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Diffstat (limited to 'sysdeps/ia64/fpu/e_powf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_powf.S | 2066 |
1 files changed, 0 insertions, 2066 deletions
diff --git a/sysdeps/ia64/fpu/e_powf.S b/sysdeps/ia64/fpu/e_powf.S deleted file mode 100644 index 1406a94b65..0000000000 --- a/sysdeps/ia64/fpu/e_powf.S +++ /dev/null @@ -1,2066 +0,0 @@ -.file "powf.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 -// 02/03/00 Added p12 to definite over/under path. With odd power we did not -// maintain the sign of x in this path. -// 04/04/00 Unwind support added -// 04/19/00 pow(+-1,inf) now returns NaN -// pow(+-val, +-inf) returns 0 or inf, but now does not call error -// support -// Added s1 to fcvt.fx because invalid flag was incorrectly set. -// 08/15/00 Bundle added after call to __libm_error_support to properly -// set [the previously overwritten] GR_Parameter_RESULT. -// 09/07/00 Improved performance by eliminating bank conflicts and other stalls, -// and tweaking the critical path -// 09/08/00 Per c99, pow(+-1,inf) now returns 1, and pow(+1,nan) returns 1 -// 09/28/00 Updated NaN**0 path -// 01/20/01 Fixed denormal flag settings. -// 02/13/01 Improved speed. -// 03/19/01 Reordered exp polynomial to improve speed and eliminate monotonicity -// problem in round up, down, and to zero modes. Also corrected -// overflow result when x negative, y odd in round up, down, zero. -// 06/14/01 Added brace missing from bundle -// 12/10/01 Corrected case where x negative, 2^23 <= |y| < 2^24, y odd integer. -// 02/08/02 Fixed overflow/underflow cases that were not calling error support. -// 05/20/02 Cleaned up namespace and sf0 syntax -// 08/29/02 Improved Itanium 2 performance -// 02/10/03 Reordered header: .section, .global, .proc, .align -// 10/09/03 Modified algorithm to improve performance, reduce table size, and -// fix boundary case powf(2.0,-150.0) -// 03/31/05 Reformatted delimiters between data tables -// -// API -//============================================================== -// float powf(float x, float y) -// -// Overview of operation -//============================================================== -// -// Three steps... -// 1. Log(x) -// 2. y Log(x) -// 3. exp(y log(x)) -// -// This means we work with the absolute value of x and merge in the sign later. -// Log(x) = G + delta + r -rsq/2 + p -// G,delta depend on the exponent of x and table entries. The table entries are -// indexed by the exponent of x, called K. -// -// The G and delta come out of the reduction; r is the reduced x. -// -// B = frcpa(x) -// xB-1 is small means that B is the approximate inverse of x. -// -// Log(x) = Log( (1/B)(Bx) ) -// = Log(1/B) + Log(Bx) -// = Log(1/B) + Log( 1 + (Bx-1)) -// -// x = 2^K 1.x_1x_2.....x_52 -// B= frcpa(x) = 2^-k Cm -// Log(1/B) = Log(1/(2^-K Cm)) -// Log(1/B) = Log((2^K/ Cm)) -// Log(1/B) = K Log(2) + Log(1/Cm) -// -// Log(x) = K Log(2) + Log(1/Cm) + Log( 1 + (Bx-1)) -// -// If you take the significand of x, set the exponent to true 0, then Cm is -// the frcpa. We tabulate the Log(1/Cm) values. There are 256 of them. -// The frcpa table is indexed by 8 bits, the x_1 thru x_8. -// m = x_1x_2...x_8 is an 8-bit index. -// -// Log(1/Cm) = log(1/frcpa(1+m/256)) where m goes from 0 to 255. -// -// We tabluate as one double, T for single precision power -// -// Log(x) = (K Log(2)_hi + T) + (K Log(2)_lo) + Log( 1 + (Bx-1)) -// Log(x) = G + delta + Log( 1 + (Bx-1)) -// -// The Log( 1 + (Bx-1)) can be calculated as a series in r = Bx-1. -// -// Log( 1 + (Bx-1)) = r - rsq/2 + p -// where p = r^3(P0 + P1*r + P2*r^2) -// -// Then, -// -// yLog(x) = yG + y delta + y(r-rsq/2) + yp -// yLog(x) = Z1 + e3 + Z2 + Z3 -// -// -// exp(yLog(x)) = exp(Z1 + Z2) exp(Z3) exp(e3) -// -// -// exp(Z3) is another series. -// exp(e3) is approximated as f3 = 1 + e3 -// -// exp(Z1 + Z2) = exp(Z) -// Z (128/log2) = number of log2/128 in Z is N -// -// s = Z - N log2/128 -// -// exp(Z) = exp(s) exp(N log2/128) -// -// exp(r) = exp(Z - N log2/128) -// -// r = s + d = (Z - N (log2/128)_hi) -N (log2/128)_lo -// = Z - N (log2/128) -// -// Z = s+d +N (log2/128) -// -// exp(Z) = exp(s) (1+d) exp(N log2/128) -// -// N = M 128 + n -// -// N log2/128 = M log2 + n log2/128 -// -// n is 8 binary digits = n_7n_6...n_1 -// -// n log2/128 = n_7n_6n_5 16 log2/128 + n_4n_3n_2n_1 log2/128 -// n log2/128 = n_7n_6n_5 log2/8 + n_4n_3n_2n_1 log2/128 -// n log2/128 = I2 log2/8 + I1 log2/128 -// -// N log2/128 = M log2 + I2 log2/8 + I1 log2/128 -// -// exp(Z) = exp(s) (1+d) exp(log(2^M) + log(2^I2/8) + log(2^I1/128)) -// exp(Z) = exp(s) f12 (2^M) 2^I2/8 2^I1/128 -// -// I1, I2 are table indices. Use a series for exp(s). -// Then get exp(Z) -// -// exp(yLog(x)) = exp(Z) exp(Z3) f3 -// exp(yLog(x)) = exp(Z)f3 exp(Z3) -// exp(yLog(x)) = A exp(Z3) -// -// We actually calculate exp(Z3) -1. -// Then, -// exp(yLog(x)) = A + A( exp(Z3) -1) -// - -// Table Generation -//============================================================== - -// The log values -// ============== -// The operation (K*log2_hi) must be exact. K is the true exponent of x. -// If we allow gradual underflow (denormals), K can be represented in 12 bits -// (as a two's complement number). We assume 13 bits as an engineering -// precaution. -// -// +------------+----------------+-+ -// | 13 bits | 50 bits | | -// +------------+----------------+-+ -// 0 1 66 -// 2 34 -// -// So we want the lsb(log2_hi) to be 2^-50 -// We get log2 as a quad-extended (15-bit exponent, 128-bit significand) -// -// 0 fffe b17217f7d1cf79ab c9e3b39803f2f6af (4...) -// -// Consider numbering the bits left to right, starting at 0 thru 127. -// Bit 0 is the 2^-1 bit; bit 49 is the 2^-50 bit. -// -// ...79ab -// 0111 1001 1010 1011 -// 44 -// 89 -// -// So if we shift off the rightmost 14 bits, then (shift back only -// the top half) we get -// -// 0 fffe b17217f7d1cf4000 e6af278ece600fcb dabc000000000000 -// -// Put the right 64-bit signficand in an FR register, convert to double; -// it is exact. Put the next 128 bits into a quad register and round to double. -// The true exponent of the low part is -51. -// -// hi is 0 fffe b17217f7d1cf4000 -// lo is 0 ffcc e6af278ece601000 -// -// Convert to double memory format and get -// -// hi is 0x3fe62e42fefa39e8 -// lo is 0x3cccd5e4f1d9cc02 -// -// log2_hi + log2_lo is an accurate value for log2. -// -// -// The T and t values -// ================== -// A similar method is used to generate the T and t values. -// -// K * log2_hi + T must be exact. -// -// Smallest T,t -// ---------- -// The smallest T,t is -// T t -// 0x3f60040155d58800, 0x3c93bce0ce3ddd81 log(1/frcpa(1+0/256))= +1.95503e-003 -// -// The exponent is 0x3f6 (biased) or -9 (true). -// For the smallest T value, what we want is to clip the significand such that -// when it is shifted right by 9, its lsb is in the bit for 2^-51. The 9 is the -// specific for the first entry. In