diff options
Diffstat (limited to 'sysdeps/ia64/fpu/e_powf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_powf.S | 984 |
1 files changed, 424 insertions, 560 deletions
diff --git a/sysdeps/ia64/fpu/e_powf.S b/sysdeps/ia64/fpu/e_powf.S index 275843f1e2..4c839cba71 100644 --- a/sysdeps/ia64/fpu/e_powf.S +++ b/sysdeps/ia64/fpu/e_powf.S @@ -64,6 +64,8 @@ // 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) // // API //============================================================== @@ -106,37 +108,33 @@ // // Log(1/Cm) = log(1/frcpa(1+m/256)) where m goes from 0 to 255. // -// We tabluate as two doubles, T and t, where T +t is the value itself. +// We tabluate as one double, T for single precision power // -// Log(x) = (K Log(2)_hi + T) + (Log(2)_hi + t) + Log( 1 + (Bx-1)) -// Log(x) = G + delta + Log( 1 + (Bx-1)) +// 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 + (e2 + e3) +// yLog(x) = Z1 + e3 + Z2 + Z3 // // -// exp(yLog(x)) = exp(Z1 + Z2 + Z3) exp(e1 + e2 + e3) +// exp(yLog(x)) = exp(Z1 + Z2) exp(Z3) exp(e3) // // // exp(Z3) is another series. -// exp(e1 + e2 + e3) is approximated as f3 = 1 + (e1 + e2 + e3) +// exp(e3) is approximated as f3 = 1 + e3 // -// Z1 (128/log2) = number of log2/128 in Z1 is N1 -// Z2 (128/log2) = number of log2/128 in Z2 is N2 -// -// s1 = Z1 - N1 log2/128 -// s2 = Z2 - N2 log2/128 +// exp(Z1 + Z2) = exp(Z) +// Z (128/log2) = number of log2/128 in Z is N // -// s = s1 + s2 -// N = N1 + N2 +// s = Z - N log2/128 // -// exp(Z1 + Z2) = exp(Z) // exp(Z) = exp(s) exp(N log2/128) // // exp(r) = exp(Z - N log2/128) @@ -161,13 +159,11 @@ // 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) (1+d1) (1+d2)(2^M) 2^I2/8 2^I1/128 -// exp(Z) = exp(s) f1 f2 (2^M) 2^I2/8 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(Z1 + Z2 + Z3) exp(e1 + e2 + e3) // exp(yLog(x)) = exp(Z) exp(Z3) f3 // exp(yLog(x)) = exp(Z)f3 exp(Z3) // exp(yLog(x)) = A exp(Z3) @@ -331,6 +327,8 @@ // +------------+----------------+-+ // | 13 bits | 50 bits | | // +------------+----------------+-+ +// +// Note: For powf only the table of T is needed // Special Cases @@ -402,10 +400,17 @@ // 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 @@ -423,9 +428,6 @@ pow_GR_offset = r29 pow_GR_exp_Xm1 = r30 pow_GR_xneg_yodd = r31 -pow_GR_signexp_Xm1 = r35 -pow_GR_int_W1 = r36 -pow_GR_int_W2 = r37 pow_GR_int_N = r38 pow_GR_index1 = r39 pow_GR_index2 = r40 @@ -465,24 +467,20 @@ POW_B = f32 POW_NORM_X = f33 POW_Xm1 = f34 POW_r1 = f34 -POW_P4 = f35 -POW_P5 = f36 POW_NORM_Y = f37 POW_Q2 = f38 -POW_Q3 = f39 +POW_eps = f39 POW_P2 = f40 -POW_P3 = f41 POW_P0 = f42 POW_log2_lo = f43 POW_r = f44 POW_Q0_half = f45 -POW_Q1 = f46 POW_tmp = f47 POW_log2_hi = f48 -POW_Q4 = f49 +POW_Q1 = f49 POW_P1 = f50 POW_log2_by_128_hi = f51 @@ -491,54 +489,33 @@ POW_rsq = f53 POW_Yrcub = f54 POW_log2_by_128_lo = f55 -POW_v6 = f56 POW_xsq = f57 -POW_v4 = f58 POW_v2 = f59 POW_T = f60 -POW_Tt = f61 POW_RSHF = f62 -POW_v21ps = f63 -POW_s4 = f64 +POW_v210 = f63 POW_twoV = f65 POW_U = f66 POW_G = f67 POW_delta = f68 -POW_v3 = f69 POW_V = f70 POW_p = f71 -POW_Z1 = f72 +POW_Z = f72 POW_e3 = f73 -POW_e2 = f74 POW_Z2 = f75 -POW_e1 = f76 POW_W1 = f77 -POW_UmZ2 = f78 -POW_W2 = f79 POW_Z3 = f80 -POW_int_W1 = f81 -POW_e12 = f82 -POW_int_W2 = f83 -POW_UmZ2pV = f84 POW_Z3sq = f85 -POW_e123 = f86 -POW_N1float = f87 -POW_N2float = f88 +POW_Nfloat = f87 POW_f3 = f89 POW_q = f90 -POW_s1 = f91 -POW_Nfloat = f92 -POW_s2 = f93 -POW_f2 = f94 -POW_f1 = f95 - POW_T1 = f96 POW_T2 = f97 POW_2M = f98 @@ -575,25 +552,18 @@ RODATA .align 16 LOCAL_OBJECT_START(pow_table_P) -data8 0x8000F7B249FF332D, 0x0000BFFC // P_5 -data8 0xAAAAAAA9E7902C7F, 0x0000BFFC // P_3 data8 0x80000000000018E5, 0x0000BFFD // P_1 data8 0xb8aa3b295c17f0bc, 0x00004006 // inv_ln2_by_128 // // data8 0x3FA5555555554A9E // Q_2 -data8 0x3F8111124F4DD9F9 // Q_3 -data8 0x3FE0000000000000 // Q_0 +data8 0x0000000000000000 // Pad data8 0x3FC5555555554733 // Q_1 -data8 0x3F56C16D9360FFA0 // Q_4 data8 0x43e8000000000000 // Right shift constant for exp data8 0xc9e3b39803f2f6af, 0x00003fb7 // ln2_by_128_lo -data8 0x0000000000000000 // pad to eliminate bank conflicts with pow_table_Q -data8 0x0000000000000000 // pad to eliminate bank conflicts with pow_table_Q LOCAL_OBJECT_END(pow_table_P) LOCAL_OBJECT_START(pow_table_Q) -data8 0x9249FE7F0DC423CF, 0x00003FFC // P_4 data8 0xCCCCCCCC4ED2BA7F, 0x00003FFC // P_2 data8 0xAAAAAAAAAAAAB505, 0x00003FFD // P_0 data8 0x3fe62e42fefa39e8, 0x3cccd5e4f1d9cc02 // log2 hi lo = +6.93147e-001 @@ -602,262 +572,262 @@ LOCAL_OBJECT_END(pow_table_Q) LOCAL_OBJECT_START(pow_Tt) -data8 0x3f60040155d58800, 0x3c93bce0ce3ddd81 // log(1/frcpa(1+0/256))= +1.95503e-003 -data8 0x3f78121214586a00, 0x3cb540e0a5cfc9bc // log(1/frcpa(1+1/256))= +5.87661e-003 -data8 0x3f841929f9683200, 0x3cbdf1d57404da1f // log(1/frcpa(1+2/256))= +9.81362e-003 -data8 0x3f8c317384c75f00, 0x3c69806208c04c22 // log(1/frcpa(1+3/256))= +1.37662e-002 -data8 0x3f91a6b91ac73380, 0x3c7874daa716eb32 // log(1/frcpa(1+4/256))= +1.72376e-002 -data8 0x3f95ba9a5d9ac000, 0x3cacbb84e08d78ac // log(1/frcpa(1+5/256))= +2.12196e-002 -data8 0x3f99d2a807432580, 0x3cbcf80538b441e1 // log(1/frcpa(1+6/256))= +2.52177e-002 -data8 0x3f9d6b2725979800, 0x3c6095e5c8f8f359 // log(1/frcpa(1+7/256))= +2.87291e-002 -data8 0x3fa0c58fa19dfa80, 0x3cb4c5d4e9d0dda2 // log(1/frcpa(1+8/256))= +3.27573e-002 -data8 0x3fa2954c78cbce00, 0x3caa932b860ab8d6 // log(1/frcpa(1+9/256))= +3.62953e-002 -data8 0x3fa4a94d2da96c40, 0x3ca670452b76bbd5 // log(1/frcpa(1+10/256))= +4.03542e-002 -data8 0x3fa67c94f2d4bb40, 0x3ca84104f9941798 // log(1/frcpa(1+11/256))= +4.39192e-002 -data8 0x3fa85188b630f040, 0x3cb40a882cbf0153 // log(1/frcpa(1+12/256))= +4.74971e-002 -data8 0x3faa6b8abe73af40, 0x3c988d46e25c9059 // log(1/frcpa(1+13/256))= +5.16017e-002 -data8 0x3fac441e06f72a80, 0x3cae3e930a1a2a96 // log(1/frcpa(1+14/256))= +5.52072e-002 -data8 0x3fae1e6713606d00, 0x3c8a796f6283b580 // log(1/frcpa(1+15/256))= +5.88257e-002 -data8 0x3faffa6911ab9300, 0x3c5193070351e88a // log(1/frcpa(1+16/256))= +6.24574e-002 -data8 0x3fb0ec139c5da600, 0x3c623f2a75eb992d // log(1/frcpa(1+17/256))= +6.61022e-002 -data8 0x3fb1dbd2643d1900, 0x3ca649b2ef8927f0 // log(1/frcpa(1+18/256))= +6.97605e-002 -data8 0x3fb2cc7284fe5f00, 0x3cbc5e86599513e2 // log(1/frcpa(1+19/256))= +7.34321e-002 -data8 0x3fb3bdf5a7d1ee60, 0x3c90bd4bb69dada3 // log(1/frcpa(1+20/256))= +7.71173e-002 -data8 0x3fb4b05d7aa012e0, 0x3c54e377c9b8a54f // log(1/frcpa(1+21/256))= +8.08161e-002 -data8 0x3fb580db7ceb5700, 0x3c7fdb2f98354cde // log(1/frcpa(1+22/256))= +8.39975e-002 -data8 0x3fb674f089365a60, 0x3cb9994c9d3301c1 // log(1/frcpa(1+23/256))= +8.77219e-002 -data8 0x3fb769ef2c6b5680, 0x3caaec639db52a79 // log(1/frcpa(1+24/256))= +9.14602e-002 -data8 0x3fb85fd927506a40, 0x3c9f9f99a3cf8e25 // log(1/frcpa(1+25/256))= +9.52125e-002 -data8 0x3fb9335e5d594980, 0x3ca15c3abd47d99a // log(1/frcpa(1+26/256))= +9.84401e-002 -data8 0x3fba2b0220c8e5e0, 0x3cb4ca639adf6fc3 // log(1/frcpa(1+27/256))= +1.02219e-001 -data8 0x3fbb0004ac1a86a0, 0x3ca7cb81bf959a59 // log(1/frcpa(1+28/256))= +1.05469e-001 -data8 0x3fbbf968769fca00, 0x3cb0c646c121418e // log(1/frcpa(1+29/256))= +1.09274e-001 -data8 0x3fbccfedbfee13a0, 0x3ca0465fce24ab4b // log(1/frcpa(1+30/256))= +1.12548e-001 -data8 0x3fbda727638446a0, 0x3c82803f4e2e6603 // log(1/frcpa(1+31/256))= +1.15832e-001 -data8 0x3fbea3257fe10f60, 0x3cb986a3f2313d1a // log(1/frcpa(1+32/256))= +1.19677e-001 -data8 0x3fbf7be9fedbfde0, 0x3c97d16a6a621cf4 // log(1/frcpa(1+33/256))= +1.22985e-001 -data8 0x3fc02ab352ff25f0, 0x3c9cc6baad365600 // log(1/frcpa(1+34/256))= +1.26303e-001 -data8 0x3fc097ce579d2040, 0x3cb9ba16d329440b // log(1/frcpa(1+35/256))= +1.29633e-001 -data8 0x3fc1178e8227e470, 0x3cb7bc671683f8e6 // log(1/frcpa(1+36/256))= +1.33531e-001 -data8 0x3fc185747dbecf30, 0x3c9d1116f66d2345 // log(1/frcpa(1+37/256))= +1.36885e-001 -data8 0x3fc1f3b925f25d40, 0x3c8162c9ef939ac6 // log(1/frcpa(1+38/256))= +1.40250e-001 -data8 0x3fc2625d1e6ddf50, 0x3caad3a1ec384fc3 // log(1/frcpa(1+39/256))= +1.43627e-001 -data8 0x3fc2d1610c868130, 0x3cb3ad997036941b // log(1/frcpa(1+40/256))= +1.47015e-001 -data8 0x3fc340c597411420, 0x3cbc2308262c7998 // log(1/frcpa(1+41/256))= +1.50414e-001 -data8 0x3fc3b08b6757f2a0, 0x3cb2170d6cdf0526 // log(1/frcpa(1+42/256))= +1.53825e-001 -data8 0x3fc40dfb08378000, 0x3c9bb453c4f7b685 // log(1/frcpa(1+43/256))= +1.56677e-001 -data8 0x3fc47e74e8ca5f70, 0x3cb836a48fdfce9d // log(1/frcpa(1+44/256))= +1.60109e-001 -data8 0x3fc4ef51f6466de0, 0x3ca07a43919aa64b // log(1/frcpa(1+45/256))= +1.63553e-001 -data8 0x3fc56092e02ba510, 0x3ca85006899d97b0 // log(1/frcpa(1+46/256))= +1.67010e-001 -data8 0x3fc5d23857cd74d0, 0x3ca30a5ba6e7abbe // log(1/frcpa(1+47/256))= +1.70478e-001 -data8 0x3fc6313a37335d70, 0x3ca905586f0ac97e // log(1/frcpa(1+48/256))= +1.73377e-001 -data8 0x3fc6a399dabbd380, 0x3c9b2c6657a96684 // log(1/frcpa(1+49/256))= +1.76868e-001 -data8 0x3fc70337dd3ce410, 0x3cb50bc52f55cdd8 // log(1/frcpa(1+50/256))= +1.79786e-001 -data8 0x3fc77654128f6120, 0x3cad2eb7c9a39efe // log(1/frcpa(1+51/256))= +1.83299e-001 -data8 0x3fc7e9d82a0b0220, 0x3cba127e90393c01 // log(1/frcpa(1+52/256))= +1.86824e-001 -data8 0x3fc84a6b759f5120, 0x3cbd7fd52079f706 // log(1/frcpa(1+53/256))= +1.89771e-001 -data8 0x3fc8ab47d5f5a300, 0x3cbfae141751a3de // log(1/frcpa(1+54/256))= +1.92727e-001 -data8 0x3fc91fe490965810, 0x3cb69cf30a1c319e // log(1/frcpa(1+55/256))= +1.96286e-001 -data8 0x3fc981634011aa70, 0x3ca5bb3d208bc42a // log(1/frcpa(1+56/256))= +1.99261e-001 -data8 0x3fc9f6c407089660, 0x3ca04d68658179a0 // log(1/frcpa(1+57/256))= +2.02843e-001 -data8 0x3fca58e729348f40, 0x3c99f5411546c286 // log(1/frcpa(1+58/256))= +2.05838e-001 -data8 0x3fcabb55c31693a0, 0x3cb9a5350eb327d5 // log(1/frcpa(1+59/256))= +2.08842e-001 -data8 0x3fcb1e104919efd0, 0x3c18965fcce7c406 // log(1/frcpa(1+60/256))= +2.11855e-001 -data8 0x3fcb94ee93e367c0, 0x3cb503716da45184 // log(1/frcpa(1+61/256))= +2.15483e-001 -data8 0x3fcbf851c0675550, 0x3cbdf1b3f7ab5378 // log(1/frcpa(1+62/256))= +2.18516e-001 -data8 0x3fcc5c0254bf23a0, 0x3ca7aab9ed0b1d7b // log(1/frcpa(1+63/256))= +2.21558e-001 -data8 0x3fccc000c9db3c50, 0x3c92a7a2a850072a // log(1/frcpa(1+64/256))= +2.24609e-001 -data8 0x3fcd244d99c85670, 0x3c9f6019120edf4c // log(1/frcpa(1+65/256))= +2.27670e-001 -data8 0x3fcd88e93fb2f450, 0x3c6affb96815e081 // log(1/frcpa(1+66/256))= +2.30741e-001 -data8 0x3fcdedd437eaef00, 0x3c72553595897976 // log(1/frcpa(1+67/256))= +2.33820e-001 -data8 0x3fce530effe71010, 0x3c90913b020fa182 // log(1/frcpa(1+68/256))= +2.36910e-001 -data8 0x3fceb89a1648b970, 0x3c837ba4045bfd25 // log(1/frcpa(1+69/256))= +2.40009e-001 -data8 0x3fcf1e75fadf9bd0, 0x3cbcea6d13e0498d // log(1/frcpa(1+70/256))= +2.43117e-001 -data8 0x3fcf84a32ead7c30, 0x3ca5e3a67b3c6d77 // log(1/frcpa(1+71/256))= +2.46235e-001 -data8 0x3fcfeb2233ea07c0, 0x3cba0c6f0049c5a6 // log(1/frcpa(1+72/256))= +2.49363e-001 -data8 0x3fd028f9c7035c18, 0x3cb0a30b06677ff6 // log(1/frcpa(1+73/256))= +2.52501e-001 -data8 0x3fd05c8be0d96358, 0x3ca0f1c77ccb5865 // log(1/frcpa(1+74/256))= +2.55649e-001 -data8 0x3fd085eb8f8ae790, 0x3cbd513f45fe7a97 // log(1/frcpa(1+75/256))= +2.58174e-001 -data8 0x3fd0b9c8e32d1910, 0x3c927449047ca006 // log(1/frcpa(1+76/256))= +2.61339e-001 -data8 0x3fd0edd060b78080, 0x3c89b52d8435f53e // log(1/frcpa(1+77/256))= +2.64515e-001 -data8 0x3fd122024cf00638, 0x3cbdd976fabda4bd // log(1/frcpa(1+78/256))= +2.67701e-001 -data8 0x3fd14be2927aecd0, 0x3cb02f90ad0bc471 // log(1/frcpa(1+79/256))= +2.70257e-001 -data8 0x3fd180618ef18ad8, 0x3cbd003792c71a98 // log(1/frcpa(1+80/256))= +2.73461e-001 -data8 0x3fd1b50bbe2fc638, 0x3ca9ae64c6403ead // log(1/frcpa(1+81/256))= +2.76675e-001 -data8 0x3fd1df4cc7cf2428, 0x3cb43f0455f7e395 // log(1/frcpa(1+82/256))= +2.79254e-001 -data8 0x3fd214456d0eb8d0, 0x3cb0fbd748d75d30 // log(1/frcpa(1+83/256))= +2.82487e-001 -data8 0x3fd23ec5991eba48, 0x3c906edd746b77e2 // log(1/frcpa(1+84/256))= +2.85081e-001 -data8 0x3fd2740d9f870af8, 0x3ca9802e6a00a670 // log(1/frcpa(1+85/256))= +2.88333e-001 -data8 0x3fd29ecdabcdfa00, 0x3cacecef70890cfa // log(1/frcpa(1+86/256))= +2.90943e-001 -data8 0x3fd2d46602adcce8, 0x3cb97911955f3521 // log(1/frcpa(1+87/256))= +2.94214e-001 -data8 0x3fd2ff66b04ea9d0, 0x3cb12dabe191d1c9 // log(1/frcpa(1+88/256))= +2.96838e-001 -data8 0x3fd335504b355a30, 0x3cbdf9139df924ec // log(1/frcpa(1+89/256))= +3.00129e-001 -data8 0x3fd360925ec44f58, 0x3cb253e68977a1e3 // log(1/frcpa(1+90/256))= +3.02769e-001 -data8 0x3fd38bf1c3337e70, 0x3cb3d283d2a2da21 // log(1/frcpa(1+91/256))= +3.05417e-001 -data8 0x3fd3c25277333180, 0x3cadaa5b035eae27 // log(1/frcpa(1+92/256))= +3.08735e-001 -data8 0x3fd3edf463c16838, 0x3cb983d680d3c108 // log(1/frcpa(1+93/256))= +3.11399e-001 -data8 0x3fd419b423d5e8c0, 0x3cbc86dd921c139d // log(1/frcpa(1+94/256))= +3.14069e-001 -data8 0x3fd44591e0539f48, 0x3c86a76d6dc2782e // log(1/frcpa(1+95/256))= +3.16746e-001 -data8 0x3fd47c9175b6f0a8, 0x3cb59a2e013c6b5f // log(1/frcpa(1+96/256))= +3.20103e-001 -data8 0x3fd4a8b341552b08, 0x3c93f1e86e468694 // log(1/frcpa(1+97/256))= +3.22797e-001 -data8 0x3fd4d4f390890198, 0x3cbf5e4ea7c5105a // log(1/frcpa(1+98/256))= +3.25498e-001 -data8 0x3fd501528da1f960, 0x3cbf58da53e9ad10 // log(1/frcpa(1+99/256))= +3.28206e-001 -data8 0x3fd52dd06347d4f0, 0x3cb98a28cebf6eef // log(1/frcpa(1+100/256))= +3.30921e-001 -data8 0x3fd55a6d3c7b8a88, 0x3c9c76b67c2d1fd4 // log(1/frcpa(1+101/256))= +3.33644e-001 -data8 0x3fd5925d2b112a58, 0x3c9029616a4331b8 // log(1/frcpa(1+102/256))= +3.37058e-001 -data8 0x3fd5bf406b543db0, 0x3c9fb8292ecfc820 // log(1/frcpa(1+103/256))= +3.39798e-001 -data8 0x3fd5ec433d5c35a8, 0x3cb71a1229d17eec // log(1/frcpa(1+104/256))= +3.42545e-001 -data8 0x3fd61965cdb02c18, 0x3cbba94fe1dbb8d2 // log(1/frcpa(1+105/256))= +3.45300e-001 -data8 0x3fd646a84935b2a0, 0x3c9ee496d2c9ae57 // log(1/frcpa(1+106/256))= +3.48063e-001 -data8 0x3fd6740add31de90, 0x3cb1da3a6c7a9dfd // log(1/frcpa(1+107/256))= +3.50833e-001 -data8 0x3fd6a18db74a58c0, 0x3cb494c257add8dc // log(1/frcpa(1+108/256))= +3.53610e-001 -data8 0x3fd6cf31058670e8, 0x3cb0b244a70a8da9 // log(1/frcpa(1+109/256))= +3.56396e-001 -data8 0x3fd6f180e852f0b8, 0x3c9db7aefa866720 // log(1/frcpa(1+110/256))= +3.58490e-001 -data8 0x3fd71f5d71b894e8, 0x3cbe91c4bf324957 // log(1/frcpa(1+111/256))= +3.61289e-001 -data8 0x3fd74d5aefd66d58, 0x3cb06b3d9bfac023 // log(1/frcpa(1+112/256))= +3.64096e-001 -data8 0x3fd77b79922bd378, 0x3cb727d8804491f4 // log(1/frcpa(1+113/256))= +3.66911e-001 -data8 0x3fd7a9b9889f19e0, 