.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#