| .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# |
