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Diffstat (limited to 'sysdeps/ia64/fpu/s_asinhl.S')
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diff --git a/sysdeps/ia64/fpu/s_asinhl.S b/sysdeps/ia64/fpu/s_asinhl.S deleted file mode 100644 index d3a5507..0000000 --- a/sysdeps/ia64/fpu/s_asinhl.S +++ /dev/null @@ -1,1347 +0,0 @@ -.file "asinhl.s" - - -// Copyright (c) 2000 - 2003, Intel Corporation -// All rights reserved. -// -// Contributed 2000 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: -// 09/04/01 Initial version -// 09/13/01 Performance improved, symmetry problems fixed -// 10/10/01 Performance improved, split issues removed -// 12/11/01 Changed huges_logp to not be global -// 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 -// -//********************************************************************* -// -// API -//============================================================== -// long double asinhl(long double); -// -// Overview of operation -//============================================================== -// -// There are 6 paths: -// 1. x = 0, [S,Q]Nan or +/-INF -// Return asinhl(x) = x + x; -// -// 2. x = + denormal -// Return asinhl(x) = x - x^2; -// -// 3. x = - denormal -// Return asinhl(x) = x + x^2; -// -// 4. 'Near 0': max denormal < |x| < 1/128 -// Return asinhl(x) = sign(x)*(x+x^3*(c3+x^2*(c5+x^2*(c7+x^2*(c9))))); -// -// 5. 'Huges': |x| > 2^63 -// Return asinhl(x) = sign(x)*(logl(2*x)); -// -// 6. 'Main path': 1/128 < |x| < 2^63 -// b_hi + b_lo = x + sqrt(x^2 + 1); -// asinhl(x) = sign(x)*(log_special(b_hi, b_lo)); -// -// Algorithm description -//============================================================== -// -// Main path algorithm -// ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! ) -// ************************************************************************* -// -// There are 3 parts of x+sqrt(x^2+1) computation: -// -// 1) p2 = (p2_hi+p2_lo) = x^2+1 obtaining -// ------------------------------------ -// p2_hi = x2_hi + 1, where x2_hi = x * x; -// p2_lo = x2_lo + p1_lo, where -// x2_lo = FMS(x*x-x2_hi), -// p1_lo = (1 - p2_hi) + x2_hi; -// -// 2) g = (g_hi+g_lo) = sqrt(p2) = sqrt(p2_hi+p2_lo) -// ---------------------------------------------- -// r = invsqrt(p2_hi) (8-bit reciprocal square root approximation); -// g = p2_hi * r (first 8 bit-approximation of sqrt); -// -// h = 0.5 * r; -// e = 0.5 - g * h; -// g = g * e + g (second 16 bit-approximation of sqrt); -// -// h = h * e + h; -// e = 0.5 - g * h; -// g = g * e + g (third 32 bit-approximation of sqrt); -// -// h = h * e + h; -// e = 0.5 - g * h; -// g_hi = g * e + g (fourth 64 bit-approximation of sqrt); -// -// Remainder computation: -// h = h * e + h; -// d = (p2_hi - g_hi * g_hi) + p2_lo; -// g_lo = d * h; -// -// 3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2+1) -// ------------------------------------------------------------------- -// b_hi = (g_hi + x) + gl; -// b_lo = (g_hi - b_hi) + x + gl; -// -// Now we pass b presented as sum b_hi + b_lo to special version -// of logl function which accept a pair of arguments as -// 'mutiprecision' value. -// -// Special log algorithm overview -// ================================ -// Here we use a table lookup method. The basic idea is that in -// order to compute logl(Arg) = logl (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 - 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 four steps. -// -// Step 0: Initialization -// -// We need to calculate logl( X ). Obtain N, S_hi such that -// -// X = 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 logl: S_lo = b_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, -// -// logl( X ) = 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 logl or log1pl function, regular path. -// -// Registers used -//============================================================== -// Floating Point registers used: -// f8, input -// f32 -> f101 (70 registers) - -// General registers used: -// r32 -> r57 (26 registers) - -// Predicate registers used: -// p6 -> p11 -// p6 for '0, NaNs, Inf' path -// p7 for '+ denormals' path -// p8 for 'near 0' path -// p9 for 'huges' path -// p10 for '- denormals' path -// p11 for negative values -// -// Data tables -//============================================================== - -RODATA -.align 64 - -// C7, C9 'near 0' polynomial coefficients -LOCAL_OBJECT_START(Poly_C_near_0_79) -data8 0xF8DC939BBEDD5A54, 0x00003FF9 -data8 0xB6DB6DAB21565AC5, 0x0000BFFA -LOCAL_OBJECT_END(Poly_C_near_0_79) - -// C3, C5 'near 0' polynomial coefficients -LOCAL_OBJECT_START(Poly_C_near_0_35) -data8 0x999999999991D582, 0x00003FFB -data8 0xAAAAAAAAAAAAAAA9, 0x0000BFFC -LOCAL_OBJECT_END(Poly_C_near_0_35) - -// Q coeffs -LOCAL_OBJECT_START(Constants_Q) -data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 -data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 -data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 -data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 -data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 -data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 -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) - -// Assembly macros -//============================================================== - -// Floating Point Registers - -FR_Arg = f8 -FR_Res = f8 -FR_AX = f32 -FR_XLog_Hi = f33 -FR_XLog_Lo = f34 - - // Special logl registers -FR_Y_hi = f35 -FR_Y_lo = f36 - -FR_Scale = f37 -FR_X_Prime = f38 -FR_S_hi = f39 -FR_W = f40 -FR_G = f41 - -FR_H = f42 -FR_wsq = f43 -FR_w4 = f44 -FR_h = f45 -FR_w6 = f46 - -FR_G2 = f47 -FR_H2 = f48 -FR_poly_lo = f49 -FR_P8 = f50 -FR_poly_hi = f51 - -FR_P7 = f52 -FR_h2 = f53 -FR_rsq = f54 -FR_P6 = f55 -FR_r = f56 - -FR_log2_hi = f57 -FR_log2_lo = f58 - -FR_float_N = f59 -FR_Q4 = f60 - -FR_G3 = f61 -FR_H3 = f62 -FR_h3 = f63 - -FR_Q3 = f64 -FR_Q2 = f65 -FR_1LN10_hi = f66 - -FR_Q1 = f67 -FR_1LN10_lo = f68 -FR_P5 = f69 -FR_rcub = f70 - -FR_Neg_One = f71 -FR_Z = f72 -FR_AA = f73 -FR_BB = f74 -FR_S_lo = f75 -FR_2_to_minus_N = f76 - - - // Huge & Main path prolog registers -FR_Half = f77 -FR_Two = f78 -FR_X2 = f79 -FR_P2 = f80 -FR_P2L = f81 -FR_Rcp = f82 -FR_GG = f83 -FR_HH = f84 -FR_EE = f85 -FR_DD = f86 -FR_GL = f87 -FR_A = f88 -FR_AL = f89 -FR_B = f90 -FR_BL = f91 -FR_Tmp = f92 - - // Near 0 & Huges path prolog registers -FR_C3 = f93 -FR_C5 = f94 -FR_C7 = f95 -FR_C9 = f96 - -FR_X3 = f97 -FR_X4 = f98 -FR_P9 = f99 -FR_P5 = f100 -FR_P3 = f101 - - -// General Purpose Registers - - // General prolog registers -GR_PFS = r32 -GR_TwoN7 = r40 -GR_TwoP63 = r41 -GR_ExpMask = r42 -GR_ArgExp = r43 -GR_Half = r44 - - // Near 0 path prolog registers -GR_Poly_C_35 = r45 -GR_Poly_C_79 = r46 - - // Special logl registers -GR_Index1 = r34 -GR_Index2 = r35 -GR_signif = r36 -GR_X_0 = r37 -GR_X_1 = r38 -GR_X_2 = r39 -GR_Z_1 = r40 -GR_Z_2 = r41 -GR_N = r42 -GR_Bias = r43 -GR_M = r44 -GR_Index3 = r45 -GR_exp_2tom80 = r45 -GR_exp_mask = r47 -GR_exp_2tom7 = r48 -GR_ad_ln10 = r49 -GR_ad_tbl_1 = r50 -GR_ad_tbl_2 = r51 -GR_ad_tbl_3 = r52 -GR_ad_q = r53 -GR_ad_z_1 = r54 -GR_ad_z_2 = r55 -GR_ad_z_3 = r56 -GR_minus_N = r57 - - - -.section .text -GLOBAL_LIBM_ENTRY(asinhl) - -{ .mfi - alloc GR_PFS = ar.pfs,0,27,0,0 - fma.s1 FR_P2 = FR_Arg, FR_Arg, f1 // p2 = x^2 + 1 - mov GR_Half = 0xfffe // 0.5's exp -} -{ .mfi - addl GR_Poly_C_79 = @ltoff(Poly_C_near_0_79), gp // C7, C9 coeffs - fma.s1 FR_X2 = FR_Arg, FR_Arg, f0 // Obtain x^2 - addl GR_Poly_C_35 = @ltoff(Poly_C_near_0_35), gp // C3, C5 coeffs -};; - -{ .mfi - getf.exp GR_ArgExp = FR_Arg // get arument's exponent - fabs FR_AX = FR_Arg // absolute value of argument - mov GR_TwoN7 = 0xfff8 // 2^-7 exp -} -{ .mfi - ld8 GR_Poly_C_79 = [GR_Poly_C_79] // get actual coeff table address - fma.s0 FR_Two = f1, f1, f1 // construct 2.0 - mov GR_ExpMask = 0x1ffff // mask for exp -};; - -{ .mfi - ld8 GR_Poly_C_35 = [GR_Poly_C_35] // get actual coeff table address - fclass.m p6,p0 = FR_Arg, 0xe7 // if arg NaN inf zero - mov GR_TwoP63 = 0x1003e // 2^63 exp -} -{ .mfi - addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp - nop.f 0 - nop.i 0 -};; - -{ .mfi - setf.exp FR_Half = GR_Half // construct 0.5 - fclass.m p7,p0 = FR_Arg, 0x09 // if arg + denorm - and GR_ArgExp = GR_ExpMask, GR_ArgExp // select exp -} -{ .mfb - ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 - nop.f 0 - nop.b 0 -};; -{ .mfi - ldfe FR_C9 = [GR_Poly_C_79],16 // load C9 - fclass.m p10,p0 = FR_Arg, 0x0a // if arg - denorm - cmp.gt p8, p0 = GR_TwoN7, GR_ArgExp // if arg < 2^-7 ('near 0') -} -{ .mfb - cmp.le p9, p0 = GR_TwoP63, GR_ArgExp // if arg > 2^63 ('huges') -(p6) fma.s0 FR_Res = FR_Arg,f1,FR_Arg // r = a + a -(p6) br.ret.spnt b0 // return -};; -// (X^2 + 1) computation -{ .mfi -(p8) ldfe FR_C5 = [GR_Poly_C_35],16 // load C5 - fms.s1 FR_Tmp = f1, f1, FR_P2 // Tmp = 1 - p2 - add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 -} -{ .mfb -(p8) ldfe FR_C7 = [GR_Poly_C_79],16 // load C7 -(p7) fnma.s0 FR_Res = FR_Arg,FR_Arg,FR_Arg // r = a - a*a -(p7) br.ret.spnt b0 // return -};; - -{ .mfi -(p8) ldfe FR_C3 = [GR_Poly_C_35],16 // load C3 - fcmp.lt.s1 p11, p12 = FR_Arg, f0 // if arg is negative - add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P -} -{ .mfb - add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 -(p10) fma.s0 FR_Res = FR_Arg,FR_Arg,FR_Arg // r = a + a*a -(p10) br.ret.spnt b0 // return -};; - -{ .mfi - add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 - frsqrta.s1 FR_Rcp, p0 = FR_P2 // Rcp = 1/p2 reciprocal appr. - add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 -} -{ .mfi - nop.m 0 - fms.s1 FR_P2L = FR_AX, FR_AX, FR_X2 //low part of p2=fma(X*X-p2) - mov GR_Bias = 0x0FFFF // Create exponent bias -};; - -{ .mfb - nop.m 0 -(p9) fms.s1 FR_XLog_Hi = FR_Two, FR_AX, f0 // Hi of log1p arg = 2*X - 1 -(p9) br.cond.spnt huges_logl // special version of log1p -};; - -{ .mfb - ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi -(p8) fma.s1 FR_X3 = FR_X2, FR_Arg, f0 // x^3 = x^2 * x -(p8) br.cond.spnt near_0 // Go to near 0 branch -};; - -{ .mfi - ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo - nop.f 0 - nop.i 0 -};; - -{ .mfi - ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 - fma.s1 FR_Tmp = FR_Tmp, f1, FR_X2 // Tmp = Tmp + x^2 - mov GR_exp_mask = 0x1FFFF // Create exponent mask -};; - -{ .mfi - ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 - fma.s1 FR_GG = FR_Rcp, FR_P2, f0 // g = Rcp * p2 - // 8 bit Newton Raphson iteration - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp - nop.i 0 -};; -{ .mfi - ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 - fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P2L = FR_Tmp, f1, FR_P2L // low part of p2 = Tmp + p2l - nop.i 0 -};; - -{ .mfi - ldfe FR_Q1 = [GR_ad_q] // Load Q1 - fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g - // 16 bit Newton Raphson iteration - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g - // 32 bit Newton Raphson iteration - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g - // 64 bit Newton Raphson iteration - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fnma.s1 FR_DD = FR_GG, FR_GG, FR_P2 // Remainder d = g * g - p2 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_XLog_Hi = FR_AX, f1, FR_GG // bh = z + gh - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_DD = FR_DD, f1, FR_P2L // add p2l: d = d + p2l - nop.i 0 -};; - - -{ .mfi - getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 - fmerge.ns FR_Neg_One = f1, f1 // Form -1.0 - mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h - extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif -} -{ .mfi - nop.m 0 - fma.s1 FR_XLog_Hi = FR_DD, FR_HH, FR_XLog_Hi // bh = bh + gl - nop.i 0 -};; - -{ .mmi - shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 - shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 - extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif. -};; - -{ .mmi - ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 - nop.m 0 - nop.i 0 -};; - -{ .mmi - ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 - nop.m 0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fms.s1 FR_XLog_Lo = FR_GG, f1, FR_XLog_Hi // bl = gh - bh - pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 -};; - -// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL! -// "DEAD" ZONE! - -{ .mfi - nop.m 0 - nop.f 0 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1| - nop.i 0 -};; - -{ .mmi - getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 - ldfd FR_h = [GR_ad_tbl_1] // Load h_1 - nop.i 0 -};; - -{ .mfi - nop.m 0 - nop.f 0 - extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 -};; - - -{ .mfi - shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 - fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_AX // bl = bl + x - mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 -} -{ .mfi - shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 - nop.f 0 - sub GR_N = GR_N, GR_Bias // sub bias from exp -};; - -{ .mmi - ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 - ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 - sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) -};; - -{ .mmi - ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 - nop.m 0 - nop.i 0 -};; - -{ .mmi - setf.sig FR_float_N = GR_N // Put integer N into rightmost sign - setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) - pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 -};; - -// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!) -// BECAUSE OF POSSIBLE 10 CLOCKS STALL! -// So we can negate Q coefficients there for negative values - -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q1 = FR_Q1, FR_Neg_One, f0 // Negate Q1 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GL // bl = bl + gl - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q2 = FR_Q2, FR_Neg_One, f0 // Negate Q2 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q3 = FR_Q3, FR_Neg_One, f0 // Negate Q3 - nop.i 0 -};; - -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q4 = FR_Q4, FR_Neg_One, f0 // Negate Q4 - extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 -};; - -{ .mfi - shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 - nop.f 0 - nop.i 0 -};; - -{ .mfi - ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 - nop.f 0 - nop.i 0 -};; - -{ .mfi - ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 - fcvt.xf FR_float_N = FR_float_N - 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 - fma.s1 FR_S_lo = FR_XLog_Lo, FR_2_to_minus_N, f0 //S_lo=S_lo*2^-N - 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 - fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+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_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 - nop.i 0 -};; - -.pred.rel "mutex",p12,p11 -{ .mfi - nop.m 0 -(p12) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r - nop.i 0 -};; - - -.pred.rel "mutex",p12,p11 -{ .mfi - nop.m 0 -(p12) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h - nop.i 0 -} -;; - -{ .mfi - nop.m 0 - fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo - // Y_lo=poly_hi+poly_lo - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fma.s0 FR_Y_hi = FR_Y_hi, FR_Neg_One, f0 // FR_Y_hi sign for neg - nop.i 0 -};; - -{ .mfb - nop.m 0 - fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi - br.ret.sptk b0 // Common exit for 2^-7 < x < inf -};; - -// * SPECIAL VERSION OF LOGL FOR HUGE ARGUMENTS * - -huges_logl: -{ .mfi - getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 - fmerge.ns FR_Neg_One = f1, f1 // Form -1.0 - mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 -};; - -{ .mfi - add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 - nop.f 0 - add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P -} -{ .mfi - add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 - nop.f 0 - add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 -};; - -{ .mfi - nop.m 0 - 