // get significand of x+1 + nop.f 0 + nop.i 0 +};; + + +{ .mfi + add GR_ad_q = -0x060,GR_ad_z_1 + nop.f 0 + extr.u GR_Index1 = GR_signif,59,4 // get high 4 bits of signif +} +{ .mfi + add GR_ad_tbl_3 = 0x280,GR_ad_z_1 // point to Constants_G_H_h3 + nop.f 0 + nop.i 0 +};; +{ .mfi + shladd GR_ad_z_1 = GR_Index1,2,GR_ad_z_1 // point to Z_1 + nop.f 0 + extr.u GR_X_0 = GR_signif,49,15 // get high 15 bits of significand +};; +{ .mfi + ld4 GR_Z_1 = [GR_ad_z_1] // load Z_1 + fmax.s1 FR_AA = FR_X,f1 // for S_lo,form AA = max(X,1.0) + nop.i 0 +} +{ .mfi + shladd GR_ad_tbl_1 = GR_Index1,4,GR_ad_tbl_1 // point to G_1 + nop.f 0 + mov GR_Bias = 0x0FFFF // exponent bias +};; +{ .mfi + ldfps FR_G,FR_H = [GR_ad_tbl_1],8 // load G_1,H_1 + fmerge.se FR_S_hi = f1,FR_Z // form |x+1| + nop.i 0 +};; +{ .mfi + getf.exp GR_N = FR_Z // get N = exponent of x+1 + nop.f 0 + nop.i 0 +} +{ .mfi + ldfd FR_h = [GR_ad_tbl_1] // load h_1 + fnma.s1 FR_R1 = FR_B_lo,FR_X,FR_R1 // r1 = r1-b_lo*x + nop.i 0 +};; +{ .mfi + ldfe FR_log2_hi = [GR_ad_q],16 // load log2_hi + nop.f 0 + pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // get bits 30-15 of X_0 * Z_1 +};; +// +// For performance,don't use result of pmpyshr2.u for 4 cycles. +// +{ .mfi + ldfe FR_log2_lo = [GR_ad_q],16 // load log2_lo + nop.f 0 + sub GR_N = GR_N,GR_Bias +};; +{ .mfi + ldfe FR_Q4 = [GR_ad_q],16 // load Q4 + fms.s1 FR_S_lo = FR_AA,f1,FR_Z // form S_lo = AA - Z + sub GR_minus_N = GR_Bias,GR_N // form exponent of 2^(-N) +};; +{ .mmf + ldfe FR_Q3 = [GR_ad_q],16 // load Q3 + // put integer N into rightmost significand + setf.sig FR_float_N = GR_N + fmin.s1 FR_BB = FR_X,f1 // for S_lo,form BB = min(X,1.0) +};; +{ .mfi + ldfe FR_Q2 = [GR_ad_q],16 // load Q2 + nop.f 0 + extr.u GR_Index2 = GR_X_1,6,4 // extract bits 6-9 of X_1 +};; +{ .mmi + ldfe FR_Q1 = [GR_ad_q] // load Q1 + shladd GR_ad_z_2 = GR_Index2,2,GR_ad_z_2 // point to Z_2 + nop.i 0 +};; +{ .mmi + ld4 GR_Z_2 = [GR_ad_z_2] // load Z_2 + shladd GR_ad_tbl_2 = GR_Index2,4,GR_ad_tbl_2 // point to G_2 + nop.i 0 +};; +{ .mfi + ldfps FR_G2,FR_H2 = [GR_ad_tbl_2],8 // load G_2,H_2 + nop.f 0 + nop.i 0 +};; +{ .mfi + ldfd FR_h2 = [GR_ad_tbl_2] // load h_2 + fma.s1 FR_S_lo = FR_S_lo,f1,FR_BB // S_lo = S_lo + BB + nop.i 0 +} +{ .mfi + setf.exp FR_2_to_minus_N = GR_minus_N // form 2^(-N) + fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3 + nop.i 0 +};; +{ .mfi + nop.m 0 + nop.f 0 + pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // get bits 30-15 of X_1 * Z_2 +};; +// +// For performance,don't use result of pmpyshr2.u for 4 cycles +// +{ .mfi + add GR_ad2_tbl_3 = 8,GR_ad_tbl_3 + nop.f 0 + nop.i 0 +} +{ .mfi + nop.m 0 + nop.f 0 + nop.i 0 +};; +{ .mfi + nop.m 0 + nop.f 0 + nop.i 0 +};; +{ .mfi + nop.m 0 + nop.f 0 + nop.i 0 +};; + +// +// Now GR_X_2 can be used +// +{ .mfi + nop.m 0 + nop.f 0 + extr.u GR_Index3 = GR_X_2,1,5 // extract bits 1-5 of X_2 +} +{ .mfi + nop.m 0 + fma.s1 FR_S_lo = FR_S_lo,f1,FR_X_lo // S_lo = S_lo + Arg_lo + nop.i 0 +};; + +{ .mfi + shladd GR_ad_tbl_3 = GR_Index3,4,GR_ad_tbl_3 // point to G_3 + fcvt.xf FR_float_N = FR_float_N + nop.i 0 +} +{ .mfi + shladd GR_ad2_tbl_3 = GR_Index3,4,GR_ad2_tbl_3 // point to h_3 + fma.s1 FR_Q1 = FR_Q1,FR_Half,f0 // sign(arg)*Q1/2 + nop.i 0 +};; +{ .mmi + ldfps FR_G3,FR_H3 = [GR_ad_tbl_3],8 // load G_3,H_3 + ldfd FR_h3 = [GR_ad2_tbl_3] // load h_3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G,FR_G2 // G = G_1 * G_2 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H,FR_H2 // H = H_1 + H_2 + nop.i 0 +};; +{ .mfi + nop.m 0 + fadd.s1 FR_h = FR_h,FR_h2 // h = h_1 + h_2 + nop.i 0 +};; +{ .mfi + nop.m 0 + // S_lo = S_lo * 2^(-N) + fma.s1 FR_S_lo = FR_S_lo,FR_2_to_minus_N,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fmpy.s1 