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Diffstat (limited to 'sysdeps/ia64/fpu/e_coshf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_coshf.S | 711 |
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diff --git a/sysdeps/ia64/fpu/e_coshf.S b/sysdeps/ia64/fpu/e_coshf.S new file mode 100644 index 0000000000..97cb4e1771 --- /dev/null +++ b/sysdeps/ia64/fpu/e_coshf.S @@ -0,0 +1,711 @@ +.file "coshf.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 +// 02/16/00 The error tag for coshf overflow changed to 65 (from 64). +// 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. +// 05/07/01 Reworked to improve speed of all paths +// 05/20/02 Cleaned up namespace and sf0 syntax +// 11/15/02 Improved algorithm based on expf +// 03/31/05 Reformatted delimiters between data tables +// +// API +//********************************************************************* +// float coshf(float) +// +// Overview of operation +//********************************************************************* +// Case 1: 0 < |x| < 0.25 +// Evaluate cosh(x) by a 8th order polynomial +// Care is take for the order of multiplication; and A2 is not exactly 1/4!, +// A3 is not exactly 1/6!, etc. +// cosh(x) = 1 + (A1*x^2 + A2*x^4 + A3*x^6 + A4*x^8) +// +// Case 2: 0.25 < |x| < 89.41598 +// Algorithm is based on the identity cosh(x) = ( exp(x) + exp(-x) ) / 2. +// The algorithm for exp is described as below. There are a number of +// economies from evaluating both exp(x) and exp(-x). Although we +// are evaluating both quantities, only where the quantities diverge do we +// duplicate the computations. The basic algorithm for exp(x) 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 +// exp(x) = T + T*P + +// Special values +//********************************************************************* +// coshf(+0) = 1.0 +// coshf(-0) = 1.0 + +// coshf(+qnan) = +qnan +// coshf(-qnan) = -qnan +// coshf(+snan) = +qnan +// coshf(-snan) = -qnan + +// coshf(-inf) = +inf +// coshf(+inf) = +inf + +// Overflow and Underflow +//********************************************************************* +// coshf(x) = largest single normal when +// x = 89.41598 = 0x42b2d4fc +// +// There is no underflow. + +// Registers used +//********************************************************************* +// Floating Point registers used: +// f8 input, output +// f6,f7, f9 -> f15, f32 -> f45 + +// General registers used: +// r2, r3, r16 -> r38 + +// Predicate registers used: +// p6 -> p15 + +// Assembly macros +//********************************************************************* +// integer registers used +// scratch +rNJ = r2 +rNJ_neg = r3 + +rJ_neg = r16 +rN_neg = r17 +rSignexp_x = r18 +rExp_x = r18 +rExp_mask = r19 +rExp_bias = r20 +rAd1 = r21 +rAd2 = r22 +rJ = r23 +rN = r24 +rTblAddr = r25 +rA3 = r26 +rExpHalf = r27 +rLn2Div64 = r28 +rGt_ln = r29 +r17ones_m1 = r29 +rRightShifter = r30 +rJ_mask = r30 +r64DivLn2 = r31 +rN_mask = 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 +fT = f33 +fMIN_SGL_OFLOW_ARG = f34 +fMAX_SGL_NORM_ARG = f35 +fRSqr = f36 +fA1 = f37 +fA21 = f37 +fA4 = f38 +fA43 = f38 +fA4321 = f38 +fX4 = f39 +fTmp = f39 +fGt_pln = f39 +fWre_urm_f8 = f40 +fXsq = f40 +fP_neg = f41 +fT_neg = f42 +fExp = f43 +fExp_neg = f44 +fAbsX = f45 + + +RODATA +.align 16 + +LOCAL_OBJECT_START(_coshf_table) +data4 0x42b2d4fd // Smallest single arg to overflow single result +data4 0x42b2d4fc // Largest single arg to give normal single result +data4 0x00000000 // pad +data4 0x00000000 // pad +// +// 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(_coshf_table) + +LOCAL_OBJECT_START(cosh_p_table) +data8 0x3efa3001dcf5905b // A4 +data8 0x3f56c1437543543e // A3 +data8 0x3fa5555572601504 // A2 +data8 0x3fdfffffffe2f097 // A1 +LOCAL_OBJECT_END(cosh_p_table) + + +.section .text +GLOBAL_IEEE754_ENTRY(coshf) + +{ .mlx + getf.exp rSignexp_x = f8 // Must recompute if x unorm + movl r64DivLn2 = 0x40571547652B82FE // 64/ln(2) +} +{ .mlx + addl rTblAddr = @ltoff(_coshf_table),gp + movl rRightShifter = 0x43E8000000000000 // DP Right Shifter +} +;; + +{ .mfi + // point to the beginning of the table + ld8 rTblAddr = [rTblAddr] + fclass.m p6, p0 = f8, 0x0b // Test for x=unorm + addl rA3 = 0x3E2AA, r0 // high bits of 1.0/6.0 rounded to SP +} +{ .mfi + nop.m 0 + fnorm.s1 fNormX = f8 // normalized x + addl rExpHalf = 0xFFFE, r0 // exponent of 1/2 +} +;; + +{ .mfi + setf.d f64DivLn2 = r64DivLn2 // load 64/ln(2) to FP reg + fclass.m p15, p0 = f8, 0x1e3 // test for NaT,NaN,Inf + nop.i 0 +} +{ .mlx + // load Right Shifter to FP reg + setf.d fRightShifter = rRightShifter + movl rLn2Div64 = 0x3F862E42FEFA39EF // DP ln(2)/64 in GR +} +;; + +{ .mfi + mov rExp_mask = 0x1ffff + fcmp.eq.s1 p13, p0 = f0, f8 // test for x = 0.0 + shl rA3 = rA3, 12 // 0x3E2AA000, approx to 1.0/6.0 in SP +} +{ .mfb + nop.m 0 + nop.f 0 +(p6) br.cond.spnt COSH_UNORM // Branch if x=unorm +} +;; + +COSH_COMMON: +{ .mfi + setf.exp fA2 = rExpHalf // load A2 to FP reg + nop.f 0 + mov rExp_bias = 0xffff +} +{ .mfb + setf.d fLn2Div64 = rLn2Div64 // load ln(2)/64 to FP reg +(p15) fma.s.s0 f8 = f8, f8, f0 // result if x = NaT,NaN,Inf +(p15) br.ret.spnt b0 // exit here if x = NaT,NaN,Inf +} +;; + +{ .mfi + // min overflow and max normal threshold + ldfps fMIN_SGL_OFLOW_ARG, fMAX_SGL_NORM_ARG = [rTblAddr], 8 + nop.f 0 + and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x +} +{ .mfb + setf.s fA3 = rA3 // load A3 to FP reg +(p13) fma.s.s0 f8 = f1, f1, f0 // result if x = 0.0 +(p13) br.ret.spnt b0 // exit here if x =0.0 +} +;; + +{ .mfi + sub rExp_x = rExp_x, rExp_bias // True exponent of x + fmerge.s fAbsX = f0, fNormX // Form |x| + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + // x*(64/ln(2)) + Right Shifter + fma.s1 fNint = fNormX, f64DivLn2, fRightShifter + add rTblAddr = 8, rTblAddr +} +{ .mfb + cmp.gt p7, p0 = -2, rExp_x // Test |x| < 2^(-2) + fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path +(p7) br.cond.spnt COSH_SMALL // Branch if 0 < |x| < 2^-2 +} +;; + +{ .mfi + nop.m 0 + // check for overflow + fcmp.ge.s1 p12, p13 = fAbsX, fMIN_SGL_OFLOW_ARG + mov rJ_mask = 0x3f // 6-bit mask for J +} +;; + +{ .mfb + nop.m 0 + fms.s1 fN = fNint, f1, fRightShifter // n in FP register + // branch out if overflow +(p12) br.cond.spnt COSH_CERTAIN_OVERFLOW +} +;; + +{ .mfi + getf.sig rNJ = fNint // bits of n, j + // check for possible overflow + fcmp.gt.s1 p13, p0 = fAbsX, fMAX_SGL_NORM_ARG + nop.i 0 +} +;; + +{ .mfi + addl rN = 0xFFBF - 63, rNJ // biased and shifted n-1,j + fnma.s1 fR = fLn2Div64, fN, fNormX // R = x - N*ln(2)/64 + and rJ = rJ_mask, rNJ // bits of j +} +{ .mfi + sub rNJ_neg = r0, rNJ // bits of n, j for -x + nop.f 0 + andcm rN_mask = -1, rJ_mask // 0xff...fc0 to mask N +} +;; + +{ .mfi + shladd rJ = rJ, 3, rTblAddr // address in the 2^(j/64) table + nop.f 0 + and rN = rN_mask, rN // biased, shifted n-1 +} +{ .mfi + addl rN_neg = 0xFFBF - 63, rNJ_neg // -x biased, shifted n-1,j + nop.f 0 + and rJ_neg = rJ_mask, rNJ_neg // bits of j for -x +} +;; + +{ .mfi + ld8 rJ = [rJ] // Table value + nop.f 0 + shl rN = rN, 46 // 2^(n-1) bits in DP format +} +{ .mfi + shladd rJ_neg = rJ_neg, 3, rTblAddr // addr in 2^(j/64) table -x + nop.f 0 + and rN_neg = rN_mask, rN_neg // biased, shifted n-1 for -x +} +;; + +{ .mfi + ld8 rJ_neg = [rJ_neg] // Table value for -x + nop.f 0 + shl rN_neg = rN_neg, 46 // 2^(n-1) bits in DP format for -x +} +;; + +{ .mfi + or rN = rN, rJ // bits of 2^n * 2^(j/64) in DP format + nop.f 0 + nop.i 0 +} +;; + +{ .mmf + setf.d fT = rN // 2^(n-1) * 2^(j/64) + or rN_neg = rN_neg, rJ_neg // -x bits of 2^n * 2^(j/64) in DP + fma.s1 fRSqr = fR, fR, f0 // R^2 +} +;; + +{ .mfi + setf.d fT_neg = rN_neg // 2^(n-1) * 2^(j/64) for -x + fma.s1 fP = fA3, fR, fA2 // A3*R + A2 + nop.i 0 +} +{ .mfi + nop.m 0 + fnma.s1 fP_neg = fA3, fR, fA2 // A3*R + A2 for -x + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fP = fP, fRSqr, fR // P = (A3*R + A2)*R^2 + R + nop.i 0 +} +{ .mfi + nop.m 0 + fms.s1 fP_neg = fP_neg, fRSqr, fR // P = (A3*R + A2)*R^2 + R, -x + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fmpy.s0 fTmp = fLn2Div64, fLn2Div64 // Force inexact + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fExp = fP, fT, fT // exp(x)/2 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s1 fExp_neg = fP_neg, fT_neg, fT_neg // exp(-x)/2 + // branch out if possible overflow result +(p13) br.cond.spnt COSH_POSSIBLE_OVERFLOW +} +;; + +{ .mfb + nop.m 0 + // final result in the absence of overflow + fma.s.s0 f8 = fExp, f1, fExp_neg // result = (exp(x)+exp(-x))/2 + // exit here in the absence of overflow + br.ret.sptk b0 // Exit main path, 0.25 <= |x| < 89.41598 +} +;; + +// Here if 0 < |x| < 0.25. Evaluate 8th order polynomial. +COSH_SMALL: +{ .mmi + add rAd1 = 0x200, rTblAddr + add rAd2 = 0x210, rTblAddr + nop.i 0 +} +;; + +{ .mmi + ldfpd fA4, fA3 = [rAd1] + ldfpd fA2, fA1 = [rAd2] + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fX4 = fXsq, fXsq, f0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fA43 = fXsq, fA4, fA3 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fA21 = fXsq, fA2, fA1 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fA4321 = fX4, fA43, fA21 + nop.i 0 +} +;; + +// Dummy multiply to generate inexact +{ .mfi + nop.m 0 + fmpy.s0 fTmp = fA4, fA4 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s.s0 f8 = fA4321, fXsq, f1 + br.ret.sptk b0 // Exit if 0 < |x| < 0.25 +} +;; + +COSH_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 single + 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, fT // 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 COSH_CERTAIN_OVERFLOW // Branch if overflow +} +;; + +{ .mfb + nop.m 0 + fma.s.s0 f8 = fP, fT, fT + br.ret.sptk b0 // Exit if really no overflow +} +;; + +// here if overflow +COSH_CERTAIN_OVERFLOW: +{ .mmi + addl r17ones_m1 = 0x1FFFE, r0 +;; + setf.exp fTmp = r17ones_m1 + nop.i 0 +} +;; + +{ .mfi + alloc r32 = ar.pfs, 0, 3, 4, 0 // get some registers + fmerge.s FR_X = f8,f8 + nop.i 0 +} +{ .mfb + mov GR_Parameter_TAG = 65 + fma.s.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region +} +;; + +// Here if x unorm +COSH_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 COSH_COMMON // Return to main path +} +;; + +GLOBAL_IEEE754_END(coshf) + + +LOCAL_LIBM_ENTRY(__libm_error_region) +.prologue +{ .mfi + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs +} +{ .mfi +.fframe 64 + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp +};; +{ .mmi + 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# |