https://git.reactos.org/?p=reactos.git;a=commitdiff;h=4afb647c786414cb5cd5ae...
commit 4afb647c786414cb5cd5ae2877b60cc0d81f1001 Author: Timo Kreuzer timo.kreuzer@reactos.org AuthorDate: Sun Jun 12 12:02:01 2022 +0200 Commit: Timo Kreuzer timo.kreuzer@reactos.org CommitDate: Thu Dec 1 15:21:59 2022 +0200
[LIBM] Import win-libm from AMD
Source: https://github.com/amd/win-libm --- sdk/lib/crt/math/libm_sse2/L2_by_pi_bits.asm | 54 + sdk/lib/crt/math/libm_sse2/Lsincos_array.asm | 62 + sdk/lib/crt/math/libm_sse2/Lsincosf_array.asm | 48 + sdk/lib/crt/math/libm_sse2/_chgsign.c | 41 + sdk/lib/crt/math/libm_sse2/_chgsignf.c | 40 + sdk/lib/crt/math/libm_sse2/_copysign.c | 44 + sdk/lib/crt/math/libm_sse2/_copysignf.c | 42 + sdk/lib/crt/math/libm_sse2/_finite.c | 39 + sdk/lib/crt/math/libm_sse2/_finitef.c | 40 + sdk/lib/crt/math/libm_sse2/acos.c | 145 ++ sdk/lib/crt/math/libm_sse2/acosf.c | 146 ++ sdk/lib/crt/math/libm_sse2/asin.c | 153 ++ sdk/lib/crt/math/libm_sse2/asinf.c | 151 ++ sdk/lib/crt/math/libm_sse2/atan.c | 132 ++ sdk/lib/crt/math/libm_sse2/atan2.c | 750 ++++++ sdk/lib/crt/math/libm_sse2/atan2f.c | 469 ++++ sdk/lib/crt/math/libm_sse2/atanf.c | 135 ++ sdk/lib/crt/math/libm_sse2/cabs.c | 34 + sdk/lib/crt/math/libm_sse2/cabsf.c | 35 + sdk/lib/crt/math/libm_sse2/ceil.c | 88 + sdk/lib/crt/math/libm_sse2/ceilf.c | 86 + sdk/lib/crt/math/libm_sse2/cos.asm | 533 +++++ sdk/lib/crt/math/libm_sse2/cosf.asm | 525 +++++ sdk/lib/crt/math/libm_sse2/cosh.c | 344 +++ sdk/lib/crt/math/libm_sse2/coshf.c | 247 ++ sdk/lib/crt/math/libm_sse2/exp.asm | 439 ++++ sdk/lib/crt/math/libm_sse2/exp2.c | 162 ++ sdk/lib/crt/math/libm_sse2/exp_special.c | 101 + sdk/lib/crt/math/libm_sse2/expf.asm | 303 +++ sdk/lib/crt/math/libm_sse2/floor.c | 85 + sdk/lib/crt/math/libm_sse2/floorf.c | 83 + sdk/lib/crt/math/libm_sse2/fm.inc | 39 + sdk/lib/crt/math/libm_sse2/fma3_available.c | 66 + sdk/lib/crt/math/libm_sse2/fmod.asm | 160 ++ sdk/lib/crt/math/libm_sse2/fmodf.asm | 160 ++ sdk/lib/crt/math/libm_sse2/hypot.c | 198 ++ sdk/lib/crt/math/libm_sse2/hypotf.c | 99 + sdk/lib/crt/math/libm_sse2/libm.h | 49 + sdk/lib/crt/math/libm_sse2/libm_errno.h | 35 + sdk/lib/crt/math/libm_sse2/libm_inlines.h | 2101 +++++++++++++++++ sdk/lib/crt/math/libm_sse2/libm_new.h | 122 + sdk/lib/crt/math/libm_sse2/libm_util.h | 150 ++ sdk/lib/crt/math/libm_sse2/log.asm | 557 +++++ sdk/lib/crt/math/libm_sse2/log10.asm | 565 +++++ .../math/libm_sse2/log10_128_lead_tail_table.asm | 297 +++ .../math/libm_sse2/log10_256_lead_tail_table.asm | 552 +++++ .../crt/math/libm_sse2/log_128_lead_tail_table.asm | 294 +++ .../crt/math/libm_sse2/log_256_lead_tail_table.asm | 554 +++++ .../crt/math/libm_sse2/log_F_inv_dword_table.asm | 164 ++ .../crt/math/libm_sse2/log_F_inv_qword_table.asm | 294 +++ sdk/lib/crt/math/libm_sse2/log_special.c | 133 ++ sdk/lib/crt/math/libm_sse2/logb.c | 84 + sdk/lib/crt/math/libm_sse2/logbf.c | 82 + sdk/lib/crt/math/libm_sse2/logf.asm | 451 ++++ sdk/lib/crt/math/libm_sse2/modf.c | 76 + sdk/lib/crt/math/libm_sse2/modff.c | 70 + sdk/lib/crt/math/libm_sse2/pow.asm | 2411 ++++++++++++++++++++ sdk/lib/crt/math/libm_sse2/pow_special.c | 130 ++ sdk/lib/crt/math/libm_sse2/remainder.c | 319 +++ sdk/lib/crt/math/libm_sse2/remainder_piby2.c | 251 ++ .../crt/math/libm_sse2/remainder_piby2_forAsm.asm | 415 ++++ .../crt/math/libm_sse2/remainder_piby2_forFMA3.asm | 283 +++ sdk/lib/crt/math/libm_sse2/remainder_piby2f.c | 173 ++ .../crt/math/libm_sse2/remainder_piby2f_forAsm.asm | 180 ++ .../crt/math/libm_sse2/remainder_piby2f_forC.asm | 341 +++ sdk/lib/crt/math/libm_sse2/remainderf.c | 247 ++ sdk/lib/crt/math/libm_sse2/simd.h | 369 +++ sdk/lib/crt/math/libm_sse2/sin.asm | 511 +++++ sdk/lib/crt/math/libm_sse2/sincos_special.c | 130 ++ sdk/lib/crt/math/libm_sse2/sinf.asm | 664 ++++++ sdk/lib/crt/math/libm_sse2/sinh.c | 340 +++ sdk/lib/crt/math/libm_sse2/sinhf.c | 256 +++ sdk/lib/crt/math/libm_sse2/sqrt.c | 88 + sdk/lib/crt/math/libm_sse2/sqrtf.c | 91 + sdk/lib/crt/math/libm_sse2/tan.asm | 762 +++++++ sdk/lib/crt/math/libm_sse2/tan.c | 242 ++ sdk/lib/crt/math/libm_sse2/tanf.asm | 551 +++++ sdk/lib/crt/math/libm_sse2/tanf.c | 193 ++ sdk/lib/crt/math/libm_sse2/tanh.c | 137 ++ sdk/lib/crt/math/libm_sse2/tanhf.c | 136 ++ .../libm_sse2/two_to_jby64_head_tail_table.asm | 165 ++ sdk/lib/crt/math/libm_sse2/two_to_jby64_table.asm | 99 + 82 files changed, 22392 insertions(+)
diff --git a/sdk/lib/crt/math/libm_sse2/L2_by_pi_bits.asm b/sdk/lib/crt/math/libm_sse2/L2_by_pi_bits.asm new file mode 100644 index 00000000000..b267015fb75 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/L2_by_pi_bits.asm @@ -0,0 +1,54 @@ +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +;; +;; Defines __L_2_by_pi_bits array +;; Used in trigonometric argument reduction +;; + +.const + +ALIGN 16 +PUBLIC __L_2_by_pi_bits +__L_2_by_pi_bits DB 224, 241, 27, 193, 12, 88, 33, 116 + DB 53, 126, 196, 126, 237, 175, 169, 75 + DB 74, 41, 222, 231, 28, 244, 236, 197 + DB 151, 175, 31, 235, 158, 212, 181, 168 + DB 127, 121, 154, 253, 24, 61, 221, 38 + DB 44, 159, 60, 251, 217, 180, 125, 180 + DB 41, 104, 45, 70, 188, 188, 63, 96 + DB 22, 120, 255, 95, 226, 127, 236, 160 + DB 228, 247, 46, 126, 17, 114, 210, 231 + DB 76, 13, 230, 88, 71, 230, 4, 249 + DB 125, 209, 154, 192, 113, 166, 19, 18 + DB 237, 186, 212, 215, 8, 162, 251, 156 + DB 166, 196, 114, 172, 119, 248, 115, 72 + DB 70, 39, 168, 187, 36, 25, 128, 75 + DB 55, 9, 233, 184, 145, 220, 134, 21 + DB 239, 122, 175, 142, 69, 249, 7, 65 + DB 14, 241, 100, 86, 138, 109, 3, 119 + DB 211, 212, 71, 95, 157, 240, 167, 84 + DB 16, 57, 185, 13, 230, 139, 2, 0 + DB 0, 0, 0, 0, 0, 0 +END diff --git a/sdk/lib/crt/math/libm_sse2/Lsincos_array.asm b/sdk/lib/crt/math/libm_sse2/Lsincos_array.asm new file mode 100644 index 00000000000..03f32d08e92 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/Lsincos_array.asm @@ -0,0 +1,62 @@ +;; +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +;; Defines __Lcosarray and __Lsinarray arrays. +;; Used in sin.asm and cos.asm +;; + +.const + +ALIGN 16 +PUBLIC __Lcosarray +__Lcosarray DQ 03fa5555555555555h ; 0.0416667 c1 + DQ 0 + DQ 0bf56c16c16c16967h ; -0.00138889 c2 + DQ 0 + DQ 03EFA01A019F4EC91h ; 2.48016e-005 c3 + DQ 0 + DQ 0bE927E4FA17F667Bh ; -2.75573e-007 c4 + DQ 0 + DQ 03E21EEB690382EECh ; 2.08761e-009 c5 + DQ 0 + DQ 0bDA907DB47258AA7h ; -1.13826e-011 c6 + DQ 0 + +ALIGN 16 +PUBLIC __Lsinarray +__Lsinarray DQ 0bfc5555555555555h ; -0.166667 s1 + DQ 0 + DQ 03f81111111110bb3h ; 0.00833333 s2 + DQ 0 + DQ 0bf2a01a019e83e5ch ; -0.000198413 s3 + DQ 0 + DQ 03ec71de3796cde01h ; 2.75573e-006 s4 + DQ 0 + DQ 0be5ae600b42fdfa7h ; -2.50511e-008 s5 + DQ 0 + DQ 03de5e0b2f9a43bb8h ; 1.59181e-010 s6 + DQ 0 + +END diff --git a/sdk/lib/crt/math/libm_sse2/Lsincosf_array.asm b/sdk/lib/crt/math/libm_sse2/Lsincosf_array.asm new file mode 100644 index 00000000000..871b9ce8410 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/Lsincosf_array.asm @@ -0,0 +1,48 @@ +;; +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +;; Defines __Lcosarray and __Lsinarray arrays. +;; Used in sin.asm and cos.asm +;; These coefficients are actually from Taylor series. +;; + +.const + +ALIGN 16 +PUBLIC __Lcosfarray +__Lcosfarray DQ 0bfe0000000000000h ; -0.5 c0 + DQ 03fa5555555555555h ; 0.0416667 c1 + DQ 0bf56c16c16c16c16h ; -0.00138889 c2 + DQ 03EFA01A01A01A019h ; 2.48016e-005 c3 + DQ 0be927e4fb7789f5ch ; -2.75573e-007 c4 + +ALIGN 16 +PUBLIC __Lsinfarray +__Lsinfarray DQ 0bfc5555555555555h ; -0.166667 s1 + DQ 03f81111111111111h ; 0.00833333 s2 + DQ 0bf2a01a01a01a01ah ; -0.000198413 s3 + DQ 03ec71de3a556c734h ; 2.75573e-006 s4 + +END diff --git a/sdk/lib/crt/math/libm_sse2/_chgsign.c b/sdk/lib/crt/math/libm_sse2/_chgsign.c new file mode 100644 index 00000000000..f22ce58a743 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_chgsign.c @@ -0,0 +1,41 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +double FN_PROTOTYPE(_chgsign)(double x) +{ + /* Returns x with its sign reversed. + NaNs are not considered special; their sign bits are handled + the same as for any other number */ + unsigned long u; + GET_BITS_DP64(x, u); + u ^= SIGNBIT_DP64; + PUT_BITS_DP64(u, x); + return x; +} + diff --git a/sdk/lib/crt/math/libm_sse2/_chgsignf.c b/sdk/lib/crt/math/libm_sse2/_chgsignf.c new file mode 100644 index 00000000000..1996aa5af96 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_chgsignf.c @@ -0,0 +1,40 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +float FN_PROTOTYPE(_chgsignf)(float x) +{ + /* Returns x with its sign reversed. + NaNs are not considered special; their sign bits are handled + the same as for any other number */ + unsigned int u; + GET_BITS_SP32(x, u); + u ^= SIGNBIT_SP32; + PUT_BITS_SP32(u, x); + return x; +} diff --git a/sdk/lib/crt/math/libm_sse2/_copysign.c b/sdk/lib/crt/math/libm_sse2/_copysign.c new file mode 100644 index 00000000000..c3944276567 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_copysign.c @@ -0,0 +1,44 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +/* Returns the absolute value of x with the sign of y. + NaNs are not considered special; their sign bits are handled + the same as for any other number. */ + +double FN_PROTOTYPE(_copysign)(double x, double y) +{ + + unsigned long ux, uy; + GET_BITS_DP64(x, ux); + GET_BITS_DP64(y, uy); + if ((ux ^ uy) & SIGNBIT_DP64) + PUT_BITS_DP64(ux ^ SIGNBIT_DP64, x); + return x; + +} diff --git a/sdk/lib/crt/math/libm_sse2/_copysignf.c b/sdk/lib/crt/math/libm_sse2/_copysignf.c new file mode 100644 index 00000000000..874f00ca0c0 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_copysignf.c @@ -0,0 +1,42 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + + /* Returns the absolute value of x with the sign of y. + NaNs are not considered special; their sign bits are handled + the same as for any other number. */ + +float FN_PROTOTYPE(_copysignf)(float x, float y) +{ + unsigned int ux, uy; + GET_BITS_SP32(x, ux); + GET_BITS_SP32(y, uy); + if ((ux ^ uy) & SIGNBIT_SP32) + PUT_BITS_SP32(ux ^ SIGNBIT_SP32, x); + return x; +} diff --git a/sdk/lib/crt/math/libm_sse2/_finite.c b/sdk/lib/crt/math/libm_sse2/_finite.c new file mode 100644 index 00000000000..c3ca86f4b05 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_finite.c @@ -0,0 +1,39 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +/* Returns 0 if x is infinite or NaN, otherwise returns 1 */ + +int FN_PROTOTYPE(_finite)(double x) +{ + + + unsigned long ux; + GET_BITS_DP64(x, ux); + return (int)(((ux & ~SIGNBIT_DP64) - PINFBITPATT_DP64) >> 63); +} diff --git a/sdk/lib/crt/math/libm_sse2/_finitef.c b/sdk/lib/crt/math/libm_sse2/_finitef.c new file mode 100644 index 00000000000..3fbfbc7c2e6 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/_finitef.c @@ -0,0 +1,40 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +/* Returns 0 if x is infinite or NaN, otherwise returns 1 */ + +int FN_PROTOTYPE(_finitef)(float x) +{ + + + unsigned int ux; + GET_BITS_SP32(x, ux); + return (int)(((ux & ~SIGNBIT_SP32) - PINFBITPATT_SP32) >> 31); + +} diff --git a/sdk/lib/crt/math/libm_sse2/acos.c b/sdk/lib/crt/math/libm_sse2/acos.c new file mode 100644 index 00000000000..cb46803e536 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/acos.c @@ -0,0 +1,145 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VAL_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_NAN_WITH_FLAGS +#undef USE_VAL_WITH_FLAGS +#undef USE_HANDLE_ERROR + +#include "libm_errno.h" + + +#pragma function(acos) + +double FN_PROTOTYPE(acos)(double x) +{ + /* Computes arccos(x). + The argument is first reduced by noting that arccos(x) + is invalid for abs(x) > 1. For denormal and small + arguments arccos(x) = pi/2 to machine accuracy. + Remaining argument ranges are handled as follows. + For abs(x) <= 0.5 use + arccos(x) = pi/2 - arcsin(x) + = pi/2 - (x + x^3*R(x^2)) + where R(x^2) is a rational minimax approximation to + (arcsin(x) - x)/x^3. + For abs(x) > 0.5 exploit the identity: + arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) + together with the above rational approximation, and + reconstruct the terms carefully. + */ + + /* Some constants and split constants. */ + + static const double + pi = 3.1415926535897933e+00, /* 0x400921fb54442d18 */ + piby2 = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */ + piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */ + piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ + + double u, y, s=0.0, r; + int xexp, xnan, transform=0; + + unsigned long ux, aux, xneg; + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + xneg = (ux & SIGNBIT_DP64); + xnan = (aux > PINFBITPATT_DP64); + xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64; + + /* Special cases */ + + if (xnan) + { + return _handle_error("acos", OP_ACOS, ux|0x0008000000000000, _DOMAIN, + 0, EDOM, x, 0.0, 1); + } + else if (xexp < -56) + { /* y small enough that arccos(x) = pi/2 */ + return val_with_flags(piby2, AMD_F_INEXACT); + } + else if (xexp >= 0) + { /* abs(x) >= 1.0 */ + if (x == 1.0) + return 0.0; + else if (x == -1.0) + return val_with_flags(pi, AMD_F_INEXACT); + else + return _handle_error("acos", OP_ACOS, INDEFBITPATT_DP64, _DOMAIN, + AMD_F_INVALID, EDOM, x, 0.0, 1); + } + + if (xneg) y = -x; + else y = x; + + transform = (xexp >= -1); /* abs(x) >= 0.5 */ + + if (transform) + { /* Transform y into the range [0,0.5) */ + r = 0.5*(1.0 - y); + /* VC++ intrinsic call */ + _mm_store_sd(&s, _mm_sqrt_sd(_mm_setzero_pd(), _mm_load_sd(&r))); + y = s; + } + else + r = y*y; + + /* Use a rational approximation for [0.0, 0.5] */ + + u = r*(0.227485835556935010735943483075 + + (-0.445017216867635649900123110649 + + (0.275558175256937652532686256258 + + (-0.0549989809235685841612020091328 + + (0.00109242697235074662306043804220 + + 0.0000482901920344786991880522822991*r)*r)*r)*r)*r)/ + (1.36491501334161032038194214209 + + (-3.28431505720958658909889444194 + + (2.76568859157270989520376345954 + + (-0.943639137032492685763471240072 + + 0.105869422087204370341222318533*r)*r)*r)*r); + + if (transform) + { /* Reconstruct acos carefully in transformed region */ + if (xneg) return pi - 2.0*(s+(y*u - piby2_tail)); + else + { + double c, s1; + unsigned long us; + GET_BITS_DP64(s, us); + PUT_BITS_DP64(0xffffffff00000000 & us, s1); + c = (r-s1*s1)/(s+s1); + return 2.0*s1 + (2.0*c+2.0*y*u); + } + } + else + return piby2_head - (x - (piby2_tail - x*u)); +} diff --git a/sdk/lib/crt/math/libm_sse2/acosf.c b/sdk/lib/crt/math/libm_sse2/acosf.c new file mode 100644 index 00000000000..5422177b317 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/acosf.c @@ -0,0 +1,146 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VALF_WITH_FLAGS +#define USE_NANF_WITH_FLAGS +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_NANF_WITH_FLAGS +#undef USE_VALF_WITH_FLAGS +#undef USE_HANDLE_ERRORF + +#include "libm_errno.h" + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(acosf) + + +float FN_PROTOTYPE(acosf)(float x) +{ + /* Computes arccos(x). + The argument is first reduced by noting that arccos(x) + is invalid for abs(x) > 1. For denormal and small + arguments arccos(x) = pi/2 to machine accuracy. + Remaining argument ranges are handled as follows. + For abs(x) <= 0.5 use + arccos(x) = pi/2 - arcsin(x) + = pi/2 - (x + x^3*R(x^2)) + where R(x^2) is a rational minimax approximation to + (arcsin(x) - x)/x^3. + For abs(x) > 0.5 exploit the identity: + arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) + together with the above rational approximation, and + reconstruct the terms carefully. + */ + + /* Some constants and split constants. */ + + static const float + piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */ + static const double + pi = 3.1415926535897933e+00, /* 0x400921fb54442d18 */ + piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */ + piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ + + float u, y, s = 0.0F, r; + int xexp, xnan, transform = 0; + + unsigned int ux, aux, xneg; + + GET_BITS_SP32(x, ux); + aux = ux & ~SIGNBIT_SP32; + xneg = (ux & SIGNBIT_SP32); + xnan = (aux > PINFBITPATT_SP32); + xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; + + /* Special cases */ + + if (xnan) + { + return _handle_errorf("acosf", OP_ACOS, ux|0x00400000, _DOMAIN, 0, + EDOM, x, 0.0F, 1); + } + else if (xexp < -26) + /* y small enough that arccos(x) = pi/2 */ + return valf_with_flags(piby2, AMD_F_INEXACT); + else if (xexp >= 0) + { /* abs(x) >= 1.0 */ + if (x == 1.0F) + return 0.0F; + else if (x == -1.0F) + return valf_with_flags((float)pi, AMD_F_INEXACT); + else + return _handle_errorf("acosf", OP_ACOS, INDEFBITPATT_SP32, _DOMAIN, + AMD_F_INVALID, EDOM, x, 0.0F, 1); + } + + if (xneg) y = -x; + else y = x; + + transform = (xexp >= -1); /* abs(x) >= 0.5 */ + + if (transform) + { /* Transform y into the range [0,0.5) */ + r = 0.5F*(1.0F - y); + /* VC++ intrinsic call */ + _mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r))); + y = s; + } + else + r = y*y; + + /* Use a rational approximation for [0.0, 0.5] */ + + u=r*(0.184161606965100694821398249421F + + (-0.0565298683201845211985026327361F + + (-0.0133819288943925804214011424456F - + 0.00396137437848476485201154797087F*r)*r)*r)/ + (1.10496961524520294485512696706F - + 0.836411276854206731913362287293F*r); + + if (transform) + { + /* Reconstruct acos carefully in transformed region */ + if (xneg) + return (float)(pi - 2.0*(s+(y*u - piby2_tail))); + else + { + float c, s1; + unsigned int us; + GET_BITS_SP32(s, us); + PUT_BITS_SP32(0xffff0000 & us, s1); + c = (r-s1*s1)/(s+s1); + return 2.0F*s1 + (2.0F*c+2.0F*y*u); + } + } + else + return (float)(piby2_head - (x - (piby2_tail - x*u))); +} diff --git a/sdk/lib/crt/math/libm_sse2/asin.c b/sdk/lib/crt/math/libm_sse2/asin.c new file mode 100644 index 00000000000..31e652b73c6 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/asin.c @@ -0,0 +1,153 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VAL_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_NAN_WITH_FLAGS +#undef USE_VAL_WITH_FLAGS +#undef USE_HANDLE_ERROR + +#include "libm_errno.h" + +#pragma function(asin) + +double FN_PROTOTYPE(asin)(double x) +{ + /* Computes arcsin(x). + The argument is first reduced by noting that arcsin(x) + is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x). + For denormal and small arguments arcsin(x) = x to machine + accuracy. Remaining argument ranges are handled as follows. + For abs(x) <= 0.5 use + arcsin(x) = x + x^3*R(x^2) + where R(x^2) is a rational minimax approximation to + (arcsin(x) - x)/x^3. + For abs(x) > 0.5 exploit the identity: + arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2) + together with the above rational approximation, and + reconstruct the terms carefully. + */ + + /* Some constants and split constants. */ + + static const double + piby2_tail = 6.1232339957367660e-17, /* 0x3c91a62633145c07 */ + hpiby2_head = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */ + piby2 = 1.5707963267948965e+00; /* 0x3ff921fb54442d18 */ + double u, v, y, s=0.0, r; + int xexp, xnan, transform=0; + + unsigned long ux, aux, xneg; + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + xneg = (ux & SIGNBIT_DP64); + xnan = (aux > PINFBITPATT_DP64); + xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64; + + /* Special cases */ + + if (xnan) + { + return _handle_error("asin", OP_ASIN, ux|0x0008000000000000, _DOMAIN, + 0, EDOM, x, 0.0, 1); + } + else if (xexp < -28) + { /* y small enough that arcsin(x) = x */ + return val_with_flags(x, AMD_F_INEXACT); + } + else if (xexp >= 0) + { /* abs(x) >= 1.0 */ + if (x == 1.0) + return val_with_flags(piby2, AMD_F_INEXACT); + else if (x == -1.0) + return val_with_flags(-piby2, AMD_F_INEXACT); + else + return _handle_error("asin", OP_ASIN, INDEFBITPATT_DP64, _DOMAIN, + AMD_F_INVALID, EDOM, x, 0.0, 1); + } + + if (xneg) y = -x; + else y = x; + + transform = (xexp >= -1); /* abs(x) >= 0.5 */ + + if (transform) + { /* Transform y into the range [0,0.5) */ + r = 0.5*(1.0 - y); + /* VC++ intrinsic call */ + _mm_store_sd(&s, _mm_sqrt_sd(_mm_setzero_pd(), _mm_load_sd(&r))); + y = s; + } + else + r = y*y; + + /* Use a rational approximation for [0.0, 0.5] */ + + u = r*(0.227485835556935010735943483075 + + (-0.445017216867635649900123110649 + + (0.275558175256937652532686256258 + + (-0.0549989809235685841612020091328 + + (0.00109242697235074662306043804220 + + 0.0000482901920344786991880522822991*r)*r)*r)*r)*r)/ + (1.36491501334161032038194214209 + + (-3.28431505720958658909889444194 + + (2.76568859157270989520376345954 + + (-0.943639137032492685763471240072 + + 0.105869422087204370341222318533*r)*r)*r)*r); + + if (transform) + { /* Reconstruct asin carefully in transformed region */ + { + double c, s1, p, q; + unsigned long us; + GET_BITS_DP64(s, us); + PUT_BITS_DP64(0xffffffff00000000 & us, s1); + c = (r-s1*s1)/(s+s1); + p = 2.0*s*u - (piby2_tail-2.0*c); + q = hpiby2_head - 2.0*s1; + v = hpiby2_head - (p-q); + } + } + else + { + /* Use a temporary variable to prevent VC++ rearranging + y + y*u + into + y * (1 + u) + and getting an incorrectly rounded result */ + double tmp; + tmp = y * u; + v = y + tmp; + } + + if (xneg) return -v; + else return v; +} diff --git a/sdk/lib/crt/math/libm_sse2/asinf.c b/sdk/lib/crt/math/libm_sse2/asinf.c new file mode 100644 index 00000000000..89dba1059ff --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/asinf.c @@ -0,0 +1,151 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VALF_WITH_FLAGS +#define USE_NANF_WITH_FLAGS +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_NANF_WITH_FLAGS +#undef USE_VALF_WITH_FLAGS +#undef USE_HANDLE_ERRORF + +#include "libm_errno.h" + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(asinf) + + +float FN_PROTOTYPE(asinf)(float x) +{ + /* Computes arcsin(x). + The argument is first reduced by noting that arcsin(x) + is invalid for abs(x) > 1 and arcsin(-x) = -arcsin(x). + For denormal and small arguments arcsin(x) = x to machine + accuracy. Remaining argument ranges are handled as follows. + For abs(x) <= 0.5 use + arcsin(x) = x + x^3*R(x^2) + where R(x^2) is a rational minimax approximation to + (arcsin(x) - x)/x^3. + For abs(x) > 0.5 exploit the identity: + arcsin(x) = pi/2 - 2*arcsin(sqrt(1-x)/2) + together with the above rational approximation, and + reconstruct the terms carefully. + */ + + /* Some constants and split constants. */ + + static const float + piby2_tail = 7.5497894159e-08F, /* 0x33a22168 */ + hpiby2_head = 7.8539812565e-01F, /* 0x3f490fda */ + piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */ + float u, v, y, s = 0.0F, r; + int xexp, xnan, transform = 0; + + unsigned int ux, aux, xneg; + GET_BITS_SP32(x, ux); + aux = ux & ~SIGNBIT_SP32; + xneg = (ux & SIGNBIT_SP32); + xnan = (aux > PINFBITPATT_SP32); + xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; + + /* Special cases */ + + if (xnan) + { + return _handle_errorf("asinf", OP_ASIN, ux|0x00400000, _DOMAIN, 0, + EDOM, x, 0.0F, 1); + } + else if (xexp < -14) + /* y small enough that arcsin(x) = x */ + return valf_with_flags(x, AMD_F_INEXACT); + else if (xexp >= 0) + { + /* abs(x) >= 1.0 */ + if (x == 1.0F) + return valf_with_flags(piby2, AMD_F_INEXACT); + else if (x == -1.0F) + return valf_with_flags(-piby2, AMD_F_INEXACT); + else + return _handle_errorf("asinf", OP_ASIN, INDEFBITPATT_SP32, _DOMAIN, + AMD_F_INVALID, EDOM, x, 0.0F, 1); + } + + if (xneg) y = -x; + else y = x; + + transform = (xexp >= -1); /* abs(x) >= 0.5 */ + + if (transform) + { /* Transform y into the range [0,0.5) */ + r = 0.5F*(1.0F - y); + /* VC++ intrinsic call */ + _mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r))); + y = s; + } + else + r = y*y; + + /* Use a rational approximation for [0.0, 0.5] */ + + u=r*(0.184161606965100694821398249421F + + (-0.0565298683201845211985026327361F + + (-0.0133819288943925804214011424456F - + 0.00396137437848476485201154797087F*r)*r)*r)/ + (1.10496961524520294485512696706F - + 0.836411276854206731913362287293F*r); + + if (transform) + { + /* Reconstruct asin carefully in transformed region */ + float c, s1, p, q; + unsigned int us; + GET_BITS_SP32(s, us); + PUT_BITS_SP32(0xffff0000 & us, s1); + c = (r-s1*s1)/(s+s1); + p = 2.0F*s*u - (piby2_tail-2.0F*c); + q = hpiby2_head - 2.0F*s1; + v = hpiby2_head - (p-q); + } + else + { + /* Use a temporary variable to prevent VC++ rearranging + y + y*u + into + y * (1 + u) + and getting an incorrectly rounded result */ + float tmp; + tmp = y * u; + v = y + tmp; + } + + if (xneg) return -v; + else return v; +} diff --git a/sdk/lib/crt/math/libm_sse2/atan.c b/sdk/lib/crt/math/libm_sse2/atan.c new file mode 100644 index 00000000000..c28e0672779 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/atan.c @@ -0,0 +1,132 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VAL_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_VAL_WITH_FLAGS +#undef USE_NAN_WITH_FLAGS +#undef USE_HANDLE_ERROR + +#include "libm_errno.h" + +#pragma function(atan) + +double FN_PROTOTYPE(atan)(double x) +{ + + /* Some constants and split constants. */ + + static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */ + double chi, clo, v, s, q, z; + + /* Find properties of argument x. */ + + unsigned long ux, aux, xneg; + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + xneg = (ux != aux); + + if (xneg) v = -x; + else v = x; + + /* Argument reduction to range [-7/16,7/16] */ + + if (aux > 0x4003800000000000) /* v > 39./16. */ + { + + if (aux > PINFBITPATT_DP64) + { + /* x is NaN */ + return _handle_error("atan", OP_ATAN, ux|0x0008000000000000, _DOMAIN, 0, + EDOM, x, 0.0, 1); + } + else if (v > 0x4370000000000000) + { /* abs(x) > 2^56 => arctan(1/x) is + insignificant compared to piby2 */ + if (xneg) + return val_with_flags(-piby2, AMD_F_INEXACT); + else + return val_with_flags(piby2, AMD_F_INEXACT); + } + + x = -1.0/v; + /* (chi + clo) = arctan(infinity) */ + chi = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */ + clo = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */ + } + else if (aux > 0x3ff3000000000000) /* 39./16. > v > 19./16. */ + { + x = (v-1.5)/(1.0+1.5*v); + /* (chi + clo) = arctan(1.5) */ + chi = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */ + clo = 1.39033110312309953701e-17; /* 0x3c7007887af0cbbc */ + } + else if (aux > 0x3fe6000000000000) /* 19./16. > v > 11./16. */ + { + x = (v-1.0)/(1.0+v); + /* (chi + clo) = arctan(1.) */ + chi = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */ + clo = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */ + } + else if (aux > 0x3fdc000000000000) /* 11./16. > v > 7./16. */ + { + x = (2.0*v-1.0)/(2.0+v); + /* (chi + clo) = arctan(0.5) */ + chi = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */ + clo = 2.26987774529616809294e-17; /* 0x3c7a2b7f222f65e0 */ + } + else /* v < 7./16. */ + { + x = v; + chi = 0.0; + clo = 0.0; + } + + /* Core approximation: Remez(4,4) on [-7/16,7/16] */ + + s = x*x; + q = x*s* + (0.268297920532545909e0 + + (0.447677206805497472e0 + + (0.220638780716667420e0 + + (0.304455919504853031e-1 + + 0.142316903342317766e-3*s)*s)*s)*s)/ + (0.804893761597637733e0 + + (0.182596787737507063e1 + + (0.141254259931958921e1 + + (0.424602594203847109e0 + + 0.389525873944742195e-1*s)*s)*s)*s); + + z = chi - ((q - clo) - x); + + if (xneg) z = -z; + return z; +} diff --git a/sdk/lib/crt/math/libm_sse2/atan2.c b/sdk/lib/crt/math/libm_sse2/atan2.c new file mode 100644 index 00000000000..fb9d1e8482f --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/atan2.c @@ -0,0 +1,750 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VAL_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_SCALEDOUBLE_1 +#define USE_SCALEDOUBLE_2 +#define USE_SCALEUPDOUBLE1024 +#define USE_SCALEDOWNDOUBLE +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_VAL_WITH_FLAGS +#undef USE_NAN_WITH_FLAGS +#undef USE_SCALEDOUBLE_1 +#undef USE_SCALEDOUBLE_2 +#undef USE_SCALEUPDOUBLE1024 +#undef USE_SCALEDOWNDOUBLE +#undef USE_HANDLE_ERROR + +#include "libm_errno.h" + +#pragma function(atan2) + +double FN_PROTOTYPE(atan2)(double y, double x) +{ + /* Arrays atan_jby256_lead and atan_jby256_tail contain + leading and trailing parts respectively of precomputed + values of atan(j/256), for j = 16, 17, ..., 256. + atan_jby256_lead contains the first 21 bits of precision, + and atan_jby256_tail contains a further 53 bits precision. */ + + static const double atan_jby256_lead[ 241] = { + 6.24187886714935302734e-02, /* 0x3faff55b00000000 */ + 6.63088560104370117188e-02, /* 0x3fb0f99e00000000 */ + 7.01969265937805175781e-02, /* 0x3fb1f86d00000000 */ + 7.40829110145568847656e-02, /* 0x3fb2f71900000000 */ + 7.79666304588317871094e-02, /* 0x3fb3f59f00000000 */ + 8.18479657173156738281e-02, /* 0x3fb4f3fd00000000 */ + 8.57268571853637695312e-02, /* 0x3fb5f23200000000 */ + 8.96031260490417480469e-02, /* 0x3fb6f03b00000000 */ + 9.34767723083496093750e-02, /* 0x3fb7ee1800000000 */ + 9.73475575447082519531e-02, /* 0x3fb8ebc500000000 */ + 1.01215422153472900391e-01, /* 0x3fb9e94100000000 */ + 1.05080246925354003906e-01, /* 0x3fbae68a00000000 */ + 1.08941912651062011719e-01, /* 0x3fbbe39e00000000 */ + 1.12800359725952148438e-01, /* 0x3fbce07c00000000 */ + 1.16655409336090087891e-01, /* 0x3fbddd2100000000 */ + 1.20507001876831054688e-01, /* 0x3fbed98c00000000 */ + 