0x3ca2ef22df5bc543 // log(1/frcpa(1+114/256))= +3.69734e-001 -data8 0x3fd7d81b037eb6a0, 0x3cb8fd3ba07a7ece // log(1/frcpa(1+115/256))= +3.72565e-001 -data8 0x3fd8069e33827230, 0x3c8bd1e25866e61a // log(1/frcpa(1+116/256))= +3.75404e-001 -data8 0x3fd82996d3ef8bc8, 0x3ca5aab9f5928928 // log(1/frcpa(1+117/256))= +3.77538e-001 -data8 0x3fd85855776dcbf8, 0x3ca56f33337789d6 // log(1/frcpa(1+118/256))= +3.80391e-001 -data8 0x3fd8873658327cc8, 0x3cbb8ef0401db49d // log(1/frcpa(1+119/256))= +3.83253e-001 -data8 0x3fd8aa75973ab8c8, 0x3cbb9961f509a680 // log(1/frcpa(1+120/256))= +3.85404e-001 -data8 0x3fd8d992dc8824e0, 0x3cb220512a53732d // log(1/frcpa(1+121/256))= +3.88280e-001 -data8 0x3fd908d2ea7d9510, 0x3c985f0e513bfb5c // log(1/frcpa(1+122/256))= +3.91164e-001 -data8 0x3fd92c59e79c0e50, 0x3cb82e073fd30d63 // log(1/frcpa(1+123/256))= +3.93332e-001 -data8 0x3fd95bd750ee3ed0, 0x3ca4aa7cdb6dd8a8 // log(1/frcpa(1+124/256))= +3.96231e-001 -data8 0x3fd98b7811a3ee58, 0x3caa93a5b660893e // log(1/frcpa(1+125/256))= +3.99138e-001 -data8 0x3fd9af47f33d4068, 0x3cac294b3b3190ba // log(1/frcpa(1+126/256))= +4.01323e-001 -data8 0x3fd9df270c1914a0, 0x3cbe1a58fd0cd67e // log(1/frcpa(1+127/256))= +4.04245e-001 -data8 0x3fda0325ed14fda0, 0x3cb1efa7950fb57e // log(1/frcpa(1+128/256))= +4.06442e-001 -data8 0x3fda33440224fa78, 0x3c8915fe75e7d477 // log(1/frcpa(1+129/256))= +4.09379e-001 -data8 0x3fda57725e80c380, 0x3ca72bd1062b1b7f // log(1/frcpa(1+130/256))= +4.11587e-001 -data8 0x3fda87d0165dd198, 0x3c91f7845f58dbad // log(1/frcpa(1+131/256))= +4.14539e-001 -data8 0x3fdaac2e6c03f890, 0x3cb6f237a911c509 // log(1/frcpa(1+132/256))= +4.16759e-001 -data8 0x3fdadccc6fdf6a80, 0x3c90ddc4b7687169 // log(1/frcpa(1+133/256))= +4.19726e-001 -data8 0x3fdb015b3eb1e790, 0x3c692dd7d90e1e8e // log(1/frcpa(1+134/256))= +4.21958e-001 -data8 0x3fdb323a3a635948, 0x3c6f85655cbe14de // log(1/frcpa(1+135/256))= +4.24941e-001 -data8 0x3fdb56fa04462908, 0x3c95252d841994de // log(1/frcpa(1+136/256))= +4.27184e-001 -data8 0x3fdb881aa659bc90, 0x3caa53a745a3642f // log(1/frcpa(1+137/256))= +4.30182e-001 -data8 0x3fdbad0bef3db160, 0x3cb32f2540dcc16a // log(1/frcpa(1+138/256))= +4.32437e-001 -data8 0x3fdbd21297781c28, 0x3cbd8e891e106f1d // log(1/frcpa(1+139/256))= +4.34697e-001 -data8 0x3fdc039236f08818, 0x3c809435af522ba7 // log(1/frcpa(1+140/256))= +4.37718e-001 -data8 0x3fdc28cb1e4d32f8, 0x3cb3944752fbd81e // log(1/frcpa(1+141/256))= +4.39990e-001 -data8 0x3fdc4e19b84723c0, 0x3c9a465260cd3fe5 // log(1/frcpa(1+142/256))= +4.42267e-001 -data8 0x3fdc7ff9c74554c8, 0x3c92447d5b6ca369 // log(1/frcpa(1+143/256))= +4.45311e-001 -data8 0x3fdca57b64e9db00, 0x3cb44344a8a00c82 // log(1/frcpa(1+144/256))= +4.47600e-001 -data8 0x3fdccb130a5ceba8, 0x3cbefaddfb97b73f // log(1/frcpa(1+145/256))= +4.49895e-001 -data8 0x3fdcf0c0d18f3268, 0x3cbd3e7bfee57898 // log(1/frcpa(1+146/256))= +4.52194e-001 -data8 0x3fdd232075b5a200, 0x3c9222599987447c // log(1/frcpa(1+147/256))= +4.55269e-001 -data8 0x3fdd490246defa68, 0x3cabafe9a767a80d // log(1/frcpa(1+148/256))= +4.57581e-001 -data8 0x3fdd6efa918d25c8, 0x3cb58a2624e1c6fd // log(1/frcpa(1+149/256))= +4.59899e-001 -data8 0x3fdd9509707ae528, 0x3cbdc3babce578e7 // log(1/frcpa(1+150/256))= +4.62221e-001 -data8 0x3fddbb2efe92c550, 0x3cb0ac0943c434a4 // log(1/frcpa(1+151/256))= +4.64550e-001 -data8 0x3fddee2f3445e4a8, 0x3cbba9d07ce820e8 // log(1/frcpa(1+152/256))= +4.67663e-001 -data8 0x3fde148a1a2726c8, 0x3cb6537e3375b205 // log(1/frcpa(1+153/256))= +4.70004e-001 -data8 0x3fde3afc0a49ff38, 0x3cbfed5518dbc20e // log(1/frcpa(1+154/256))= +4.72350e-001 -data8 0x3fde6185206d5168, 0x3cb6572601f73d5c // log(1/frcpa(1+155/256))= +4.74702e-001 -data8 0x3fde882578823d50, 0x3c9b24abd4584d1a // log(1/frcpa(1+156/256))= +4.77060e-001 -data8 0x3fdeaedd2eac9908, 0x3cb0ceb5e4d2c8f7 // log(1/frcpa(1+157/256))= +4.79423e-001 -data8 0x3fded5ac5f436be0, 0x3ca72f21f1f5238e // log(1/frcpa(1+158/256))= +4.81792e-001 -data8 0x3fdefc9326d16ab8, 0x3c85081a1639a45c // log(1/frcpa(1+159/256))= +4.84166e-001 -data8 0x3fdf2391a21575f8, 0x3cbf11015bdd297a // log(1/frcpa(1+160/256))= +4.86546e-001 -data8 0x3fdf4aa7ee031928, 0x3cb3795bc052a2d1 // log(1/frcpa(1+161/256))= +4.88932e-001 -data8 0x3fdf71d627c30bb0, 0x3c35c61f0f5a88f3 // log(1/frcpa(1+162/256))= +4.91323e-001 -data8 0x3fdf991c6cb3b378, 0x3c97d99419be6028 // log(1/frcpa(1+163/256))= +4.93720e-001 -data8 0x3fdfc07ada69a908, 0x3cbfe9341ded70b1 // log(1/frcpa(1+164/256))= +4.96123e-001 -data8 0x3fdfe7f18eb03d38, 0x3cb85718a640c33f // log(1/frcpa(1+165/256))= +4.98532e-001 -data8 0x3fe007c053c5002c, 0x3cb3addc9c065f09 // log(1/frcpa(1+166/256))= +5.00946e-001 -data8 0x3fe01b942198a5a0, 0x3c9d5aa4c77da6ac // log(1/frcpa(1+167/256))= +5.03367e-001 -data8 0x3fe02f74400c64e8, 0x3cb5a0ee4450ef52 // log(1/frcpa(1+168/256))= +5.05793e-001 -data8 0x3fe04360be7603ac, 