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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 new file mode 100644 index 0000000..d3a5507 --- /dev/null +++ b/sysdeps/ia64/fpu/s_asinhl.S @@ -0,0 +1,1347 @@ +.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) + + + |