1.24354958534240722656e-01, /* 0x3fbfd5ba00000000 */ + 1.28199219703674316406e-01, /* 0x3fc068d500000000 */ + 1.32039666175842285156e-01, /* 0x3fc0e6ad00000000 */ + 1.35876297950744628906e-01, /* 0x3fc1646500000000 */ + 1.39708757400512695312e-01, /* 0x3fc1e1fa00000000 */ + 1.43537282943725585938e-01, /* 0x3fc25f6e00000000 */ + 1.47361397743225097656e-01, /* 0x3fc2dcbd00000000 */ + 1.51181221008300781250e-01, /* 0x3fc359e800000000 */ + 1.54996633529663085938e-01, /* 0x3fc3d6ee00000000 */ + 1.58807516098022460938e-01, /* 0x3fc453ce00000000 */ + 1.62613749504089355469e-01, /* 0x3fc4d08700000000 */ + 1.66415214538574218750e-01, /* 0x3fc54d1800000000 */ + 1.70211911201477050781e-01, /* 0x3fc5c98100000000 */ + 1.74003481864929199219e-01, /* 0x3fc645bf00000000 */ + 1.77790164947509765625e-01, /* 0x3fc6c1d400000000 */ + 1.81571602821350097656e-01, /* 0x3fc73dbd00000000 */ + 1.85347914695739746094e-01, /* 0x3fc7b97b00000000 */ + 1.89118742942810058594e-01, /* 0x3fc8350b00000000 */ + 1.92884206771850585938e-01, /* 0x3fc8b06e00000000 */ + 1.96644186973571777344e-01, /* 0x3fc92ba300000000 */ + 2.00398445129394531250e-01, /* 0x3fc9a6a800000000 */ + 2.04147100448608398438e-01, /* 0x3fca217e00000000 */ + 2.07889914512634277344e-01, /* 0x3fca9c2300000000 */ + 2.11626768112182617188e-01, /* 0x3fcb169600000000 */ + 2.15357661247253417969e-01, /* 0x3fcb90d700000000 */ + 2.19082474708557128906e-01, /* 0x3fcc0ae500000000 */ + 2.22801089286804199219e-01, /* 0x3fcc84bf00000000 */ + 2.26513504981994628906e-01, /* 0x3fccfe6500000000 */ + 2.30219483375549316406e-01, /* 0x3fcd77d500000000 */ + 2.33919143676757812500e-01, /* 0x3fcdf11000000000 */ + 2.37612247467041015625e-01, /* 0x3fce6a1400000000 */ + 2.41298794746398925781e-01, /* 0x3fcee2e100000000 */ + 2.44978547096252441406e-01, /* 0x3fcf5b7500000000 */ + 2.48651623725891113281e-01, /* 0x3fcfd3d100000000 */ + 2.52317905426025390625e-01, /* 0x3fd025fa00000000 */ + 2.55977153778076171875e-01, /* 0x3fd061ee00000000 */ + 2.59629487991333007812e-01, /* 0x3fd09dc500000000 */ + 2.63274669647216796875e-01, /* 0x3fd0d97e00000000 */ + 2.66912937164306640625e-01, /* 0x3fd1151a00000000 */ + 2.70543813705444335938e-01, /* 0x3fd1509700000000 */ + 2.74167299270629882812e-01, /* 0x3fd18bf500000000 */ + 2.77783632278442382812e-01, /* 0x3fd1c73500000000 */ + 2.81392335891723632812e-01, /* 0x3fd2025500000000 */ + 2.84993648529052734375e-01, /* 0x3fd23d5600000000 */ + 2.88587331771850585938e-01, /* 0x3fd2783700000000 */ + 2.92173147201538085938e-01, /* 0x3fd2b2f700000000 */ + 2.95751571655273437500e-01, /* 0x3fd2ed9800000000 */ + 2.99322128295898437500e-01, /* 0x3fd3281800000000 */ + 3.02884817123413085938e-01, /* 0x3fd3627700000000 */ + 3.06439399719238281250e-01, /* 0x3fd39cb400000000 */ + 3.09986352920532226562e-01, /* 0x3fd3d6d100000000 */ + 3.13524961471557617188e-01, /* 0x3fd410cb00000000 */ + 3.17055702209472656250e-01, /* 0x3fd44aa400000000 */ + 3.20578098297119140625e-01, /* 0x3fd4845a00000000 */ + 3.24092388153076171875e-01, /* 0x3fd4bdee00000000 */ + 3.27598333358764648438e-01, /* 0x3fd4f75f00000000 */ + 3.31095933914184570312e-01, /* 0x3fd530ad00000000 */ + 3.34585189819335937500e-01, /* 0x3fd569d800000000 */ + 3.38066101074218750000e-01, /* 0x3fd5a2e000000000 */ + 3.41538190841674804688e-01, /* 0x3fd5dbc300000000 */ + 3.45002174377441406250e-01, /* 0x3fd6148400000000 */ + 3.48457098007202148438e-01, /* 0x3fd64d1f00000000 */ + 3.51903676986694335938e-01, /* 0x3fd6859700000000 */ + 3.55341434478759765625e-01, /* 0x3fd6bdea00000000 */ + 3.58770608901977539062e-01, /* 0x3fd6f61900000000 */ + 3.62190723419189453125e-01, /* 0x3fd72e2200000000 */ + 3.65602254867553710938e-01, /* 0x3fd7660700000000 */ + 3.69004726409912109375e-01, /* 0x3fd79dc600000000 */ + 3.72398376464843750000e-01, /* 0x3fd7d56000000000 */ + 3.75782966613769531250e-01, /* 0x3fd80cd400000000 */ + 3.79158496856689453125e-01, /* 0x3fd8442200000000 */ + 3.82525205612182617188e-01, /* 0x3fd87b4b00000000 */ + 3.85882616043090820312e-01, /* 0x3fd8b24d00000000 */ + 3.89230966567993164062e-01, /* 0x3fd8e92900000000 */ + 3.92570018768310546875e-01, /* 0x3fd91fde00000000 */ + 3.95900011062622070312e-01, /* 0x3fd9566d00000000 */ + 3.99220705032348632812e-01, /* 0x3fd98cd500000000 */ + 4.02532100677490234375e-01, /* 0x3fd9c31600000000 */ + 4.05834197998046875000e-01, /* 0x3fd9f93000000000 */ + 4.09126996994018554688e-01, /* 0x3fda2f2300000000 */ + 4.12410259246826171875e-01, /* 0x3fda64ee00000000 */ + 4.15684223175048828125e-01, /* 0x3fda9a9200000000 */ + 4.18948888778686523438e-01, /* 0x3fdad00f00000000 */ + 4.22204017639160156250e-01, /* 0x3fdb056400000000 */ + 4.25449609756469726562e-01, /* 0x3fdb3a9100000000 */ + 4.28685665130615234375e-01, /* 0x3fdb6f9600000000 */ + 4.31912183761596679688e-01, /* 0x3fdba47300000000 */ + 4.35129165649414062500e-01, /* 0x3fdbd92800000000 */ + 4.38336372375488281250e-01, /* 0x3fdc0db400000000 */ + 4.41534280776977539062e-01, /* 0x3fdc421900000000 */ + 4.44722414016723632812e-01, /* 0x3fdc765500000000 */ + 4.47900772094726562500e-01, /* 0x3fdcaa6800000000 */ + 4.51069593429565429688e-01, /* 0x3fdcde5300000000 */ + 4.54228639602661132812e-01, /* 0x3fdd121500000000 */ + 4.57377910614013671875e-01, /* 0x3fdd45ae00000000 */ + 4.60517644882202148438e-01, /* 0x3fdd791f00000000 */ + 4.63647603988647460938e-01, /* 0x3fddac6700000000 */ + 4.66767549514770507812e-01, /* 0x3fdddf8500000000 */ + 4.69877958297729492188e-01, /* 0x3fde127b00000000 */ + 4.72978591918945312500e-01, /* 0x3fde454800000000 */ + 4.76069211959838867188e-01, /* 0x3fde77eb00000000 */ + 4.79150056838989257812e-01, /* 0x3fdeaa6500000000 */ + 4.82221126556396484375e-01, /* 0x3fdedcb600000000 */ + 4.85282421112060546875e-01, /* 0x3fdf0ede00000000 */ + 4.88333940505981445312e-01, /* 0x3fdf40dd00000000 */ + 4.91375446319580078125e-01, /* 0x3fdf72b200000000 */ + 4.94406938552856445312e-01, /* 0x3fdfa45d00000000 */ + 4.97428894042968750000e-01, /* 0x3fdfd5e000000000 */ + 5.00440597534179687500e-01, /* 0x3fe0039c00000000 */ + 5.03442764282226562500e-01, /* 0x3fe01c3400000000 */ + 5.06434917449951171875e-01, /* 0x3fe034b700000000 */ + 5.09417057037353515625e-01, /* 0x3fe04d2500000000 */ + 5.12389183044433593750e-01, /* 0x3fe0657e00000000 */ + 5.15351772308349609375e-01, /* 0x3fe07dc300000000 */ + 5.18304347991943359375e-01, /* 0x3fe095f300000000 */ + 5.21246910095214843750e-01, /* 0x3fe0ae0e00000000 */ + 5.24179458618164062500e-01, /* 0x3fe0c61400000000 */ + 5.27101993560791015625e-01, /* 0x3fe0de0500000000 */ + 5.30014991760253906250e-01, /* 0x3fe0f5e200000000 */ + 5.32917976379394531250e-01, /* 0x3fe10daa00000000 */ + 5.35810947418212890625e-01, /* 0x3fe1255d00000000 */ + 5.38693904876708984375e-01, /* 0x3fe13cfb00000000 */ + 5.41567325592041015625e-01, /* 0x3fe1548500000000 */ + 5.44430732727050781250e-01, /* 0x3fe16bfa00000000 */ + 5.47284126281738281250e-01, /* 0x3fe1835a00000000 */ + 5.50127506256103515625e-01, /* 0x3fe19aa500000000 */ + 5.52961349487304687500e-01, /* 0x3fe1b1dc00000000 */ + 5.55785179138183593750e-01, /* 0x3fe1c8fe00000000 */ + 5.58598995208740234375e-01, /* 0x3fe1e00b00000000 */ + 5.61403274536132812500e-01, /* 0x3fe1f70400000000 */ + 5.64197540283203125000e-01, /* 0x3fe20de800000000 */ + 5.66981792449951171875e-01, /* 0x3fe224b700000000 */ + 5.69756031036376953125e-01, /* 0x3fe23b7100000000 */ + 5.72520732879638671875e-01, /* 0x3fe2521700000000 */ + 5.75275897979736328125e-01, /* 0x3fe268a900000000 */ + 5.78021049499511718750e-01, /* 0x3fe27f2600000000 */ + 5.80756187438964843750e-01, /* 0x3fe2958e00000000 */ + 5.83481788635253906250e-01, /* 0x3fe2abe200000000 */ + 5.86197376251220703125e-01, /* 0x3fe2c22100000000 */ + 5.88903427124023437500e-01, /* 0x3fe2d84c00000000 */ + 5.91599464416503906250e-01, /* 0x3fe2ee6200000000 */ + 5.94285964965820312500e-01, /* 0x3fe3046400000000 */ + 5.96962928771972656250e-01, /* 0x3fe31a5200000000 */ + 5.99629878997802734375e-01, /* 0x3fe3302b00000000 */ + 6.02287292480468750000e-01, /* 0x3fe345f000000000 */ + 6.04934692382812500000e-01, /* 0x3fe35ba000000000 */ + 6.07573032379150390625e-01, /* 0x3fe3713d00000000 */ + 6.10201358795166015625e-01, /* 0x3fe386c500000000 */ + 6.12820148468017578125e-01, /* 0x3fe39c3900000000 */ + 6.15428924560546875000e-01, /* 0x3fe3b19800000000 */ + 6.18028640747070312500e-01, /* 0x3fe3c6e400000000 */ + 6.20618820190429687500e-01, /* 0x3fe3dc1c00000000 */ + 6.23198986053466796875e-01, /* 0x3fe3f13f00000000 */ + 6.25770092010498046875e-01, /* 0x3fe4064f00000000 */ + 6.28331184387207031250e-01, /* 0x3fe41b4a00000000 */ + 6.30883216857910156250e-01, /* 0x3fe4303200000000 */ + 6.33425712585449218750e-01, /* 0x3fe4450600000000 */ + 6.35958671569824218750e-01, /* 0x3fe459c600000000 */ + 6.38482093811035156250e-01, /* 0x3fe46e7200000000 */ + 6.40995979309082031250e-01, /* 0x3fe4830a00000000 */ + 6.43500804901123046875e-01, /* 0x3fe4978f00000000 */ + 6.45996093750000000000e-01, /* 0x3fe4ac0000000000 */ + 6.48482322692871093750e-01, /* 0x3fe4c05e00000000 */ + 6.50959014892578125000e-01, /* 0x3fe4d4a800000000 */ + 6.53426170349121093750e-01, /* 0x3fe4e8de00000000 */ + 6.55884265899658203125e-01, /* 0x3fe4fd0100000000 */ + 6.58332824707031250000e-01, /* 0x3fe5111000000000 */ + 6.60772323608398437500e-01, /* 0x3fe5250c00000000 */ + 6.63202762603759765625e-01, /* 0x3fe538f500000000 */ + 6.65623664855957031250e-01, /* 0x3fe54cca00000000 */ + 6.68035984039306640625e-01, /* 0x3fe5608d00000000 */ + 6.70438766479492187500e-01, /* 0x3fe5743c00000000 */ + 6.72832489013671875000e-01, /* 0x3fe587d800000000 */ + 6.75216674804687500000e-01, /* 0x3fe59b6000000000 */ + 6.77592277526855468750e-01, /* 0x3fe5aed600000000 */ + 6.79958820343017578125e-01, /* 0x3fe5c23900000000 */ + 6.82316303253173828125e-01, /* 0x3fe5d58900000000 */ + 6.84664726257324218750e-01, /* 0x3fe5e8c600000000 */ + 6.87004089355468750000e-01, /* 0x3fe5fbf000000000 */ + 6.89334869384765625000e-01, /* 0x3fe60f0800000000 */ + 6.91656589508056640625e-01, /* 0x3fe6220d00000000 */ + 6.93969249725341796875e-01, /* 0x3fe634ff00000000 */ + 6.96272850036621093750e-01, /* 0x3fe647de00000000 */ + 6.98567867279052734375e-01, /* 0x3fe65aab00000000 */ + 7.00854301452636718750e-01, /* 0x3fe66d6600000000 */ + 7.03131675720214843750e-01, /* 0x3fe6800e00000000 */ + 7.05400466918945312500e-01, /* 0x3fe692a400000000 */ + 7.07660198211669921875e-01, /* 0x3fe6a52700000000 */ + 7.09911346435546875000e-01, /* 0x3fe6b79800000000 */ + 7.12153911590576171875e-01, /* 0x3fe6c9f700000000 */ + 7.14387893676757812500e-01, /* 0x3fe6dc4400000000 */ + 7.16613292694091796875e-01, /* 0x3fe6ee7f00000000 */ + 7.18829631805419921875e-01, /* 0x3fe700a700000000 */ + 7.21037864685058593750e-01, /* 0x3fe712be00000000 */ + 7.23237514495849609375e-01, /* 0x3fe724c300000000 */ + 7.25428581237792968750e-01, /* 0x3fe736b600000000 */ + 7.27611064910888671875e-01, /* 0x3fe7489700000000 */ + 7.29785442352294921875e-01, /* 0x3fe75a6700000000 */ + 7.31950759887695312500e-01, /* 0x3fe76c2400000000 */ + 7.34108448028564453125e-01, /* 0x3fe77dd100000000 */ + 7.36257076263427734375e-01, /* 0x3fe78f6b00000000 */ + 7.38397598266601562500e-01, /* 0x3fe7a0f400000000 */ + 7.40530014038085937500e-01, /* 0x3fe7b26c00000000 */ + 7.42654323577880859375e-01, /* 0x3fe7c3d300000000 */ + 7.44770050048828125000e-01, /* 0x3fe7d52800000000 */ + 7.46877670288085937500e-01, /* 0x3fe7e66c00000000 */ + 7.48976707458496093750e-01, /* 0x3fe7f79e00000000 */ + 7.51068115234375000000e-01, /* 0x3fe808c000000000 */ + 7.53150939941406250000e-01, /* 0x3fe819d000000000 */ + 7.55226135253906250000e-01, /* 0x3fe82ad000000000 */ + 7.57292747497558593750e-01, /* 0x3fe83bbe00000000 */ + 7.59351730346679687500e-01, /* 0x3fe84c9c00000000 */ + 7.61402606964111328125e-01, /* 0x3fe85d6900000000 */ + 7.63445377349853515625e-01, /* 0x3fe86e2500000000 */ + 7.65480041503906250000e-01, /* 0x3fe87ed000000000 */ + 7.67507076263427734375e-01, /* 0x3fe88f6b00000000 */ + 7.69526004791259765625e-01, /* 0x3fe89ff500000000 */ + 7.71537303924560546875e-01, /* 0x3fe8b06f00000000 */ + 7.73540973663330078125e-01, /* 0x3fe8c0d900000000 */ + 7.75536537170410156250e-01, /* 0x3fe8d13200000000 */ + 7.77523994445800781250e-01, /* 0x3fe8e17a00000000 */ + 7.79504299163818359375e-01, /* 0x3fe8f1b300000000 */ + 7.81476497650146484375e-01, /* 0x3fe901db00000000 */ + 7.83441066741943359375e-01, /* 0x3fe911f300000000 */ + 7.85398006439208984375e-01}; /* 0x3fe921fb00000000 */ + + static const double atan_jby256_tail[ 241] = { + 2.13244638182005395671e-08, /* 0x3e56e59fbd38db2c */ + 3.89093864761712760656e-08, /* 0x3e64e3aa54dedf96 */ + 4.44780900009437454576e-08, /* 0x3e67e105ab1bda88 */ + 1.15344768460112754160e-08, /* 0x3e48c5254d013fd0 */ + 3.37271051945395312705e-09, /* 0x3e2cf8ab3ad62670 */ + 2.40857608736109859459e-08, /* 0x3e59dca4bec80468 */ + 1.85853810450623807768e-08, /* 0x3e53f4b5ec98a8da */ + 5.14358299969225078306e-08, /* 0x3e6b9d49619d81fe */ + 8.85023985412952486748e-09, /* 0x3e43017887460934 */ + 1.59425154214358432060e-08, /* 0x3e511e3eca0b9944 */ + 1.95139937737755753164e-08, /* 0x3e54f3f73c5a332e */ + 2.64909755273544319715e-08, /* 0x3e5c71c8ae0e00a6 */ + 4.43388037881231070144e-08, /* 0x3e67cde0f86fbdc7 */ + 2.14757072421821274557e-08, /* 0x3e570f328c889c72 */ + 2.61049792670754218852e-08, /* 0x3e5c07ae9b994efe */ + 7.81439350674466302231e-09, /* 0x3e40c8021d7b1698 */ + 3.60125207123751024094e-08, /* 0x3e635585edb8cb22 */ + 6.15276238179343767917e-08, /* 0x3e70842567b30e96 */ + 9.54387964641184285058e-08, /* 0x3e799e811031472e */ + 3.02789566851502754129e-08, /* 0x3e6041821416bcee */ + 1.16888650949870856331e-07, /* 0x3e7f6086e4dc96f4 */ + 1.07580956468653338863e-08, /* 0x3e471a535c5f1b58 */ + 8.33454265379535427653e-08, /* 0x3e765f743fe63ca1 */ + 1.10790279272629526068e-07, /* 0x3e7dbd733472d014 */ + 1.08394277896366207424e-07, /* 0x3e7d18cc4d8b0d1d */ + 9.22176086126841098800e-08, /* 0x3e78c12553c8fb29 */ + 7.90938592199048786990e-08, /* 0x3e753b49e2e8f991 */ + 8.66445407164293125637e-08, /* 0x3e77422ae148c141 */ + 1.40839973537092438671e-08, /* 0x3e4e3ec269df56a8 */ + 1.19070438507307600689e-07, /* 0x3e7ff6754e7e0ac9 */ + 6.40451663051716197071e-08, /* 0x3e7131267b1b5aad */ + 1.08338682076343674522e-07, /* 0x3e7d14fa403a94bc */ + 3.52999550187922736222e-08, /* 0x3e62f396c089a3d8 */ + 1.05983273930043077202e-07, /* 0x3e7c731d78fa95bb */ + 1.05486124078259553339e-07, /* 0x3e7c50f385177399 */ + 5.82167732281776477773e-08, /* 0x3e6f41409c6f2c20 */ + 1.08696483983403942633e-07, /* 0x3e7d2d90c4c39ec0 */ + 4.47335086122377542835e-08, /* 0x3e680420696f2106 */ + 1.26896287162615723528e-08, /* 0x3e4b40327943a2e8 */ + 4.06534471589151404531e-08, /* 0x3e65d35e02f3d2a2 */ + 