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Diffstat (limited to 'sysdeps/ia64/fpu/s_expm1f.S')
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diff --git a/sysdeps/ia64/fpu/s_expm1f.S b/sysdeps/ia64/fpu/s_expm1f.S new file mode 100644 index 0000000..55264a9 --- /dev/null +++ b/sysdeps/ia64/fpu/s_expm1f.S @@ -0,0 +1,671 @@ +.file "expf_m1.s" + + +// Copyright (c) 2000 - 2005, 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 +//********************************************************************* +// 02/02/00 Initial Version +// 04/04/00 Unwind support added +// 08/15/00 Bundle added after call to __libm_error_support to properly +// set [the previously overwritten] GR_Parameter_RESULT. +// 07/07/01 Improved speed of all paths +// 05/20/02 Cleaned up namespace and sf0 syntax +// 11/20/02 Improved speed, algorithm based on expf +// 03/31/05 Reformatted delimiters between data tables +// +// +// API +//********************************************************************* +// float expm1f(float) +// +// Overview of operation +//********************************************************************* +// 1. Inputs of Nan, Inf, Zero, NatVal handled with special paths +// +// 2. |x| < 2^-40 +// Result = x, computed by x + x*x to handle appropriate flags and rounding +// +// 3. 2^-40 <= |x| < 2^-2 +// Result determined by 8th order Taylor series polynomial +// expm1f(x) = x + A2*x^2 + ... + A8*x^8 +// +// 4. x < -24.0 +// Here we know result is essentially -1 + eps, where eps only affects +// rounded result. Set I. +// +// 5. x >= 88.7228 +// Result overflows. Set I, O, and call error support +// +// 6. 2^-2 <= x < 88.7228 or -24.0 <= x < -2^-2 +// This is the main path. The algorithm is described below: + +// Take the input x. w is "how many log2/128 in x?" +// w = x * 64/log2 +// NJ = int(w) +// x = NJ*log2/64 + R + +// NJ = 64*n + j +// x = n*log2 + (log2/64)*j + R +// +// So, exp(x) = 2^n * 2^(j/64)* exp(R) +// +// T = 2^n * 2^(j/64) +// Construct 2^n +// Get 2^(j/64) table +// actually all the entries of 2^(j/64) table are stored in DP and +// with exponent bits set to 0 -> multiplication on 2^n can be +// performed by doing logical "or" operation with bits presenting 2^n + +// exp(R) = 1 + (exp(R) - 1) +// P = exp(R) - 1 approximated by Taylor series of 3rd degree +// P = A3*R^3 + A2*R^2 + R, A3 = 1/6, A2 = 1/2 +// + +// The final result is reconstructed as follows +// expm1f(x) = T*P + (T - 1.0) + +// Special values +//********************************************************************* +// expm1f(+0) = +0.0 +// expm1f(-0) = -0.0 + +// expm1f(+qnan) = +qnan +// expm1f(-qnan) = -qnan +// expm1f(+snan) = +qnan +// expm1f(-snan) = -qnan + +// expm1f(-inf) = -1.0 +// expm1f(+inf) = +inf + +// Overflow and Underflow +//********************************************************************* +// expm1f(x) = largest single normal when +// x = 88.7228 = 0x42b17217 +// +// Underflow