.file "cbrtl.s" // Copyright (c) 2000 - 2004, 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 //============================================================== // 04/28/00 Initial version // 05/20/02 Cleaned up namespace and sf0 syntax // 02/06/03 Reordered header:.section,.global,.proc,.align // 11/23/04 Reformatted routine and improved speed // // API //============================================================== // long double cbrtl(long double) // // Overview of operation //============================================================== // Background // // Implementation // // The result is computed as // cbrt(x)= cbrt(1 - (1 - x*y)) * (1/cbrt(y)) // where y = frcpa(x) = (-1)^sgn_y * 2^(3*k+j) * m_y, // m_y in [1,2), j in {0,1,2} // // cbrt(1 - (1 - x*y)) is approximated by a degree-6 polynomial // in r= 1 - x*y : // P = 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6 // // // The values (1/cbrt(y)) are stored as two tables of constants T_hi // (double-extended precision) and D (single precision) as follows: // T_hi (1 + D)= 1/cbrt(y) to about 80 bits of accuracy // // The tables are only stored for three exponent values (i.e. // only for 2^j * m_y, where j in {0,1,2} and m_y covers the 256 // possible mantissas for an frcpa result); the index is formed // by the 8 leading mantissa bits of x, which is the same index used // by the hardware to get frcpa(x). // // The table values are multiplied by 2^k where e is the exponent of // the input number. This multiplication is carried out in parallel with // the polynomial evaluation: // T= 2^(k) * T_hi // //======================================================================= //=============== // Special values //============================================================== // Registers used //============================================================== // p6, p7, p12 FR_R = f6 FR_C1 = f7 FR_C2 = f9 FR_C3 = f10 FR_C4 = f11 FR_C5 = f12 FR_C6 = f13 FR_XNORM = f14 FR_D = f15 FR_SPECIAL = f32 FR_RCP = f33 FR_R2 = f34 FR_P1 = f35 FR_P2 = f36 FR_P3 = f37 FR_P4 = f38 FR_P5 = f39 FR_R3 = f40 FR_T = f41 FR_TF = f42 FR_P = f43 FR_SGNEXP = f44 GR_ADDR = r2 GR_C_START = r2 GR_ARGSIG = r3 GR_NORMSIG = r15 GR_D_ADDR = r16 GR_D_START = r16 GR_INDEX2 = r17 GR_IX2 = r17 GR_NORMEXP = r18 GR_EXP5 = r19 GR_EXP3 = r20 GR_EXP6 = r20 GR_EXP17 = r21 GR_TMP1 = r21 GR_SGNMASK = r22 GR_T_INDEX = r23 GR_IX_T = r23 GR_IX_D = r24 GR_D_INDEX = r24 GR_TMP2 = r25 GR_TMP3 = r25 GR_TMP4 = r25 GR_EXP_RES = r26 GR_BIAS23 = r27 GR_EXPBIAS = r27 GR_EXP_MOD_3 = r28 GR_SIGN = r29 GR_EXPSIGNRES = r29 GR_REMTMP = r30 GR_NORMEXPSGN = r31 // Data tables //============================================================== RODATA .align 16 LOCAL_OBJECT_START(poly_coeffs) data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1 data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2 data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4 data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6 LOCAL_OBJECT_END(poly_coeffs) LOCAL_OBJECT_START(T_table) data8 0x80155c748c374836, 0x8040404b0879f7f9 data8 0x806b5dce4b405c10, 0x8096b586974669b1 data8 0x80bcd273d952a028, 0x80e898c52813f2f3 data8 0x81149add67c2d208, 0x813b4e2c856b6e9a data8 0x8167c1dde03de7aa, 0x818ed973b811135e data8 0x81bbc0c33e13ec98, 0x81e33e69fbe7504a data8 0x820aec524e3c23e9, 0x823880f78e70b805 data8 0x826097a62a8e5200, 0x8288dfe00e9b5eaf data8 0x82b15a10c5371624, 0x82da06a527b18937 data8 0x8302e60b635ab394, 0x832bf8b2feec2f0e data8 0x83553f0ce00e276b, 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data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229 data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259 data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959 data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967 data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804 data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2 data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030 data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40 data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7 data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894 data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4 data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3 data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8 data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383 data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6 data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727 data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9 data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6 data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5 data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29 data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496 data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2 data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398 data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92 data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662 data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70 data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1 data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2 data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045 data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516 data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3 data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381 data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871 data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4 data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2 data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3 data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8 data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912 data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6 data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0 data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6 data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7 data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37 data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1 data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36 data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5 data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57 data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748 data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225 data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109 data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9 data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1 data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991 data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48 data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26 