3.84504846300557026690e-08, /* 0x3e64a498288117b0 */ + 3.60715006404807269080e-08, /* 0x3e635da119afb324 */ + 6.44725903165522722801e-08, /* 0x3e714e85cdb9a908 */ + 3.63749249976409461305e-08, /* 0x3e638754e5547b9a */ + 1.03901294413833913794e-07, /* 0x3e7be40ae6ce3246 */ + 6.25379756302167880580e-08, /* 0x3e70c993b3bea7e7 */ + 6.63984302368488828029e-08, /* 0x3e71d2dd89ac3359 */ + 3.21844598971548278059e-08, /* 0x3e61476603332c46 */ + 1.16030611712765830905e-07, /* 0x3e7f25901bac55b7 */ + 1.17464622142347730134e-07, /* 0x3e7f881b7c826e28 */ + 7.54604017965808996596e-08, /* 0x3e7441996d698d20 */ + 1.49234929356206556899e-07, /* 0x3e8407ac521ea089 */ + 1.41416924523217430259e-07, /* 0x3e82fb0c6c4b1723 */ + 2.13308065617483489011e-07, /* 0x3e8ca135966a3e18 */ + 5.04230937933302320146e-08, /* 0x3e6b1218e4d646e4 */ + 5.45874922281655519035e-08, /* 0x3e6d4e72a350d288 */ + 1.51849028914786868886e-07, /* 0x3e84617e2f04c329 */ + 3.09004308703769273010e-08, /* 0x3e6096ec41e82650 */ + 9.67574548184738317664e-08, /* 0x3e79f91f25773e6e */ + 4.02508285529322212824e-08, /* 0x3e659c0820f1d674 */ + 3.01222268096861091157e-08, /* 0x3e602bf7a2df1064 */ + 2.36189860670079288680e-07, /* 0x3e8fb36bfc40508f */ + 1.14095158111080887695e-07, /* 0x3e7ea08f3f8dc892 */ + 7.42349089746573467487e-08, /* 0x3e73ed6254656a0e */ + 5.12515583196230380184e-08, /* 0x3e6b83f5e5e69c58 */ + 2.19290391828763918102e-07, /* 0x3e8d6ec2af768592 */ + 3.83263512187553886471e-08, /* 0x3e6493889a226f94 */ + 1.61513486284090523855e-07, /* 0x3e85ad8fa65279ba */ + 5.09996743535589922261e-08, /* 0x3e6b615784d45434 */ + 1.23694037861246766534e-07, /* 0x3e809a184368f145 */ + 8.23367955351123783984e-08, /* 0x3e761a2439b0d91c */ + 1.07591766213053694014e-07, /* 0x3e7ce1a65e39a978 */ + 1.42789947524631815640e-07, /* 0x3e832a39a93b6a66 */ + 1.32347123024711878538e-07, /* 0x3e81c3699af804e7 */ + 2.17626067316598149229e-08, /* 0x3e575e0f4e44ede8 */ + 2.34454866923044288656e-07, /* 0x3e8f77ced1a7a83b */ + 2.82966370261766916053e-09, /* 0x3e284e7f0cb1b500 */ + 2.29300919890907632975e-07, /* 0x3e8ec6b838b02dfe */ + 1.48428270450261284915e-07, /* 0x3e83ebf4dfbeda87 */ + 1.87937408574313982512e-07, /* 0x3e89397aed9cb475 */ + 6.13685946813334055347e-08, /* 0x3e707937bc239c54 */ + 1.98585022733583817493e-07, /* 0x3e8aa754553131b6 */ + 7.68394131623752961662e-08, /* 0x3e74a05d407c45dc */ + 1.28119052312436745644e-07, /* 0x3e8132231a206dd0 */ + 7.02119104719236502733e-08, /* 0x3e72d8ecfdd69c88 */ + 9.87954793820636301943e-08, /* 0x3e7a852c74218606 */ + 1.72176752381034986217e-07, /* 0x3e871bf2baeebb50 */ + 1.12877225146169704119e-08, /* 0x3e483d7db7491820 */ + 5.33549829555851737993e-08, /* 0x3e6ca50d92b6da14 */ + 2.13833275710816521345e-08, /* 0x3e56f5cde8530298 */ + 1.16243518048290556393e-07, /* 0x3e7f343198910740 */ + 6.29926408369055877943e-08, /* 0x3e70e8d241ccd80a */ + 6.45429039328021963791e-08, /* 0x3e71535ac619e6c8 */ + 8.64001922814281933403e-08, /* 0x3e77316041c36cd2 */ + 9.50767572202325800240e-08, /* 0x3e7985a000637d8e */ + 5.80851497508121135975e-08, /* 0x3e6f2f29858c0a68 */ + 1.82350561135024766232e-07, /* 0x3e8879847f96d909 */ + 1.98948680587390608655e-07, /* 0x3e8ab3d319e12e42 */ + 7.83548663450197659846e-08, /* 0x3e75088162dfc4c2 */ + 3.04374234486798594427e-08, /* 0x3e605749a1cd9d8c */ + 2.76135725629797411787e-08, /* 0x3e5da65c6c6b8618 */ + 4.32610105454203065470e-08, /* 0x3e6739bf7df1ad64 */ + 5.17107515324127256994e-08, /* 0x3e6bc31252aa3340 */ + 2.82398327875841444660e-08, /* 0x3e5e528191ad3aa8 */ + 1.87482469524195595399e-07, /* 0x3e8929d93df19f18 */ + 2.97481891662714096139e-08, /* 0x3e5ff11eb693a080 */ + 9.94421570843584316402e-09, /* 0x3e455ae3f145a3a0 */ + 1.07056210730391848428e-07, /* 0x3e7cbcd8c6c0ca82 */ + 6.25589580466881163081e-08, /* 0x3e70cb04d425d304 */ + 9.56641013869464593803e-08, /* 0x3e79adfcab5be678 */ + 1.88056307148355440276e-07, /* 0x3e893d90c5662508 */ + 8.38850689379557880950e-08, /* 0x3e768489bd35ff40 */ + 5.01215865527674122924e-09, /* 0x3e3586ed3da2b7e0 */ + 1.74166095998522089762e-07, /* 0x3e87604d2e850eee */ + 9.96779574395363585849e-08, /* 0x3e7ac1d12bfb53d8 */ + 5.98432026368321460686e-09, /* 0x3e39b3d468274740 */ + 1.18362922366887577169e-07, /* 0x3e7fc5d68d10e53c */ + 1.86086833284154215946e-07, /* 0x3e88f9e51884becb */ + 1.97671457251348941011e-07, /* 0x3e8a87f0869c06d1 */ + 1.42447160717199237159e-07, /* 0x3e831e7279f685fa */ + 1.05504240785546574184e-08, /* 0x3e46a8282f9719b0 */ + 3.13335218371639189324e-08, /* 0x3e60d2724a8a44e0 */ + 1.96518418901914535399e-07, /* 0x3e8a60524b11ad4e */ + 2.17692035039173536059e-08, /* 0x3e575fdf832750f0 */ + 2.15613114426529981675e-07, /* 0x3e8cf06902e4cd36 */ + 5.68271098300441214948e-08, /* 0x3e6e82422d4f6d10 */ + 1.70331455823369124256e-08, /* 0x3e524a091063e6c0 */ + 9.17590028095709583247e-08, /* 0x3e78a1a172dc6f38 */ + 2.77266304112916566247e-07, /* 0x3e929b6619f8a92d */ + 9.37041937614656939690e-08, /* 0x3e79274d9c1b70c8 */ + 1.56116346368316796511e-08, /* 0x3e50c34b1fbb7930 */ + 4.13967433808382727413e-08, /* 0x3e6639866c20eb50 */ + 1.70164749185821616276e-07, /* 0x3e86d6d0f6832e9e */ + 4.01708788545600086008e-07, /* 0x3e9af54def99f25e */ + 2.59663539226050551563e-07, /* 0x3e916cfc52a00262 */ + 2.22007487655027469542e-07, /* 0x3e8dcc1e83569c32 */ + 2.90542250809644081369e-07, /* 0x3e937f7a551ed425 */ + 4.67720537666628903341e-07, /* 0x3e9f6360adc98887 */ + 2.79799803956772554802e-07, /* 0x3e92c6ec8d35a2c1 */ + 2.07344552327432547723e-07, /* 0x3e8bd44df84cb036 */ + 2.54705698692735196368e-07, /* 0x3e9117cf826e310e */ + 4.26848589539548450728e-07, /* 0x3e9ca533f332cfc9 */ + 2.52506723633552216197e-07, /* 0x3e90f208509dbc2e */ + 2.14684129933849704964e-07, /* 0x3e8cd07d93c945de */ + 3.20134822201596505431e-07, /* 0x3e957bdfd67e6d72 */ + 9.93537565749855712134e-08, /* 0x3e7aab89c516c658 */ + 3.70792944827917252327e-08, /* 0x3e63e823b1a1b8a0 */ + 1.41772749369083698972e-07, /* 0x3e8307464a9d6d3c */ + 4.22446601490198804306e-07, /* 0x3e9c5993cd438843 */ + 4.11818433724801511540e-07, /* 0x3e9ba2fca02ab554 */ + 1.19976381502605310519e-07, /* 0x3e801a5b6983a268 */ + 3.43703078571520905265e-08, /* 0x3e6273d1b350efc8 */ + 1.66128705555453270379e-07, /* 0x3e864c238c37b0c6 */ + 5.00499610023283006540e-08, /* 0x3e6aded07370a300 */ + 1.75105139941208062123e-07, /* 0x3e878091197eb47e */ + 7.70807146729030327334e-08, /* 0x3e74b0f245e0dabc */ + 2.45918607526895836121e-07, /* 0x3e9080d9794e2eaf */ + 2.18359020958626199345e-07, /* 0x3e8d4ec242b60c76 */ + 8.44342887976445333569e-09, /* 0x3e4221d2f940caa0 */ + 1.07506148687888629299e-07, /* 0x3e7cdbc42b2bba5c */ + 5.36544954316820904572e-08, /* 0x3e6cce37bb440840 */ + 3.39109101518396596341e-07, /* 0x3e96c1d999cf1dd0 */ + 2.60098720293920613340e-08, /* 0x3e5bed8a07eb0870 */ + 8.42678991664621455827e-08, /* 0x3e769ed88f490e3c */ + 5.36972237470183633197e-08, /* 0x3e6cd41719b73ef0 */ + 4.28192558171921681288e-07, /* 0x3e9cbc4ac95b41b7 */ + 2.71535491483955143294e-07, /* 0x3e9238f1b890f5d7 */ + 7.84094998145075780203e-08, /* 0x3e750c4282259cc4 */ + 3.43880599134117431863e-07, /* 0x3e9713d2de87b3e2 */ + 1.32878065060366481043e-07, /* 0x3e81d5a7d2255276 */ + 4.18046802627967629428e-07, /* 0x3e9c0dfd48227ac1 */ + 2.65042411765766019424e-07, /* 0x3e91c964dab76753 */ + 1.70383695347518643694e-07, /* 0x3e86de56d5704496 */ + 1.54096497259613515678e-07, /* 0x3e84aeb71fd19968 */ + 2.36543402412459813461e-07, /* 0x3e8fbf91c57b1918 */ + 4.38416350106876736790e-07, /* 0x3e9d6bef7fbe5d9a */ + 3.03892161339927775731e-07, /* 0x3e9464d3dc249066 */ + 3.31136771605664899240e-07, /* 0x3e9638e2ec4d9073 */ + 6.49494294526590682218e-08, /* 0x3e716f4a7247ea7c */ + 4.10423429887181345747e-09, /* 0x3e31a0a740f1d440 */ + 1.70831640869113847224e-07, /* 0x3e86edbb0114a33c */ + 1.10811512657909180966e-07, /* 0x3e7dbee8bf1d513c */ + 3.23677724749783611964e-07, /* 0x3e95b8bdb0248f73 */ + 3.55662734259192678528e-07, /* 0x3e97de3d3f5eac64 */ + 2.30102333489738219140e-07, /* 0x3e8ee24187ae448a */ + 4.47429004000738629714e-07, /* 0x3e9e06c591ec5192 */ + 7.78167135617329598659e-08, /* 0x3e74e3861a332738 */ + 9.90345291908535415737e-08, /* 0x3e7a9599dcc2bfe4 */ + 5.85800913143113728314e-08, /* 0x3e6f732fbad43468 */ + 4.57859062410871843857e-07, /* 0x3e9eb9f573b727d9 */ + 3.67993069723390929794e-07, /* 0x3e98b212a2eb9897 */ + 2.90836464322977276043e-07, /* 0x3e9384884c167215 */ + 2.51621574250131388318e-07, /* 0x3e90e2d363020051 */ + 2.75789824740652815545e-07, /* 0x3e92820879fbd022 */ + 3.88985776250314403593e-07, /* 0x3e9a1ab9893e4b30 */ + 1.40214080183768019611e-07, /* 0x3e82d1b817a24478 */ + 3.23451432223550478373e-08, /* 0x3e615d7b8ded4878 */ + 9.15979180730608444470e-08, /* 0x3e78968f9db3a5e4 */ + 3.44371402498640470421e-07, /* 0x3e971c4171fe135f */ + 3.40401897215059498077e-07, /* 0x3e96d80f605d0d8c */ + 1.06431813453707950243e-07, /* 0x3e7c91f043691590 */ + 1.46204238932338846248e-07, /* 0x3e839f8a15fce2b2 */ + 9.94610376972039046878e-09, /* 0x3e455beda9d94b80 */ + 2.01711528092681771039e-07, /* 0x3e8b12c15d60949a */ + 2.72027977986191568296e-07, /* 0x3e924167b312bfe3 */ + 2.48402602511693757964e-07, /* 0x3e90ab8633070277 */ + 1.58480011219249621715e-07, /* 0x3e854554ebbc80ee */ + 3.00372828113368713281e-08, /* 0x3e60204aef5a4bb8 */ + 3.67816204583541976394e-07, /* 0x3e98af08c679cf2c */ + 2.46169793032343824291e-07, /* 0x3e90852a330ae6c8 */ + 1.70080468270204253247e-07, /* 0x3e86d3eb9ec32916 */ + 1.67806717763872914315e-07, /* 0x3e8685cb7fcbbafe */ + 2.67715622006907942620e-07, /* 0x3e91f751c1e0bd95 */ + 2.14411342550299170574e-08, /* 0x3e5705b1b0f72560 */ + 4.11228221283669073277e-07, /* 0x3e9b98d8d808ca92 */ + 3.52311752396749662260e-08, /* 0x3e62ea22c75cc980 */ + 3.52718000397367821054e-07, /* 0x3e97aba62bca0350 */ + 4.38857387992911129814e-07, /* 0x3e9d73833442278c */ + 3.22574606753482540743e-07, /* 0x3e95a5ca1fb18bf9 */ + 3.28730371182804296828e-08, /* 0x3e61a6092b6ecf28 */ + 7.56672470607639279700e-08, /* 0x3e744fd049aac104 */ + 3.26750155316369681821e-09, /* 0x3e2c114fd8df5180 */ + 3.21724445362095284743e-07, /* 0x3e95972f130feae5 */ + 1.06639427371776571151e-07, /* 0x3e7ca034a55fe198 */ + 3.41020788139524715063e-07, /* 0x3e96e2b149990227 */ + 1.00582838631232552824e-07, /* 0x3e7b00000294592c */ + 3.68439433859276640065e-07, /* 0x3e98b9bdc442620e */ + 2.20403078342388012027e-07, /* 0x3e8d94fdfabf3e4e */ + 1.62841467098298142534e-07, /* 0x3e85db30b145ad9a */ + 2.25325348296680733838e-07, /* 0x3e8e3e1eb95022b0 */ + 4.37462238226421614339e-07, /* 0x3e9d5b8b45442bd6 */ + 3.52055880555040706500e-07, /* 0x3e97a046231ecd2e */ + 4.75614398494781776825e-07, /* 0x3e9feafe3ef55232 */ + 3.60998399033215317516e-07, /* 0x3e9839e7bfd78267 */ + 3.79292434611513945954e-08, /* 0x3e645cf49d6fa900 */ + 1.29859015528549300061e-08, /* 0x3e4be3132b27f380 */ + 3.15927546985474913188e-07, /* 0x3e9533980bb84f9f */ + 2.28533679887379668031e-08, /* 0x3e5889e2ce3ba390 */ + 1.17222541823553133877e-07, /* 0x3e7f7778c3ad0cc8 */ + 1.51991208405464415857e-07, /* 0x3e846660cec4eba2 */ + 1.56958239325240655564e-07}; /* 0x3e85110b4611a626 */ + + /* Some constants and split constants. */ + + static double pi = 3.1415926535897932e+00, /* 0x400921fb54442d18 */ + piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */ + piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */ + three_piby4 = 2.3561944901923449e+00, /* 0x4002d97c7f3321d2 */ + pi_head = 3.1415926218032836e+00, /* 0x400921fb50000000 */ + pi_tail = 3.1786509547056392e-08, /* 0x3e6110b4611a6263 */ + piby2_head = 1.5707963267948965e+00, /* 0x3ff921fb54442d18 */ + piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */ + + double u, v, vbyu, q1, q2, s, u1, vu1, u2, vu2, uu, c, r; + unsigned int swap_vu, index, xzero, yzero, xnan, ynan, xinf, yinf; + int m, xexp, yexp, diffexp; + + /* Find properties of arguments x and y. */ + + unsigned long ux, ui, aux, xneg, uy, auy, yneg; + + GET_BITS_DP64(x, ux); + GET_BITS_DP64(y, uy); + aux = ux & ~SIGNBIT_DP64; + auy = uy & ~SIGNBIT_DP64; + xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + xneg = ux & SIGNBIT_DP64; + yneg = uy & SIGNBIT_DP64; + xzero = (aux == 0); + yzero = (auy == 0); + xnan = (aux > PINFBITPATT_DP64); + ynan = (auy > PINFBITPATT_DP64); + xinf = (aux == PINFBITPATT_DP64); + yinf = (auy == PINFBITPATT_DP64); + + diffexp = yexp - xexp; + + /* Special cases */ + + if (xnan) + return _handle_error("atan2", OP_ATAN2, ux|0x0008000000000000, _DOMAIN, 0, + EDOM, x, y, 2); + else if (ynan) + return _handle_error("atan2", OP_ATAN2, uy|0x0008000000000000, _DOMAIN, 0, + EDOM, x, y, 2); + else if (yzero) + { /* Zero y gives +-0 for positive x + and +-pi for negative x */ + if (xneg) + { + if (yneg) return val_with_flags(-pi,AMD_F_INEXACT); + else return val_with_flags(pi,AMD_F_INEXACT); + } + else return y; + } + else if (xzero) + { /* Zero x gives +- pi/2 + depending on sign of y */ + if (yneg) return val_with_flags(-piby2,AMD_F_INEXACT); + else val_with_flags(piby2,AMD_F_INEXACT); + } + + /* Scale up both x and y if they are both below 1/4. + This avoids any possible later denormalised arithmetic. */ + + if ((xexp < 1021 && yexp < 1021)) + { + scaleUpDouble1024(ux, &ux); + scaleUpDouble1024(uy, &uy); + PUT_BITS_DP64(ux, x); + PUT_BITS_DP64(uy, y); + xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + diffexp = yexp - xexp; + } + + if (diffexp > 56) + { /* abs(y)/abs(x) > 2^56 => arctan(x/y) + is insignificant compared to piby2 */ + if (yneg) return val_with_flags(-piby2,AMD_F_INEXACT); + else return val_with_flags(piby2,AMD_F_INEXACT); + } + else if (diffexp < -28 && (!xneg)) + { /* x positive and dominant over y by a factor of 2^28. + In this case atan(y/x) is y/x to machine accuracy. */ + + if (diffexp < -1074) /* Result underflows */ + { + if (yneg) + return val_with_flags(-0.0,AMD_F_INEXACT | AMD_F_UNDERFLOW); + else + return val_with_flags(0.0,AMD_F_INEXACT | AMD_F_UNDERFLOW); + } + else + { + if (diffexp < -1022) + { + /* Result will likely be denormalized */ + y = scaleDouble_1(y, 100); + y /= x; + /* Now y is 2^100 times the true result. Scale it back down. */ + GET_BITS_DP64(y, uy); + scaleDownDouble(uy, 100, &uy); + PUT_BITS_DP64(uy, y); + if ((uy & EXPBITS_DP64) == 0) + return val_with_flags(y, AMD_F_INEXACT | AMD_F_UNDERFLOW); + else + return y; + } + else + return y / x; + } + } + else if (diffexp < -56 && xneg) + { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x) + is insignificant compared to pi */ + if (yneg) return val_with_flags(-pi,AMD_F_INEXACT); + else return val_with_flags(pi,AMD_F_INEXACT); + } + else if (yinf && xinf) + { /* If abs(x) and abs(y) are both infinity + return +-pi/4 or +- 3pi/4 according to + signs. */ + if (xneg) + { + if (yneg) return val_with_flags(-three_piby4,AMD_F_INEXACT); + else return val_with_flags(three_piby4,AMD_F_INEXACT); + } + else + { + if (yneg) return val_with_flags(-piby4,AMD_F_INEXACT); + else return val_with_flags(piby4,AMD_F_INEXACT); + } + } + + /* General case: take absolute values of arguments */ + + u = x; v = y; + if (xneg) u = -x; + if (yneg) v = -y; + + /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */ + + swap_vu = (u < v); + if (swap_vu) { uu = u; u = v; v = uu; } + vbyu = v/u; + + if (vbyu > 0.0625) + { /* General values of v/u. Use a look-up + table and series expansion. */ + + index = (int)(256*vbyu + 0.5); + q1 = atan_jby256_lead[index-16]; + q2 = atan_jby256_tail[index-16]; + c = index*1./256; + GET_BITS_DP64(u, ui); + m = (int)((ui & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64; + u = scaleDouble_2(u,-m); + v = scaleDouble_2(v,-m); + GET_BITS_DP64(u, ui); + PUT_BITS_DP64(0xfffffffff8000000 & ui, u1); /* 26 leading bits of u */ + u2 = u - u1; + + r = ((v-c*u1)-c*u2)/(u+c*v); + + /* Polynomial approximation to atan(r) */ + + s = r*r; + q2 = q2 + r - r*(s * (0.33333333333224095522 - s*(0.19999918038989143496))); + } + else if (vbyu < 1.e-8) + { /* v/u is small enough that atan(v/u) = v/u */ + q1 = 0.0; + q2 = vbyu; + } + else /* vbyu <= 0.0625 */ + { + /* Small values of v/u. Use a series expansion + computed carefully to minimise cancellation */ + + GET_BITS_DP64(u, ui); + PUT_BITS_DP64(0xffffffff00000000 & ui, u1); + GET_BITS_DP64(vbyu, ui); + PUT_BITS_DP64(0xffffffff00000000 & ui, vu1); + u2 = u - u1; + vu2 = vbyu - vu1; + + q1 = 0.0; + s = vbyu*vbyu; + q2 = vbyu + + ((((v - u1*vu1) - u2*vu1) - u*vu2)/u - + (vbyu*s*(0.33333333333333170500 - + s*(0.19999999999393223405 - + s*(0.14285713561807169030 - + s*(0.11110736283514525407 - + s*(0.90029810285449784439E-01))))))); + } + + /* Tidy-up according to which quadrant the arguments lie in */ + + if (swap_vu) {q1 = piby2_head - q1; q2 = piby2_tail - q2;} + if (xneg) {q1 = pi_head - q1; q2 = pi_tail - q2;} + q1 = q1 + q2; + + if (yneg) q1 = - q1; + + return q1; +} diff --git a/sdk/lib/crt/math/libm_sse2/atan2f.c b/sdk/lib/crt/math/libm_sse2/atan2f.c new file mode 100644 index 00000000000..42d54cda2d5 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/atan2f.c @@ -0,0 +1,469 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VALF_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_SCALEDOUBLE_1 +#define USE_SCALEDOWNDOUBLE +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_VALF_WITH_FLAGS +#undef USE_NAN_WITH_FLAGS +#undef USE_SCALEDOUBLE_1 +#undef USE_SCALEDOWNDOUBLE +#undef USE_HANDLE_ERRORF + +#include "libm_errno.h" + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(atan2f) + +float FN_PROTOTYPE(atan2f)(float fy, float fx) +{ + /* Array atan_jby256 contains precomputed values of atan(j/256), + for j = 16, 17, ..., 256. */ + + static const double atan_jby256[ 241] = { + 6.24188099959573430842e-02, /* 0x3faff55bb72cfde9 */ + 6.63088949198234745008e-02, /* 0x3fb0f99ea71d52a6 */ + 7.01969710718705064423e-02, /* 0x3fb1f86dbf082d58 */ + 7.40829225490337306415e-02, /* 0x3fb2f719318a4a9a */ + 7.79666338315423007588e-02, /* 0x3fb3f59f0e7c559d */ + 8.18479898030765457007e-02, /* 0x3fb4f3fd677292fb */ + 8.57268757707448092464e-02, /* 0x3fb5f2324fd2d7b2 */ + 8.96031774848717321724e-02, /* 0x3fb6f03bdcea4b0c */ + 9.34767811585894559112e-02, /* 0x3fb7ee182602f10e */ + 9.73475734872236708739e-02, /* 0x3fb8ebc54478fb28 */ + 1.01215441667466668485e-01, /* 0x3fb9e94153cfdcf1 */ + 1.05080273416329528224e-01, /* 0x3fbae68a71c722b8 */ + 1.08941956989865793015e-01, /* 0x3fbbe39ebe6f07c3 */ + 1.12800381201659388752e-01, /* 0x3fbce07c5c3cca32 */ + 1.16655435441069349478e-01, /* 0x3fbddd21701eba6e */ + 1.20507009691224548087e-01, /* 0x3fbed98c2190043a */ + 1.24354994546761424279e-01, /* 0x3fbfd5ba9aac2f6d */ + 1.28199281231298117811e-01, /* 0x3fc068d584212b3d */ + 1.32039761614638734288e-01, /* 0x3fc0e6adccf40881 */ + 1.35876328229701304195e-01, /* 0x3fc1646541060850 */ + 1.39708874289163620386e-01, /* 0x3fc1e1fafb043726 */ + 1.43537293701821222491e-01, /* 0x3fc25f6e171a535c */ + 1.47361481088651630200e-01, /* 0x3fc2dcbdb2fba1ff */ + 1.51181331798580037562e-01, /* 0x3fc359e8edeb99a3 */ + 1.54996741923940972718e-01, /* 0x3fc3d6eee8c6626c */ + 1.58807608315631065832e-01, /* 0x3fc453cec6092a9e */ + 1.62613828597948567589e-01, /* 0x3fc4d087a9da4f17 */ + 1.66415301183114927586e-01, /* 0x3fc54d18ba11570a */ + 1.70211925285474380276e-01, /* 0x3fc5c9811e3ec269 */ + 1.74003600935367680469e-01, /* 0x3fc645bfffb3aa73 */ + 1.77790228992676047071e-01, /* 0x3fc6c1d4898933d8 */ + 1.81571711160032150945e-01, /* 0x3fc73dbde8a7d201 */ + 1.85347949995694760705e-01, /* 0x3fc7b97b4bce5b02 */ + 1.89118848926083965578e-01, /* 0x3fc8350be398ebc7 */ + 1.92884312257974643856e-01, /* 0x3fc8b06ee2879c28 */ + 1.96644245190344985064e-01, /* 0x3fc92ba37d050271 */ + 2.00398553825878511514e-01, /* 0x3fc9a6a8e96c8626 */ + 2.04147145182116990236e-01, /* 0x3fca217e601081a5 */ + 2.07889927202262986272e-01, /* 0x3fca9c231b403279 */ + 2.11626808765629753628e-01, /* 0x3fcb1696574d780b */ + 2.15357699697738047551e-01, /* 0x3fcb90d7529260a2 */ + 2.19082510780057748701e-01, /* 0x3fcc0ae54d768466 */ + 2.22801153759394493514e-01, /* 0x3fcc84bf8a742e6d */ + 2.26513541356919617664e-01, /* 0x3fccfe654e1d5395 */ + 2.30219587276843717927e-01, /* 0x3fcd77d5df205736 */ + 2.33919206214733416127e-01, /* 0x3fcdf110864c9d9d */ + 2.37612313865471241892e-01, /* 0x3fce6a148e96ec4d */ + 2.41298826930858800743e-01, /* 0x3fcee2e1451d980c */ + 2.44978663126864143473e-01, /* 0x3fcf5b75f92c80dd */ + 2.48651741190513253521e-01, /* 0x3fcfd3d1fc40dbe4 */ + 2.52317980886427151166e-01, /* 0x3fd025fa510665b5 */ + 2.55977303013005474952e-01, /* 0x3fd061eea03d6290 */ + 2.59629629408257511791e-01, /* 0x3fd09dc597d86362 */ + 2.63274882955282396590e-01, /* 0x3fd0d97ee509acb3 */ + 2.66912987587400396539e-01, /* 0x3fd1151a362431c9 */ + 2.70543868292936529052e-01, /* 0x3fd150973a9ce546 */ + 2.74167451119658789338e-01, /* 0x3fd18bf5a30bf178 */ + 2.77783663178873208022e-01, /* 0x3fd1c735212dd883 */ + 2.81392432649178403370e-01, /* 0x3fd2025567e47c95 */ + 2.84993688779881237938e-01, /* 0x3fd23d562b381041 */ + 2.88587361894077354396e-01, /* 0x3fd278372057ef45 */ + 2.92173383391398755471e-01, /* 0x3fd2b2f7fd9b5fe2 */ + 2.95751685750431536626e-01, /* 0x3fd2ed987a823cfe */ + 2.99322202530807379706e-01, /* 0x3fd328184fb58951 */ + 3.02884868374971361060e-01, /* 0x3fd362773707ebcb */ + 3.06439619009630070945e-01, /* 0x3fd39cb4eb76157b */ + 3.09986391246883430384e-01, /* 0x3fd3d6d129271134 */ + 3.13525122985043869228e-01, /* 0x3fd410cbad6c7d32 */ + 3.17055753209146973237e-01, /* 0x3fd44aa436c2af09 */ + 3.20578221991156986359e-01, /* 0x3fd4845a84d0c21b */ + 3.24092470489871664618e-01, /* 0x3fd4bdee586890e6 */ + 3.27598440950530811477e-01, /* 0x3fd4f75f73869978 */ + 3.31096076704132047386e-01, /* 0x3fd530ad9951cd49 */ + 3.34585322166458920545e-01, /* 0x3fd569d88e1b4cd7 */ + 3.38066122836825466713e-01, /* 0x3fd5a2e0175e0f4e */ + 3.41538425296541714449e-01, /* 0x3fd5dbc3fbbe768d */ + 3.45002177207105076295e-01, /* 0x3fd614840309cfe1 */ + 3.48457327308122011278e-01, /* 0x3fd64d1ff635c1c5 */ + 3.51903825414964732676e-01, /* 0x3fd685979f5fa6fd */ + 3.55341622416168290144e-01, /* 0x3fd6bdeac9cbd76c */ + 3.58770670270572189509e-01, /* 0x3fd6f61941e4def0 */ + 3.62190922004212156882e-01, /* 0x3fd72e22d53aa2a9 */ + 3.65602331706966821034e-01, /* 0x3fd7660752817501 */ + 3.69004854528964421068e-01, /* 0x3fd79dc6899118d1 */ + 3.72398446676754202311e-01, /* 0x3fd7d5604b63b3f7 */ + 3.75783065409248884237e-01, /* 0x3fd80cd46a14b1d0 */ + 3.79158669033441808605e-01, /* 0x3fd84422b8df95d7 */ + 3.82525216899905096124e-01, /* 0x3fd87b4b0c1ebedb */ + 3.85882669398073752109e-01, /* 0x3fd8b24d394a1b25 */ + 3.89230987951320717144e-01, /* 0x3fd8e92916f5cde8 */ + 3.92570135011828580396e-01, /* 0x3fd91fde7cd0c662 */ + 3.95900074055262896078e-01, /* 0x3fd9566d43a34907 */ + 3.99220769575252543149e-01, /* 0x3fd98cd5454d6b18 */ + 4.02532187077682512832e-01, /* 0x3fd9c3165cc58107 */ + 4.05834293074804064450e-01, /* 0x3fd9f93066168001 */ + 4.09127055079168300278e-01, /* 0x3fda2f233e5e530b */ + 4.12410441597387267265e-01, /* 0x3fda64eec3cc23fc */ + 4.15684422123729413467e-01, /* 0x3fda9a92d59e98cf */ + 4.18948967133552840902e-01, /* 0x3fdad00f5422058b */ + 4.22204048076583571270e-01, /* 0x3fdb056420ae9343 */ + 4.25449637370042266227e-01, /* 0x3fdb3a911da65c6c */ + 4.28685708391625730496e-01, /* 0x3fdb6f962e737efb */ + 4.31912235472348193799e-01, /* 0x3fdba473378624a5 */ + 4.35129193889246812521e-01, /* 0x3fdbd9281e528191 */ + 4.38336559857957774877e-01, /* 0x3fdc0db4c94ec9ef */ + 4.41534310525166673322e-01, /* 0x3fdc42191ff11eb6 */ + 4.44722423960939305942e-01, /* 0x3fdc76550aad71f8 */ + 4.47900879150937292206e-01, /* 0x3fdcaa6872f3631b */ + 4.51069655988523443568e-01, /* 0x3fdcde53432c1350 */ + 4.54228735266762495559e-01, /* 0x3fdd121566b7f2ad */ + 4.57378098670320809571e-01, /* 0x3fdd45aec9ec862b */ + 4.60517728767271039558e-01, /* 0x3fdd791f5a1226f4 */ + 4.63647609000806093515e-01, /* 0x3fddac670561bb4f */ + 4.66767723680866497560e-01, /* 0x3fdddf85bb026974 */ + 4.69878057975686880265e-01, /* 0x3fde127b6b0744af */ + 4.72978597903265574054e-01, /* 0x3fde4548066cf51a */ + 4.76069330322761219421e-01, /* 0x3fde77eb7f175a34 */ + 4.79150242925822533735e-01, /* 0x3fdeaa65c7cf28c4 */ + 4.82221324227853687105e-01, /* 0x3fdedcb6d43f8434 */ + 4.85282563559221225002e-01, /* 0x3fdf0ede98f393cf */ + 4.88333951056405479729e-01, /* 0x3fdf40dd0b541417 */ + 4.91375477653101910835e-01, /* 0x3fdf72b221a4e495 */ + 4.94407135071275316562e-01, /* 0x3fdfa45dd3029258 */ + 4.97428915812172245392e-01, /* 0x3fdfd5e0175fdf83 */ + 5.00440813147294050189e-01, /* 0x3fe0039c73c1a40b */ + 5.03442821109336358099e-01, /* 0x3fe01c341e82422d */ + 5.06434934483096732549e-01, /* 0x3fe034b709250488 */ + 5.09417148796356245022e-01, /* 0x3fe04d25314342e5 */ + 5.12389460310737621107e-01, /* 0x3fe0657e94db30cf */ + 5.15351866012543347040e-01, /* 0x3fe07dc3324e9b38 */ + 5.18304363603577900044e-01, /* 0x3fe095f30861a58f */ + 5.21246951491958210312e-01, /* 0x3fe0ae0e1639866c */ + 5.24179628782913242802e-01, /* 0x3fe0c6145b5b43da */ + 5.27102395269579471204e-01, /* 0x3fe0de05d7aa6f7c */ + 5.30015251423793132268e-01, /* 0x3fe0f5e28b67e295 */ + 5.32918198386882147055e-01, /* 0x3fe10daa77307a0d */ + 5.35811237960463593311e-01, /* 0x3fe1255d9bfbd2a8 */ + 5.38694372597246617929e-01, /* 0x3fe13cfbfb1b056e */ + 5.41567605391844897333e-01, /* 0x3fe1548596376469 */ + 5.44430940071603086672e-01, /* 0x3fe16bfa6f5137e1 */ + 5.47284380987436924748e-01, /* 0x3fe1835a88be7c13 */ + 5.50127933104692989907e-01, /* 0x3fe19aa5e5299f99 */ + 5.52961601994028217888e-01, /* 0x3fe1b1dc87904284 */ + 5.55785393822313511514e-01, /* 0x3fe1c8fe7341f64f */ + 5.58599315343562330405e-01, /* 0x3fe1e00babdefeb3 */ + 5.61403373889889367732e-01, /* 0x3fe1f7043557138a */ + 5.64197577362497537656e-01, /* 0x3fe20de813e823b1 */ + 5.66981934222700489912e-01, /* 0x3fe224b74c1d192a */ + 5.69756453482978431069e-01, /* 0x3fe23b71e2cc9e6a */ + 5.72521144698072359525e-01, /* 0x3fe25217dd17e501 */ + 5.75276017956117824426e-01, /* 0x3fe268a940696da6 */ + 5.78021083869819540801e-01, /* 0x3fe27f261273d1b3 */ + 5.80756353567670302596e-01, /* 0x3fe2958e59308e30 */ + 5.83481838685214859730e-01, /* 0x3fe2abe21aded073 */ + 5.86197551356360535557e-01, /* 0x3fe2c2215e024465 */ + 5.88903504204738026395e-01, /* 0x3fe2d84c2961e48b */ + 5.91599710335111383941e-01, /* 0x3fe2ee628406cbca */ + 5.94286183324841177367e-01, /* 0x3fe30464753b090a */ + 5.96962937215401501234e-01, /* 0x3fe31a52048874be */ + 5.99629986503951384336e-01, /* 0x3fe3302b39b78856 */ + 6.02287346134964152178e-01, /* 0x3fe345f01cce37bb */ + 6.04935031491913965951e-01, /* 0x3fe35ba0b60eccce */ + 6.07573058389022313541e-01, /* 0x3fe3713d0df6c503 */ + 6.10201443063065118722e-01, /* 0x3fe386c52d3db11e */ + 6.12820202165241245673e-01, /* 0x3fe39c391cd41719 */ + 6.15429352753104952356e-01, /* 0x3fe3b198e5e2564a */ + 6.18028912282561737612e-01, /* 0x3fe3c6e491c78dc4 */ + 6.20618898599929469384e-01, /* 0x3fe3dc1c2a188504 */ + 6.23199329934065904268e-01, /* 0x3fe3f13fb89e96f4 */ + 6.25770224888563042498e-01, /* 0x3fe4064f47569f48 */ + 6.28331602434009650615e-01, /* 0x3fe41b4ae06fea41 */ + 6.30883481900321840818e-01, /* 0x3fe430328e4b26d5 */ + 6.33425882969144482537e-01, /* 0x3fe445065b795b55 */ + 6.35958825666321447834e-01, /* 0x3fe459c652badc7f */ + 6.38482330354437466191e-01, /* 0x3fe46e727efe4715 */ + 6.40996417725432032775e-01, /* 0x3fe4830aeb5f7bfd */ + 6.43501108793284370968e-01, /* 0x3fe4978fa3269ee1 */ + 6.45996424886771558604e-01, /* 0x3fe4ac00b1c71762 */ + 6.48482387642300484032e-01, /* 0x3fe4c05e22de94e4 */ + 6.50959018996812410762e-01, /* 0x3fe4d4a8023414e8 */ + 6.53426341180761927063e-01, /* 0x3fe4e8de5bb6ec04 */ + 6.55884376711170835605e-01, /* 0x3fe4fd013b7dd17e */ + 6.58333148384755983962e-01, /* 0x3fe51110adc5ed81 */ + 6.60772679271132590273e-01, /* 0x3fe5250cbef1e9fa */ + 6.63202992706093175102e-01, /* 0x3fe538f57b89061e */ + 6.65624112284960989250e-01, /* 0x3fe54ccaf0362c8f */ + 6.68036061856020157990e-01, /* 0x3fe5608d29c70c34 */ + 6.70438865514021320458e-01, /* 0x3fe5743c352b33b9 */ + 6.72832547593763097282e-01, /* 0x3fe587d81f732fba */ + 6.75217132663749830535e-01, /* 0x3fe59b60f5cfab9d */ + 6.77592645519925151909e-01, /* 0x3fe5aed6c5909517 */ + 6.79959111179481823228e-01, /* 0x3fe5c2399c244260 */ + 6.82316554874748071313e-01, /* 0x3fe5d58987169b18 */ + 6.84665002047148862907e-01, /* 0x3fe5e8c6941043cf */ + 6.87004478341244895212e-01, /* 0x3fe5fbf0d0d5cc49 */ + 6.89335009598845749323e-01, /* 0x3fe60f084b46e05e */ + 6.91656621853199760075e-01, /* 0x3fe6220d115d7b8d */ + 6.93969341323259825138e-01, /* 0x3fe634ff312d1f3b */ + 6.96273194408023488045e-01, /* 0x3fe647deb8e20b8f */ + 6.98568207680949848637e-01, /* 0x3fe65aabb6c07b02 */ + 7.00854407884450081312e-01, /* 0x3fe66d663923e086 */ + 7.03131821924453670469e-01, /* 0x3fe6800e4e7e2857 */ + 7.05400476865049030906e-01, /* 0x3fe692a40556fb6a */ + 7.07660399923197958039e-01, /* 0x3fe6a5276c4b0575 */ + 7.09911618463524796141e-01, /* 0x3fe6b798920b3d98 */ + 7.12154159993178659249e-01, /* 0x3fe6c9f7855c3198 */ + 7.14388052156768926793e-01, /* 0x3fe6dc44551553ae */ + 7.16613322731374569052e-01, /* 0x3fe6ee7f10204aef */ + 7.18829999621624415873e-01, /* 0x3fe700a7c5784633 */ + 7.21038110854851588272e-01, /* 0x3fe712be84295198 */ + 7.23237684576317874097e-01, /* 0x3fe724c35b4fae7b */ + 7.25428749044510712274e-01, /* 0x3fe736b65a172dff */ + 7.27611332626510676214e-01, /* 