is handled as described in case 2 above. + + +// Registers used +//********************************************************************* +// Floating Point registers used: +// f8, input +// f6,f7, f9 -> f15, f32 -> f45 + +// General registers used: +// r3, r20 -> r38 + +// Predicate registers used: +// p9 -> p15 + +// Assembly macros +//********************************************************************* +// integer registers used +// scratch +rNJ = r3 + +rExp_half = r20 +rSignexp_x = r21 +rExp_x = r22 +rExp_mask = r23 +rExp_bias = r24 +rTmp = r25 +rM1_lim = r25 +rGt_ln = r25 +rJ = r26 +rN = r27 +rTblAddr = r28 +rLn2Div64 = r29 +rRightShifter = r30 +r64DivLn2 = r31 +// stacked +GR_SAVE_PFS = r32 +GR_SAVE_B0 = r33 +GR_SAVE_GP = r34 +GR_Parameter_X = r35 +GR_Parameter_Y = r36 +GR_Parameter_RESULT = r37 +GR_Parameter_TAG = r38 + +// floating point registers used +FR_X = f10 +FR_Y = f1 +FR_RESULT = f8 +// scratch +fRightShifter = f6 +f64DivLn2 = f7 +fNormX = f9 +fNint = f10 +fN = f11 +fR = f12 +fLn2Div64 = f13 +fA2 = f14 +fA3 = f15 +// stacked +fP = f32 +fX3 = f33 +fT = f34 +fMIN_SGL_OFLOW_ARG = f35 +fMAX_SGL_NORM_ARG = f36 +fMAX_SGL_MINUS_1_ARG = f37 +fA4 = f38 +fA43 = f38 +fA432 = f38 +fRSqr = f39 +fA5 = f40 +fTmp = f41 +fGt_pln = f41 +fXsq = f41 +fA7 = f42 +fA6 = f43 +fA65 = f43 +fTm1 = f44 +fA8 = f45 +fA87 = f45 +fA8765 = f45 +fA8765432 = f45 +fWre_urm_f8 = f45 + +RODATA +.align 16 +LOCAL_OBJECT_START(_expf_table) +data8 0x3efa01a01a01a01a // A8 = 1/8! +data8 0x3f2a01a01a01a01a // A7 = 1/7! +data8 0x3f56c16c16c16c17 // A6 = 1/6! +data8 0x3f81111111111111 // A5 = 1/5! +data8 0x3fa5555555555555 // A4 = 1/4! +data8 0x3fc5555555555555 // A3 = 1/3! +// +data4 0x42b17218 // Smallest sgl arg to overflow sgl result +data4 0x42b17217 // Largest sgl arg to give sgl result +// +// 2^(j/64) table, j goes from 0 to 63 +data8 0x0000000000000000 // 2^(0/64) +data8 0x00002C9A3E778061 // 2^(1/64) +data8 0x000059B0D3158574 // 2^(2/64) +data8 0x0000874518759BC8 // 2^(3/64) +data8 0x0000B5586CF9890F // 2^(4/64) +data8 0x0000E3EC32D3D1A2 // 2^(5/64) +data8 0x00011301D0125B51 // 2^(6/64) +data8 0x0001429AAEA92DE0 // 2^(7/64) +data8 0x000172B83C7D517B // 2^(8/64) +data8 0x0001A35BEB6FCB75 // 2^(9/64) +data8 0x0001D4873168B9AA // 2^(10/64) +data8 0x0002063B88628CD6 // 2^(11/64) +data8 0x0002387A6E756238 // 2^(12/64) +data8 0x00026B4565E27CDD // 2^(13/64) +data8 0x00029E9DF51FDEE1 // 2^(14/64) +data8 0x0002D285A6E4030B // 2^(15/64) +data8 0x000306FE0A31B715 // 2^(16/64) +data8 0x00033C08B26416FF // 2^(17/64) +data8 0x000371A7373AA9CB // 2^(18/64) +data8 0x0003A7DB34E59FF7 // 2^(19/64) +data8 0x0003DEA64C123422 // 2^(20/64) +data8 0x0004160A21F72E2A // 2^(21/64) +data8 0x00044E086061892D // 2^(22/64) +data8 0x000486A2B5C13CD0 // 2^(23/64) +data8 0x0004BFDAD5362A27 // 2^(24/64) +data8 0x0004F9B2769D2CA7 // 2^(25/64) +data8 0x0005342B569D4F82 // 2^(26/64) +data8 0x00056F4736B527DA // 2^(27/64) +data8 0x0005AB07DD485429 // 2^(28/64) +data8 0x0005E76F15AD2148 // 2^(29/64) +data8 0x0006247EB03A5585 // 2^(30/64) +data8 0x0006623882552225 // 2^(31/64) +data8 0x0006A09E667F3BCD // 2^(32/64) +data8 0x0006DFB23C651A2F // 2^(33/64) +data8 0x00071F75E8EC5F74 // 2^(34/64) +data8 0x00075FEB564267C9 // 2^(35/64) +data8 0x0007A11473EB0187 // 2^(36/64) +data8 0x0007E2F336CF4E62 // 2^(37/64) +data8 0x00082589994CCE13 // 2^(38/64) +data8 0x000868D99B4492ED // 2^(39/64) +data8 0x0008ACE5422AA0DB // 2^(40/64) +data8 0x0008F1AE99157736 // 2^(41/64) +data8 0x00093737B0CDC5E5 // 2^(42/64) +data8 0x00097D829FDE4E50 // 2^(43/64) +data8 0x0009C49182A3F090 // 2^(44/64) +data8 0x000A0C667B5DE565 // 2^(45/64) +data8 0x000A5503B23E255D // 2^(46/64) +data8 0x000A9E6B5579FDBF // 2^(47/64) +data8 0x000AE89F995AD3AD // 2^(48/64) +data8 0x000B33A2B84F15FB // 2^(49/64) +data8 0x000B7F76F2FB5E47 // 2^(50/64) +data8 0x000BCC1E904BC1D2 // 2^(51/64) +data8 0x000C199BDD85529C // 2^(52/64) +data8 0x000C67F12E57D14B // 2^(53/64) +data8 0x000CB720DCEF9069 // 2^(54/64) +data8 0x000D072D4A07897C // 2^(55/64) +data8 0x000D5818DCFBA487 // 2^(56/64) +data8 0x000DA9E603DB3285 // 2^(57/64) +data8 0x000DFC97337B9B5F // 2^(58/64) +data8 0x000E502EE78B3FF6 // 2^(59/64) +data8 0x000EA4AFA2A490DA // 2^(60/64) +data8 0x000EFA1BEE615A27 // 2^(61/64) +data8 0x000F50765B6E4540 // 2^(62/64) +data8 0x000FA7C1819E90D8 // 2^(63/64) +LOCAL_OBJECT_END(_expf_table) + + +.section .text +GLOBAL_IEEE754_ENTRY(expm1f) + +{ .mlx + getf.exp rSignexp_x = f8 // Must recompute if x unorm + movl r64DivLn2 = 0x40571547652B82FE // 64/ln(2) +} +{ .mlx + addl rTblAddr = @ltoff(_expf_table),gp + movl rRightShifter = 0x43E8000000000000 // DP Right Shifter +} +;; + +{ .mfi + // point to the beginning of the table + ld8 rTblAddr = [rTblAddr] + fclass.m p14, p0 = f8 , 0x22 // test for -INF + mov rExp_mask = 0x1ffff // Exponent mask +} +{ .mfi + nop.m 0 + fnorm.s1 fNormX = f8 // normalized x + nop.i 0 +} +;; + +{ .mfi + setf.d f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg + fclass.m p9, p0 = f8 , 0x0b // test for x unorm + mov rExp_bias = 0xffff // Exponent bias +} +{ .mlx + // load Right Shifter to FP reg + setf.d fRightShifter = rRightShifter + movl rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR +} +;; + +{ .mfi + ldfpd fA8, fA7 = [rTblAddr], 16 + fcmp.eq.s1 p13, p0 = f0, f8 // test for x = 0.0 + mov rExp_half = 0xfffe +} +{ .mfb + setf.d fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg + nop.f 0 +(p9) br.cond.spnt EXPM1_UNORM // Branch if x unorm +} +;; + +EXPM1_COMMON: +{ .mfb + ldfpd fA6, fA5 = [rTblAddr], 16 +(p14) fms.s.s0 f8 = f0, f0, f1 // result if x = -inf +(p14) br.ret.spnt b0 // exit here if x = -inf +} +;; + +{ .mfb + ldfpd fA4, fA3 = [rTblAddr], 16 + fclass.m p15, p0 = f8 , 0x1e1 // test for NaT,NaN,+Inf +(p13) br.ret.spnt b0 // exit here if x =0.0, result is x +} +;; + +{ .mfi + // overflow thresholds + ldfps fMIN_SGL_OFLOW_ARG, fMAX_SGL_NORM_ARG = [rTblAddr], 8 + fma.s1 fXsq = fNormX, fNormX, f0 // x^2 for small path + and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x +} +{ .mlx + nop.m 0 + movl rM1_lim = 0xc1c00000 // Minus -1 limit (-24.0), SP +} +;; + +{ .mfi + setf.exp fA2 = rExp_half + // x*(64/ln(2)) + Right Shifter + fma.s1 fNint = fNormX, f64DivLn2, fRightShifter + sub rExp_x = rExp_x, rExp_bias // True exponent of x +} +{ .mfb + nop.m 0 +(p15) fma.s.s0 f8 = f8, f1, f0 // result if x = NaT,NaN,+Inf +(p15) br.ret.spnt b0 // exit here if x = NaT,NaN,+Inf +} +;; + +{ .mfi + setf.s fMAX_SGL_MINUS_1_ARG = rM1_lim // -1 threshold, -24.0 + nop.f 0 + cmp.gt p7, p8 = -2, rExp_x // Test |x| < 2^(-2) +} +;; + +{ .mfi +(p7) cmp.gt.unc p6, p7 = -40, rExp_x // Test |x| < 2^(-40) + fma.s1 fA87 = fA8, fNormX, fA7 // Small path, A8*x+A7 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA65 = fA6, fNormX, fA5 // Small path, A6*x+A5 + nop.i 0 +} +;; + +{ .mfb + nop.m 0 +(p6) fma.s.s0 f8 = f8, f8, f8 // If x < 2^-40, result=x+x*x +(p6) br.ret.spnt b0 // Exit if x < 2^-40 +} +;; + +{ .mfi + nop.m 0 + // check for overflow + fcmp.gt.s1 p15, p14 = fNormX, fMIN_SGL_OFLOW_ARG + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fN = fNint, f1, fRightShifter // n in FP register + nop.i 0 +} +;; + +{ .mfi + nop.m 0 +(p7) fma.s1 fA43 = fA4, fNormX, fA3 // Small path, A4*x+A3 + nop.i 0 +} +;; + +{ .mfi + getf.sig rNJ = fNint // bits of n, j +(p7) fma.s1 fA8765 = fA87, fXsq, fA65 // Small path, A87*xsq+A65 + nop.i 0 +} +{ .mfb + nop.m 0 +(p7) fma.s1 fX3 = fXsq, fNormX, f0 // Small path, x^3 + // branch out if overflow +(p15) br.cond.spnt EXPM1_CERTAIN_OVERFLOW +} +;; + +{ .mfi + addl rN = 0xffff-63, rNJ // biased and shifted n + fnma.s1 fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64 + extr.u rJ = rNJ , 0 , 6 // bits of j +} +;; + +{ .mfi + shladd rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table + // check for certain -1 + fcmp.le.s1 p13, p0 = fNormX, fMAX_SGL_MINUS_1_ARG + shr rN = rN, 6 // biased n +} +{ .mfi + nop.m 0 +(p7) fma.s1 fA432 = fA43, fNormX, fA2 // Small path, A43*x+A2 + nop.i 0 +} +;; + +{ .mfi + ld8 rJ = [rJ] + nop.f 0 + shl rN = rN , 52 // 2^n bits in DP format +} +;; + +{ .mmi + or rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format +(p13) mov rTmp = 1 // Make small value for -1 path + nop.i 0 +} +;; + +{ .mfi + setf.d fT = rN // 2^n + // check for possible overflow (only happens if input higher precision) +(p14) fcmp.gt.s1 p14, p0 = fNormX, fMAX_SGL_NORM_ARG + nop.i 0 +} +{ .mfi + nop.m 0 +(p7) fma.s1 fA8765432 = fA8765, fX3, fA432 // A8765*x^3+A432 + nop.i 0 +} +;; + +{ .mfi +(p13) setf.exp fTmp = rTmp // Make small value for -1 path + fma.s1 fP = fA3, fR, fA2 // A3*R + A2 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s1 fRSqr = fR, fR, f0 // R^2 +(p13) br.cond.spnt EXPM1_CERTAIN_MINUS_ONE // Branch if x < -24.0 +} +;; + +{ .mfb + nop.m 0 +(p7) fma.s.s0 f8 = fA8765432, fXsq, fNormX // Small path, + // result=xsq*A8765432+x +(p7) br.ret.spnt b0 // Exit if 2^-40 <= |x| < 2^-2 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fP = fP, fRSqr, fR // P = (A3*R + A2)*Rsqr + R + nop.i 0 +} +;; + +{ .mfb + nop.m 0 + fms.s1 fTm1 = fT, f1, f1 // T - 1.0 +(p14) br.cond.spnt EXPM1_POSSIBLE_OVERFLOW +} +;; + +{ .mfb + nop.m 0 + fma.s.s0 f8 = fP, fT, fTm1 + br.ret.sptk b0 // Result for main path + // minus_one_limit < x < -2^-2 + // and +2^-2 <= x < overflow_limit +} +;; + +// Here if x unorm +EXPM1_UNORM: +{ .mfb + getf.exp rSignexp_x = fNormX // Must recompute if x unorm + fcmp.eq.s0 p6, p0 = f8, f0 // Set D flag + br.cond.sptk EXPM1_COMMON +} +;; + +// here if result will be -1 and inexact, x <= -24.0 +EXPM1_CERTAIN_MINUS_ONE: +{ .mfb + nop.m 0 + fms.s.s0 f8 = fTmp, fTmp, f1 // Result -1, and Inexact set + br.ret.sptk b0 +} +;; + +EXPM1_POSSIBLE_OVERFLOW: + +// Here if fMAX_SGL_NORM_ARG < x < fMIN_SGL_OFLOW_ARG +// This cannot happen if input is a single, only if input higher precision. +// Overflow is a possibility, not a certainty. + +// Recompute result using status field 2 with user's rounding mode, +// and wre set. If result is larger than largest single, then we have +// overflow + +{ .mfi + mov rGt_ln = 0x1007f // Exponent for largest sgl + 1 ulp + fsetc.s2 0x7F,0x42 // Get user's round mode, set wre + nop.i 0 +} +;; + +{ .mfi + setf.exp fGt_pln = rGt_ln // Create largest single + 1 ulp + fma.s.s2 fWre_urm_f8 = fP, fT, fTm1 // Result with wre set + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fsetc.s2 0x7F,0x40 // Turn off wre in sf2 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fcmp.ge.s1 p6, p0 = fWre_urm_f8, fGt_pln // Test for overflow + nop.i 0 +} +;; + +{ .mfb + nop.m 0 + nop.f 0 +(p6) br.cond.spnt EXPM1_CERTAIN_OVERFLOW // Branch if overflow +} +;; + +{ .mfb + nop.m 0 + fma.s.s0 f8 = fP, fT, fTm1 + br.ret.sptk b0 // Exit if really no overflow +} +;; + +// here if overflow +EXPM1_CERTAIN_OVERFLOW: +{ .mmi + addl rTmp = 0x1FFFE, r0;; + setf.exp fTmp = rTmp + nop.i 999 +} +;; + +{ .mfi + alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers + fmerge.s FR_X = fNormX,fNormX + nop.i 0 +} +{ .mfb + mov GR_Parameter_TAG = 43 + fma.s.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region +} +;; + +GLOBAL_IEEE754_END(expm1f) + + +LOCAL_LIBM_ENTRY(__libm_error_region) +.prologue +{ .mfi + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 999 +.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 + stfs [GR_Parameter_Y] = FR_Y,16 // Store 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 +{ .mfi + stfs [GR_Parameter_X] = FR_X // Store Parameter 1 on stack + nop.f 0 + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address +} +{ .mib + stfs [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 + add GR_Parameter_RESULT = 48,sp + nop.m 0 + nop.i 0 +};; + +{ .mmi + ldfs 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# |