general, it is 0xffff - (biased 15-bit -// exponent). - -// Independently, what we have calculated is the table value as a quad -// precision number. -// Table entry 1 is -// 0 fff6 80200aaeac44ef38 338f77605fdf8000 -// -// We store this quad precision number in a data structure that is -// sign: 1 -// exponent: 15 -// signficand_hi: 64 (includes explicit bit) -// signficand_lo: 49 -// Because the explicit bit is included, the significand is 113 bits. -// -// Consider significand_hi for table entry 1. -// -// -// +-+--- ... -------+--------------------+ -// | | -// +-+--- ... -------+--------------------+ -// 0 1 4444444455555555556666 -// 2345678901234567890123 -// -// Labeled as above, bit 0 is 2^0, bit 1 is 2^-1, etc. -// Bit 42 is 2^-42. If we shift to the right by 9, the bit in -// bit 42 goes in 51. -// -// So what we want to do is shift bits 43 thru 63 into significand_lo. -// This is shifting bit 42 into bit 63, taking care to retain shifted-off bits. -// Then shifting (just with signficaand_hi) back into bit 42. -// -// The shift_value is 63-42 = 21. In general, this is -// 63 - (51 -(0xffff - 0xfff6)) -// For this example, it is -// 63 - (51 - 9) = 63 - 42 = 21 -// -// This means we are shifting 21 bits into significand_lo. We must maintain more -// that a 128-bit signficand not to lose bits. So before the shift we put the -// 128-bit significand into a 256-bit signficand and then shift. -// The 256-bit significand has four parts: hh, hl, lh, and ll. -// -// Start off with -// hh hl lh ll -// <64> <49><15_0> <64_0> <64_0> -// -// After shift by 21 (then return for significand_hi), -// <43><21_0> <21><43> <6><58_0> <64_0> -// -// Take the hh part and convert to a double. There is no rounding here. -// The conversion is exact. The true exponent of the high part is the same as -// the true exponent of the input quad. -// -// We have some 64 plus significand bits for the low part. In this example, we -// have 70 bits. We want to round this to a double. Put them in a quad and then -// do a quad fnorm. -// For this example the true exponent of the low part is -// true_exponent_of_high - 43 = true_exponent_of_high - (64-21) -// In general, this is -// true_exponent_of_high - (64 - shift_value) -// -// -// Largest T,t -// ---------- -// The largest T,t is -// 0x3fe62643fecf9742, 0x3c9e3147684bd37d log(1/frcpa(1+255/256))=+6.92171e-001 -// -// Table entry 256 is -// 0 fffe b1321ff67cba178c 51da12f4df5a0000 -// -// The shift value is -// 63 - (51 -(0xffff - 0xfffe)) = 13 -// -// The true exponent of the low part is -// true_exponent_of_high - (64 - shift_value) -// -1 - (64-13) = -52 -// Biased as a double, this is 0x3cb -// -// -// -// So then lsb(T) must be >= 2^-51 -// msb(Klog2_hi) <= 2^12 -// -// +--------+---------+ -// | 51 bits | <== largest T -// +--------+---------+ -// | 9 bits | 42 bits | <== smallest T -// +------------+----------------+-+ -// | 13 bits | 50 bits | | -// +------------+----------------+-+ -// -// Note: For powf only the table of T is needed - - -// Special Cases -//============================================================== - -// double float -// overflow error 24 30 - -// underflow error 25 31 - -// X zero Y zero -// +0 +0 +1 error 26 32 -// -0 +0 +1 error 26 32 -// +0 -0 +1 error 26 32 -// -0 -0 +1 error 26 32 - -// X zero Y negative -// +0 -odd integer +inf error 27 33 divide-by-zero -// -0 -odd integer -inf error 27 33 divide-by-zero -// +0 !-odd integer +inf error 27 33 divide-by-zero -// -0 !-odd integer +inf error 27 33 divide-by-zero -// +0 -inf +inf error 27 33 divide-by-zero -// -0 -inf +inf error 27 33 divide-by-zero - -// X zero Y positve -// +0 +odd integer +0 -// -0 +odd integer -0 -// +0 !+odd integer +0 -// -0 !+odd integer +0 -// +0 +inf +0 -// -0 +inf +0 -// +0 Y NaN quiet Y invalid if Y SNaN -// -0 Y NaN quiet Y invalid if Y SNaN - -// X one -// -1 Y inf +1 -// -1 Y NaN quiet Y invalid if Y SNaN -// +1 Y NaN +1 invalid if Y SNaN -// +1 Y any else +1 - -// X - Y not integer QNAN error 28 34 invalid - -// X NaN Y 0 +1 error 29 35 -// X NaN Y NaN quiet X invalid if X or Y SNaN -// X NaN Y any else quiet X invalid if X SNaN -// X !+1 Y NaN quiet Y invalid if Y SNaN - - -// X +inf Y >0 +inf -// X -inf Y >0, !odd integer +inf -// X -inf Y >0, odd integer -inf - -// X +inf Y <0 +0 -// X -inf Y <0, !odd integer +0 -// X -inf Y <0, odd integer -0 - -// X +inf Y =0 +1 -// X -inf Y =0 +1 - -// |X|<1 Y +inf +0 -// |X|<1 Y -inf +inf -// |X|>1 Y +inf +inf -// |X|>1 Y -inf +0 - -// X any Y =0 +1 - -// Assembly macros -//============================================================== - -// integer registers used - -pow_GR_exp_half = r10 -pow_GR_signexp_Xm1 = r11 -pow_GR_tmp = r11 - -pow_GR_signexp_X = r14 -pow_GR_17ones = r15 -pow_GR_Fpsr = r15 -pow_AD_P = r16 -pow_GR_rcs0_mask = r16 -pow_GR_exp_2tom8 = r17 -pow_GR_rcs0 = r17 -pow_GR_sig_X = r18 -pow_GR_10033 = r19 -pow_GR_16ones = r20 - -pow_AD_Tt = r21 -pow_GR_exp_X = r22 -pow_AD_Q = r23 -pow_GR_true_exp_X = r24 -pow_GR_y_zero = r25 - -pow_GR_exp_Y = r26 -pow_AD_tbl1 = r27 -pow_AD_tbl2 = r28 -pow_GR_offset = r29 -pow_GR_exp_Xm1 = r30 -pow_GR_xneg_yodd = r31 - -pow_GR_int_N = r38 -pow_GR_index1 = r39 -pow_GR_index2 = r40 - -pow_AD_T1 = r41 -pow_AD_T2 = r42 -pow_int_GR_M = r43 -pow_GR_sig_int_Y = r44 -pow_GR_sign_Y_Gpr = r45 - -pow_GR_17ones_m1 = r46 -pow_GR_one = r47 -pow_GR_sign_Y = r48 -pow_GR_signexp_Y_Gpr = r49 -pow_GR_exp_Y_Gpr = r50 - -pow_GR_true_exp_Y_Gpr = r51 -pow_GR_signexp_Y = r52 -pow_GR_x_one = r53 -pow_GR_big_pos = r55 - -pow_GR_big_neg = r56 - -GR_SAVE_B0 = r50 -GR_SAVE_GP = r51 -GR_SAVE_PFS = r52 - -GR_Parameter_X = r53 -GR_Parameter_Y = r54 -GR_Parameter_RESULT = r55 -pow_GR_tag = r56 - - -// floating point registers used - -POW_B = f32 -POW_NORM_X = f33 -POW_Xm1 = f34 -POW_r1 = f34 - -POW_NORM_Y = f37 -POW_Q2 = f38 -POW_eps = f39 -POW_P2 = f40 - -POW_P0 = f42 -POW_log2_lo = f43 -POW_r = f44 -POW_Q0_half = f45 - -POW_tmp = f47 -POW_log2_hi = f48 -POW_Q1 = f49 -POW_P1 = f50 - -POW_log2_by_128_hi = f51 -POW_inv_log2_by_128 = f52 -POW_rsq = f53 -POW_Yrcub = f54 -POW_log2_by_128_lo = f55 - -POW_xsq = f57 -POW_v2 = f59 -POW_T = f60 - -POW_RSHF = f62 -POW_v210 = f63 -POW_twoV = f65 - -POW_U = f66 -POW_G = f67 -POW_delta = f68 -POW_V = f70 - -POW_p = f71 -POW_Z = f72 -POW_e3 = f73 -POW_Z2 = f75 - -POW_W1 = f77 -POW_Z3 = f80 - -POW_Z3sq = f85 - -POW_Nfloat = f87 -POW_f3 = f89 -POW_q = f90 - -POW_T1 = f96 -POW_T2 = f97 -POW_2M = f98 -POW_s = f99 -POW_f12 = f100 - -POW_ssq = f101 -POW_T1T2 = f102 -POW_1ps = f103 -POW_A = f104 -POW_es = f105 - -POW_Xp1 = f106 -POW_int_K = f107 -POW_K = f108 -POW_f123 = f109 -POW_Gpr = f110 - -POW_Y_Gpr = f111 -POW_int_Y = f112 -POW_2Mqp1 = f113 - -POW_float_int_Y = f116 -POW_ftz_urm_f8 = f117 -POW_wre_urm_f8 = f118 -POW_big_neg = f119 -POW_big_pos = f120 - -// Data tables -//============================================================== - -RODATA - -.align 16 - -LOCAL_OBJECT_START(pow_table_P) -data8 