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Diffstat (limited to 'sysdeps/ia64/fpu/s_expm1f.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_expm1f.S | 671 |
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diff --git a/sysdeps/ia64/fpu/s_expm1f.S b/sysdeps/ia64/fpu/s_expm1f.S deleted file mode 100644 index 8996977..0000000 --- a/sysdeps/ia64/fpu/s_expm1f.S +++ /dev/null @@ -1,671 +0,0 @@ -.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# |