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 signif. -};; - -{ .mfi - ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 - nop.f 0 - mov GR_exp_mask = 0x1FFFF // Create exponent mask -} -{ .mfi - shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 - nop.f 0 - mov GR_Bias = 0x0FFFF // Create 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_XLog_Hi // Form |x+1| - nop.i 0 -};; - -{ .mmi - getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 - ldfd FR_h = [GR_ad_tbl_1] // Load h_1 - 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 -};; - -// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL! -// "DEAD" ZONE! - -{ .mmi - ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo - sub GR_N = GR_N, GR_Bias - mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 -};; - -{ .mfi - ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 - nop.f 0 - sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) -};; - -{ .mmf - ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 - setf.sig FR_float_N = GR_N // Put integer N into rightmost sign - nop.f 0 -};; - -{ .mmi - nop.m 0 - ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 - 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 -};; - -{ .mmi - ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 - nop.m 0 - nop.i 0 -};; - -{ .mfi - ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 - nop.f 0 - nop.i 0 -} -{ .mfi - setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) - nop.f 0 - 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 -};; - -// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL! -// "DEAD" ZONE! -// JUST HAVE TO INSERT 3 NOP CYCLES (nothing to do here) - -{ .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 -};; - -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q4 = FR_Q4, FR_Neg_One, f0 // Negate Q4 - extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 - };; - -{ .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 - nop.m 0 -(p11) fma.s1 FR_Q3 = FR_Q3, FR_Neg_One, f0 // Negate Q3 - nop.i 0 -};; - -{ .mfi - ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 -(p11) fma.s1 FR_Q2 = FR_Q2, FR_Neg_One, f0 // Negate Q2 - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fma.s1 FR_Q1 = FR_Q1, FR_Neg_One, f0 // Negate Q1 - nop.i 0 -};; - -{ .mfi - ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 - 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 -};; - -{ .mmf - nop.m 0 - nop.m 0 - fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 -};; - -{ .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 - fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+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_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_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 - nop.i 0 -};; - -.pred.rel "mutex",p12,p11 -{ .mfi - nop.m 0 -(p12) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r - nop.i 0 -};; - - -.pred.rel "mutex",p12,p11 -{ .mfi - nop.m 0 -(p12) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fms.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h - nop.i 0 -};; - -{ .mfi - nop.m 0 - fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo - nop.i 0 -} -{ .mfi - nop.m 0 -(p11) fma.s0 FR_Y_hi = FR_Y_hi, FR_Neg_One, f0 // FR_Y_hi sign for neg - nop.i 0 -};; - -{ .mfb - nop.m 0 - fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi - br.ret.sptk b0 // Common exit for 2^-7 < x < inf -};; - -// NEAR ZERO POLYNOMIAL INTERVAL -near_0: -{ .mfi - nop.m 0 - fma.s1 FR_X4 = FR_X2, FR_X2, f0 // x^4 = x^2 * x^2 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_P9 = FR_C9,FR_X2,FR_C7 // p9 = C9*x^2 + C7 - nop.i 0 -} -{ .mfi - nop.m 0 - fma.s1 FR_P5 = FR_C5,FR_X2,FR_C3 // p5 = C5*x^2 + C3 - nop.i 0 -};; - -{ .mfi - nop.m 0 - fma.s1 FR_P3 = FR_P9,FR_X4,FR_P5 // p3 = p9*x^4 + p5 - nop.i 0 -};; - -{ .mfb - nop.m 0 - fma.s0 FR_Res = FR_P3,FR_X3,FR_Arg // res = p3*C3 + x - br.ret.sptk b0 // Near 0 path return -};; - -GLOBAL_LIBM_END(asinhl) - - - |