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Diffstat (limited to 'sysdeps/ia64/fpu/e_acosl.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_acosl.S | 2552 |
1 files changed, 2552 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_acosl.S b/sysdeps/ia64/fpu/e_acosl.S new file mode 100644 index 0000000000..4fd345bedd --- /dev/null +++ b/sysdeps/ia64/fpu/e_acosl.S @@ -0,0 +1,2552 @@ +.file "acosl.s" + + +// Copyright (c) 2001 - 2003, Intel Corporation +// All rights reserved. +// +// Contributed 2001 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 +//============================================================== +// 08/28/01 New version +// 05/20/02 Cleaned up namespace and sf0 syntax +// 02/06/03 Reordered header: .section, .global, .proc, .align +// +// API +//============================================================== +// long double acosl(long double) +// +// Overview of operation +//============================================================== +// Background +// +// Implementation +// +// For |s| in [2^{-4}, sqrt(2)/2]: +// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52 +// acos(s)= pi/2-asin(t)-asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e. +// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1) +// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9) +// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table, +// along with the high and low parts of asin(t) (stored as two double precision +// values) +// +// |s| in (sqrt(2)/2, sqrt(255/256)): +// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6.. +// acos(|s|)= asin(t)-asin(r) +// acos(-|s|)=pi-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2) +// To minimize accumulated errors, r is computed as +// r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+ +// +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+ +// +ez*z'*y*(1-s^2)*(1-x), +// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits) +// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2 +// +// |s|<2^{-4}: evaluate asin(s) as 17-degree polynomial, return pi/2-asin(s) +// (or simply return pi/2-s, if|s|<2^{-64}) +// +// |s| in [sqrt(255/256), 1): acos(|s|)= asin(sqrt(1-s^2)) +// acos(-|s|)= pi-asin(sqrt(1-s^2)) +// use 17-degree polynomial for asin(sqrt(1-s^2)), +// 9-degree polynomial to evaluate sqrt(1-s^2) +// High order term is (pi)_high-(y*(1-s^2))_high, for s<0, +// or y*(1-s^2)_s, for s>0 +// + + + +// Registers used +//============================================================== +// f6-f15, f32-f36 +// r2-r3, r23-r23 +// p6, p7, p8, p12 +// + + + GR_SAVE_B0= r33 + GR_SAVE_PFS= r34 + GR_SAVE_GP= r35 // This reg. can safely be used + GR_SAVE_SP= r36 + + GR_Parameter_X= r37 + GR_Parameter_Y= r38 + GR_Parameter_RESULT= r39 + GR_Parameter_TAG= r40 + + FR_X= f10 + FR_Y= f1 + FR_RESULT= f8 + + + +RODATA + +.align 16 + +LOCAL_OBJECT_START(T_table) + +// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2), +// asin(t)_high (double precision), asin(t)_low (double precision) + +data8 0x80828692b71c4391, 0xff7ddcec2d87e879 +data8 0x3fb022bc0ae531a0, 0x3c9f599c7bb42af6 +data8 0x80869f0163d0b082, 0xff79cad2247914d3 +data8 0x3fb062dd26afc320, 0x3ca4eff21bd49c5c +data8 0x808ac7d5a8690705, 0xff75a89ed6b626b9 +data8 0x3fb0a2ff4a1821e0, 0x3cb7e33b58f164cc +data8 0x808f0112ad8ad2e0, 0xff7176517c2cc0cb +data8 0x3fb0e32279319d80, 0x3caee31546582c43 +data8 0x80934abba8a1da0a, 0xff6d33e949b1ed31 +data8 0x3fb12346b8101da0, 0x3cb8bfe463d087cd +data8 0x8097a4d3dbe63d8f, 0xff68e16571015c63 +data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f +data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0 +data8 0x3fb1a392756ed280, 0x3c964f1a927461ae +data8 0x80a08a5f33fadc66, 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0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d +data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b +data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321 +data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91 +data8 0x3fe76840418978a0, 0x3ccda46e85432c3d +data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3 +data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3 +data8 0xf049183c3f53c39b, 0xbad848720223d3a8 +data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b +data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48 +data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f +data8 0xfa718f05adbf2c33, 0xb70432500286b185 +data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9 +data8 0xfff200c3f5489608, 0xb509e6454dca33cc +data8 0x3fe9211b54441080, 0x3cb789cb53515688 +// The following table entries are not used +//data8 0x82e138a0fac48700, 0xb3044a513a8e6132 +//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0 +//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88 +//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039 +//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c +//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58 +//data8 0x8cad7a2c98dec333, 0xacab929ce114d451 +//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f +//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec +//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5 +//data8 0x9446d8191f80dd42, 0xa82ff92687235baf +//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e +//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58 +//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613 +//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b +//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177 +//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03 +//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959 +//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec +//data8 0x3fece4f404e29b20, 0x3cea3413401132b5 +//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c +//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276 +//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb +//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2 +//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c +//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71 +//data8 0xbfea427678945732, 0x93d5990f9ee787af +//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5 +//data8 0xc79611399b8c90c5, 0x90f72bde80febc31 +//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56 +//data8 0xcffa8425040624d7, 0x8e02b4418574ebed +//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f +//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024 +//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94 +//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b +//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc +//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a +//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02 +//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6 +//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3 +//data8 0x84ac1fcec4203245, 0xfb73a828893df19e +//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de +//data8 0x8ca50621110c60e6, 0xf438a14c158d867c</ |