0x3c9dd00c35630fe0 // log(1/frcpa(1+169/256))= +5.08225e-001 -data8 0x3fe05759ac47fe30, 0x3cbd063e1f0bd82c // log(1/frcpa(1+170/256))= +5.10663e-001 -data8 0x3fe06b5f1911cf50, 0x3cae8da674af5289 // log(1/frcpa(1+171/256))= +5.13107e-001 -data8 0x3fe078bf0533c568, 0x3c62241edf5fd1f7 // log(1/frcpa(1+172/256))= +5.14740e-001 -data8 0x3fe08cd9687e7b0c, 0x3cb3007febcca227 // log(1/frcpa(1+173/256))= +5.17194e-001 -data8 0x3fe0a10074cf9018, 0x3ca496e84603816b // log(1/frcpa(1+174/256))= +5.19654e-001 -data8 0x3fe0b5343a234474, 0x3cb46098d14fc90a // log(1/frcpa(1+175/256))= +5.22120e-001 -data8 0x3fe0c974c89431cc, 0x3cac0a7cdcbb86c6 // log(1/frcpa(1+176/256))= +5.24592e-001 -data8 0x3fe0ddc2305b9884, 0x3cb2f753210410ff // log(1/frcpa(1+177/256))= +5.27070e-001 -data8 0x3fe0eb524bafc918, 0x3c88affd6682229e // log(1/frcpa(1+178/256))= +5.28726e-001 -data8 0x3fe0ffb54213a474, 0x3cadeefbab9af993 // log(1/frcpa(1+179/256))= +5.31214e-001 -data8 0x3fe114253da97d9c, 0x3cbaf1c2b8bc160a // log(1/frcpa(1+180/256))= +5.33709e-001 -data8 0x3fe128a24f1d9afc, 0x3cb9cf4df375e650 // log(1/frcpa(1+181/256))= +5.36210e-001 -data8 0x3fe1365252bf0864, 0x3c985a621d4be111 // log(1/frcpa(1+182/256))= +5.37881e-001 -data8 0x3fe14ae558b4a92c, 0x3ca104c4aa8977d1 // log(1/frcpa(1+183/256))= +5.40393e-001 -data8 0x3fe15f85a19c7658, 0x3cbadf26e540f375 // log(1/frcpa(1+184/256))= +5.42910e-001 -data8 0x3fe16d4d38c119f8, 0x3cb3aea11caec416 // log(1/frcpa(1+185/256))= +5.44592e-001 -data8 0x3fe18203c20dd130, 0x3cba82d1211d1d6d // log(1/frcpa(1+186/256))= +5.47121e-001 -data8 0x3fe196c7bc4b1f38, 0x3cb6267acc4f4f4a // log(1/frcpa(1+187/256))= +5.49656e-001 -data8 0x3fe1a4a738b7a33c, 0x3c858930213c987d // log(1/frcpa(1+188/256))= +5.51349e-001 -data8 0x3fe1b981c0c9653c, 0x3c9bc2a4a30f697b // log(1/frcpa(1+189/256))= +5.53895e-001 -data8 0x3fe1ce69e8bb1068, 0x3cb7ae6199cf2a00 // log(1/frcpa(1+190/256))= +5.56447e-001 -data8 0x3fe1dc619de06944, 0x3c6b50bb38388177 // log(1/frcpa(1+191/256))= +5.58152e-001 -data8 0x3fe1f160a2ad0da0, 0x3cbd05b2778a5e1d // log(1/frcpa(1+192/256))= +5.60715e-001 -data8 0x3fe2066d7740737c, 0x3cb32e828f9c6bd6 // log(1/frcpa(1+193/256))= +5.63285e-001 -data8 0x3fe2147dba47a390, 0x3cbd579851b8b672 // log(1/frcpa(1+194/256))= +5.65001e-001 -data8 0x3fe229a1bc5ebac0, 0x3cbb321be5237ce8 // log(1/frcpa(1+195/256))= +5.67582e-001 -data8 0x3fe237c1841a502c, 0x3cb3b56e0915ea64 // log(1/frcpa(1+196/256))= +5.69306e-001 -data8 0x3fe24cfce6f80d98, 0x3cb34a4d1a422919 // log(1/frcpa(1+197/256))= +5.71898e-001 -data8 0x3fe25b2c55cd5760, 0x3cb237401ea5015e // log(1/frcpa(1+198/256))= +5.73630e-001 -data8 0x3fe2707f4d5f7c40, 0x3c9d30f20acc8341 // log(1/frcpa(1+199/256))= +5.76233e-001 -data8 0x3fe285e0842ca380, 0x3cbc4d866d5f21c0 // log(1/frcpa(1+200/256))= +5.78842e-001 -data8 0x3fe294294708b770, 0x3cb85e14d5dc54fa // log(1/frcpa(1+201/256))= +5.80586e-001 -data8 0x3fe2a9a2670aff0c, 0x3c7e6f8f468bbf91 // log(1/frcpa(1+202/256))= +5.83207e-001 -data8 0x3fe2b7fb2c8d1cc0, 0x3c930ffcf63c8b65 // log(1/frcpa(1+203/256))= +5.84959e-001 -data8 0x3fe2c65a6395f5f4, 0x3ca0afe20b53d2d2 // log(1/frcpa(1+204/256))= +5.86713e-001 -data8 0x3fe2dbf557b0df40, 0x3cb646be1188fbc9 // log(1/frcpa(1+205/256))= +5.89350e-001 -data8 0x3fe2ea64c3f97654, 0x3c96516fa8df33b2 // log(1/frcpa(1+206/256))= +5.91113e-001 -data8 0x3fe3001823684d70, 0x3cb96d64e16d1360 // log(1/frcpa(1+207/256))= +5.93762e-001 -data8 0x3fe30e97e9a8b5cc, 0x3c98ef96bc97cca0 // log(1/frcpa(1+208/256))= +5.95531e-001 -data8 0x3fe32463ebdd34e8, 0x3caef1dc9a56c1bf // log(1/frcpa(1+209/256))= +5.98192e-001 -data8 0x3fe332f4314ad794, 0x3caa4f0ac5d5fa11 // log(1/frcpa(1+210/256))= +5.99970e-001 -data8 0x3fe348d90e7464cc, 0x3cbe7889f0516acd // log(1/frcpa(1+211/256))= +6.02643e-001 -data8 0x3fe35779f8c43d6c, 0x3ca96bbab7245411 // log(1/frcpa(1+212/256))= +6.04428e-001 -data8 0x3fe36621961a6a98, 0x3ca31f32262db9fb // log(1/frcpa(1+213/256))= +6.06217e-001 -data8 0x3fe37c299f3c3668, 0x3cb15c72c107ee29 // log(1/frcpa(1+214/256))= +6.08907e-001 -data8 0x3fe38ae2171976e4, 0x3cba42a2554b2dd4 // log(1/frcpa(1+215/256))= +6.10704e-001 -data8 0x3fe399a157a603e4, 0x3cb99c62286d8919 // log(1/frcpa(1+216/256))= +6.12504e-001 -data8 0x3fe3afccfe77b9d0, 0x3ca11048f96a43bd // log(1/frcpa(1+217/256))= +6.15210e-001 -data8 0x3fe3be9d503533b4, 0x3ca4022f47588c3e // log(1/frcpa(1+218/256))= +6.17018e-001 -data8 0x3fe3cd7480b4a8a0, 0x3cb4ba7afc2dc56a // log(1/frcpa(1+219/256))= +6.18830e-001 -data8 0x3fe3e3c43918f76c, 0x3c859673d064b8ba // log(1/frcpa(1+220/256))= +6.21554e-001 -data8 0x3fe3f2acb27ed6c4, 0x3cb55c6b452a16a8 // log(1/frcpa(1+221/256))= +6.23373e-001 -data8 0x3fe4019c2125ca90, 0x3cb8c367879c5a31 // log(1/frcpa(1+222/256))= +6.25197e-001 -data8 0x3fe4181061389720, 0x3cb2c17a79c5cc6c // log(1/frcpa(1+223/256))= +6.27937e-001 -data8 0x3fe42711518df544, 0x3ca5f38d47012fc5 // log(1/frcpa(1+224/256))= +6.29769e-001 -data8 0x3fe436194e12b6bc, 0x3cb9854d65a9b426 // log(1/frcpa(1+225/256))= +6.31604e-001 -data8 0x3fe445285d68ea68, 0x3ca3ff9b3a81cd81 // log(1/frcpa(1+226/256))= +6.33442e-001 -data8 0x3fe45bcc464c8938, 0x3cb0a2d8011a6c05 // log(1/frcpa(1+227/256))= +6.36206e-001 -data8 0x3fe46aed21f117fc, 0x3c8a2be41f8e9f3d // log(1/frcpa(1+228/256))= +6.38053e-001 -data8 0x3fe47a1527e8a2d0, 0x3cba4a83594fab09 // log(1/frcpa(1+229/256))= +6.39903e-001 -data8 0x3fe489445efffcc8, 0x3cbf306a23dcbcde // log(1/frcpa(1+230/256))= +6.41756e-001 -data8 0x3fe4a018bcb69834, 0x3ca46c9285029fd1 // log(1/frcpa(1+231/256))= +6.44543e-001 -data8 0x3fe4af5a0c9d65d4, 0x3cbbc1db897580e3 // log(1/frcpa(1+232/256))= +6.46405e-001 -data8 0x3fe4bea2a5bdbe84, 0x3cb84d880d7ef775 // log(1/frcpa(1+233/256))= +6.48271e-001 -data8 0x3fe4cdf28f10ac44, 0x3cb3ec4b7893ce1f // log(1/frcpa(1+234/256))= +6.50140e-001 -data8 0x3fe4dd49cf994058, 0x3c897224d59d3408 // log(1/frcpa(1+235/256))= +6.52013e-001 -data8 0x3fe4eca86e64a680, 0x3cbccf620f24f0cd // log(1/frcpa(1+236/256))= +6.53889e-001 -data8 0x3fe503c43cd8eb68, 0x3c3f872c65971084 // log(1/frcpa(1+237/256))= +6.56710e-001 -data8 0x3fe513356667fc54, 0x3cb9ca64cc3d52c8 // log(1/frcpa(1+238/256))= +6.58595e-001 -data8 0x3fe522ae0738a3d4, 0x3cbe708164c75968 // log(1/frcpa(1+239/256))= +6.60483e-001 -data8 0x3fe5322e26867854, 0x3cb9988ba4aea615 // log(1/frcpa(1+240/256))= +6.62376e-001 -data8 0x3fe541b5cb979808, 0x3ca1662e3a6b95f5 // log(1/frcpa(1+241/256))= +6.64271e-001 -data8 0x3fe55144fdbcbd60, 0x3cb3acd4ca45c1e0 // log(1/frcpa(1+242/256))= +6.66171e-001 -data8 0x3fe560dbc45153c4, 0x3cb4988947959fed // log(1/frcpa(1+243/256))= +6.68074e-001 -data8 0x3fe5707a26bb8c64, 0x3cb3017fe6607ba9 // log(1/frcpa(1+244/256))= +6.69980e-001 -data8 0x3fe587f60ed5b8fc, 0x3cbe7a3266366ed4 // log(1/frcpa(1+245/256))= +6.72847e-001 -data8 0x3fe597a7977c8f30, 0x3ca1e12b9959a90e // log(1/frcpa(1+246/256))= +6.74763e-001 -data8 0x3fe5a760d634bb88, 0x3cb7c365e53d9602 // log(1/frcpa(1+247/256))= +6.76682e-001 -data8 0x3fe5b721d295f10c, 0x3cb716c2551ccbf0 // log(1/frcpa(1+248/256))= +6.78605e-001 -data8 0x3fe5c6ea94431ef8, 0x3ca02b2ed0e28261 // log(1/frcpa(1+249/256))= +6.80532e-001 -data8 0x3fe5d6bb22ea86f4, 0x3caf43a8bbb2f974 // log(1/frcpa(1+250/256))= +6.82462e-001 -data8 0x3fe5e6938645d38c, 0x3cbcedc98821b333 // log(1/frcpa(1+251/256))= +6.84397e-001 -data8 0x3fe5f673c61a2ed0, 0x3caa385eef5f2789 // log(1/frcpa(1+252/256))= +6.86335e-001 -data8 0x3fe6065bea385924, 0x3cb11624f165c5b4 // log(1/frcpa(1+253/256))= +6.88276e-001 -data8 0x3fe6164bfa7cc068, 0x3cbad884f87073fa // log(1/frcpa(1+254/256))= +6.90222e-001 -data8 0x3fe62643fecf9740, 0x3cb78c51da12f4df // log(1/frcpa(1+255/256))= +6.92171e-001 +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) @@ -909,14 +879,14 @@ GLOBAL_LIBM_ENTRY(powf) 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 - nop.i 999 + mov pow_GR_exp_half = 0xFFFE // Exponent for 0.5 } { .mfi ld8 pow_AD_P = [pow_AD_P] @@ -925,11 +895,10 @@ GLOBAL_LIBM_ENTRY(powf) } ;; -// p13 = TRUE ==> X is unorm // DOUBLE 0x10033 exponent limit at which y is an integer { .mfi nop.m 999 - fclass.m p13,p0 = f8, 0x0b // Test for x unorm + fcmp.lt.s1 p8,p9 = f8, f0 // Test for x<0 addl pow_GR_10033 = 0x10033, r0 } { .mfi @@ -939,11 +908,11 @@ GLOBAL_LIBM_ENTRY(powf) } ;; -// p14 = TRUE ==> X is ZERO +// 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 - fclass.m p14,p0 = f8, 0x07 - and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones } { .mfi adds pow_AD_Q = pow_table_Q - pow_table_P, pow_AD_P @@ -952,14 +921,16 @@ GLOBAL_LIBM_ENTRY(powf) } ;; +// p14 = TRUE ==> X is ZERO { .mfi - ldfe POW_P5 = [pow_AD_P], 16 - fcmp.lt.s1 p8,p9 = f8, f0 // Test for x<0 + ldfe POW_P2 = [pow_AD_Q], 16 + fclass.m p14,p0 = f8, 0x07 nop.i 999 } -{ .mib - ldfe POW_P4 = [pow_AD_Q], 16 - sub pow_GR_true_exp_X = pow_GR_exp_X, pow_GR_16ones +// 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 } ;; @@ -968,26 +939,33 @@ GLOBAL_LIBM_ENTRY(powf) POW_COMMON: // p11 = TRUE ==> Y is a NAN { .mfi - ldfe POW_P3 = [pow_AD_P], 16 + and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones fclass.m p11,p0 = f9, 0xc3 nop.i 999 } { .mfi - ldfe POW_P2 = [pow_AD_Q], 16 - nop.f 999 + nop.m 999 + fms.s1 POW_r = POW_B, POW_NORM_X,f1 mov pow_GR_y_zero = 0 } ;; -// Note POW_Xm1 and POW_r1 are used interchangably +// 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 - fms.s1 POW_r = POW_B, POW_NORM_X,f1 - nop.i 999 + 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 -(p8) fnma.s1 POW_Xm1 = POW_Xp1,f1,f0 + nop.f 999 nop.i 999 } ;; @@ -997,7 +975,7 @@ POW_COMMON: { .mfi ldfe POW_P1 = [pow_AD_P], 16 fclass.m p12,p0 = f9, 0x07 - shl pow_GR_offset = pow_GR_sig_X, 1 + nop.i 999 } { .mfb ldfe POW_P0 = [pow_AD_Q], 16 @@ -1006,19 +984,18 @@ POW_COMMON: } ;; -// Get exponent of |x|-1 to use in comparison to 2^-8 -{ .mfi - getf.exp pow_GR_signexp_Xm1 = POW_Xm1 - fcvt.fx.s1 POW_int_Y = POW_NORM_Y - shr.u pow_GR_offset = pow_GR_offset,56 +{ .