0x80000000000018E5, 0x0000BFFD // P_1 -data8 0xb8aa3b295c17f0bc, 0x00004006 // inv_ln2_by_128 -// -// -data8 0x3FA5555555554A9E // Q_2 -data8 0x0000000000000000 // Pad -data8 0x3FC5555555554733 // Q_1 -data8 0x43e8000000000000 // Right shift constant for exp -data8 0xc9e3b39803f2f6af, 0x00003fb7 // ln2_by_128_lo -LOCAL_OBJECT_END(pow_table_P) - -LOCAL_OBJECT_START(pow_table_Q) -data8 0xCCCCCCCC4ED2BA7F, 0x00003FFC // P_2 -data8 0xAAAAAAAAAAAAB505, 0x00003FFD // P_0 -data8 0x3fe62e42fefa39e8, 0x3cccd5e4f1d9cc02 // log2 hi lo = +6.93147e-001 -data8 0xb17217f7d1cf79ab, 0x00003ff7 // ln2_by_128_hi -LOCAL_OBJECT_END(pow_table_Q) - - -LOCAL_OBJECT_START(pow_Tt) -data8 0x3f60040155d58800 // log(1/frcpa(1+0/256))= +1.95503e-003 -data8 0x3f78121214586a00 // log(1/frcpa(1+1/256))= +5.87661e-003 -data8 0x3f841929f9683200 // log(1/frcpa(1+2/256))= +9.81362e-003 -data8 0x3f8c317384c75f00 // log(1/frcpa(1+3/256))= +1.37662e-002 -data8 0x3f91a6b91ac73380 // log(1/frcpa(1+4/256))= +1.72376e-002 -data8 0x3f95ba9a5d9ac000 // log(1/frcpa(1+5/256))= +2.12196e-002 -data8 0x3f99d2a807432580 // log(1/frcpa(1+6/256))= +2.52177e-002 -data8 0x3f9d6b2725979800 // log(1/frcpa(1+7/256))= +2.87291e-002 -data8 0x3fa0c58fa19dfa80 // log(1/frcpa(1+8/256))= +3.27573e-002 -data8 0x3fa2954c78cbce00 // log(1/frcpa(1+9/256))= +3.62953e-002 -data8 0x3fa4a94d2da96c40 // log(1/frcpa(1+10/256))= +4.03542e-002 -data8 0x3fa67c94f2d4bb40 // log(1/frcpa(1+11/256))= +4.39192e-002 -data8 0x3fa85188b630f040 // log(1/frcpa(1+12/256))= +4.74971e-002 -data8 0x3faa6b8abe73af40 // log(1/frcpa(1+13/256))= +5.16017e-002 -data8 0x3fac441e06f72a80 // log(1/frcpa(1+14/256))= +5.52072e-002 -data8 0x3fae1e6713606d00 // log(1/frcpa(1+15/256))= +5.88257e-002 -data8 0x3faffa6911ab9300 // log(1/frcpa(1+16/256))= +6.24574e-002 -data8 0x3fb0ec139c5da600 // log(1/frcpa(1+17/256))= +6.61022e-002 -data8 0x3fb1dbd2643d1900 // log(1/frcpa(1+18/256))= +6.97605e-002 -data8 0x3fb2cc7284fe5f00 // log(1/frcpa(1+19/256))= +7.34321e-002 -data8 0x3fb3bdf5a7d1ee60 // log(1/frcpa(1+20/256))= +7.71173e-002 -data8 0x3fb4b05d7aa012e0 // log(1/frcpa(1+21/256))= +8.08161e-002 -data8 0x3fb580db7ceb5700 // log(1/frcpa(1+22/256))= +8.39975e-002 -data8 0x3fb674f089365a60 // log(1/frcpa(1+23/256))= +8.77219e-002 -data8 0x3fb769ef2c6b5680 // log(1/frcpa(1+24/256))= +9.14602e-002 -data8 0x3fb85fd927506a40 // log(1/frcpa(1+25/256))= +9.52125e-002 -data8 0x3fb9335e5d594980 // log(1/frcpa(1+26/256))= +9.84401e-002 -data8 0x3fba2b0220c8e5e0 // log(1/frcpa(1+27/256))= +1.02219e-001 -data8 0x3fbb0004ac1a86a0 // log(1/frcpa(1+28/256))= +1.05469e-001 -data8 0x3fbbf968769fca00 // log(1/frcpa(1+29/256))= +1.09274e-001 -data8 0x3fbccfedbfee13a0 // log(1/frcpa(1+30/256))= +1.12548e-001 -data8 0x3fbda727638446a0 // log(1/frcpa(1+31/256))= +1.15832e-001 -data8 0x3fbea3257fe10f60 // log(1/frcpa(1+32/256))= +1.19677e-001 -data8 0x3fbf7be9fedbfde0 // log(1/frcpa(1+33/256))= +1.22985e-001 -data8 0x3fc02ab352ff25f0 // log(1/frcpa(1+34/256))= +1.26303e-001 -data8 0x3fc097ce579d2040 // log(1/frcpa(1+35/256))= +1.29633e-001 -data8 0x3fc1178e8227e470 // log(1/frcpa(1+36/256))= +1.33531e-001 -data8 0x3fc185747dbecf30 // log(1/frcpa(1+37/256))= +1.36885e-001 -data8 0x3fc1f3b925f25d40 // log(1/frcpa(1+38/256))= +1.40250e-001 -data8 0x3fc2625d1e6ddf50 // log(1/frcpa(1+39/256))= +1.43627e-001 -data8 0x3fc2d1610c868130 // log(1/frcpa(1+40/256))= +1.47015e-001 -data8 0x3fc340c597411420 // log(1/frcpa(1+41/256))= +1.50414e-001 -data8 0x3fc3b08b6757f2a0 // log(1/frcpa(1+42/256))= +1.53825e-001 -data8 0x3fc40dfb08378000 // log(1/frcpa(1+43/256))= +1.56677e-001 -data8 0x3fc47e74e8ca5f70 // log(1/frcpa(1+44/256))= +1.60109e-001 -data8 0x3fc4ef51f6466de0 // log(1/frcpa(1+45/256))= +1.63553e-001 -data8 0x3fc56092e02ba510 // log(1/frcpa(1+46/256))= +1.67010e-001 -data8 0x3fc5d23857cd74d0 // log(1/frcpa(1+47/256))= +1.70478e-001 -data8 0x3fc6313a37335d70 // log(1/frcpa(1+48/256))= +1.73377e-001 -data8 0x3fc6a399dabbd380 // log(1/frcpa(1+49/256))= +1.76868e-001 -data8 0x3fc70337dd3ce410 // log(1/frcpa(1+50/256))= +1.79786e-001 -data8 0x3fc77654128f6120 // log(1/frcpa(1+51/256))= +1.83299e-001 -data8 0x3fc7e9d82a0b0220 // log(1/frcpa(1+52/256))= +1.86824e-001 -data8 0x3fc84a6b759f5120 // log(1/frcpa(1+53/256))= +1.89771e-001 -data8 0x3fc8ab47d5f5a300 // log(1/frcpa(1+54/256))= +1.92727e-001 -data8 0x3fc91fe490965810 // log(1/frcpa(1+55/256))= +1.96286e-001 -data8 0x3fc981634011aa70 // log(1/frcpa(1+56/256))= +1.99261e-001 -data8 0x3fc9f6c407089660 // log(1/frcpa(1+57/256))= +2.02843e-001 -data8 0x3fca58e729348f40 // log(1/frcpa(1+58/256))= +2.05838e-001 -data8 0x3fcabb55c31693a0 // log(1/frcpa(1+59/256))= +2.08842e-001 -data8 0x3fcb1e104919efd0 // log(1/frcpa(1+60/256))= +2.11855e-001 -data8 0x3fcb94ee93e367c0 // log(1/frcpa(1+61/256))= +2.15483e-001 -data8 0x3fcbf851c0675550 // log(1/frcpa(1+62/256))= +2.18516e-001 -data8 0x3fcc5c0254bf23a0 // log(1/frcpa(1+63/256))= +2.21558e-001 -data8 0x3fccc000c9db3c50 // log(1/frcpa(1+64/256))= +2.24609e-001 -data8 0x3fcd244d99c85670 // log(1/frcpa(1+65/256))= +2.27670e-001 -data8 0x3fcd88e93fb2f450 // log(1/frcpa(1+66/256))= +2.30741e-001 -data8 0x3fcdedd437eaef00 // log(1/frcpa(1+67/256))= +2.33820e-001 -data8 0x3fce530effe71010 // log(1/frcpa(1+68/256))= +2.36910e-001 -data8 0x3fceb89a1648b970 // log(1/frcpa(1+69/256))= +2.40009e-001 -data8 0x3fcf1e75fadf9bd0 // log(1/frcpa(1+70/256))= +2.43117e-001 -data8 0x3fcf84a32ead7c30 // log(1/frcpa(1+71/256))= +2.46235e-001 -data8 0x3fcfeb2233ea07c0 // log(1/frcpa(1+72/256))= +2.49363e-001 -data8 0x3fd028f9c7035c18 // log(1/frcpa(1+73/256))= +2.52501e-001 -data8 0x3fd05c8be0d96358 // log(1/frcpa(1+74/256))= +2.55649e-001 -data8 0x3fd085eb8f8ae790 // log(1/frcpa(1+75/256))= +2.58174e-001 -data8 0x3fd0b9c8e32d1910 // log(1/frcpa(1+76/256))= +2.61339e-001 -data8 0x3fd0edd060b78080 // log(1/frcpa(1+77/256))= +2.64515e-001 -data8 0x3fd122024cf00638 // log(1/frcpa(1+78/256))= +2.67701e-001 -data8 0x3fd14be2927aecd0 // log(1/frcpa(1+79/256))= +2.70257e-001 -data8 0x3fd180618ef18ad8 // log(1/frcpa(1+80/256))= +2.73461e-001 -data8 0x3fd1b50bbe2fc638 // log(1/frcpa(1+81/256))= +2.76675e-001 -data8 0x3fd1df4cc7cf2428 // log(1/frcpa(1+82/256))= +2.79254e-001 -data8 0x3fd214456d0eb8d0 // log(1/frcpa(1+83/256))= +2.82487e-001 -data8 0x3fd23ec5991eba48 // log(1/frcpa(1+84/256))= +2.85081e-001 -data8 0x3fd2740d9f870af8 // log(1/frcpa(1+85/256))= +2.88333e-001 -data8 0x3fd29ecdabcdfa00 // log(1/frcpa(1+86/256))= +2.90943e-001 -data8 0x3fd2d46602adcce8 // log(1/frcpa(1+87/256))= +2.94214e-001 -data8 0x3fd2ff66b04ea9d0 // log(1/frcpa(1+88/256))= +2.96838e-001 -data8 0x3fd335504b355a30 // log(1/frcpa(1+89/256))= +3.00129e-001 -data8 0x3fd360925ec44f58 // log(1/frcpa(1+90/256))= +3.02769e-001 -data8 0x3fd38bf1c3337e70 // log(1/frcpa(1+91/256))= +3.05417e-001 -data8 0x3fd3c25277333180 // log(1/frcpa(1+92/256))= +3.08735e-001 -data8 0x3fd3edf463c16838 // log(1/frcpa(1+93/256))= +3.11399e-001 -data8 0x3fd419b423d5e8c0 // log(1/frcpa(1+94/256))= +3.14069e-001 -data8 0x3fd44591e0539f48 // log(1/frcpa(1+95/256))= +3.16746e-001 -data8 0x3fd47c9175b6f0a8 // log(1/frcpa(1+96/256))= +3.20103e-001 -data8 0x3fd4a8b341552b08 // log(1/frcpa(1+97/256))= +3.22797e-001 -data8 0x3fd4d4f390890198 // log(1/frcpa(1+98/256))= +3.25498e-001 -data8 0x3fd501528da1f960 // log(1/frcpa(1+99/256))= +3.28206e-001 -data8 0x3fd52dd06347d4f0 // log(1/frcpa(1+100/256))= +3.30921e-001 -data8 0x3fd55a6d3c7b8a88 // log(1/frcpa(1+101/256))= +3.33644e-001 -data8 0x3fd5925d2b112a58 // log(1/frcpa(1+102/256))= +3.37058e-001 -data8 0x3fd5bf406b543db0 // log(1/frcpa(1+103/256))= +3.39798e-001 -data8 0x3fd5ec433d5c35a8 // log(1/frcpa(1+104/256))= +3.42545e-001 -data8 0x3fd61965cdb02c18 // log(1/frcpa(1+105/256))= +3.45300e-001 -data8 0x3fd646a84935b2a0 // log(1/frcpa(1+106/256))= +3.48063e-001 -data8 0x3fd6740add31de90 // log(1/frcpa(1+107/256))= +3.50833e-001 -data8 0x3fd6a18db74a58c0 // log(1/frcpa(1+108/256))= +3.53610e-001 -data8 0x3fd6cf31058670e8 // log(1/frcpa(1+109/256))= +3.56396e-001 -data8 0x3fd6f180e852f0b8 // log(1/frcpa(1+110/256))= +3.58490e-001 -data8 0x3fd71f5d71b894e8 // log(1/frcpa(1+111/256))= +3.61289e-001 -data8 0x3fd74d5aefd66d58 // log(1/frcpa(1+112/256))= +3.64096e-001 -data8 0x3fd77b79922bd378 // log(1/frcpa(1+113/256))= +3.66911e-001 -data8 0x3fd7a9b9889f19e0 // log(1/frcpa(1+114/256))= +3.69734e-001 -data8 0x3fd7d81b037eb6a0 // log(1/frcpa(1+115/256))= +3.72565e-001 -data8 0x3fd8069e33827230 // log(1/frcpa(1+116/256))= +3.75404e-001 -data8 0x3fd82996d3ef8bc8 // log(1/frcpa(1+117/256))= +3.77538e-001 -data8 0x3fd85855776dcbf8 // log(1/frcpa(1+118/256))= +3.80391e-001 -data8 0x3fd8873658327cc8 // log(1/frcpa(1+119/256))= +3.83253e-001 -data8 0x3fd8aa75973ab8c8 // log(1/frcpa(1+120/256))= +3.85404e-001 -data8 0x3fd8d992dc8824e0 // log(1/frcpa(1+121/256))= +3.88280e-001 -data8 0x3fd908d2ea7d9510 // log(1/frcpa(1+122/256))= +3.91164e-001 -data8 0x3fd92c59e79c0e50 // log(1/frcpa(1+123/256))= +3.93332e-001 -data8 0x3fd95bd750ee3ed0 // log(1/frcpa(1+124/256))= +3.96231e-001 -data8 0x3fd98b7811a3ee58 // log(1/frcpa(1+125/256))= +3.99138e-001 -data8 0x3fd9af47f33d4068 // log(1/frcpa(1+126/256))= +4.01323e-001 -data8 0x3fd9df270c1914a0 // log(1/frcpa(1+127/256))= +4.04245e-001 -data8 0x3fda0325ed14fda0 // log(1/frcpa(1+128/256))= +4.06442e-001 -data8 0x3fda33440224fa78 // log(1/frcpa(1+129/256))= +4.09379e-001 -data8 0x3fda57725e80c380 // log(1/frcpa(1+130/256))= +4.11587e-001 -data8 0x3fda87d0165dd198 // log(1/frcpa(1+131/256))= +4.14539e-001 -data8 0x3fdaac2e6c03f890 // log(1/frcpa(1+132/256))= +4.16759e-001 -data8 0x3fdadccc6fdf6a80 // log(1/frcpa(1+133/256))= +4.19726e-001 -data8 0x3fdb015b3eb1e790 // log(1/frcpa(1+134/256))= +4.21958e-001 -data8 0x3fdb323a3a635948 // log(1/frcpa(1+135/256))= +4.24941e-001 -data8 0x3fdb56fa04462908 // log(1/frcpa(1+136/256))= +4.27184e-001 -data8 0x3fdb881aa659bc90 // log(1/frcpa(1+137/256))= +4.30182e-001 -data8 0x3fdbad0bef3db160 // log(1/frcpa(1+138/256))= +4.32437e-001 -data8 0x3fdbd21297781c28 // log(1/frcpa(1+139/256))= +4.34697e-001 -data8 0x3fdc039236f08818 // log(1/frcpa(1+140/256))= +4.37718e-001 -data8 0x3fdc28cb1e4d32f8 // log(1/frcpa(1+141/256))= +4.39990e-001 -data8 0x3fdc4e19b84723c0 // log(1/frcpa(1+142/256))= +4.42267e-001 -data8 0x3fdc7ff9c74554c8 // log(1/frcpa(1+143/256))= +4.45311e-001 -data8 0x3fdca57b64e9db00 // log(1/frcpa(1+144/256))= +4.47600e-001 -data8 0x3fdccb130a5ceba8 // log(1/frcpa(1+145/256))= +4.49895e-001 -data8 0x3fdcf0c0d18f3268 // log(1/frcpa(1+146/256))= +4.52194e-001 -data8 0x3fdd232075b5a200 // log(1/frcpa(1+147/256))= +4.55269e-001 -data8 0x3fdd490246defa68 // log(1/frcpa(1+148/256))= +4.57581e-001 -data8 0x3fdd6efa918d25c8 // log(1/frcpa(1+149/256))= +4.59899e-001 -data8 0x3fdd9509707ae528 // log(1/frcpa(1+150/256))= +4.62221e-001 -data8 0x3fddbb2efe92c550 // log(1/frcpa(1+151/256))= +4.64550e-001 -data8 0x3fddee2f3445e4a8 // log(1/frcpa(1+152/256))= +4.67663e-001 -data8 0x3fde148a1a2726c8 // log(1/frcpa(1+153/256))= +4.70004e-001 -data8 0x3fde3afc0a49ff38 // log(1/frcpa(1+154/256))= +4.72350e-001 -data8 0x3fde6185206d5168 // log(1/frcpa(1+155/256))= +4.74702e-001 -data8 0x3fde882578823d50 // log(1/frcpa(1+156/256))= +4.77060e-001 -data8 0x3fdeaedd2eac9908 // log(1/frcpa(1+157/256))= +4.79423e-001 -data8 0x3fded5ac5f436be0 // log(1/frcpa(1+158/256))= +4.81792e-001 -data8 0x3fdefc9326d16ab8 // log(1/frcpa(1+159/256))= +4.84166e-001 -data8 0x3fdf2391a21575f8 // log(1/frcpa(1+160/256))= +4.86546e-001 -data8 0x3fdf4aa7ee031928 // log(1/frcpa(1+161/256))= +4.88932e-001 -data8 0x3fdf71d627c30bb0 // log(1/frcpa(1+162/256))= +4.91323e-001 -data8 0x3fdf991c6cb3b378 // log(1/frcpa(1+163/256))= +4.93720e-001 -data8 0x3fdfc07ada69a908 // log(1/frcpa(1+164/256))= +4.96123e-001 -data8 0x3fdfe7f18eb03d38 // log(1/frcpa(1+165/256))= +4.98532e-001 -data8 0x3fe007c053c5002c // log(1/frcpa(1+166/256))= +5.00946e-001 -data8 0x3fe01b942198a5a0 // log(1/frcpa(1+167/256))= +5.03367e-001 -data8 0x3fe02f74400c64e8 // log(1/frcpa(1+168/256))= +5.05793e-001 -data8 0x3fe04360be7603ac // log(1/frcpa(1+169/256))= +5.08225e-001 -data8 0x3fe05759ac47fe30 // log(1/frcpa(1+170/256))= +5.10663e-001 -data8 0x3fe06b5f1911cf50 // log(1/frcpa(1+171/256))= +5.13107e-001 -data8 0x3fe078bf0533c568 // log(1/frcpa(1+172/256))= +5.14740e-001 -data8 0x3fe08cd9687e7b0c // log(1/frcpa(1+173/256))= +5.17194e-001 -data8 0x3fe0a10074cf9018 // log(1/frcpa(1+174/256))= +5.19654e-001 -data8 0x3fe0b5343a234474 // log(1/frcpa(1+175/256))= +5.22120e-001 -data8 0x3fe0c974c89431cc // log(1/frcpa(1+176/256))= +5.24592e-001 -data8 0x3fe0ddc2305b9884 // log(1/frcpa(1+177/256))= +5.27070e-001 -data8 0x3fe0eb524bafc918 // log(1/frcpa(1+178/256))= +5.28726e-001 -data8 0x3fe0ffb54213a474 // log(1/frcpa(1+179/256))= +5.31214e-001 -data8 0x3fe114253da97d9c // log(1/frcpa(1+180/256))= +5.33709e-001 -data8 0x3fe128a24f1d9afc // log(1/frcpa(1+181/256))= +5.36210e-001 -data8 0x3fe1365252bf0864 // log(1/frcpa(1+182/256))= +5.37881e-001 -data8 0x3fe14ae558b4a92c // log(1/frcpa(1+183/256))= +5.40393e-001 -data8 0x3fe15f85a19c7658 // log(1/frcpa(1+184/256))= +5.42910e-001 -data8 0x3fe16d4d38c119f8 // log(1/frcpa(1+185/256))= +5.44592e-001 -data8 0x3fe18203c20dd130 // log(1/frcpa(1+186/256))= +5.47121e-001 -data8 0x3fe196c7bc4b1f38 // log(1/frcpa(1+187/256))= +5.49656e-001 -data8 0x3fe1a4a738b7a33c // log(1/frcpa(1+188/256))= +5.51349e-001 -data8 0x3fe1b981c0c9653c // log(1/frcpa(1+189/256))= +5.53895e-001 -data8 0x3fe1ce69e8bb1068 // log(1/frcpa(1+190/256))= +5.56447e-001 -data8 0x3fe1dc619de06944 // log(1/frcpa(1+191/256))= +5.58152e-001 -data8 0x3fe1f160a2ad0da0 // log(1/frcpa(1+192/256))= +5.60715e-001 -data8 0x3fe2066d7740737c // log(1/frcpa(1+193/256))= +5.63285e-001 -data8 0x3fe2147dba47a390 // log(1/frcpa(1+194/256))= +5.65001e-001 -data8 0x3fe229a1bc5ebac0 // log(1/frcpa(1+195/256))= +5.67582e-001 -data8 