FR_G = FR_G,FR_G3 // G = (G_1 * G_2) * G_3 + nop.i 0 +} +{ .mfi + nop.m 0 + fadd.s1 FR_H = FR_H,FR_H3 // H = (H_1 + H_2) + H_3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fadd.s1 FR_h = FR_h,FR_h3 // h = (h_1 + h_2) + h_3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fms.s1 FR_r = FR_G,FR_S_hi,f1 // r = G * S_hi - 1 + nop.i 0 +} +{ .mfi + nop.m 0 + // Y_hi = N * log2_hi + H + fma.s1 FR_Y_hi = FR_float_N,FR_log2_hi,FR_H + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_h = FR_float_N,FR_log2_lo,FR_h // h = N * log2_lo + h + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_r = FR_G,FR_S_lo,FR_r // r = G * S_lo + (G * S_hi - 1) + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_poly_lo = FR_r,FR_Q4,FR_Q3 // poly_lo = r * Q4 + Q3 + nop.i 0 +} +{ .mfi + nop.m 0 + fmpy.s1 FR_rsq = FR_r,FR_r // rsq = r * r + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_05r = FR_r,FR_Half,f0 // sign(arg)*r/2 + nop.i 0 +};; +{ .mfi + nop.m 0 + // poly_lo = poly_lo * r + Q2 + fma.s1 FR_poly_lo = FR_poly_lo,FR_r,FR_Q2 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_rcub = FR_rsq,FR_r,f0 // rcub = r^3 + nop.i 0 +};; +{ .mfi + nop.m 0 + // poly_hi = sing(arg)*(Q1*r^2 + r)/2 + fma.s1 FR_poly_hi = FR_Q1,FR_rsq,FR_05r + nop.i 0 +};; +{ .mfi + nop.m 0 + // poly_lo = poly_lo*r^3 + h + fma.s1 FR_poly_lo = FR_poly_lo,FR_rcub,FR_h + nop.i 0 +};; +{ .mfi + nop.m 0 + // Y_lo = poly_hi + poly_lo/2 + fma.s0 FR_Y_lo = FR_poly_lo,FR_Half,FR_poly_hi + nop.i 0 +};; +{ .mfb + nop.m 0 + // Result = arctanh(x) = Y_hi/2 + Y_lo + fma.s0 f8 = FR_Y_hi,FR_Half,FR_Y_lo + br.ret.sptk b0 +};; + +// Taylor's series +atanhl_near_zero: +{ .mfi + nop.m 0 + fma.s1 FR_x3 = FR_x2,f8,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_x4 = FR_x2,FR_x2,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C17 = FR_C17,FR_x2,FR_C15 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_C13 = FR_C13,FR_x2,FR_C11 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C9 = FR_C9,FR_x2,FR_C7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 FR_C5 = FR_C5,FR_x2,FR_C3 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_x8 = FR_x4,FR_x4,f0 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C17 = FR_C17,FR_x4,FR_C13 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C9 = FR_C9,FR_x4,FR_C5 + nop.i 0 +};; +{ .mfi + nop.m 0 + fma.s1 FR_C17 = FR_C17,FR_x8,FR_C9 + nop.i 0 +};; +{ .mfb + nop.m 0 + fma.s0 f8 = FR_C17,FR_x3,f8 + br.ret.sptk b0 +};; + +atanhl_eq_one: +{ .mfi + nop.m 0 + frcpa.s0 FR_Rcp,p0 = f1,f0 // get inf,and raise Z flag + nop.i 0 +} +{ .mfi + nop.m 0 + fmerge.s FR_Arg_X = f8, f8 + nop.i 0 +};; +{ .mfb + mov GR_Parameter_TAG = 130 + fmerge.s FR_RESULT = f8,FR_Rcp // result is +-inf + br.cond.sptk __libm_error_region // exit if |x| = 1.0 +};; + +atanhl_gt_one: +{ .mfi + nop.m 0 + fmerge.s FR_Arg_X = f8, f8 + nop.i 0 +};; +{ .mfb + mov GR_Parameter_TAG = 129 + frcpa.s0 FR_RESULT,p0 = f0,f0 // get QNaN,and raise invalid + br.cond.sptk __libm_error_region // exit if |x| > 1.0 +};; + +GLOBAL_LIBM_END(atanhl) +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 + stfe [GR_Parameter_Y] = FR_Arg_Y,16 // Save 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 + stfe [GR_Parameter_X] = FR_Arg_X // Store Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y + nop.b 0 // Parameter 3 address +} +{ .mib + stfe [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 + ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack +.restore sp + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address +};; +{ .mib + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return +};; + +LOCAL_LIBM_END(__libm_error_region#) + +.type __libm_error_support#,@function +.global __libm_error_support# |