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 = f8, 0xc3 - shladd pow_AD_Tt = pow_GR_offset, 4, pow_AD_Tt + fclass.m p11,p0 = POW_NORM_X, 0xc3 + nop.i 999 } { .mfi ldfe POW_inv_log2_by_128 = [pow_AD_P], 16 @@ -1028,28 +1005,33 @@ POW_COMMON: ;; { .mfi - ldfpd POW_Q2, POW_Q3 = [pow_AD_P], 16 - fma.s1 POW_G = f0,f0,f0 // G=0 in case |x| near 1 + 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 - getf.exp pow_GR_signexp_Y = POW_NORM_Y - nop.f 999 + nop.m 999 + fcvt.xf POW_K = POW_int_K cmp.lt p6,p7 = pow_GR_exp_Xm1, pow_GR_exp_2tom8 } { .mfb - ldfpd POW_T, POW_Tt = [pow_AD_Tt], 16 - fma.s1 POW_rsq = POW_r, POW_r,f0 + 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 and r1*r1 to rsq +// If on the x near 1 path, assign r1 to r { .mfi - ldfpd POW_Q0_half, POW_Q1 = [pow_AD_P], 16 + ldfpd POW_Q1, POW_RSHF = [pow_AD_P], 16 (p6) fma.s1 POW_r = POW_r1, f1, f0 nop.i 999 } @@ -1061,57 +1043,25 @@ POW_COMMON: ;; { .mfi - ldfpd POW_Q4, POW_RSHF = [pow_AD_P], 16 -(p7) fma.s1 POW_v6 = POW_r, POW_P5, POW_P4 - nop.i 999 -} -{ .mfi - nop.m 999 -(p6) fma.s1 POW_v6 = POW_r1, POW_P5, POW_P4 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p7) fma.s1 POW_v4 = POW_P3, POW_r, POW_P2 - nop.i 999 -} -{ .mfi - nop.m 999 -(p6) fma.s1 POW_v4 = POW_P3, POW_r1, POW_P2 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fcvt.xf POW_K = POW_int_K - nop.i 999 -} -;; - -{ .mfi getf.sig pow_GR_sig_int_Y = POW_int_Y - fnma.s1 POW_twoV = POW_NORM_Y, POW_rsq,f0 +(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 - fma.s1 POW_U = POW_NORM_Y,POW_r,f0 +(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 } ;; -// p11 = TRUE ==> X is NEGATIVE but not inf { .mfi ldfe POW_log2_by_128_lo = [pow_AD_P], 16 - fclass.m p11,p0 = f8, 0x1a +(p7) fma.s1 POW_Z2 = POW_twoV, POW_U, f0 nop.i 999 } { .mfi ldfe POW_log2_by_128_hi = [pow_AD_Q], 16 - fma.s1 POW_v2 = POW_P1, POW_r, POW_P0 + nop.f 999 nop.i 999 } ;; @@ -1123,43 +1073,32 @@ POW_COMMON: } { .mfi nop.m 999 - fma.s1 POW_v3 = POW_v6, POW_rsq, POW_v4 +(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 -(p7) fma.s1 POW_delta = POW_K, POW_log2_lo, POW_Tt + fclass.m p11,p0 = POW_NORM_X, 0x1a nop.i 999 } { .mfi nop.m 999 -(p7) fma.s1 POW_G = POW_K, POW_log2_hi, POW_T +(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 - fms.s1 POW_e2 = POW_NORM_Y, POW_r, POW_U +(p6) fma.s1 POW_Z = POW_twoV, POW_U, f0 nop.i 999 } { .mfi nop.m 999 - fma.s1 POW_Z2 = POW_twoV, POW_Q0_half, POW_U - 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_v3, POW_v2 + fma.s1 POW_v2 = POW_P1, POW_r, POW_P0 nop.i 999 } ;; @@ -1169,7 +1108,7 @@ POW_COMMON: // p13 = TRUE ==> X is NEGATIVE AND Y possible int { .mfi nop.m 999 - fma.s1 POW_Z1 = POW_NORM_Y, POW_G, f0 +(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 @@ -1179,35 +1118,28 @@ POW_COMMON: } ;; -// By adding RSHF (1.1000...*2^63) we put integer part in rightmost significand { .mfi nop.m 999 - fma.s1 POW_W2 = POW_Z2, POW_inv_log2_by_128, POW_RSHF + fma.s1 POW_Yrcub = POW_rsq, POW_U, f0 nop.i 999 } { .mfi nop.m 999 - fms.s1 POW_UmZ2 = POW_U, f1, POW_Z2 + fma.s1 POW_p = POW_rsq, POW_P2, POW_v2 nop.i 999 } ;; +// Test if x inf { .mfi nop.m 999 - fma.s1 POW_Z3 = POW_p, POW_Yrcub, f0 + 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 - fms.s1 POW_e1 = POW_NORM_Y, POW_G, POW_Z1 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_W1 = POW_Z1, POW_inv_log2_by_128, POW_RSHF + fma.s1 POW_W1 = POW_Z, POW_inv_log2_by_128, POW_RSHF nop.i 999 } ;; @@ -1227,93 +1159,38 @@ POW_COMMON: } ;; -// By subtracting RSHF we get rounded integer POW_N2float -{ .mfi - nop.m 999 - fms.s1 POW_N2float = POW_W2, f1, POW_RSHF - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_UmZ2pV = POW_twoV,POW_Q0_half,POW_UmZ2 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_Z3sq = POW_Z3, POW_Z3, f0 - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_v4 = POW_Z3, POW_Q3, POW_Q2 - nop.i 999 -} -;; - -// Extract rounded integer from rightmost significand of POW_W2 -// By subtracting RSHF we get rounded integer POW_N1float -{ .mfi - getf.sig pow_GR_int_W2 = POW_W2 - fms.s1 POW_N1float = POW_W1, f1, POW_RSHF - nop.i 999 -} -{ .mfi - nop.m 999 - fma.s1 POW_v2 = POW_Z3, POW_Q1, POW_Q0_half - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fnma.s1 POW_s2 = POW_N2float, POW_log2_by_128_hi, POW_Z2 - nop.i 999 -} +// p11 = TRUE ==> X is +1.0 { .mfi nop.m 999 - fma.s1 POW_e2 = POW_e2,f1,POW_UmZ2pV + fcmp.eq.s1 p11,p0 = POW_NORM_X, f1 nop.i 999 } ;; // Extract rounded integer from rightmost significand of POW_W1 -// Test if x inf +// By subtracting RSHF we get rounded integer POW_Nfloat { .mfi - getf.sig pow_GR_int_W1 = POW_W1 - fclass.m p15,p0 = POW_NORM_X, 0x23 + getf.sig pow_GR_int_N = POW_W1 + fms.s1 POW_Nfloat = POW_W1, f1, POW_RSHF nop.i 999 } { .mfb nop.m 999 - fnma.s1 POW_f2 = POW_N2float, POW_log2_by_128_lo, f1 + 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 } ;; -// p11 = TRUE ==> X is +1.0 +// 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 p11,p0 = POW_NORM_X, f1 + 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 } -{ .mfi - nop.m 999 - fma.s1 POW_v3 = POW_Z3sq, POW_Q4, POW_v4 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fnma.s1 POW_f1 = POW_N1float, POW_log2_by_128_lo, f1 - nop.i 999 -} { .mfb nop.m 999 - fnma.s1 POW_s1 = POW_N1float, POW_log2_by_128_hi, POW_Z1 +(p11) fma.s.s0 f8 = f1,f1,f0 // If x=1, result is +1 (p15) br.cond.spnt POW_X_INF } ;; @@ -1324,77 +1201,73 @@ POW_COMMON: fcmp.eq.s0 p15,p0 = f8,f9 nop.i 999 } -{ .mfi +{ .mfb nop.m 999 fma.s1 POW_e3 = POW_NORM_Y, POW_delta, f0 - nop.i 999 +(p11) br.ret.spnt b0 // Early exit if x=1.0, result is +1 } ;; { .mfi - nop.m 999 - fcmp.eq.s1 p7,p0 = POW_NORM_Y, f1 // Test for y=1.0 +(p12) mov pow_GR_xneg_yodd = 1 + fnma.s1 POW_f12 = POW_Nfloat, POW_log2_by_128_lo, f1 nop.i 999 } -{ .mfi +{ .mfb nop.m 999 - fma.s1 POW_e12 = POW_e1,f1,POW_e2 - nop.i 999 -} -;; - -{ .mfi - add pow_GR_int_N = pow_GR_int_W1, pow_GR_int_W2 -(p11) fma.s.s0 f8 = f1,f1,f0 // If x=1, result is +1 - nop.i 999 -} -{ .mib -(p12) mov pow_GR_xneg_yodd = 1 - nop.i 999 -(p11) br.ret.spnt b0 // Early exit if x=1.0, result is +1 + 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 } ;; -{ .mfi +{ .mmi and pow_GR_index1 = 0x0f, pow_GR_int_N - fma.s1 POW_q = POW_Z3sq, POW_v3, POW_v2 - shr pow_int_GR_M = pow_GR_int_N, 7 // M = N/128 -} -{ .mib and pow_GR_index2 = 0x70, pow_GR_int_N - nop.i 999 -(p7) br.ret.spnt b0 // Early exit if y=1.0, result is x + 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_s = POW_s1, f1, POW_s2 + 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_f12 = POW_f1, POW_f2,f0 + fma.s1 POW_Z3sq = POW_Z3, POW_Z3, f0 nop.i 999 } ;; -{ .mmf +{ .mmi ldfe POW_T1 = [pow_AD_T1] ldfe POW_T2 = [pow_AD_T2] - nop.f 999 + nop.i 999 } ;; +// f123 = f12*(e3+1) = f12*e3+f12 { .mfi setf.exp POW_2M = pow_int_GR_M - fma.s1 POW_e123 = POW_e12, f1, POW_e3 - and pow_GR_exp_Y_Gpr = pow_GR_signexp_Y_Gpr, pow_GR_17ones + 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 } @@ -1411,88 +1284,62 @@ POW_COMMON: // Form signexp of constants to indicate overflow { .mfi mov pow_GR_big_pos = 0x1007f - fma.s1 POW_ssq = POW_s, POW_s, f0 + nop.f 999 cmp.le p8,p9 = 7, pow_GR_true_exp_Y_Gpr } { .mfi mov pow_GR_big_neg = 0x3007f - fma.s1 POW_v4 = POW_s, POW_Q3, POW_Q2 + 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_v2 = POW_s, POW_Q1, POW_Q0_half + 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 = f1,f1,POW_s + fma.s1 POW_1ps = POW_s, POW_f123, POW_f123 (p8) br.cond.spnt POW_OVER_UNDER_X_NOT_INF } ;; -// f123 = f12*(e123+1) = f12*e123+f12 { .mfi nop.m 999 - fma.s1 POW_f123 = POW_e123,POW_f12,POW_f12 +(p12) fnma.s1 POW_T1T2 = POW_T1, POW_T2, f0 nop.i 999 } -;; - { .mfi nop.m 999 - fma.s1 POW_T1T2 = POW_T1, POW_T2, f0 +(p13) fma.s1 POW_T1T2 = POW_T1, POW_T2, f0 nop.i 999 } -{ .mfi - nop.m 999 - fma.s1 POW_v3 = POW_ssq, POW_Q4, POW_v4 - cmp.ne p12,p13 = pow_GR_xneg_yodd, r0 -} ;; { .mfi nop.m 999 - fma.s1 POW_2Mqp1 = POW_2M, POW_q, POW_2M - nop.i 999 -} -;; - -{ .mfi - nop.m 999 - fma.s1 POW_v21ps = POW_ssq, POW_v2, POW_1ps + fma.s1 POW_v210 = POW_s, POW_v2, POW_Q0_half nop.i 999 } { .mfi nop.m 999 - fma.s1 POW_s4 = POW_ssq, POW_ssq, f0 - nop.i 999 -} -;; - -{ .mfi - nop.m 999 -(p12) fnma.s1 POW_A = POW_T1T2, POW_f123, f0 - nop.i 999 -} -{ .mfi - nop.m 999 -(p13) fma.s1 POW_A = POW_T1T2, POW_f123, f0 + fma.s1 POW_2Mqp1 = POW_2M, POW_q, POW_2M nop.i 999 } ;; { .mfi nop.m 999 - fma.s1 POW_es = POW_s4, POW_v3, POW_v21ps + fma.s1 POW_es = POW_ssq, POW_v210, POW_1ps nop.i 999 } { .mfi nop.m 999 - fma.s1 POW_A = POW_A, POW_2Mqp1, f0 + fma.s1 POW_A = POW_T1T2, POW_2Mqp1, f0 nop.i 999 } ;; @@ -1623,16 +1470,25 @@ POW_POSSIBLE_UNDER: // 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 - nop.m 999 + mov pow_GR_Fpsr = ar40 // Read the fpsr--need to check rc.s0 fsetc.s2 0x7F,0x41 - nop.i 999 + 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 - nop.m 999 + 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 } @@ -1654,6 +1510,21 @@ POW_POSSIBLE_UNDER: } ;; +{ .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 @@ -1671,16 +1542,8 @@ POW_X_DENORM: } ;; -{ .mmi - getf.sig pow_GR_sig_X = POW_NORM_X -;; - and pow_GR_exp_X = pow_GR_signexp_X, pow_GR_17ones - nop.i 999 -} -;; - { .mib - sub pow_GR_true_exp_X = pow_GR_exp_X, pow_GR_16ones + getf.sig pow_GR_sig_X = POW_NORM_X nop.i 999 br.cond.sptk POW_COMMON } @@ -2140,6 +2003,7 @@ POW_OVER_UNDER_ERROR: GLOBAL_LIBM_END(powf) + LOCAL_LIBM_ENTRY(__libm_error_region) .prologue |