0x3fe237c1841a502c // log(1/frcpa(1+196/256))= +5.69306e-001 -data8 0x3fe24cfce6f80d98 // log(1/frcpa(1+197/256))= +5.71898e-001 -data8 0x3fe25b2c55cd5760 // log(1/frcpa(1+198/256))= +5.73630e-001 -data8 0x3fe2707f4d5f7c40 // log(1/frcpa(1+199/256))= +5.76233e-001 -data8 0x3fe285e0842ca380 // log(1/frcpa(1+200/256))= +5.78842e-001 -data8 0x3fe294294708b770 // log(1/frcpa(1+201/256))= +5.80586e-001 -data8 0x3fe2a9a2670aff0c // log(1/frcpa(1+202/256))= +5.83207e-001 -data8 0x3fe2b7fb2c8d1cc0 // log(1/frcpa(1+203/256))= +5.84959e-001 -data8 0x3fe2c65a6395f5f4 // log(1/frcpa(1+204/256))= +5.86713e-001 -data8 0x3fe2dbf557b0df40 // log(1/frcpa(1+205/256))= +5.89350e-001 -data8 0x3fe2ea64c3f97654 // log(1/frcpa(1+206/256))= +5.91113e-001 -data8 0x3fe3001823684d70 // log(1/frcpa(1+207/256))= +5.93762e-001 -data8 0x3fe30e97e9a8b5cc // log(1/frcpa(1+208/256))= +5.95531e-001 -data8 0x3fe32463ebdd34e8 // log(1/frcpa(1+209/256))= +5.98192e-001 -data8 0x3fe332f4314ad794 // log(1/frcpa(1+210/256))= +5.99970e-001 -data8 0x3fe348d90e7464cc // log(1/frcpa(1+211/256))= +6.02643e-001 -data8 0x3fe35779f8c43d6c // log(1/frcpa(1+212/256))= +6.04428e-001 -data8 0x3fe36621961a6a98 // log(1/frcpa(1+213/256))= +6.06217e-001 -data8 0x3fe37c299f3c3668 // log(1/frcpa(1+214/256))= +6.08907e-001 -data8 0x3fe38ae2171976e4 // log(1/frcpa(1+215/256))= +6.10704e-001 -data8 0x3fe399a157a603e4 // log(1/frcpa(1+216/256))= +6.12504e-001 -data8 0x3fe3afccfe77b9d0 // log(1/frcpa(1+217/256))= +6.15210e-001 -data8 0x3fe3be9d503533b4 // log(1/frcpa(1+218/256))= +6.17018e-001 -data8 0x3fe3cd7480b4a8a0 // log(1/frcpa(1+219/256))= +6.18830e-001 -data8 0x3fe3e3c43918f76c // log(1/frcpa(1+220/256))= +6.21554e-001 -data8 0x3fe3f2acb27ed6c4 // log(1/frcpa(1+221/256))= +6.23373e-001 -data8 0x3fe4019c2125ca90 // log(1/frcpa(1+222/256))= +6.25197e-001 -data8 0x3fe4181061389720 // log(1/frcpa(1+223/256))= +6.27937e-001 -data8 0x3fe42711518df544 // log(1/frcpa(1+224/256))= +6.29769e-001 -data8 0x3fe436194e12b6bc // log(1/frcpa(1+225/256))= +6.31604e-001 -data8 0x3fe445285d68ea68 // log(1/frcpa(1+226/256))= +6.33442e-001 -data8 0x3fe45bcc464c8938 // log(1/frcpa(1+227/256))= +6.36206e-001 -data8 0x3fe46aed21f117fc // log(1/frcpa(1+228/256))= +6.38053e-001 -data8 0x3fe47a1527e8a2d0 // log(1/frcpa(1+229/256))= +6.39903e-001 -data8 0x3fe489445efffcc8 // log(1/frcpa(1+230/256))= +6.41756e-001 -data8 0x3fe4a018bcb69834 // log(1/frcpa(1+231/256))= +6.44543e-001 -data8 0x3fe4af5a0c9d65d4 // log(1/frcpa(1+232/256))= +6.46405e-001 -data8 0x3fe4bea2a5bdbe84 // log(1/frcpa(1+233/256))= +6.48271e-001 -data8 0x3fe4cdf28f10ac44 // log(1/frcpa(1+234/256))= +6.50140e-001 -data8 0x3fe4dd49cf994058 // log(1/frcpa(1+235/256))= +6.52013e-001 -data8 0x3fe4eca86e64a680 // log(1/frcpa(1+236/256))= +6.53889e-001 -data8 0x3fe503c43cd8eb68 // log(1/frcpa(1+237/256))= +6.56710e-001 -data8 0x3fe513356667fc54 // log(1/frcpa(1+238/256))= +6.58595e-001 -data8 0x3fe522ae0738a3d4 // log(1/frcpa(1+239/256))= +6.60483e-001 -data8 0x3fe5322e26867854 // log(1/frcpa(1+240/256))= +6.62376e-001 -data8 0x3fe541b5cb979808 // log(1/frcpa(1+241/256))= +6.64271e-001 -data8 0x3fe55144fdbcbd60 // log(1/frcpa(1+242/256))= +6.66171e-001 -data8 0x3fe560dbc45153c4 // log(1/frcpa(1+243/256))= +6.68074e-001 -data8 0x3fe5707a26bb8c64 // log(1/frcpa(1+244/256))= +6.69980e-001 -data8 0x3fe587f60ed5b8fc // log(1/frcpa(1+245/256))= +6.72847e-001 -data8 0x3fe597a7977c8f30 // log(1/frcpa(1+246/256))= +6.74763e-001 -data8 0x3fe5a760d634bb88 // log(1/frcpa(1+247/256))= +6.76682e-001 -data8 0x3fe5b721d295f10c // log(1/frcpa(1+248/256))= +6.78605e-001 -data8 0x3fe5c6ea94431ef8 // log(1/frcpa(1+249/256))= +6.80532e-001 -data8 0x3fe5d6bb22ea86f4 // log(1/frcpa(1+250/256))= +6.82462e-001 -data8 0x3fe5e6938645d38c // log(1/frcpa(1+251/256))= +6.84397e-001 -data8 0x3fe5f673c61a2ed0 // log(1/frcpa(1+252/256))= +6.86335e-001 -data8 0x3fe6065bea385924 // log(1/frcpa(1+253/256))= +6.88276e-001 -data8 0x3fe6164bfa7cc068 // log(1/frcpa(1+254/256))= +6.90222e-001 -data8 0x3fe62643fecf9740 // log(1/frcpa(1+255/256))= +6.92171e-001 -LOCAL_OBJECT_END(pow_Tt) - - -// Table 1 is 2^(index_1/128) where -// index_1 goes from 0 to 15 -LOCAL_OBJECT_START(pow_tbl1) -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(pow_tbl1) - - -// Table 2 is 2^(index_1/8) where -// index_2 goes from 0 to 7 -LOCAL_OBJECT_START(pow_tbl2) -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(pow_tbl2) - -.section .text -GLOBAL_LIBM_ENTRY(powf) - -// Get exponent of x. Will be used to calculate K. -{ .mfi - getf.exp pow_GR_signexp_X = f8 - fms.s1 POW_Xm1 = f8,f1,f1 // Will be used for r1 if x>0 - mov pow_GR_17ones = 0x1FFFF -} -{ .mfi - addl pow_AD_P = @ltoff(pow_table_P), gp - fma.s1 POW_Xp1 = f8,f1,f1 // Will be used for r1 if x<0 - nop.i 999 -} -;; - -// Get significand of x. Will be used to get index to fetch T, Tt. -{ .mfi - getf.sig pow_GR_sig_X = f8 - frcpa.s1 POW_B, p6 = f1,f8 - mov pow_GR_exp_half = 0xFFFE // Exponent for 0.5 -} -{ .mfi - ld8 pow_AD_P = [pow_AD_P] - fma.s1 POW_NORM_X = f8,f1,f0 - mov pow_GR_exp_2tom8 = 0xFFF7 -} -;; - -// DOUBLE 0x10033 exponent limit at which y is an integer -{ .mfi - nop.m 999 - fcmp.lt.s1 p8,p9 = f8, f0 // Test for x<0 - addl pow_GR_10033 = 0x10033, r0 -} -{ .mfi - mov pow_GR_16ones = 0xFFFF - fma.s1 POW_NORM_Y = f9,f1,f0 - nop.i 999 -} -;; - -// p13 = TRUE ==> X is unorm -{ .mfi - setf.exp POW_Q0_half = pow_GR_exp_half // Form 0.5 - fclass.m p13,p0 = f8, 0x0b // Test for x unorm - adds pow_AD_Tt = pow_Tt - pow_table_P, pow_AD_P -} -{ .mfi - adds pow_AD_Q = pow_table_Q - pow_table_P, pow_AD_P - nop.f 999 - nop.i 999 -} -;; - -// p14 = TRUE ==> X is ZERO -{ .mfi - ldfe POW_P2 = [pow_AD_Q], 16 - fclass.m p14,p0 = f8, 0x07 - nop.i 999 -} -// Note POW_Xm1 and POW_r1 are used interchangably -{ .mfb - nop.m 999 -(p8) fnma.s1 POW_Xm1 = POW_Xp1,f1,f0 -(p13) br.cond.spnt POW_X_DENORM -} -;; - -// Continue normal and denormal paths here -POW_COMMON: -// p11 = TRUE ==> Y is a NAN -{ .mfi - and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones - fclass.m p11,p0 = f9, 0xc3 - nop.i 999 -} -{ .mfi - nop.m 999 - fms.s1 POW_r = POW_B, POW_NORM_X,f1 - mov pow_GR_y_zero = 0 -} -;; - -// Get exponent of |x|-1 to use in comparison to 2^-8 -{ .mmi - getf.exp pow_GR_signexp_Xm1 = POW_Xm1 - sub pow_GR_true_exp_X = pow_GR_exp_X, pow_GR_16ones - extr.u pow_GR_offset = pow_GR_sig_X, 55, 8 -} -;; - -{ .mfi - alloc r32=ar.pfs,2,19,4,0 - fcvt.fx.s1 POW_int_Y = POW_NORM_Y - shladd pow_AD_Tt = pow_GR_offset, 3, pow_AD_Tt -} -{ .mfi - setf.sig POW_int_K = pow_GR_true_exp_X - nop.f 999 - nop.i 999 -} -;; - -// p12 = TRUE if Y is ZERO -// Compute xsq to decide later if |x|=1 -{ .mfi - ldfe POW_P1 = [pow_AD_P], 16 - fclass.m p12,p0 = f9, 0x07 - nop.i 999 -} -{ .mfb - ldfe POW_P0 = [pow_AD_Q], 16 - fma.s1 POW_xsq = POW_NORM_X, POW_NORM_X, f0 -(p11) br.cond.spnt POW_Y_NAN // Branch if y=nan -} -;; - -{ .mmf - getf.exp pow_GR_signexp_Y = POW_NORM_Y - ldfd POW_T = [pow_AD_Tt] - fma.s1 POW_rsq = POW_r, POW_r,f0 -} -;; - -// p11 = TRUE ==> X is a NAN -{ .mfi - ldfpd POW_log2_hi, POW_log2_lo = [pow_AD_Q], 16 - fclass.m p11,p0 = POW_NORM_X, 0xc3 - nop.i 999 -} -{ .mfi - ldfe POW_inv_log2_by_128 = [pow_AD_P], 16 - fma.s1 POW_delta = f0,f0,f0 // delta=0 in case |x| near 1 -(p12) mov pow_GR_y_zero = 1 -} -;; - -{ .mfi - ldfd POW_Q2 = [pow_AD_P], 16 - fnma.s1 POW_twoV = POW_r, POW_Q0_half,f1 - and pow_GR_exp_Xm1 = pow_GR_signexp_Xm1, pow_GR_17ones -} -{ .mfi - nop.m 999 - fma.s1 POW_U = POW_NORM_Y,POW_r,f0 - nop.i 999 -} -;; - -// Determine if we will use the |x| near 1 path (p6) or normal path (p7) -{ .mfi - nop.m 999 - fcvt.xf POW_K = POW_int_K - cmp.lt p6,p7 = pow_GR_exp_Xm1, pow_GR_exp_2tom8 -} -{ .mfb - nop.m 999 - fma.s1 POW_G = f0,f0,f0 // G=0 in case |x| near 1 -(p11) br.cond.spnt POW_X_NAN // Branch if x=nan and y not nan -} -;; - -// If on the x near 1 path, assign r1 to r -{ .mfi - ldfpd POW_Q1, POW_RSHF = [pow_AD_P], 16 -(p6) fma.s1 POW_r = POW_r1, f1, f0 - nop.i 999 -} -{ .mfb - nop.m 999 -(p6) fma.s1 POW_rsq = POW_r1, POW_r1, f0 -(p14) br.cond.spnt POW_X_0 // Branch if x zero and y not nan -} -;; - -{ .mfi - getf.sig pow_GR_sig_int_Y = POW_int_Y -(p6) fnma.s1 POW_twoV = POW_r1, POW_Q0_half,f1 - and pow_GR_exp_Y = pow_GR_signexp_Y, pow_GR_17ones -} -{ .mfb - andcm pow_GR_sign_Y = pow_GR_signexp_Y, pow_GR_17ones -(p6) fma.s1 POW_U = POW_NORM_Y,POW_r1,f0 -(p12) br.cond.spnt POW_Y_0 // Branch if y=zero, x not zero or nan -} -;; - -{ .mfi - ldfe POW_log2_by_128_lo = [pow_AD_P], 16 -(p7) fma.s1 POW_Z2 = POW_twoV, POW_U, f0 - nop.i 999 -} -{ .mfi - ldfe POW_log2_by_128_hi = [pow_AD_Q], 16 - nop.f 999 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fcvt.xf POW_float_int_Y = POW_int_Y - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 POW_G = POW_K, POW_log2_hi, POW_T - adds pow_AD_tbl1 = pow_tbl1 - pow_Tt, pow_AD_Q -} -;; - -// p11 = TRUE ==> X is NEGATIVE but not inf -{ .mfi - nop.m 999 - fclass.m p11,p0 = POW_NORM_X, 0x1a - nop.i 999 -} -{ .mfi - nop.m 999 -(p7) fma.s1 POW_delta = POW_K, POW_log2_lo, f0 - adds pow_AD_tbl2 = pow_tbl2 - pow_tbl1, pow_AD_tbl1 -} -;; - -{ .mfi - nop.m 999 -(p6) fma.s1 POW_Z = POW_twoV, POW_U, f0 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_v2 = POW_P1, POW_r, POW_P0 - nop.i 999 -} -;; - -// p11 = TRUE ==> X is NEGATIVE but not inf -// p12 = TRUE ==> X is NEGATIVE AND Y already even int -// p13 = TRUE ==> X is NEGATIVE AND Y possible int -{ .mfi - nop.m 999 -(p7) fma.s1 POW_Z = POW_NORM_Y, POW_G, POW_Z2 -(p11) cmp.gt.unc p12,p13 = pow_GR_exp_Y, pow_GR_10033 -} -{ .mfi - nop.m 999 - fma.s1 POW_Gpr = POW_G, f1, POW_r - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_Yrcub = POW_rsq, POW_U, f0 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_p = POW_rsq, POW_P2, POW_v2 - nop.i 999 -} -;; - -// Test if x inf -{ .mfi - nop.m 999 - fclass.m p15,p0 = POW_NORM_X, 0x23 - nop.i 999 -} -// By adding RSHF (1.1000...*2^63) we put integer part in rightmost significand -{ .mfi - nop.m 999 - fma.s1 POW_W1 = POW_Z, POW_inv_log2_by_128, POW_RSHF - nop.i 999 -} -;; - -// p13 = TRUE ==> X is NEGATIVE AND Y possible int -// p10 = TRUE ==> X is NEG and Y is an int -// p12 = TRUE ==> X is NEG and Y is not an int -{ .mfi - nop.m 999 -(p13) fcmp.eq.unc.s1 p10,p12 = POW_float_int_Y, POW_NORM_Y - mov pow_GR_xneg_yodd = 0 -} -{ .mfi - nop.m 999 - fma.s1 POW_Y_Gpr = POW_NORM_Y, POW_Gpr, f0 - nop.i 999 -} -;; - -// p11 = TRUE ==> X is +1.0 -{ .mfi - nop.m 999 - fcmp.eq.s1 p11,p0 = POW_NORM_X, f1 - nop.i 999 -} -;; - -// Extract rounded integer from rightmost significand of POW_W1 -// By subtracting RSHF we get rounded integer POW_Nfloat -{ .mfi - getf.sig pow_GR_int_N = POW_W1 - fms.s1 POW_Nfloat = POW_W1, f1, POW_RSHF - nop.i 999 -} -{ .mfb - nop.m 999 - fma.s1 POW_Z3 = POW_p, POW_Yrcub, f0 -(p12) br.cond.spnt POW_X_NEG_Y_NONINT // Branch if x neg, y not integer -} -;; - -// p7 = TRUE ==> Y is +1.0 -// p12 = TRUE ==> X is NEGATIVE AND Y is an odd integer -{ .mfi - getf.exp pow_GR_signexp_Y_Gpr = POW_Y_Gpr - fcmp.eq.s1 p7,p0 = POW_NORM_Y, f1 // Test for y=1.0 -(p10) tbit.nz.unc p12,p0 = pow_GR_sig_int_Y,0 -} -{ .mfb - nop.m 999 -(p11) fma.s.s0 f8 = f1,f1,f0 // If x=1, result is +1 -(p15) br.cond.spnt POW_X_INF -} -;; - -// Test x and y and flag denormal -{ .mfi - nop.m 999 - fcmp.eq.s0 p15,p0 = f8,f9 - nop.i 999 -} -{ .mfb - nop.m 999 - fma.s1 POW_e3 = POW_NORM_Y, POW_delta, f0 -(p11) br.ret.spnt b0 // Early exit if x=1.0, result is +1 -} -;; - -{ .mfi -(p12) mov pow_GR_xneg_yodd = 1 - fnma.s1 POW_f12 = POW_Nfloat, POW_log2_by_128_lo, f1 - nop.i 999 -} -{ .mfb - nop.m 999 - fnma.s1 POW_s = POW_Nfloat, POW_log2_by_128_hi, POW_Z -(p7) br.ret.spnt b0 // Early exit if y=1.0, result is x -} -;; - -{ .mmi - and pow_GR_index1 = 0x0f, pow_GR_int_N - and pow_GR_index2 = 0x70, pow_GR_int_N - shr pow_int_GR_M = pow_GR_int_N, 7 // M = N/128 -} -;; - -{ .mfi - shladd pow_AD_T1 = pow_GR_index1, 4, pow_AD_tbl1 - fma.s1 POW_q = POW_Z3, POW_Q1, POW_Q0_half - add pow_int_GR_M = pow_GR_16ones, pow_int_GR_M -} -{ .mfi - add pow_AD_T2 = pow_AD_tbl2, pow_GR_index2 - fma.s1 POW_Z3sq = POW_Z3, POW_Z3, f0 - nop.i 999 -} -;; - -{ .mmi - ldfe POW_T1 = [pow_AD_T1] - ldfe POW_T2 = [pow_AD_T2] - nop.i 999 -} -;; - -// f123 = f12*(e3+1) = f12*e3+f12 -{ .mfi - setf.exp POW_2M = pow_int_GR_M - fma.s1 POW_f123 = POW_e3,POW_f12,POW_f12 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_ssq = POW_s, POW_s, f0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_v2 = POW_s, POW_Q2, POW_Q1 - and pow_GR_exp_Y_Gpr = pow_GR_signexp_Y_Gpr, pow_GR_17ones -} -;; - -{ .mfi - cmp.ne p12,p13 = pow_GR_xneg_yodd, r0 - fma.s1 POW_q = POW_Z3sq, POW_q, POW_Z3 - sub pow_GR_true_exp_Y_Gpr = pow_GR_exp_Y_Gpr, pow_GR_16ones -} -;; - -// p8 TRUE ==> |Y(G + r)| >= 7 - -// single -// -2^7 -2^6 2^6 2^7 -// -----+-----+----+ ... +-----+-----+----- -// p8 | p9 | p8 -// | | p10 | | - -// Form signexp of constants to indicate overflow -{ .mfi - mov pow_GR_big_pos = 0x1007f - nop.f 999 - cmp.le p8,p9 = 7, pow_GR_true_exp_Y_Gpr -} -{ .mfi - mov pow_GR_big_neg = 0x3007f - nop.f 999 - andcm pow_GR_sign_Y_Gpr = pow_GR_signexp_Y_Gpr, pow_GR_17ones -} -;; - -// Form big positive and negative constants to test for possible overflow -// Scale both terms of the polynomial by POW_f123 -{ .mfi - setf.exp POW_big_pos = pow_GR_big_pos - fma.s1 POW_ssq = POW_ssq, POW_f123, f0 -(p9) cmp.le.unc p0,p10 = 6, pow_GR_true_exp_Y_Gpr -} -{ .mfb - setf.exp POW_big_neg = pow_GR_big_neg - fma.s1 POW_1ps = POW_s, POW_f123, POW_f123 -(p8) br.cond.spnt POW_OVER_UNDER_X_NOT_INF -} -;; - -{ .mfi - nop.m 999 -(p12) fnma.s1 POW_T1T2 = POW_T1, POW_T2, f0 - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fma.s1 POW_T1T2 = POW_T1, POW_T2, f0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_v210 = POW_s, POW_v2, POW_Q0_half - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_2Mqp1 = POW_2M, POW_q, POW_2M - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_es = POW_ssq, POW_v210, POW_1ps - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_A = POW_T1T2, POW_2Mqp1, f0 - nop.i 999 -} -;; - -// Dummy op to set inexact -{ .mfi - nop.m 999 - fma.s0 POW_tmp = POW_2M, POW_q, POW_2M - nop.i 999 -} -;; - -{ .mfb - nop.m 999 - fma.s.s0 f8 = POW_A, POW_es, f0 -(p10) br.ret.sptk b0 // Exit main branch if no over/underflow -} -;; - -// POSSIBLE_OVER_UNDER -// p6 = TRUE ==> Y_Gpr negative -// Result is already computed. We just need to know if over/underflow occurred. - -{ .mfb - cmp.eq p0,p6 = pow_GR_sign_Y_Gpr, r0 - nop.f 999 -(p6) br.cond.spnt POW_POSSIBLE_UNDER -} -;; - -// POSSIBLE_OVER -// We got an answer. -// overflow is a possibility, not a certainty - - -// We define an overflow when the answer with -// WRE set -// user-defined rounding mode - -// double -// Largest double is 7FE (biased double) -// 7FE - 3FF + FFFF = 103FE -// Create + largest_double_plus_ulp -// Create - largest_double_plus_ulp -// Calculate answer with WRE set. - -// single -// Largest single is FE (biased double) -// FE - 7F + FFFF = 1007E -// Create + largest_single_plus_ulp -// Create - largest_single_plus_ulp -// Calculate answer with WRE set. - -// Cases when answer is ldn+1 are as follows: -// ldn ldn+1 -// --+----------|----------+------------ -// | -// +inf +inf -inf -// RN RN -// RZ - -// Put in s2 (td set, wre set) -{ .mfi - nop.m 999 - fsetc.s2 0x7F,0x42 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s.s2 POW_wre_urm_f8 = POW_A, POW_es, f0 - nop.i 999 -} -;; - -// Return s2 to default -{ .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - nop.i 999 -} -;; - -// p7 = TRUE ==> yes, we have an overflow -{ .mfi - nop.m 999 - fcmp.ge.s1 p7, p8 = POW_wre_urm_f8, POW_big_pos - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p8) fcmp.le.s1 p7, p0 = POW_wre_urm_f8, POW_big_neg - nop.i 999 -} -;; - -{ .mbb -(p7) mov pow_GR_tag = 30 -(p7) br.cond.spnt __libm_error_region // Branch if overflow - br.ret.sptk b0 // Exit if did not overflow -} -;; - - -POW_POSSIBLE_UNDER: -// We got an answer. input was < -2^9 but > -2^10 (double) -// We got an answer. input was < -2^6 but > -2^7 (float) -// underflow is a possibility, not a certainty - -// We define an underflow when the answer with -// ftz set -// is zero (tiny numbers become zero) -// Notice (from below) that if we have an unlimited exponent range, -// then there is an extra machine number E between the largest denormal and -// the smallest normal. -// So if with unbounded exponent we round to E or below, then we are -// tiny and underflow has occurred. -// But notice that you can be in a situation where we are tiny, namely -// rounded to E, but when the exponent is bounded we round to smallest -// normal. So the answer can be the smallest normal with underflow. -// E -// -----+--------------------+--------------------+----- -// | | | -// 1.1...10 2^-3fff 1.1...11 2^-3fff 1.0...00 2^-3ffe -// 0.1...11 2^-3ffe (biased, 1) -// largest dn smallest normal - -// Form small constant (2^-170) to correct underflow result near region of -// smallest denormal in round-nearest. - -// Put in s2 (td set, ftz set) -.pred.rel "mutex",p12,p13 -{ .mfi - mov pow_GR_Fpsr = ar40 // Read the fpsr--need to check rc.s0 - fsetc.s2 0x7F,0x41 - mov pow_GR_rcs0_mask = 0x0c00 // Set mask for rc.s0 -} -{ .mfi -(p12) mov pow_GR_tmp = 0x2ffff - 170 - nop.f 999 -(p13) mov pow_GR_tmp = 0x0ffff - 170 -} -;; - -{ .mfi - setf.exp POW_eps = pow_GR_tmp // Form 2^-170 - fma.s.s2 POW_ftz_urm_f8 = POW_A, POW_es, f0 - nop.i 999 -} -;; - -// Return s2 to default -{ .mfi - nop.m 999 - fsetc.s2 0x7F,0x40 - nop.i 999 -} -;; - -// p7 = TRUE ==> yes, we have an underflow -{ .mfi - nop.m 999 - fcmp.eq.s1 p7, p0 = POW_ftz_urm_f8, f0 - nop.i 999 -} -;; - -{ .mmi -(p7) and pow_GR_rcs0 = pow_GR_rcs0_mask, pow_GR_Fpsr // Isolate rc.s0 -;; -(p7) cmp.eq.unc p6,p0 = pow_GR_rcs0, r0 // Test for round to nearest - nop.i 999 -} -;; - -// Tweak result slightly if underflow to get correct rounding near smallest -// denormal if round-nearest -{ .mfi - nop.m 999 -(p6) fms.s.s0 f8 = POW_A, POW_es, POW_eps - nop.i 999 -} -{ .mbb -(p7) mov pow_GR_tag = 31 -(p7) br.cond.spnt __libm_error_region // Branch if underflow - br.ret.sptk b0 // Exit if did not underflow -} -;; - -POW_X_DENORM: -// Here if x unorm. Use the NORM_X for getf instructions, and then back -// to normal path -{ .mfi - getf.exp pow_GR_signexp_X = POW_NORM_X - nop.f 999 - nop.i 999 -} -;; - -{ .mib - getf.sig pow_GR_sig_X = POW_NORM_X - nop.i 999 - br.cond.sptk POW_COMMON -} -;; - -POW_X_0: -// Here if x=0 and y not nan -// -// We have the following cases: -// p6 x=0 and y>0 and is an integer (may be even or odd) -// p7 x=0 and y>0 and is NOT an integer, return +0 -// p8 x=0 and y>0 and so big as to always be an even integer, return +0 -// p9 x=0 and y>0 and may not be integer -// p10 x=0 and y>0 and is an odd integer, return x -// p11 x=0 and y>0 and is an even integer, return +0 -// p12 used in dummy fcmp to set denormal flag if y=unorm -// p13 x=0 and y>0 -// p14 x=0 and y=0, branch to code for calling error handling -// p15 x=0 and y<0, branch to code for calling error handling -// -{ .mfi - getf.sig pow_GR_sig_int_Y = POW_int_Y // Get signif of int_Y - fcmp.lt.s1 p15,p13 = f9, f0 // Test for y<0 - and pow_GR_exp_Y = pow_GR_signexp_Y, pow_GR_17ones -} -{ .mfb - cmp.ne p14,p0 = pow_GR_y_zero,r0 // Test for y=0 - fcvt.xf POW_float_int_Y = POW_int_Y -(p14) br.cond.spnt POW_X_0_Y_0 // Branch if x=0 and y=0 -} -;; - -// If x=0 and y>0, test y and flag denormal -{ .mfb -(p13) cmp.gt.unc p8,p9 = pow_GR_exp_Y, pow_GR_10033 // Test y +big = even int -(p13) fcmp.eq.s0 p12,p0 = f9,f0 // If x=0, y>0 dummy op to flag denormal -(p15) br.cond.spnt POW_X_0_Y_NEG // Branch if x=0 and y<0 -} -;; - -// Here if x=0 and y>0 -{ .mfi - nop.m 999 -(p9) fcmp.eq.unc.s1 p6,p7 = POW_float_int_Y, POW_NORM_Y // Test y=int - nop.i 999 -} -{ .mfi - nop.m 999 -(p8) fma.s.s0 f8 = f0,f0,f0 // If x=0, y>0 and large even int, return +0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p7) fma.s.s0 f8 = f0,f0,f0 // Result +0 if x=0 and y>0 and not integer -(p6) tbit.nz.unc p10,p11 = pow_GR_sig_int_Y,0 // If y>0 int, test y even/odd -} -;; - -// Note if x=0, y>0 and odd integer, just return x -{ .mfb - nop.m 999 -(p11) fma.s.s0 f8 = f0,f0,f0 // Result +0 if x=0 and y even integer - br.ret.sptk b0 // Exit if x=0 and y>0 -} -;; - -POW_X_0_Y_0: -// When X is +-0 and Y is +-0, IEEE returns 1.0 -// We call error support with this value - -{ .mfb - mov pow_GR_tag = 32 - fma.s.s0 f8 = f1,f1,f0 - br.cond.sptk __libm_error_region -} -;; - -POW_X_0_Y_NEG: -// When X is +-0 and Y is negative, IEEE returns -// X Y answer -// +0 -odd int +inf -// -0 -odd int -inf - -// +0 !-odd int +inf -// -0 !