data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66 data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2 data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304 data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01 data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3 data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6 data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0 data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8 data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114 data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745 data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2 data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0 data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640 data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817 data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059 data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6 data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821 data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944 data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93 data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7 data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19 data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3 data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8 data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030 data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7 data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5 data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43 data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978 data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3 data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6 data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849 data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85 data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7 data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107 data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249 data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20 data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4 data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467 data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d LOCAL_OBJECT_END(D_table) .section .text GLOBAL_LIBM_ENTRY(cbrtl) { .mfi getf.sig GR_ARGSIG = f8 // will continue on main path only for normal/denormal numbers // all other values will be filtered out and will exit early fclass.nm.unc p12, p7 = f8, 0x1b // GR_ADDR = pointer to C_1...C_6 followed by T_table addl GR_ADDR = @ltoff(poly_coeffs), gp } { .mfi // GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b mov GR_BIAS23 = 0xaa6b // normalize a fma.s1 FR_XNORM = f8, f1, f0 // GR_D_ADDR = pointer to D table addl GR_D_ADDR = @ltoff(D_table), gp } ;; { .mmf // load start address for C_1...C_6 followed by T_table ld8 GR_C_START = [ GR_ADDR ] // load start address of D table ld8 GR_D_START = [ GR_D_ADDR ] // y = frcpa(a) frcpa.s1 FR_RCP, p6 = f1, f8 } ;; { .mmi // get normalized significand getf.sig GR_NORMSIG = FR_XNORM // get exponent getf.exp GR_NORMEXPSGN = FR_XNORM (p7) cmp.eq p12, p0 = GR_ARGSIG, r0 } ;; { .mii // load C_1 ldfe FR_C1 = [ GR_C_START ], 16 mov GR_SGNMASK = 0x20000 nop.i 0 } ;; { .mfb // load C_2 ldfe FR_C2 = [ GR_C_START ], 16 (p12) fma.s0 f8 = f8, f1, f0 // NaN/Infinities exit early (p12) br.ret.spnt b0 } ;; { .mfi // load C_3, C_4 ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16 // y = frcpa(a), set flags and result when argument is 0 // only used when p6=0 frcpa.s0 f8, p0 = f1, f8 nop.i 0 } ;; { .mii // get GR_SIGN = sign and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK // eliminate leading 1 from GR_NORMSIG = 2nd table index shl GR_INDEX2 = GR_NORMSIG, 1 // eliminate sign from exponent andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK } ;; { .mfi // load C_5, C_6 (p6) ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16 // r = 1-a*y (p6) fnma.s1 FR_R = FR_RCP, FR_XNORM, f1 // Start computation of floor(exponent/3) by // computing (2^20+2)/3*exponent = exponent*0x55556 // 1: exponent* = 5; // (2^{16}-1)/3 = 0x5555: // will form 0x5555*exponent by using shladd's shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP } ;; { .mib // Next several integer steps compute floor(exponent/3) // GR_TMP1 = (5*expon)*16 shladd GR_TMP1 = GR_EXP5, 4, r0 // GR_EXP3 = 3*exponent shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP nop.b 0 } ;; { .mmi // GR_EXP6 = 6*exponent shladd GR_EXP6 = GR_EXP3, 1, r0 // GR_EXP17 = 17*expon add GR_EXP17 = GR_EXP5, GR_TMP1 // GR_IX2 = 2nd table index (8 bits) shr.u GR_IX2 = GR_INDEX2, 56 } ;; { .mmi // adjust T_table pointer by 2nd index shladd GR_T_INDEX = GR_IX2, 3, GR_C_START // adjust D_table pointer by 2nd index shladd GR_D_INDEX = GR_IX2, 2, GR_D_START // GR_TMP2 = (17*expon)*16^2 shl GR_TMP2 = GR_EXP17, 8 } ;; { .mmi // GR_TMP3 = expon*(2^16-1)/3 add GR_TMP3 = GR_EXP17, GR_TMP2 ;; // GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556 shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6 nop.i 0 } ;; { .mii nop.m 0 // GR_EXP_RES = floor(expon/3) shr.u GR_EXP_RES = GR_TMP4, 20 nop.i 0 } ;; { .mmi nop.m 0 // r16 = 3*exponent shladd r16 = GR_EXP_RES, 1, GR_EXP_RES // bias exponent add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES } ;; { .mmi // get remainder of exponent/3 sub GR_EXP_MOD_3 = GR_NORMEXP, r16 ;; // add sign to exponent or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN // remainder << = 8 shl GR_REMTMP = GR_EXP_MOD_3, 8 } ;; { .mfi // adjust D_table pointer by 1st index shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX // P_1 = C_1+C_2*r (p6) fma.s1 FR_P1 = FR_C2, FR_R, FR_C1 // adjust T_table pointer by 1st index shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX } { .mfi // FR_SGNEXP = sign*2^{exponent/3} (p6) setf.exp FR_SGNEXP = GR_EXPSIGNRES // r^2 = r*r (p6) fma.s1 FR_R2 = FR_R, FR_R, f0 nop.i 0 } ;; { .mfi // load D (p6) ldfs FR_D = [ GR_IX_D ] // P_2 = C_3+C_4*r (p6) fma.s1 FR_P2 = FR_C4, FR_R, FR_C3 nop.i 0 } { .mfi // load T (p6) ldf8 FR_T = [ GR_IX_T ] // P_3 = C_5+C_6*r (p6) fma.s1 FR_P3 = FR_C6, FR_R, FR_C5 nop.i 0 } ;; { .mfi nop.m 0 // P_4 = D-r*P_1 (p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D nop.i 0 } { .mfi nop.m 0 // r^3 = r*r^2 (p6) fma.s1 FR_R3 = FR_R, FR_R2, f0 nop.i 0 } ;; { .mfi nop.m 0 // P_5 = P_2+r2*P_3 (p6) fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2 nop.i 0 } ;; { .mfi nop.m 0 // T = T*(sign*2^{exponent/3}) (p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0 nop.i 0 } { .mfi nop.m 0 // P = P_4-r3*P_5 (p6) fnma.s1 FR_P = FR_R3, FR_P5, FR_P4 nop.i 0 } ;; { .mfb nop.m 0 // result = T+T*p (p6) fma.s0 f8 = FR_TF, FR_P, FR_TF br.ret.sptk b0 } ;; GLOBAL_LIBM_END(cbrtl)