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Diffstat (limited to 'ports/sysdeps/ia64/fpu/s_expm1.S')
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diff --git a/ports/sysdeps/ia64/fpu/s_expm1.S b/ports/sysdeps/ia64/fpu/s_expm1.S new file mode 100644 index 0000000000..f0b911e295 --- /dev/null +++ b/ports/sysdeps/ia64/fpu/s_expm1.S @@ -0,0 +1,886 @@ +.file "exp_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 exp +// 03/31/05 Reformatted delimiters between data tables + +// API +//============================================================== +// double expm1(double) + +// Overview of operation +//============================================================== +// 1. Inputs of Nan, Inf, Zero, NatVal handled with special paths +// +// 2. |x| < 2^-60 +// Result = x, computed by x + x*x to handle appropriate flags and rounding +// +// 3. 2^-60 <= |x| < 2^-2 +// Result determined by 13th order Taylor series polynomial +// expm1f(x) = x + Q2*x^2 + ... + Q13*x^13 +// +// 4. x < -48.0 +// Here we know result is essentially -1 + eps, where eps only affects +// rounded result. Set I. +// +// 5. x >= 709.7827 +// Result overflows. Set I, O, and call error support +// +// 6. 2^-2 <= x < 709.7827 or -48.0 <= 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 * 128/log2 +// n = int(w) +// x = n log2/128 + r + delta + +// n = 128M + index_1 + 2^4 index_2 +// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta + +// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta) +// Construct 2^M +// Get 2^(index_1/128) from table_1; +// Get 2^(index_2/8) from table_2; +// Calculate exp(r) by series by 5th order polynomial +// r = x - n (log2/128)_high +// delta = - n (log2/128)_low +// Calculate exp(delta) as 1 + delta + + +// Special values +//============================================================== +// expm1(+0) = +0.0 +// expm1(-0) = -0.0 + +// expm1(+qnan) = +qnan +// expm1(-qnan) = -qnan +// expm1(+snan) = +qnan +// expm1(-snan) = -qnan + +// expm1(-inf) = -1.0 +// expm1(+inf) = +inf + +// Overflow and Underflow +//======================= +// expm1(x) = largest double normal when +// x = 709.7827 = 40862e42fefa39ef +// +// Underflow is handled as described in case 2 above. + + +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f9 -> f15, f32 -> f75 + +// General registers used: +// r14 -> r40 + +// Predicate registers used: +// p6 -> p15 + +// Assembly macros +//============================================================== + +rRshf = r14 +rAD_TB1 = r15 +rAD_T1 = r15 +rAD_TB2 = r16 +rAD_T2 = r16 +rAD_Ln2_lo = r17 +rAD_P = r17 + +rN = r18 +rIndex_1 = r19 +rIndex_2_16 = r20 + +rM = r21 +rBiased_M = r21 +rIndex_1_16 = r22 +rSignexp_x = r23 +rExp_x = r24 +rSig_inv_ln2 = r25 + +rAD_Q1 = r26 +rAD_Q2 = r27 +rTmp = r27 +rExp_bias = r28 +rExp_mask = r29 +rRshf_2to56 = r30 + +rGt_ln = r31 +rExp_2tom56 = r31 + + +GR_SAVE_B0 = r33 +GR_SAVE_PFS = r34 +GR_SAVE_GP = r35 +GR_SAVE_SP = r36 + +GR_Parameter_X = r37 +GR_Parameter_Y = r38 +GR_Parameter_RESULT = r39 +GR_Parameter_TAG = r40 + + +FR_X = f10 +FR_Y = f1 +FR_RESULT = f8 + +fRSHF_2TO56 = f6 +fINV_LN2_2TO63 = f7 +fW_2TO56_RSH = f9 +f2TOM56 = f11 +fP5 = f12 +fP54 = f50 +fP5432 = f50 +fP4 = f13 +fP3 = f14 +fP32 = f14 +fP2 = f15 + +fLn2_by_128_hi = f33 +fLn2_by_128_lo = f34 + +fRSHF = f35 +fNfloat = f36 +fW = f37 +fR = f38 +fF = f39 + +fRsq = f40 +fRcube = f41 + +f2M = f42 +fS1 = f43 +fT1 = f44 + +fMIN_DBL_OFLOW_ARG = f45 +fMAX_DBL_MINUS_1_ARG = f46 +fMAX_DBL_NORM_ARG = f47 +fP_lo = f51 +fP_hi = f52 +fP = f53 +fS = f54 + +fNormX = f56 + +fWre_urm_f8 = f57 + +fGt_pln = f58 +fTmp = f58 + +fS2 = f59 +fT2 = f60 +fSm1 = f61 + +fXsq = f62 +fX6 = f63 +fX4 = f63 +fQ7 = f64 +fQ76 = f64 +fQ7654 = f64 +fQ765432 = f64 +fQ6 = f65 +fQ5 = f66 +fQ54 = f66 +fQ4 = f67 +fQ3 = f68 +fQ32 = f68 +fQ2 = f69 +fQD = f70 +fQDC = f70 +fQDCBA = f70 +fQDCBA98 = f70 +fQDCBA98765432 = f70 +fQC = f71 +fQB = f72 +fQBA = f72 +fQA = f73 +fQ9 = f74 +fQ98 = f74 +fQ8 = f75 + +// Data tables +//============================================================== + +RODATA +.align 16 + +// ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** + +// double-extended 1/ln(2) +// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88 +// 3fff b8aa 3b29 5c17 f0bc +// For speed the significand will be loaded directly with a movl and setf.sig +// and the exponent will be bias+63 instead of bias+0. Thus subsequent +// computations need to scale appropriately. +// The constant 128/ln(2) is needed for the computation of w. This is also +// obtained by scaling the computations. +// +// Two shifting constants are loaded directly with movl and setf.d. +// 1. fRSHF_2TO56 = 1.1000..00 * 2^(63-7) +// This constant is added to x*1/ln2 to shift the integer part of +// x*128/ln2 into the rightmost bits of the significand. +// The result of this fma is fW_2TO56_RSH. +// 2. fRSHF = 1.1000..00 * 2^(63) +// This constant is subtracted from fW_2TO56_RSH * 2^(-56) to give +// the integer part of w, n, as a floating-point number. +// The result of this fms is fNfloat. + + +LOCAL_OBJECT_START(exp_Table_1) +data8 0x40862e42fefa39f0 // smallest dbl overflow arg +data8 0xc048000000000000 // approx largest arg for minus one result +data8 0x40862e42fefa39ef // largest dbl arg to give normal dbl result +data8 0x0 // pad +data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi +data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo +// +// Table 1 is 2^(index_1/128) where +// index_1 goes from 0 to 15 +// +data8 0x8000000000000000 , 0x00003FFF +data8 0x80B1ED4FD999AB6C , 0x00003FFF +data8 0x8164D1F3BC030773 , 0x00003FFF +data8 0x8218AF4373FC25EC , 0x00003FFF +data8 0x82CD8698AC2BA1D7 , 0x00003FFF +data8 0x8383594EEFB6EE37 , 0x00003FFF +data8 0x843A28C3ACDE4046 , 0x00003FFF +data8 0x84F1F656379C1A29 , 0x00003FFF +data8 0x85AAC367CC487B15 , 0x00003FFF +data8 0x8664915B923FBA04 , 0x00003FFF +data8 0x871F61969E8D1010 , 0x00003FFF +data8 0x87DB357FF698D792 , 0x00003FFF +data8 0x88980E8092DA8527 , 0x00003FFF +data8 0x8955EE03618E5FDD , 0x00003FFF +data8 0x8A14D575496EFD9A , 0x00003FFF +data8 0x8AD4C6452C728924 , 0x00003FFF +LOCAL_OBJECT_END(exp_Table_1) + +// Table 2 is 2^(index_1/8) where +// index_2 goes from 0 to 7 +LOCAL_OBJECT_START(exp_Table_2) +data8 0x8000000000000000 , 0x00003FFF +data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF +data8 0x9837F0518DB8A96F , 0x00003FFF +data8 0xA5FED6A9B15138EA , 0x00003FFF +data8 0xB504F333F9DE6484 , 0x00003FFF +data8 0xC5672A115506DADD , 0x00003FFF +data8 0xD744FCCAD69D6AF4 , 0x00003FFF +data8 0xEAC0C6E7DD24392F , 0x00003FFF +LOCAL_OBJECT_END(exp_Table_2) + + +LOCAL_OBJECT_START(exp_p_table) +data8 0x3f8111116da21757 //P5 +data8 0x3fa55555d787761c //P4 +data8 0x3fc5555555555414 //P3 +data8 0x3fdffffffffffd6a //P2 +LOCAL_OBJECT_END(exp_p_table) + +LOCAL_OBJECT_START(exp_Q1_table) +data8 0x3de6124613a86d09 // QD = 1/13! +data8 0x3e21eed8eff8d898 // QC = 1/12! +data8 0x3ec71de3a556c734 // Q9 = 1/9! +data8 0x3efa01a01a01a01a // Q8 = 1/8! +data8 0x8888888888888889,0x3ff8 // Q5 = 1/5! +data8 0xaaaaaaaaaaaaaaab,0x3ffc // Q3 = 1/3! +data8 0x0,0x0 // Pad to avoid bank conflicts +LOCAL_OBJECT_END(exp_Q1_table) + +LOCAL_OBJECT_START(exp_Q2_table) +data8 0x3e5ae64567f544e4 // QB = 1/11! +data8 0x3e927e4fb7789f5c // QA = 1/10! +data8 0x3f2a01a01a01a01a // Q7 = 1/7! +data8 0x3f56c16c16c16c17 // Q6 = 1/6! +data8 0xaaaaaaaaaaaaaaab,0x3ffa // Q4 = 1/4! +data8 0x8000000000000000,0x3ffe // Q2 = 1/2! +LOCAL_OBJECT_END(exp_Q2_table) + + +.section .text +GLOBAL_IEEE754_ENTRY(expm1) + +{ .mlx + getf.exp rSignexp_x = f8 // Must recompute if x unorm + movl rSig_inv_ln2 = 0xb8aa3b295c17f0bc // signif of 1/ln2 +} +{ .mlx + addl rAD_TB1 = @ltoff(exp_Table_1), gp + movl rRshf_2to56 = 0x4768000000000000 // 1.10000 2^(63+56) +} +;; + +// We do this fnorm right at the beginning to normalize +// any input unnormals so that SWA is not taken. +{ .mfi + ld8 rAD_TB1 = [rAD_TB1] + fclass.m p6,p0 = f8,0x0b // Test for x=unorm + mov rExp_mask = 0x1ffff +} +{ .mfi + mov rExp_bias = 0xffff + fnorm.s1 fNormX = f8 + mov rExp_2tom56 = 0xffff-56 +} +;; + +// Form two constants we need +// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128 +// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand + +{ .mfi + setf.sig fINV_LN2_2TO63 = rSig_inv_ln2 // form 1/ln2 * 2^63 + fclass.m p8,p0 = f8,0x07 // Test for x=0 + nop.i 0 +} +{ .mlx + setf.d fRSHF_2TO56 = rRshf_2to56 // Form 1.100 * 2^(63+56) + movl rRshf = 0x43e8000000000000 // 1.10000 2^63 for rshift +} +;; + +{ .mfi + setf.exp f2TOM56 = rExp_2tom56 // form 2^-56 for scaling Nfloat + fclass.m p9,p0 = f8,0x22 // Test for x=-inf + add rAD_TB2 = 0x140, rAD_TB1 // Point to Table 2 +} +{ .mib + add rAD_Q1 = 0x1e0, rAD_TB1 // Point to Q table for small path + add rAD_Ln2_lo = 0x30, rAD_TB1 // Point to ln2_by_128_lo +(p6) br.cond.spnt EXPM1_UNORM // Branch if x unorm +} +;; + +EXPM1_COMMON: +{ .mfi + ldfpd fMIN_DBL_OFLOW_ARG, fMAX_DBL_MINUS_1_ARG = [rAD_TB1],16 + fclass.m p10,p0 = f8,0x1e1 // Test for x=+inf, NaN, NaT + add rAD_Q2 = 0x50, rAD_Q1 // Point to Q table for small path +} +{ .mfb + nop.m 0 + nop.f 0 +(p8) br.ret.spnt b0 // Exit for x=0, return x +} +;; + +{ .mfi + ldfd fMAX_DBL_NORM_ARG = [rAD_TB1],16 + nop.f 0 + and rExp_x = rExp_mask, rSignexp_x // Biased exponent of x +} +{ .mfb + setf.d fRSHF = rRshf // Form right shift const 1.100 * 2^63 +(p9) fms.d.s0 f8 = f0,f0,f1 // quick exit for x=-inf +(p9) br.ret.spnt b0 +} +;; + +{ .mfi + ldfpd fQD, fQC = [rAD_Q1], 16 // Load coeff for small path + nop.f 0 + sub rExp_x = rExp_x, rExp_bias // True exponent of x +} +{ .mfb + ldfpd fQB, fQA = [rAD_Q2], 16 // Load coeff for small path +(p10) fma.d.s0 f8 = f8, f1, f0 // For x=+inf, NaN, NaT +(p10) br.ret.spnt b0 // Exit for x=+inf, NaN, NaT +} +;; + +{ .mfi + ldfpd fQ9, fQ8 = [rAD_Q1], 16 // Load coeff for small path + fma.s1 fXsq = fNormX, fNormX, f0 // x*x for small path + cmp.gt p7, p8 = -2, rExp_x // Test |x| < 2^(-2) +} +{ .mfi + ldfpd fQ7, fQ6 = [rAD_Q2], 16 // Load coeff for small path + nop.f 0 + nop.i 0 +} +;; + +{ .mfi + ldfe fQ5 = [rAD_Q1], 16 // Load coeff for small path + nop.f 0 + nop.i 0 +} +{ .mib + ldfe fQ4 = [rAD_Q2], 16 // Load coeff for small path +(p7) cmp.gt.unc p6, p7 = -60, rExp_x // Test |x| < 2^(-60) +(p7) br.cond.spnt EXPM1_SMALL // Branch if 2^-60 <= |x| < 2^-2 +} +;; + +// W = X * Inv_log2_by_128 +// By adding 1.10...0*2^63 we shift and get round_int(W) in significand. +// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing. + +{ .mfi + ldfe fLn2_by_128_hi = [rAD_TB1],32 + fma.s1 fW_2TO56_RSH = fNormX, fINV_LN2_2TO63, fRSHF_2TO56 + nop.i 0 +} +{ .mfb + ldfe fLn2_by_128_lo = [rAD_Ln2_lo] +(p6) fma.d.s0 f8 = f8, f8, f8 // If x < 2^-60, result=x+x*x +(p6) br.ret.spnt b0 // Exit if x < 2^-60 +} +;; + +// Divide arguments into the following categories: +// Certain minus one p11 - -inf < x <= MAX_DBL_MINUS_1_ARG +// Possible Overflow p14 - MAX_DBL_NORM_ARG < x < MIN_DBL_OFLOW_ARG +// Certain Overflow p15 - MIN_DBL_OFLOW_ARG <= x < +inf +// +// If the input is really a double arg, then there will never be "Possible +// Overflow" arguments. +// + +// After that last load, rAD_TB1 points to the beginning of table 1 + +{ .mfi + nop.m 0 + fcmp.ge.s1 p15,p14 = fNormX,fMIN_DBL_OFLOW_ARG + nop.i 0 +} +;; + +{ .mfi + add rAD_P = 0x80, rAD_TB2 + fcmp.le.s1 p11,p0 = fNormX,fMAX_DBL_MINUS_1_ARG + nop.i 0 +} +;; + +{ .mfb + ldfpd fP5, fP4 = [rAD_P] ,16 +(p14) fcmp.gt.unc.s1 p14,p0 = fNormX,fMAX_DBL_NORM_ARG +(p15) br.cond.spnt EXPM1_CERTAIN_OVERFLOW +} +;; + +// Nfloat = round_int(W) +// The signficand of fW_2TO56_RSH contains the rounded integer part of W, +// as a twos complement number in the lower bits (that is, it may be negative). +// That twos complement number (called N) is put into rN. + +// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56 +// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat. +// Thus, fNfloat contains the floating point version of N + +{ .mfb + ldfpd fP3, fP2 = [rAD_P] + fms.s1 fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF +(p11) br.cond.spnt EXPM1_CERTAIN_MINUS_ONE +} +;; + +{ .mfi + getf.sig rN = fW_2TO56_RSH + nop.f 0 + nop.i 0 +} +;; + +// rIndex_1 has index_1 +// rIndex_2_16 has index_2 * 16 +// rBiased_M has M +// rIndex_1_16 has index_1 * 16 + +// r = x - Nfloat * ln2_by_128_hi +// f = 1 - Nfloat * ln2_by_128_lo +{ .mfi + and rIndex_1 = 0x0f, rN + fnma.s1 fR = fNfloat, fLn2_by_128_hi, fNormX + shr rM = rN, 0x7 +} +{ .mfi + and rIndex_2_16 = 0x70, rN + fnma.s1 fF = fNfloat, fLn2_by_128_lo, f1 + nop.i 0 +} +;; + +// rAD_T1 has address of T1 +// rAD_T2 has address if T2 + +{ .mmi + add rBiased_M = rExp_bias, rM + add rAD_T2 = rAD_TB2, rIndex_2_16 + shladd rAD_T1 = rIndex_1, 4, rAD_TB1 +} +;; + +// Create Scale = 2^M +// Load T1 and T2 +{ .mmi + setf.exp f2M = rBiased_M + ldfe fT2 = [rAD_T2] + nop.i 0 +} +;; + +{ .mfi + ldfe fT1 = [rAD_T1] + fmpy.s0 fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fP54 = fR, fP5, fP4 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fP32 = fR, fP3, fP2 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fRsq = fR, fR, f0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fP5432 = fRsq, fP54, fP32 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fS2 = fF,fT2,f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fS1 = f2M,fT1,f0 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fP = fRsq, fP5432, fR + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fms.s1 fSm1 = fS1,fS2,f1 // S - 1.0 + nop.i 0 +} +{ .mfb + nop.m 0 + fma.s1 fS = fS1,fS2,f0 +(p14) br.cond.spnt EXPM1_POSSIBLE_OVERFLOW +} +;; + +{ .mfb + nop.m 0 + fma.d.s0 f8 = fS, fP, fSm1 + br.ret.sptk b0 // Normal path exit +} +;; + +// Here if 2^-60 <= |x| <2^-2 +// Compute 13th order polynomial +EXPM1_SMALL: +{ .mmf + ldfe fQ3 = [rAD_Q1], 16 + ldfe fQ2 = [rAD_Q2], 16 + fma.s1 fX4 = fXsq, fXsq, f0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQDC = fQD, fNormX, fQC + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fQBA = fQB, fNormX, fQA + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQ98 = fQ9, fNormX, fQ8 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fQ76= fQ7, fNormX, fQ6 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQ54 = fQ5, fNormX, fQ4 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fX6 = fX4, fXsq, f0 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fQ32= fQ3, fNormX, fQ2 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQDCBA = fQDC, fXsq, fQBA + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fQ7654 = fQ76, fXsq, fQ54 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQDCBA98 = fQDCBA, fXsq, fQ98 + nop.i 0 +} +{ .mfi + nop.m 0 + fma.s1 fQ765432 = fQ7654, fXsq, fQ32 + nop.i 0 +} +;; + +{ .mfi + nop.m 0 + fma.s1 fQDCBA98765432 = fQDCBA98, fX6, fQ765432 + nop.i 0 +} +;; + +{ .mfb + nop.m 0 + fma.d.s0 f8 = fQDCBA98765432, fXsq, fNormX + br.ret.sptk b0 // Exit small branch +} +;; + + +EXPM1_POSSIBLE_OVERFLOW: + +// Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG +// This cannot happen if input is a double, 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 double, then we have +// overflow + +{ .mfi + mov rGt_ln = 0x103ff // Exponent for largest dbl + 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 double + 1 ulp + fma.d.s2 fWre_urm_f8 = fS, fP, fSm1 // 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.d.s0 f8 = fS, fP, fSm1 + br.ret.sptk b0 // Exit if really no overflow +} +;; + +EXPM1_CERTAIN_OVERFLOW: +{ .mmi + sub rTmp = rExp_mask, r0, 1 +;; + setf.exp fTmp = rTmp + nop.i 0 +} +;; + +{ .mfi + alloc r32=ar.pfs,1,4,4,0 + fmerge.s FR_X = f8,f8 + nop.i 0 +} +{ .mfb + mov GR_Parameter_TAG = 41 + fma.d.s0 FR_RESULT = fTmp, fTmp, f0 // Set I,O and +INF result + br.cond.sptk __libm_error_region +} +;; + +// 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 <= -48.0 +EXPM1_CERTAIN_MINUS_ONE: +{ .mmi + mov rTmp = 1 +;; + setf.exp fTmp = rTmp + nop.i 0 +} +;; + +{ .mfb + nop.m 0 + fms.d.s0 FR_RESULT = fTmp, fTmp, f1 // Set I, rounded -1+eps result + br.ret.sptk b0 +} +;; + +GLOBAL_IEEE754_END(expm1) + + +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 + stfd [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 +{ .mib + stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 +} +{ .mib + stfd [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 + ldfd 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# |