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Diffstat (limited to 'ports/sysdeps/ia64/fpu/e_atanhl.S')
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diff --git a/ports/sysdeps/ia64/fpu/e_atanhl.S b/ports/sysdeps/ia64/fpu/e_atanhl.S deleted file mode 100644 index 5d828d5ffa..0000000000 --- a/ports/sysdeps/ia64/fpu/e_atanhl.S +++ /dev/null @@ -1,1156 +0,0 @@ -.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 -// algorithm 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# |