-odd int +inf - -// p6 == Y is a floating point number outside the integer. -// Hence it is an integer and is even. -// return +inf - -// p7 == Y is a floating point number within the integer range. -// p9 == (int_Y = NORM_Y), Y is an integer, which may be odd or even. -// p11 odd -// return (sign_of_x)inf -// p12 even -// return +inf -// p10 == Y is not an integer -// return +inf -// - -{ .mfi - nop.m 999 - nop.f 999 - cmp.gt p6,p7 = pow_GR_exp_Y, pow_GR_10033 -} -;; - -{ .mfi - mov pow_GR_tag = 33 -(p7) fcmp.eq.unc.s1 p9,p10 = POW_float_int_Y, POW_NORM_Y - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p6) frcpa.s0 f8,p13 = f1, f0 -(p6) br.cond.sptk __libm_error_region // x=0, y<0, y large neg int -} -;; - -{ .mfb - nop.m 999 -(p10) frcpa.s0 f8,p13 = f1, f0 -(p10) br.cond.sptk __libm_error_region // x=0, y<0, y not int -} -;; - -// x=0, y<0, y an int -{ .mib - nop.m 999 -(p9) tbit.nz.unc p11,p12 = pow_GR_sig_int_Y,0 - nop.b 999 -} -;; - -{ .mfi - nop.m 999 -(p12) frcpa.s0 f8,p13 = f1,f0 - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p11) frcpa.s0 f8,p13 = f1,f8 - br.cond.sptk __libm_error_region -} -;; - - -POW_Y_0: -// Here for y zero, x anything but zero and nan -// Set flag if x denormal -// Result is +1.0 -{ .mfi - nop.m 999 - fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag if x denormal - nop.i 999 -} -{ .mfb - nop.m 999 - fma.s.s0 f8 = f1,f1,f0 - br.ret.sptk b0 -} -;; - - -POW_X_INF: -// Here when X is +-inf - -// X +inf Y +inf +inf -// X -inf Y +inf +inf - -// X +inf Y >0 +inf -// X -inf Y >0, !odd integer +inf <== (-inf)^0.5 = +inf !! -// X -inf Y >0, odd integer -inf - -// X +inf Y -inf +0 -// X -inf Y -inf +0 - -// X +inf Y <0 +0 -// X -inf Y <0, !odd integer +0 -// X -inf Y <0, odd integer -0 - -// X + inf Y=+0 +1 -// X + inf Y=-0 +1 -// X - inf Y=+0 +1 -// X - inf Y=-0 +1 - -// p13 == Y negative -// p14 == Y positive - -// p6 == Y is a floating point number outside the integer. -// Hence it is an integer and is even. -// p13 == (Y negative) -// return +inf -// p14 == (Y positive) -// return +0 - -// p7 == Y is a floating point number within the integer range. -// p9 == (int_Y = NORM_Y), Y is an integer, which may be odd or even. -// p11 odd -// p13 == (Y negative) -// return (sign_of_x)inf -// p14 == (Y positive) -// return (sign_of_x)0 -// pxx even -// p13 == (Y negative) -// return +inf -// p14 == (Y positive) -// return +0 - -// pxx == Y is not an integer -// p13 == (Y negative) -// return +inf -// p14 == (Y positive) -// return +0 -// - -// If x=inf, test y and flag denormal -{ .mfi - nop.m 999 - fcmp.eq.s0 p10,p11 = f9,f0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fcmp.lt.s0 p13,p14 = POW_NORM_Y,f0 - cmp.gt p6,p7 = pow_GR_exp_Y, pow_GR_10033 -} -{ .mfi - nop.m 999 - fclass.m p12,p0 = f9, 0x23 //@inf - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fclass.m p15,p0 = f9, 0x07 //@zero - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p15) fmerge.s f8 = f1,f1 // Return +1.0 if x=inf, y=0 -(p15) br.ret.spnt b0 // Exit if x=inf, y=0 -} -;; - -{ .mfi - nop.m 999 -(p14) frcpa.s1 f8,p10 = f1,f0 // If x=inf, y>0, assume result +inf - nop.i 999 -} -{ .mfb - nop.m 999 -(p13) fma.s.s0 f8 = f0,f0,f0 // If x=inf, y<0, assume result +0.0 -(p12) br.ret.spnt b0 // Exit if x=inf, y=inf -} -;; - -// Here if x=inf, and 0 < |y| < inf. Need to correct results if y odd integer. -{ .mfi - nop.m 999 -(p7) fcmp.eq.unc.s1 p9,p0 = POW_float_int_Y, POW_NORM_Y // Is y integer? - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - nop.f 999 -(p9) tbit.nz.unc p11,p0 = pow_GR_sig_int_Y,0 // Test for y odd integer -} -;; - -{ .mfb - nop.m 999 -(p11) fmerge.s f8 = POW_NORM_X,f8 // If y odd integer use sign of x - br.ret.sptk b0 // Exit for x=inf, 0 < |y| < inf -} -;; - - -POW_X_NEG_Y_NONINT: -// When X is negative and Y is a non-integer, IEEE -// returns a qnan indefinite. -// We call error support with this value - -{ .mfb - mov pow_GR_tag = 34 - frcpa.s0 f8,p6 = f0,f0 - br.cond.sptk __libm_error_region -} -;; - -POW_X_NAN: -// Here if x=nan, y not nan -{ .mfi - nop.m 999 - fclass.m p9,p13 = f9, 0x07 // Test y=zero - nop.i 999 -} -;; - -{ .mfb - nop.m 999 -(p13) fma.s.s0 f8 = f8,f1,f0 -(p13) br.ret.sptk b0 // Exit if x nan, y anything but zero or nan -} -;; - -POW_X_NAN_Y_0: -// When X is a NAN and Y is zero, IEEE returns 1. -// We call error support with this value. -{ .mfi - nop.m 999 - fcmp.eq.s0 p6,p0 = f8,f0 // Dummy op to set invalid on snan - nop.i 999 -} -{ .mfb - mov pow_GR_tag = 35 - fma.s.s0 f8 = f0,f0,f1 - br.cond.sptk __libm_error_region -} -;; - - -POW_OVER_UNDER_X_NOT_INF: - -// p8 is TRUE for overflow -// p9 is TRUE for underflow - -// if y is infinity, we should not over/underflow - -{ .mfi - nop.m 999 - fcmp.eq.s1 p14, p13 = POW_xsq,f1 // Test |x|=1 - cmp.eq p8,p9 = pow_GR_sign_Y_Gpr, r0 -} -;; - -{ .mfi - nop.m 999 -(p14) fclass.m.unc p15, p0 = f9, 0x23 // If |x|=1, test y=inf - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fclass.m.unc p11,p0 = f9, 0x23 // If |x| not 1, test y=inf - nop.i 999 -} -;; - -// p15 = TRUE if |x|=1, y=inf, return +1 -{ .mfb - nop.m 999 -(p15) fma.s.s0 f8 = f1,f1,f0 // If |x|=1, y=inf, result +1 -(p15) br.ret.spnt b0 // Exit if |x|=1, y=inf -} -;; - -.pred.rel "mutex",p8,p9 -{ .mfb -(p8) setf.exp f8 = pow_GR_17ones // If exp(+big), result inf -(p9) fmerge.s f8 = f0,f0 // If exp(-big), result 0 -(p11) br.ret.sptk b0 // Exit if |x| not 1, y=inf -} -;; - -{ .mfb - nop.m 999 - nop.f 999 - br.cond.sptk POW_OVER_UNDER_ERROR // Branch if y not inf -} -;; - - -POW_Y_NAN: -// Here if y=nan, x anything -// If x = +1 then result is +1, else result is quiet Y -{ .mfi - nop.m 999 - fcmp.eq.s1 p10,p9 = POW_NORM_X, f1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p10) fcmp.eq.s0 p6,p0 = f9,f1 // Set invalid, even if x=+1 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p10) fma.s.s0 f8 = f1,f1,f0 - nop.i 999 -} -{ .mfb - nop.m 999 -(p9) fma.s.s0 f8 = f9,f8,f0 - br.ret.sptk b0 // Exit y=nan -} -;; - - -POW_OVER_UNDER_ERROR: -// Here if we have overflow or underflow. -// Enter with p12 true if x negative and y odd int to force -0 or -inf - -{ .mfi - sub pow_GR_17ones_m1 = pow_GR_17ones, r0, 1 - nop.f 999 - mov pow_GR_one = 0x1 -} -;; - -// overflow, force inf with O flag -{ .mmb -(p8) mov pow_GR_tag = 30 -(p8) setf.exp POW_tmp = pow_GR_17ones_m1 - nop.b 999 -} -;; - -// underflow, force zero with I, U flags -{ .mmi -(p9) mov pow_GR_tag = 31 -(p9) setf.exp POW_tmp = pow_GR_one - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s.s0 f8 = POW_tmp, POW_tmp, f0 - nop.i 999 -} -;; - -// p12 x is negative and y is an odd integer, change sign of result -{ .mfi - nop.m 999 -(p12) fnma.s.s0 f8 = POW_tmp, POW_tmp, f0 - nop.i 999 -} -;; - -GLOBAL_LIBM_END(powf) - - -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] = POW_NORM_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 - stfs [GR_Parameter_X] = POW_NORM_X // STORE Parameter 1 on stack - add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address - nop.b 0 -} -{ .mib - stfs [GR_Parameter_Y] = f8 // 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# - |