0x3fe748978fba8e0f */ + 7.29785463793429123314e-01, /* 0x3fe75a670b82d8d8 */ + 7.31951171115916565668e-01, /* 0x3fe76c24dcc6c6c0 */ + 7.34108483259739652560e-01, /* 0x3fe77dd112ea22c7 */ + 7.36257428981428097003e-01, /* 0x3fe78f6bbd5d315e */ + 7.38398037123989547936e-01, /* 0x3fe7a0f4eb9c19a2 */ + 7.40530336612692630105e-01, /* 0x3fe7b26cad2e50fd */ + 7.42654356450917929600e-01, /* 0x3fe7c3d311a6092b */ + 7.44770125716075148681e-01, /* 0x3fe7d528289fa093 */ + 7.46877673555587429099e-01, /* 0x3fe7e66c01c114fd */ + 7.48977029182941400620e-01, /* 0x3fe7f79eacb97898 */ + 7.51068221873802288613e-01, /* 0x3fe808c03940694a */ + 7.53151280962194302759e-01, /* 0x3fe819d0b7158a4c */ + 7.55226235836744863583e-01, /* 0x3fe82ad036000005 */ + 7.57293115936992444759e-01, /* 0x3fe83bbec5cdee22 */ + 7.59351950749757920178e-01, /* 0x3fe84c9c7653f7ea */ + 7.61402769805578416573e-01, /* 0x3fe85d69576cc2c5 */ + 7.63445602675201784315e-01, /* 0x3fe86e2578f87ae5 */ + 7.65480478966144461950e-01, /* 0x3fe87ed0eadc5a2a */ + 7.67507428319308182552e-01, /* 0x3fe88f6bbd023118 */ + 7.69526480405658186434e-01, /* 0x3fe89ff5ff57f1f7 */ + 7.71537664922959498526e-01, /* 0x3fe8b06fc1cf3dfe */ + 7.73541011592573490852e-01, /* 0x3fe8c0d9145cf49d */ + 7.75536550156311621507e-01, /* 0x3fe8d13206f8c4ca */ + 7.77524310373347682379e-01, /* 0x3fe8e17aa99cc05d */ + 7.79504322017186335181e-01, /* 0x3fe8f1b30c44f167 */ + 7.81476614872688268854e-01, /* 0x3fe901db3eeef187 */ + 7.83441218733151756304e-01, /* 0x3fe911f35199833b */ + 7.85398163397448278999e-01}; /* 0x3fe921fb54442d18 */ + + /* Some constants. */ + + static double pi = 3.1415926535897932e+00, /* 0x400921fb54442d18 */ + piby2 = 1.5707963267948966e+00, /* 0x3ff921fb54442d18 */ + piby4 = 7.8539816339744831e-01, /* 0x3fe921fb54442d18 */ + three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */ + + double u, v, vbyu, q, s, uu, r; + unsigned int swap_vu, index, xzero, yzero, xnan, ynan, xinf, yinf; + int xexp, yexp, diffexp; + + double x = fx; + double y = fy; + + /* Find properties of arguments x and y. */ + + unsigned long ux, aux, xneg, uy, auy, yneg; + + GET_BITS_DP64(x, ux); + GET_BITS_DP64(y, uy); + aux = ux & ~SIGNBIT_DP64; + auy = uy & ~SIGNBIT_DP64; + xexp = (int)((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + yexp = (int)((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + xneg = ux & SIGNBIT_DP64; + yneg = uy & SIGNBIT_DP64; + xzero = (aux == 0); + yzero = (auy == 0); + xnan = (aux > PINFBITPATT_DP64); + ynan = (auy > PINFBITPATT_DP64); + xinf = (aux == PINFBITPATT_DP64); + yinf = (auy == PINFBITPATT_DP64); + + diffexp = yexp - xexp; + + /* Special cases */ + + if (xnan) + { + unsigned int ufx; + GET_BITS_SP32(fx, ufx); + return _handle_errorf("atan2f", OP_ATAN2, ufx|0x00400000, _DOMAIN, 0, + EDOM, fx, fy, 2); + } + else if (ynan) + { + unsigned int ufy; + GET_BITS_SP32(fy, ufy); + return _handle_errorf("atan2f", OP_ATAN2, ufy|0x00400000, _DOMAIN, 0, + EDOM, fx, fy, 2); + } + else if (yzero) + { /* Zero y gives +-0 for positive x + and +-pi for negative x */ + if (xneg) + { + if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); + else return valf_with_flags((float)pi, AMD_F_INEXACT); + } + else return (float)y; + } + else if (xzero) + { /* Zero x gives +- pi/2 + depending on sign of y */ + if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); + else valf_with_flags((float)piby2, AMD_F_INEXACT); + } + + if (diffexp > 26) + { /* abs(y)/abs(x) > 2^26 => arctan(x/y) + is insignificant compared to piby2 */ + if (yneg) return valf_with_flags((float)-piby2, AMD_F_INEXACT); + else return valf_with_flags((float)piby2, AMD_F_INEXACT); + } + else if (diffexp < -13 && (!xneg)) + { /* x positive and dominant over y by a factor of 2^13. + In this case atan(y/x) is y/x to machine accuracy. */ + + if (diffexp < -150) /* Result underflows */ + { + if (yneg) + return valf_with_flags(-0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); + else + return valf_with_flags(0.0F, AMD_F_INEXACT | AMD_F_UNDERFLOW); + } + else + { + if (diffexp < -126) + { + /* Result will likely be denormalized */ + y = scaleDouble_1(y, 100); + y /= x; + /* Now y is 2^100 times the true result. Scale it back down. */ + GET_BITS_DP64(y, uy); + scaleDownDouble(uy, 100, &uy); + PUT_BITS_DP64(uy, y); + if ((uy & EXPBITS_DP64) == 0) + return valf_with_flags((float)y, AMD_F_INEXACT | AMD_F_UNDERFLOW); + else + return (float)y; + } + else + return (float)(y / x); + } + } + else if (diffexp < -26 && xneg) + { /* abs(x)/abs(y) > 2^56 and x < 0 => arctan(y/x) + is insignificant compared to pi */ + if (yneg) return valf_with_flags((float)-pi, AMD_F_INEXACT); + else return valf_with_flags((float)pi, AMD_F_INEXACT); + } + else if (yinf && xinf) + { /* If abs(x) and abs(y) are both infinity + return +-pi/4 or +- 3pi/4 according to + signs. */ + if (xneg) + { + if (yneg) return valf_with_flags((float)-three_piby4, AMD_F_INEXACT); + else return valf_with_flags((float)three_piby4, AMD_F_INEXACT); + } + else + { + if (yneg) return valf_with_flags((float)-piby4, AMD_F_INEXACT); + else return valf_with_flags((float)piby4, AMD_F_INEXACT); + } + } + + /* General case: take absolute values of arguments */ + + u = x; v = y; + if (xneg) u = -x; + if (yneg) v = -y; + + /* Swap u and v if necessary to obtain 0 < v < u. Compute v/u. */ + + swap_vu = (u < v); + if (swap_vu) { uu = u; u = v; v = uu; } + vbyu = v/u; + + if (vbyu > 0.0625) + { /* General values of v/u. Use a look-up + table and series expansion. */ + + index = (int)(256*vbyu + 0.5); + r = (256*v-index*u)/(256*u+index*v); + + /* Polynomial approximation to atan(vbyu) */ + + s = r*r; + q = atan_jby256[index-16] + r - r*s*0.33333333333224095522; + } + else if (vbyu < 1.e-4) + { /* v/u is small enough that atan(v/u) = v/u */ + q = vbyu; + } + else /* vbyu <= 0.0625 */ + { + /* Small values of v/u. Use a series expansion */ + + s = vbyu*vbyu; + q = vbyu - + vbyu*s*(0.33333333333333170500 - + s*(0.19999999999393223405 - + s*0.14285713561807169030)); + } + + /* Tidy-up according to which quadrant the arguments lie in */ + + if (swap_vu) {q = piby2 - q;} + if (xneg) {q = pi - q;} + if (yneg) q = - q; + return (float)q; +} diff --git a/sdk/lib/crt/math/libm_sse2/atanf.c b/sdk/lib/crt/math/libm_sse2/atanf.c new file mode 100644 index 00000000000..08c4eb7ff43 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/atanf.c @@ -0,0 +1,135 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_VALF_WITH_FLAGS +#define USE_NAN_WITH_FLAGS +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_VALF_WITH_FLAGS +#undef USE_NAN_WITH_FLAGS +#undef USE_HANDLE_ERRORF + +#include "libm_errno.h" + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(atanf) + +float FN_PROTOTYPE(atanf)(float fx) +{ + + /* Some constants and split constants. */ + + static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */ + + double c, v, s, q, z; + unsigned int xnan; + + double x = fx; + + /* Find properties of argument fx. */ + + unsigned long ux, aux, xneg; + + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + xneg = ux & SIGNBIT_DP64; + + v = x; + if (xneg) v = -x; + + /* Argument reduction to range [-7/16,7/16] */ + + if (aux < 0x3fdc000000000000) /* v < 7./16. */ + { + x = v; + c = 0.0; + } + else if (aux < 0x3fe6000000000000) /* v < 11./16. */ + { + x = (2.0*v-1.0)/(2.0+v); + /* c = arctan(0.5) */ + c = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */ + } + else if (aux < 0x3ff3000000000000) /* v < 19./16. */ + { + x = (v-1.0)/(1.0+v); + /* c = arctan(1.) */ + c = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */ + } + else if (aux < 0x4003800000000000) /* v < 39./16. */ + { + x = (v-1.5)/(1.0+1.5*v); + /* c = arctan(1.5) */ + c = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */ + } + else + { + + xnan = (aux > PINFBITPATT_DP64); + + if (xnan) + { + /* x is NaN */ + unsigned int uhx; + GET_BITS_SP32(fx, uhx); + return _handle_errorf("atanf", OP_ATAN, uhx|0x00400000, _DOMAIN, + 0, EDOM, fx, 0.0F, 1); + } + else if (v > 0x4c80000000000000) + { /* abs(x) > 2^26 => arctan(1/x) is + insignificant compared to piby2 */ + if (xneg) + return valf_with_flags((float)-piby2, AMD_F_INEXACT); + else + return valf_with_flags((float)piby2, AMD_F_INEXACT); + } + + x = -1.0/v; + /* c = arctan(infinity) */ + c = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */ + } + + /* Core approximation: Remez(2,2) on [-7/16,7/16] */ + + s = x*x; + q = x*s* + (0.296528598819239217902158651186e0 + + (0.192324546402108583211697690500e0 + + 0.470677934286149214138357545549e-2*s)*s)/ + (0.889585796862432286486651434570e0 + + (0.111072499995399550138837673349e1 + + 0.299309699959659728404442796915e0*s)*s); + + z = c - (q - x); + + if (xneg) z = -z; + return (float)z; +} diff --git a/sdk/lib/crt/math/libm_sse2/cabs.c b/sdk/lib/crt/math/libm_sse2/cabs.c new file mode 100644 index 00000000000..fa1b22a9b62 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/cabs.c @@ -0,0 +1,34 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" + +double __cdecl _cabs(COMPLEX z) +{ + /* Returns the absolute value of a complex number z + with real part a and complex part b. */ +return _hypot(z.x, z.y); +} diff --git a/sdk/lib/crt/math/libm_sse2/cabsf.c b/sdk/lib/crt/math/libm_sse2/cabsf.c new file mode 100644 index 00000000000..c9235ce97bf --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/cabsf.c @@ -0,0 +1,35 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" + +float _hypotf(float,float); +float _cabsf(COMPLEX z) +{ + /* Returns the absolute value of a complex number z + with real part a and complex part b. */ +return _hypotf((float)z.x, (float)z.y); +} diff --git a/sdk/lib/crt/math/libm_sse2/ceil.c b/sdk/lib/crt/math/libm_sse2/ceil.c new file mode 100644 index 00000000000..cb0f155e1d8 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/ceil.c @@ -0,0 +1,88 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#include "libm_errno.h" +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_HANDLE_ERROR + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(ceil) + +double FN_PROTOTYPE(ceil)(double x) +{ + double r; + long rexp, xneg; + unsigned long ux, ax, ur, mask; + + GET_BITS_DP64(x, ux); + ax = ux & (~SIGNBIT_DP64); + xneg = (ux != ax); + + if (ax >= 0x4340000000000000) + { + /* abs(x) is either NaN, infinity, or >= 2^53 */ + if (ax > 0x7ff0000000000000) + /* x is NaN */ + return _handle_error("ceil", OP_CEIL, ux|0x0008000000000000, _DOMAIN, 0, + EDOM, x, 0.0, 1); + else + return x; + } + else if (ax < 0x3ff0000000000000) /* abs(x) < 1.0 */ + { + if (ax == 0x0000000000000000) + /* x is +zero or -zero; return the same zero */ + return x; + else if (xneg) /* x < 0.0 */ + { + PUT_BITS_DP64(SIGNBIT_DP64, r); /* return -0.0 */ + return r; + } + else + return 1.0; + } + else + { + rexp = ((ux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64; + /* Mask out the bits of r that we don't want */ + mask = 1; + mask = (mask << (EXPSHIFTBITS_DP64 - rexp)) - 1; + ur = (ux & ~mask); + PUT_BITS_DP64(ur, r); + if (xneg || (ur == ux)) + return r; + else + /* We threw some bits away and x was positive */ + return r + 1.0; + } + +} diff --git a/sdk/lib/crt/math/libm_sse2/ceilf.c b/sdk/lib/crt/math/libm_sse2/ceilf.c new file mode 100644 index 00000000000..22f85b9777b --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/ceilf.c @@ -0,0 +1,86 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#include "libm_errno.h" +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_HANDLE_ERRORF + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(ceilf) + +float FN_PROTOTYPE(ceilf)(float x) +{ + float r; + int rexp, xneg; + unsigned int ux, ax, ur, mask; + + GET_BITS_SP32(x, ux); + ax = ux & (~SIGNBIT_SP32); + xneg = (ux != ax); + + if (ax >= 0x4b800000) + { + /* abs(x) is either NaN, infinity, or >= 2^24 */ + if (ax > 0x7f800000) + /* x is NaN */ + return _handle_errorf("ceilf", OP_CEIL, ux, _DOMAIN, 0, EDOM, x, + 0.0F, 1); + else + return x; + } + else if (ax < 0x3f800000) /* abs(x) < 1.0 */ + { + if (ax == 0x00000000) + /* x is +zero or -zero; return the same zero */ + return x; + else if (xneg) /* x < 0.0 */ + { + PUT_BITS_SP32(SIGNBIT_SP32, r); /* return -0.0 */ + return r; + } + else + return 1.0F; + } + else + { + rexp = ((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; + /* Mask out the bits of r that we don't want */ + mask = (1 << (EXPSHIFTBITS_SP32 - rexp)) - 1; + ur = (ux & ~mask); + PUT_BITS_SP32(ur, r); + + if (xneg || (ux == ur)) return r; + else + /* We threw some bits away and x was positive */ + return r + 1.0F; + } +} diff --git a/sdk/lib/crt/math/libm_sse2/cos.asm b/sdk/lib/crt/math/libm_sse2/cos.asm new file mode 100644 index 00000000000..850b8f1a34d --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/cos.asm @@ -0,0 +1,533 @@ +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +; +; An implementation of the cos function. +; +; Prototype: +; +; double cos(double x); +; +; Computes cos(x). +; It will provide proper C99 return values, +; but may not raise floating point status bits properly. +; Based on the NAG C implementation. +; +; If FMA3 hardware is available, an FMA3 implementation of cos will be used. + +.const +ALIGN 16 +L_real_piby2_1 DQ 03ff921fb54400000h ; piby2_1 + DQ 0 +L_real_piby2_1tail DQ 03dd0b4611a626331h ; piby2_1tail + DQ 0 +L_real_piby2_2 DQ 03dd0b4611a600000h ; piby2_2 + DQ 0 +L_real_piby2_2tail DQ 03ba3198a2e037073h ; piby2_2tail + DQ 0 + +ALIGN 16 +L_one DQ 03FF0000000000000h, 03FF0000000000000h +L_signbit DQ 08000000000000000h, 00000000000000000h +L_int_one DQ 00000000000000001h, 00000000000000000h +L_int_two DQ 00000000000000002h, 00000000000000000h + +L_2_by_pi DQ 03fe45f306dc9c883h ; 2/pi +L_one_half DQ 03FE0000000000000h ; .5 +L_neg_one_half DQ 0bfe0000000000000h ; - 0.5 +L_two_to_neg_27 DQ 03e40000000000000h ; 2^-27 +L_two_to_neg_13 DQ 03f20000000000000h ; 2^-13 +L_piby4 DQ 03FE921FB54442D18h ; pi/4 +L_small_arg_cw DQ 0411E848000000000h ; 5.e5, appropriate for CW +L_small_arg_bdl DQ 0417312D000000000h ; 2e7, works for BDL +L_sign_mask DQ 07FFFFFFFFFFFFFFFh + +L__inf_mask_64 DQ 07FF0000000000000h ; +Inf + + + +EXTRN __Lcosarray:QWORD +EXTRN __Lsinarray:QWORD +EXTRN __use_fma3_lib:DWORD + +; local storage offsets +p_temp EQU 020h ; temporary for get/put bits operation +p_temp1 EQU 030h ; temporary for get/put bits operation +dummy_space EQU 040h +stack_size EQU 068h + +include fm.inc + +fname TEXTEQU <cos> +fname_special TEXTEQU <_cos_special> + +;Define name and any external functions being called +EXTERN __remainder_piby2_forAsm : PROC +EXTERN __remainder_piby2_fma3 : PROC +EXTERN __remainder_piby2_fma3_bdl : PROC +EXTERN fname_special : PROC + +.code + +PUBLIC fname +fname PROC FRAME + StackAllocate stack_size + .ENDPROLOG + + cmp DWORD PTR __use_fma3_lib, 0 + jne L_cos_fma3 + +Lcos_sse2: + movd rdx, xmm0 + xorpd xmm2, xmm2 ; zeroed out for later use + + mov r10, rdx + btr r10, 63 ; r10 <-- |x| + cmp r10, L_piby4 + jb Lcos_sse2_absx_lt_piby4 + +Lcos_absx_nlt_piby4: ; common case + +; Here rdx has x, r10 has |x| + movd xmm0, r10 ; xmm0 <-- |x| + + cmp r10, QWORD PTR L_small_arg_cw + jae Lcos_reduce_precise ; Note NaN/Inf will branch + +; At this point we have |x| < L_small_arg_cw, which is currently 500000. +; Note that if |x| were too large, conversion of npi2 to integer would fail. +; We reduce the argument to be in a range from -pi/4 to +pi/4 +; by subtracting multiples of pi/2 + movapd xmm2, xmm0 + mulsd xmm2, L_2_by_pi + movapd xmm4, xmm0 + +; xexp = ax >> EXPSHIFTBITS_DP64; + mov r9, r10 + shr r9, 52 ; >>EXPSHIFTBITS_DP64 + +; How many pi/2 is |x| a multiple of? +; npi2 = (int)(x * twobypi + 0.5); + addsd xmm2, L_one_half ; npi2 + + movsd xmm3, L_real_piby2_1 + cvttpd2dq xmm0, xmm2 ; convert npi2 to integer + movsd xmm1, L_real_piby2_1tail + cvtdq2pd xmm2, xmm0 ; and back to double. + +; Subtract the multiple from x to get an extra-precision remainder +; rhead = x - npi2 * piby2_1; + mulsd xmm3, xmm2 + subsd xmm4, xmm3 ; rhead + +; rtail = npi2 * piby2_1tail; + mulsd xmm1, xmm2 ; rtail + movd eax, xmm0 ; eax <-- npi2 + +; GET_BITS_DP64(rhead-rtail, uy); +; originally only rhead + movapd xmm0, xmm4 + subsd xmm0, xmm1 + + movsd xmm3, L_real_piby2_2 + movd rcx, xmm0 ; rcx <-- rhead - rtail + movsd xmm5, L_real_piby2_2tail ; piby2_2tail + +; xmm0=r, xmm1=rtail, xmm2=npi2, xmm3=temp for calc, +; xmm4=rhead xmm5= temp for calc +; expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); +; expdiff measures how close rhead - rtail is to |x| +; (larger expdiff ==> more cancellation in |x| - (rhead-rtail) ==> closer) + shl rcx, 1 ; strip any sign bit + shr rcx, 53 ; >> EXPSHIFTBITS_DP64 +1 + sub r9, rcx ; expdiff + +;; if (expdiff > 15) + cmp r9, 15 + jle Lcos_sse2_cw_reduction_done + +; Here the remainder is pretty small compared with x, which +; implies that x is a near multiple of pi/2 +; (x matches the multiple to at least 15 bits) +; So we do another stage of argument reduction. + +; t = rhead; + movapd xmm1, xmm4 + +; rtail = npi2 * piby2_2; + mulsd xmm3, xmm2 + +; rhead = t - rtail; + mulsd xmm5, xmm2 ; npi2 * piby2_2tail + subsd xmm4, xmm3 ; rhead + +; rtail = npi2 * piby2_2tail - ((t - rhead) - rtail); + subsd xmm1, xmm4 ; t - rhead + subsd xmm1, xmm3 ; -rtail + subsd xmm5, xmm1 ; rtail + +; r = rhead - rtail; + movapd xmm0, xmm4 + +;HARSHA +;xmm1=rtail + movapd xmm1, xmm5 ; xmm1 <-- copy of rtail + subsd xmm0, xmm5 + +; xmm0=r, xmm4=rhead, xmm1=rtail +Lcos_sse2_cw_reduction_done: +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +;; if the input was close to a pi/2 multiple +; The original NAG code missed this trick. +; If the input is very close to n*pi/2 after reduction, so r < 2^-27, +; then the cos is either ~ 1.0 or ~r, to within 53 bits. + +; NOTE: Unfortunately, this introduces two jcc instructions close to each +; other and to other branches. As r < 2^-13 should be rather uncommon, +; the problems for branch prediction outweigh the computational savings. - WAT +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; region = npi2 & 3; + subsd xmm4, xmm0 ; rhead-r + subsd xmm4, xmm1 ; rr = (rhead-r) - rtail + +Lcos_piby4: +; perform taylor series to calc sinx or cosx +; x2 = r * r; + +;xmm4 = a part of rr for the sin path, xmm4 is overwritten in the cos path +;instead use xmm3 because that was freed up in the sin path, xmm3 is overwritten in sin path + movapd xmm3, xmm0 + movapd xmm2, xmm0 + mulsd xmm2, xmm0 ;x2 + + bt eax,0 + jnc Lcos_sse2_calc_cos + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; region 1 or 3 do a sin calculation + movsd xmm3, __Lsinarray+50h ; s6 + mulsd xmm3, xmm2 ; x2s6 + movsd xmm5, __Lsinarray+20h ; s3 + movsd QWORD PTR p_temp[rsp], xmm4 ; store xx + movapd xmm1, xmm2 ; move for x4 + mulsd xmm1, xmm2 ; x4 + movsd QWORD PTR p_temp1[rsp], xmm0 ; store x + mulsd xmm5, xmm2 ; x2s3 + movapd xmm4, xmm0 ; move for x3 + addsd xmm3, __Lsinarray+40h ; s5+x2s6 + mulsd xmm1, xmm2 ; x6 + mulsd xmm3, xmm2 ; x2(s5+x2s6) + mulsd xmm4, xmm2 ; x3 + addsd xmm5, __Lsinarray+10h ; s2+x2s3 + mulsd xmm5, xmm2 ; x2(s2+x2s3) + addsd xmm3, __Lsinarray+30h ; s4 + x2(s5+x2s6) + mulsd xmm2, L_one_half ; 0.5 *x2 + movsd xmm0, QWORD PTR p_temp[rsp] ; load xx + mulsd xmm3, xmm1 ; x6(s4 + x2(s5+x2s6)) + addsd xmm5, __Lsinarray ; s1+x2(s2+x2s3) + mulsd xmm2, xmm0 ; 0.5 * x2 *xx + addsd xmm3, xmm5 ; zs + mulsd xmm4, xmm3 ; *x3 + subsd xmm4, xmm2 ; x3*zs - 0.5 * x2 *xx + addsd xmm0, xmm4 ; +xx + addsd xmm0, QWORD PTR p_temp1[rsp] ; +x + + jmp Lcos_sse2_adjust_region + +ALIGN 16 +Lcos_sse2_calc_cos: +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; region 0 or 2 - do a cos calculation +; zc = (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * c6)))); + mulsd xmm4, xmm0 ; x*xx + movsd xmm5, L_one_half + movsd xmm1, __Lcosarray+50h ; c6 + movsd xmm0, __Lcosarray+20h ; c3 + mulsd xmm5, xmm2 ; r = 0.5 *x2 + movapd xmm3, xmm2 ; copy of x2 + movsd QWORD PTR p_temp[rsp], xmm4 ; store x*xx + mulsd xmm1, xmm2 ; c6*x2 + mulsd xmm0, xmm2 ; c3*x2 + subsd xmm5, L_one ; -t=r-1.0, trash r + mulsd xmm3, xmm2 ; x4 + addsd xmm1, __Lcosarray+40h ; c5+x2c6 + addsd xmm0, __Lcosarray+10h ; c2+x2C3 + addsd xmm5, L_one ; 1 + (-t), trash t + mulsd xmm3, xmm2 ; x6 + mulsd xmm1, xmm2 ; x2(c5+x2c6) + mulsd xmm0, xmm2 ; x2(c2+x2C3) + movapd xmm4, xmm2 ; copy of x2 + mulsd xmm4, L_one_half ; r recalculate + addsd xmm1, __Lcosarray+30h ; c4 + x2(c5+x2c6) + addsd xmm0, __Lcosarray ; c1+x2(c2+x2C3) + mulsd xmm2, xmm2 ; x4 recalculate + subsd xmm5, xmm4 ; (1 + (-t)) - r + mulsd xmm1, xmm3 ; x6(c4 + x2(c5+x2c6)) + addsd xmm0, xmm1 ; zc + subsd xmm4, L_one ; t relaculate + subsd xmm5, QWORD PTR p_temp[rsp] ; ((1 + (-t)) - r) - x*xx + mulsd xmm0, xmm2 ; x4 * zc + addsd xmm0, xmm5 ; x4 * zc + ((1 + (-t)) - r -x*xx) + subsd xmm0, xmm4 ; result - (-t) + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; + +Lcos_sse2_adjust_region: +; switch (region) + add eax, 1 + and eax, 2 + jz Lcos_sse2_cleanup + +;; if the original region 1 or 2 then we negate the result. + movapd xmm2, xmm0 + xorpd xmm0, xmm0 + subsd xmm0, xmm2 + +ALIGN 16 +Lcos_sse2_cleanup: + StackDeallocate stack_size + ret + + + + + + +ALIGN 16 +Lcos_sse2_absx_lt_piby4: +; cos = cos_piby4(x, 0.0); + +; x2 = r * r; + cmp r10, L_two_to_neg_13 + jb Lcos_sse2_x_small + movapd xmm2, xmm0 + mulsd xmm2, xmm0 ; x2 + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; region 0 - do a cos calculation +; zc = (c2 + x2 * (c3 + x2 * (c4 + x2 * (c5 + x2 * c6)))); + movsd xmm1, __Lcosarray+10h ; c2 + movapd xmm4, xmm2 ; move for x4 + mulsd xmm4, xmm2 ; x4 + movsd xmm3, __Lcosarray+30h ; c4 + mulsd xmm1, xmm2 ; c2x2 + movsd xmm5, __Lcosarray+50h ; c6 + mulsd xmm3, xmm2 ; c4x2 + movapd xmm0, xmm4 ; move for x8 + mulsd xmm5, xmm2 ; c6x2 + mulsd xmm0, xmm4 ; x8 + addsd xmm1, __Lcosarray ; c1 + c2x2 + mulsd xmm1, xmm4 ; c1x4 + c2x6 + addsd xmm3, __Lcosarray+20h ; c3 + c4x2 + mulsd xmm2, L_neg_one_half ; -0.5x2, destroy xmm2 + addsd xmm5, __Lcosarray+40h ; c5 + c6x2 + mulsd xmm3, xmm0 ; c3x8 + c4x10 + mulsd xmm4, xmm0 ; x12 + mulsd xmm4, xmm5 ; c5x12 + c6x14 + + movsd xmm0, L_one + addsd xmm1, xmm3 ; c1x4 + c2x6 + c3x8 + c4x10 + movapd xmm3, xmm2 ; preserve -0.5x2 + addsd xmm2, xmm0 ; t = 1 - 0.5x2 + subsd xmm0, xmm2 ; 1-t + addsd xmm0, xmm3 ; (1-t) - r + addsd xmm1, xmm4 ; c1x4 + c2x6 + c3x8 + c4x10 + c5x12 + c6x14 + addsd xmm0, xmm1 ; (1-t) - r + c1x4 + c2x6 + c3x8 + c4x10 + c5x12 + c6x14 + addsd xmm0, xmm2 ; 1 - 0.5x2 + above + + StackDeallocate stack_size + ret + +ALIGN 16 +Lcos_sse2_x_small: + movsd xmm2, xmm0 + movsd xmm0, L_one + cmp r10, L_two_to_neg_27 + jb Lcos_sse2_x_smaller + mulsd xmm2, xmm2 + mulsd xmm2, L_one_half + subsd xmm0, xmm2 + StackDeallocate stack_size + ret + +ALIGN 16 +Lcos_sse2_x_smaller: + movsd xmm0, L_one + addsd xmm0, L_int_one ; really adding smallest subnormal; set inexact + StackDeallocate stack_size + ret + +ALIGN 16 +Lcos_reduce_precise: +; Reduce x into range [-pi/4, pi/4] + cmp r10, L__inf_mask_64 + jae Lcos_x_naninf + call __remainder_piby2_forAsm + + ; At this point xmm0 has r, xmm1 has rr, rax has region + + movapd xmm4, xmm1 ; xmm4 <-- rr + jmp Lcos_piby4 + +; xmm0 = x, xmm4 = xx, eax= region + + +ALIGN 16 +Lcos_x_naninf: + call fname_special + StackDeallocate stack_size + ret + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; From this point we assume that FMA3 and AVX hardware are present. + +ALIGN 16 +L_cos_fma3: + vmovq r9,xmm0 + mov rax,r9 + and r9,L_sign_mask ; clear sign + +Lcos_early_exit_s_1: ;; unused label + cmp r9,L_piby4 + jg Lcos_early_exit_s ; Note that NaN will branch + cmp r9,L_two_to_neg_13 + jge Lcompute_cos_pyby_4 + cmp r9,L_two_to_neg_27 + jge Lcompute_1_xx_5 + vmovq xmm0,L_one ; for tiniest args, cos is 1 + jmp Lreturn_no_restore + +Lcompute_1_xx_5: + vmulsd xmm1,xmm0,L_one_half ; xmm1l <-- .5*x + vfnmadd213sd xmm0,xmm1,L_one ; xmm0l <-- 1.0 - (.5*x)*x + jmp Lreturn_no_restore + +Lcompute_cos_pyby_4: + ; make sure this is accurate enough + ; note that x^2 can't be all that close to 1 here + vmulsd xmm3,xmm0,xmm0 ; xmm3 <-- xx = x*x + vmovapd xmm0,__Lcosarray+050h ; xmm0 <-- c5 + vfmadd213sd xmm0,xmm3,__Lcosarray+040h ; xmm0 <-- c5*xx + c4 + vfmadd213sd xmm0,xmm3,__Lcosarray+030h ; xmm0 <-- (c5*xx + c4)*xx + c3 + vfmadd213sd xmm0,xmm3,__Lcosarray+020h + vfmadd213sd xmm0,xmm3,__Lcosarray+010h + vfmadd213sd xmm0,xmm3,__Lcosarray + vfmsub213sd xmm0,xmm3,L_one_half + vfmadd213sd xmm0,xmm3,L_one + + jmp Lreturn_no_restore + +Lcos_early_exit_s: + mov r8,L__inf_mask_64 + and rax,r8 + cmp rax, r8 + jz Lcos_x_naninf + +Lrange_reduce: + vmovq xmm0,r9 ; r9 <-- |x| + cmp r9,L_small_arg_bdl + jae Lcos_remainder_piby2 + + ; For __remainder_piby2_fma3 and __remainder_piby2_fma3_bdl + ; on input + ; x is in xmm0 + ; on output + ; r is in xmm0 + ; rr is in xmm1 + ; region is in rax + + ; Boldo-Daumas-Li reduction for reasonably small |x| + call __remainder_piby2_fma3_bdl + +;; if region is 0 or 2 do a cos calc. +;; if region is 1 or 3 do a sin calc. +Lcos_exit_s: + bt rax,0 + jc Lsin_piby4_compute + +Lcos_piby4_compute: ;; unused label + ; compute the cosine of r+rr, where this sum is in [-pi/4,pi/4] + vmovapd xmm2,L_one + vmulsd xmm3,xmm0,xmm0 ; xmm3 <-- x * x + vmulsd xmm5,xmm3,L_one_half ; xmm5 <-- x*x*.5 == r + vsubsd xmm4,xmm2,xmm5 ; xmm4 <-- t = 1. - x*x*.5 + vsubsd xmm2,xmm2,xmm4 ; 1-t + vsubsd xmm2,xmm2,xmm5 ; xmm2 <-- (1-t) - r + vmovapd xmm5,__Lcosarray+040h + vfnmadd231sd xmm2,xmm0,xmm1 ; (1.0 - t) - r) - x * xx) xmm2 + vmulsd xmm1,xmm3,xmm3 ; x2 * x2 xmm1 + vfmadd231sd xmm5,xmm3,__Lcosarray+050h + vfmadd213sd xmm5,xmm3,__Lcosarray+030h + vfmadd213sd xmm5,xmm3,__Lcosarray+020h + vfmadd213sd xmm5,xmm3,__Lcosarray+010h + vfmadd213sd xmm5,xmm3,__Lcosarray + vfmadd213sd xmm5,xmm1,xmm2 + vaddsd xmm0,xmm5,xmm4 + + jmp Lcos_exit_s_1 + +ALIGN 16 +Lsin_piby4_compute: + ; compute the sine of r+rr, where this sum is in [-pi/4,pi/4] + vmovapd xmm5,__Lsinarray+040h + vmulsd xmm3,xmm0,xmm0 ; xmm3 <-- x2 = x * x + vfmadd231sd xmm5,xmm3,__Lsinarray+050h + vfmadd213sd xmm5,xmm3,__Lsinarray+030h + vfmadd213sd xmm5,xmm3,__Lsinarray+020h + vfmadd213sd xmm5,xmm3,__Lsinarray+010h ; xmm5 <-- r + + vmulsd xmm4,xmm0,xmm3 ; xmm4 <-- x3 = x*x*x + vmulsd xmm2,xmm4,xmm5 ; xmm2 <-- x*x*x * r + vmulsd xmm5,xmm1,L_one_half ; xmm5 <-- .5*x*x + vsubsd xmm2,xmm5,xmm2 ; xmm2 <-- .5*x*x - x*x*x*r + vmulsd xmm2,xmm3,xmm2 + vsubsd xmm2,xmm2,xmm1 + vfnmadd231sd xmm2, xmm4,__Lsinarray + vsubsd xmm0,xmm0,xmm2 + +Lcos_exit_s_1: + xor r8,r8 + add eax, 1 + and eax, 2 + cmovnz r8, L_signbit + vmovq xmm3,r8 + vxorpd xmm0,xmm0,xmm3 + +Lreturn_restore_regs: + StackDeallocate stack_size + ret + +Lreturn_no_restore: + StackDeallocate stack_size + ret + +ALIGN 16 +Lcos_remainder_piby2: + ; argument reduction for general x + call __remainder_piby2_fma3 + jmp Lcos_exit_s + + +fname endp +END diff --git a/sdk/lib/crt/math/libm_sse2/cosf.asm b/sdk/lib/crt/math/libm_sse2/cosf.asm new file mode 100644 index 00000000000..6b232472a23 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/cosf.asm @@ -0,0 +1,525 @@ +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +; An implementation of the cosf function. +; +; Prototype: +; +; float cosf(float x); +; +; Computes cosf(x). +; Based on the NAG C implementation. +; It will provide proper C99 return values, +; but may not raise floating point status bits properly. +; Original Author: Harsha Jagasia + +.const +ALIGN 16 +L_real_one DQ 03ff0000000000000h ; 1.0 + DQ 0 ; for alignment +L_one_half DQ 03fe0000000000000h ; 0.5 + DQ 0 +L_2bypi DQ 03fe45f306dc9c883h ; 2./pi + DQ 0 +L_one_sixth DQ 03fc5555555555555h ; 0.166666666666 + DQ 0 +L_piby2 DQ 03fe921fb54442d18h + DQ 0 +L_piby2_1 DQ 03ff921fb54400000h ; piby2_1 + DQ 0 +L_piby2_1tail DQ 03dd0b4611a626331h ; piby2_1tail + DQ 0 +L_piby2_2 DQ 03dd0b4611a600000h ; piby2_2 + DQ 0 +L_piby2_2tail DQ 03ba3198a2e037073h ; piby2_2tail + DQ 0 +L_large_x_sse2 DQ 0411E848000000000h ; 5e5 + DQ 0 +L_large_x_fma3 DQ 041E921FB60000000h ; 3.37325952e9 + DQ 0 +L_sign_mask DQ 07FFFFFFFFFFFFFFFh + DQ 07FFFFFFFFFFFFFFFh +L__int_three DQ 00000000000000003h + DQ 00000000000000003h +L__min_norm_double DQ 00010000000000000h + DQ 00010000000000000h +L_two_to_neg_7 DQ 03f80000000000000h + DQ 0 +L_two_to_neg_13 DQ 03f20000000000000h + DQ 0 +L_inf_mask_32 DD 07F800000h + DQ 0 + +fname TEXTEQU <cosf> +fname_special TEXTEQU <_cosf_special> + +;Define name and any external functions being called +EXTERN __remainder_piby2d2f_forAsm : PROC ; NEAR +EXTERN __remainder_piby2_fma3_bdl : PROC ; NEAR +EXTERN __remainder_piby2_fma3 : PROC ; NEAR +EXTERN fname_special : PROC +EXTERN _set_statfp : PROC + + +EXTRN __Lcosfarray:QWORD +EXTRN __Lsinfarray:QWORD +EXTRN __use_fma3_lib:DWORD + +; define local variable storage offsets +p_temp equ 020h ; temporary for get/put bits operation +p_temp1 equ 030h ; temporary for get/put bits operation +dummy_space EQU 040h +stack_size EQU 068h + +include fm.inc + +.code + +ALIGN 16 +PUBLIC fname +fname PROC FRAME + StackAllocate stack_size + .ENDPROLOG + cmp DWORD PTR __use_fma3_lib, 0 + jne Lcosf_fma3 + +Lcosf_sse2: + + xorpd xmm2, xmm2 ; zeroed out for later use + +;; if NaN or inf + movd edx, xmm0 + mov eax, 07f800000h + mov r10d, eax + and r10d, edx + cmp r10d, eax + jz Lcosf_sse2_naninf + + cvtss2sd xmm0, xmm0 + movd rdx, xmm0 + +; ax = (ux & ~SIGNBIT_DP64); + mov r10, rdx + btr r10, 63 ; r10 <-- |x| + mov r8d, 1 ; for determining region later on + + movapd xmm1, xmm0 ; xmm1 <-- copy of x + + +;; if (ax <= 3fe921fb54442d18h) /* abs(x) <= pi/4 */ + mov rax, 03fe921fb54442d18h + cmp r10, rax + jg Lcosf_sse2_absx_gt_piby4 + +; *c = cos_piby4(x, 0.0); + movapd xmm2, xmm0 + mulsd xmm2, xmm2 ;x^2 + xor eax, eax + mov rdx, r10 + movsd xmm5, QWORD PTR L_one_half + jmp Lcosf_sse2_calc_sincosf_piby4 ; done + + +ALIGN 16 +Lcosf_sse2_absx_gt_piby4: +; reduce the argument to be in a range from -pi/4 to +pi/4 +; by subtracting multiples of pi/2 +; xneg = (ax != ux); + movd xmm0, r10 ; xmm0 <-- |x| + cmp r10, QWORD PTR L_large_x_sse2 + jae Lcosf_sse2_reduce_precise + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; xmm0=abs(x), xmm1=x +;/* How many pi/2 is x a multiple of? */ + + movapd xmm2, xmm0 + movsd xmm3, QWORD PTR L_2bypi + movapd xmm4, xmm0 + movsd xmm5, QWORD PTR L_one_half + mulsd xmm2, xmm3 + +; movsd xmm5, QWORD PTR L_one_half +; movapd xmm2, xmm0 +; mulsd xmm2, QWORD PTR L_2bypi +; movapd xmm4, xmm0 + + mov r9, r10 + shr r9, 52 ; r9 <-- biased exponent of x + +; npi2 = (int)(x * twobypi + 0.5); + addsd xmm2, xmm5 ; npi2 + + movsd xmm3, QWORD PTR L_piby2_1 ; piby2_1 + cvttpd2dq xmm0, xmm2 ; xmm0 <-- npi2 + movsd xmm1, QWORD PTR L_piby2_1tail ; piby2_1tail + cvtdq2pd xmm2, xmm0 ; xmm2 <-- (double)npi2 + +; Subtract the multiple from x to get an extra-precision remainder +; rhead = x - npi2 * piby2_1; + + mulsd xmm3, xmm2 ; use piby2_1 + subsd xmm4, xmm3 ; rhead + +; rtail = npi2 * piby2_1tail; + mulsd xmm1, xmm2 ; rtail + movd eax, xmm0 + +; GET_BITS_DP64(rhead-rtail, uy); +; originally only rhead + movapd xmm0, xmm4 + subsd xmm0, xmm1 + + movsd xmm3, QWORD PTR L_piby2_2 ; piby2_2 + movd rcx, xmm0 ; rcx <-- rhead-rtail + movsd xmm5, QWORD PTR L_piby2_2tail ; piby2_2tail + +; region = npi2 & 3; +; and eax, 3 +; expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); + shl rcx, 1 ; strip any sign bit + shr rcx, 53 ; >> EXPSHIFTBITS_DP64 +1 + sub r9, rcx ; expdiff + +;; if (expdiff > 15) + cmp r9, 15 + jle Lcosf_sse2_expdiff_le_15 + +; The remainder is pretty small compared with x, which +; implies that x is a near multiple of pi/2 +; (x matches the multiple to at least 15 bits) +; t = rhead; + movapd xmm1, xmm4 + +; rtail = npi2 * piby2_2; + mulsd xmm3, xmm2 + +; rhead = t - rtail; + mulsd xmm5, xmm2 ; npi2 * piby2_2tail + subsd xmm4, xmm3 ; rhead + +; rtail = npi2 * piby2_2tail - ((t - rhead) - rtail); + subsd xmm1, xmm4 ; t - rhead + subsd xmm1, xmm3 ; -rtail + subsd xmm5, xmm1 ; rtail + +; r = rhead - rtail; + movapd xmm0, xmm4 + +;HARSHA +;xmm1=rtail + movapd xmm1, xmm5 + subsd xmm0, xmm5 + +; xmm0=r, xmm4=rhead, xmm1=rtail + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +Lcosf_sse2_expdiff_le_15: + cmp rcx, 03f2h ; is r < 2^-13 ? + jge Lcosf_sse2_calc_sincosf_piby4 ; use taylor series if not + cmp rcx, 03deh ; is r < 2^-33 ? + jle Lcosf_sse2_r_very_small ; then cosf(r) ~ 1 or r + + movapd xmm2, xmm0 + mulsd xmm2, xmm0 ; xmm2 <-- x^2 + +;; if region is 1 or 3 do a sinf calc. + and r8d, eax + jz Lcosf_sse2_r_small_calc_sin + +Lcosf_sse2_r_small_calc_cos: +; region 1 or 3 +; use simply polynomial +; *s = x - x*x*x*0.166666666666666666; + movsd xmm3, QWORD PTR L_one_sixth + mulsd xmm3, xmm0 ; * x + mulsd xmm3, xmm2 ; * x^2 + subsd xmm0, xmm3 ; xs + jmp Lcosf_sse2_adjust_region + +ALIGN 16 +Lcosf_sse2_r_small_calc_sin: +; region 0 or 2 +; cos = 1.0 - x*x*0.5; + movsd xmm0, QWORD PTR L_real_one ; 1.0 + mulsd xmm2, QWORD PTR L_one_half ; 0.5 *x^2 + subsd xmm0, xmm2 + jmp Lcosf_sse2_adjust_region + +ALIGN 16 +Lcosf_sse2_r_very_small: +; then sin(r) = r +; if region is 1 or 3 do a sin calc. + and r8d, eax + jnz Lcosf_sse2_adjust_region + + movsd xmm0, QWORD PTR L_real_one ; cosf(r) is a 1 + ; By this point, calculations should already have set inexact + jmp Lcosf_sse2_adjust_region + +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +ALIGN 16 +Lcosf_sse2_reduce_precise: +; Reduce abs(x) into range [-pi/4, pi/4] +; remainder_piby2d2f(ax, &r, ®ion); + mov QWORD PTR p_temp[rsp], rdx ; save ux for use later + mov QWORD PTR p_temp1[rsp], r10 ; save ax for use later + + call __remainder_piby2d2f_forAsm + mov rdx, QWORD PTR p_temp[rsp] ; restore ux for use later + mov r10, QWORD PTR p_temp1[rsp] ; restore ax for use later + mov r8d, 1 ; for determining region later + + ; Reduced argument is in xmm0. No second word; after all, we started in + ; single precision. Region is in rax. + movapd xmm1, xmm0 + movsd xmm5, QWORD PTR L_one_half + + jmp Lcosf_sse2_calc_sincosf_piby4 + + +; done with reducing the argument. Now perform the sin/cos calculations. +ALIGN 16 +Lcosf_sse2_calc_sincosf_piby4: + movapd xmm2, xmm0 + mulsd xmm2, xmm0 ; x^2 + +;; if region is 0 or 2, do a cosf calc + and r8d, eax + jz Lcosf_sse2_do_cosf_calc +; region is 1 or 3: do a sinf calc. +Lcosf_sse2_do_sinf_calc: + movsd xmm1, QWORD PTR __Lsinfarray+18h ; s4 + mulsd xmm1, xmm2 ; s4x2 + movsd xmm4, xmm2 ; move for x4 + mulsd xmm4, xmm2 ; x4 + movsd xmm5, QWORD PTR __Lsinfarray+8h ; s2 + mulsd xmm5, xmm2 ; s2x2 + movsd xmm3, xmm0 ; move for x3 + mulsd xmm3, xmm2 ; x3 + addsd xmm1, QWORD PTR __Lsinfarray+10h ; s3+s4x2 + mulsd xmm1, xmm4 ; s3x4+s4x6 + addsd xmm5, QWORD PTR __Lsinfarray ; s1+s2x2 + addsd xmm1, xmm5 ; s1+s2x2+s3x4+s4x6 + mulsd xmm1, xmm3 ; x3(s1+s2x2+s3x4+s4x6) + addsd xmm0, xmm1 ; x + x3(s1+s2x2+s3x4+s4x6) + jmp Lcosf_sse2_adjust_region + +ALIGN 16 +Lcosf_sse2_do_cosf_calc: +; region 0 or 2 - do a cos calculation +; zc = 1-0.5*x2+ c1*x4 +c2*x6 +c3*x8; +; zc = 1-0.5*x2+ c1*x4 +c2*x6 +c3*x8 + c4*x10 for a higher precision + movsd xmm1, QWORD PTR __Lcosfarray+20h ; c4 + movsd xmm4, xmm2 ; move for x4 + mulsd xmm1, xmm2 ; c4x2 + movsd xmm3, QWORD PTR __Lcosfarray+10h ; c2 + mulsd xmm4, xmm2 ; x4 + movsd xmm0, QWORD PTR __Lcosfarray ; c0 + mulsd xmm3, xmm2 ; c2x2 + mulsd xmm0, xmm2 ; c0x2 (=-0.5x2) + addsd xmm1, QWORD PTR __Lcosfarray+18h ; c3+c4x2 + mulsd xmm1, xmm4 ; c3x4 + c4x6 + addsd xmm3, QWORD PTR __Lcosfarray+8h ; c1+c2x2 + addsd xmm1, xmm3 ; c1 + c2x2 + c3x4 + c4x6 + mulsd xmm1, xmm4 ; c1x4 + c2x6 + c3x8 + c4x10 + addsd xmm0, QWORD PTR L_real_one ; 1 - 0.5x2 + addsd xmm0, xmm1 ; 1 - 0.5x2 + c1x4 + c2x6 + c3x8 + c4x10 + +Lcosf_sse2_adjust_region: +; xmm1 is cos or sin, relies on previous sections to +; switch (region) + add eax, 1 + and eax, 2 + jz Lcosf_sse2_cleanup +;; if region 1 or 2 then we negate the result. + xorpd xmm2, xmm2 + subsd xmm2, xmm0 + movapd xmm0, xmm2 + +ALIGN 16 +Lcosf_sse2_cleanup: + cvtsd2ss xmm0, xmm0 + StackDeallocate stack_size + ret + + +Lcosf_sse2_naninf: + call fname_special + StackDeallocate stack_size + ret + + +ALIGN 16 +Lcosf_fma3: + vmovd eax,xmm0 + mov r8d,L_inf_mask_32 + and eax,r8d + cmp eax, r8d + jz Lcosf_fma3_naninf + + vcvtss2sd xmm5,xmm0,xmm0 + vmovq r9,xmm5 + btr r9,63 ;clear sign + + cmp r9,L_piby2 + jg Lcosf_fma3_range_reduce + cmp r9,L_two_to_neg_7 + jge Lcosf_fma3_compute_cosf_piby_4 + cmp r9,L_two_to_neg_13 + jge Lcosf_fma3_compute_1_xx_5 + + vmovq xmm0,QWORD PTR L_real_one + ; Here we need to set inexact + vaddsd xmm0,xmm0,L__min_norm_double ; this will set inexact + jmp Lcosf_fma3_return + +ALIGN 16 +Lcosf_fma3_compute_1_xx_5: + vmulsd xmm0,xmm5,QWORD PTR L_one_half + vfnmadd213sd xmm0,xmm5,L_real_one ; xmm9 1.0 - x*x*(double2)0.5 + jmp Lcosf_fma3_return + +ALIGN 16 +Lcosf_fma3_compute_cosf_piby_4: + movsd xmm0,xmm5 + vmovapd xmm2,L_real_one + vmulsd xmm3,xmm0,xmm0 + vmulsd xmm1,xmm3,L_one_half ; xmm1 <-- r + vsubsd xmm2,xmm2,xmm1 + vmovsd xmm1,__Lcosfarray+018h + vfmadd231sd xmm1,xmm3,__Lcosfarray+020h + vfmadd213sd xmm1,xmm3,__Lcosfarray+010h + vfmadd213sd xmm1,xmm3,__Lcosfarray+008h + vmulsd xmm3,xmm3,xmm3 ; xmm3 <-- x^4 + vmovdqa xmm0,xmm2 + vfmadd231sd xmm0,xmm1,xmm3 + jmp Lcosf_fma3_return + +ALIGN 16 +Lcosf_fma3_range_reduce: + vmovq xmm0,r9 ; xmm0 <-- |x| + cmp r9,L_large_x_fma3 + jge Lcosf_reduce_precise + +;cosff_range_e_5_s: + vandpd xmm1,xmm0,L_sign_mask + vmovapd xmm2,L_2bypi + vfmadd213sd xmm2,xmm1,L_one_half + vcvttpd2dq xmm2,xmm2 + vpmovsxdq xmm1,xmm2 + vandpd xmm4,xmm1,L__int_three ; region xmm4 + vshufps xmm1 ,xmm1,xmm1,8 + vcvtdq2pd xmm1,xmm1 + vmovdqa xmm2,xmm0 + vfnmadd231sd xmm2,xmm1,L_piby2_1 ; xmm2 rhead + vmulsd xmm3,xmm1,L_piby2_1tail ; xmm3 rtail + vsubsd xmm0,xmm2,xmm3 ; r_1 xmm0 + vsubsd xmm2,xmm2,xmm0 + vsubsd xmm1,xmm2,xmm3 + vmovq rax,xmm4 + jmp Lcosf_exit_s + +ALIGN 16 +Lcosf_reduce_precise: + + vmovq xmm0,r9 ; r9 <-- |x| + cmp r9,L_large_x_fma3 + jge Lcos_remainder_piby2 + + ; __remainder_piby2_fma3 and __remainder_piby2_fma3_bdl + ; have the following conventions: + ; on input + ; x is in xmm0 + ; on output + ; r is in xmm0 + ; rr is in xmm1 + ; region is in rax + ; The _bdl routine is guaranteed not to touch r10 + +Lcos_remainder_piby2_small: ;; unused label + ; Boldo-Daumas-Li reduction for reasonably small |x| + call __remainder_piby2_fma3_bdl + jmp Lcosf_exit_s + +ALIGN 16 +Lcos_remainder_piby2: + ; argument reduction for general x + call __remainder_piby2_fma3 +Lcosf_exit_s: + bt rax,0 + jnc Lcosf_piby4_compute + +;sinf_piby4_compute: +; vmovapd xmm1,__Lsinfarray+010h + vmovsd xmm1,__Lsinfarray+010h + vmulsd xmm3,xmm0,xmm0 + vfmadd231sd xmm1,xmm3,__Lsinfarray+018h + vfmadd213sd xmm1,xmm3,__Lsinfarray+008h + vfmadd213sd xmm1,xmm3,__Lsinfarray + vmulsd xmm3,xmm0,xmm3 ; xmm3 <-- x^3 + vfmadd231sd xmm0,xmm1,xmm3 + jmp Lcosf_fma3_adjust_sign + +ALIGN 16 +Lcosf_piby4_compute: + vmovapd xmm2,L_real_one + vmulsd xmm3,xmm0,xmm0 + vmulsd xmm1,xmm3,L_one_half ; xmm1 <-- r + vsubsd xmm2,xmm2,xmm1 + vmovsd xmm1,__Lcosfarray+018h + vfmadd231sd xmm1 ,xmm3,__Lcosfarray+020h + vfmadd213sd xmm1 ,xmm3,__Lcosfarray+010h + vfmadd213sd xmm1 ,xmm3,__Lcosfarray+008h + vmulsd xmm3,xmm3,xmm3 ; xmm3 <-- x^4 + vmovdqa xmm0, xmm2 + vfmadd231sd xmm0 ,xmm1,xmm3 + +Lcosf_fma3_adjust_sign: + ; assuming FMA3 ==> AVX ==> SSE4.1 +; vpcmpeqq xmm1,xmm4,XMMWORD PTR L_int_one +; vpcmpeqq xmm2,xmm4,XMMWORD PTR L_int_two +; vorpd xmm3,xmm2,xmm1 + +; vandpd xmm3,xmm3,L_signbit + + add rax,1 ; 1,2 --> 2,3 + shr rax,1 ; 2,3 --> 1 + shl rax,63 ; 1 --> sign bit + vmovq xmm3,rax + + vxorpd xmm0,xmm0,xmm3 + +Lcosf_fma3_return: + vcvtsd2ss xmm0,xmm0,xmm0 + StackDeallocate stack_size + ret + +Lcosf_fma3_naninf: + call fname_special + StackDeallocate stack_size + ret + +fname endp +END diff --git a/sdk/lib/crt/math/libm_sse2/cosh.c b/sdk/lib/crt/math/libm_sse2/cosh.c new file mode 100644 index 00000000000..9eb06d0c261 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/cosh.c @@ -0,0 +1,344 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_SPLITEXP +#define USE_SCALEDOUBLE_1 +#define USE_SCALEDOUBLE_2 +#define USE_INFINITY_WITH_FLAGS +#define USE_VAL_WITH_FLAGS +#define USE_HANDLE_ERROR +#include "libm_inlines.h" +#undef USE_SPLITEXP +#undef USE_SCALEDOUBLE_1 +#undef USE_SCALEDOUBLE_2 +#undef USE_INFINITY_WITH_FLAGS +#undef USE_VAL_WITH_FLAGS +#undef USE_HANDLE_ERROR + + +#pragma function(cosh) +double cosh(double x) +{ + /* + Derived from sinh subroutine + + After dealing with special cases the computation is split into + regions as follows: + + abs(x) >= max_cosh_arg: + cosh(x) = sign(x)*Inf + + abs(x) >= small_threshold: + cosh(x) = sign(x)*exp(abs(x))/2 computed using the + splitexp and scaleDouble functions as for exp_amd(). + + abs(x) < small_threshold: + compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) + cosh(x) is then sign(x)*z. */ + + static const double + max_cosh_arg = 7.10475860073943977113e+02, /* 0x408633ce8fb9f87e */ + thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */ + log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */ + log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */ +// small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889; + small_threshold = 20.0; + /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */ + + /* Lead and tail tabulated values of sinh(i) and cosh(i) + for i = 0,...,36. The lead part has 26 leading bits. */ + + static const double sinh_lead[ 37] = { + 0.00000000000000000000e+00, /* 0x0000000000000000 */ + 1.17520117759704589844e+00, /* 0x3ff2cd9fc0000000 */ + 3.62686038017272949219e+00, /* 0x400d03cf60000000 */ + 1.00178747177124023438e+01, /* 0x40240926e0000000 */ + 2.72899169921875000000e+01, /* 0x403b4a3800000000 */ + 7.42032089233398437500e+01, /* 0x40528d0160000000 */ + 2.01713153839111328125e+02, /* 0x406936d228000000 */ + 5.48316116333007812500e+02, /* 0x4081228768000000 */ + 1.49047882080078125000e+03, /* 0x409749ea50000000 */ + 4.05154187011718750000e+03, /* 0x40afa71570000000 */ + 1.10132326660156250000e+04, /* 0x40c5829dc8000000 */ + 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */ + 8.13773945312500000000e+04, /* 0x40f3de1650000000 */ + 2.21206695312500000000e+05, /* 0x410b00b590000000 */ + 6.01302140625000000000e+05, /* 0x412259ac48000000 */ + 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */ + 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */ + 1.20774762500000000000e+07, /* 0x4167093488000000 */ + 3.28299845000000000000e+07, /* 0x417f4f2208000000 */ + 8.92411500000000000000e+07, /* 0x419546d8f8000000 */ + 2.42582596000000000000e+08, /* 0x41aceb0888000000 */ + 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */ + 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */ + 4.87240166400000000000e+09, /* 0x41f226af30000000 */ + 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */ + 3.60024494080000000000e+10, /* 0x4220c3d390000000 */ + 9.78648043520000000000e+10, /* 0x4236c93268000000 */ + 2.66024116224000000000e+11, /* 0x424ef822f0000000 */ + 7.23128516608000000000e+11, /* 0x42650bba30000000 */ + 1.96566712320000000000e+12, /* 0x427c9aae40000000 */ + 5.34323724288000000000e+12, /* 0x4293704708000000 */ + 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */ + 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */ + 1.07321789251584000000e+14, /* 0x42d866f348000000 */ + 2.91730863685632000000e+14, /* 0x42f0953e28000000 */ + 7.93006722514944000000e+14, /* 0x430689e220000000 */ + 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */ + + static const double sinh_tail[ 37] = { + 0.00000000000000000000e+00, /* 0x0000000000000000 */ + 1.60467555584448807892e-08, /* 0x3e513ae6096a0092 */ + 2.76742892754807136947e-08, /* 0x3e5db70cfb79a640 */ + 2.09697499555224576530e-07, /* 0x3e8c2526b66dc067 */ + 2.04940252448908240062e-07, /* 0x3e8b81b18647f380 */ + 1.65444891522700935932e-06, /* 0x3ebbc1cdd1e1eb08 */ + 3.53116789999998198721e-06, /* 0x3ecd9f201534fb09 */ + 6.94023870987375490695e-06, /* 0x3edd1c064a4e9954 */ + 4.98876893611587449271e-06, /* 0x3ed4eca65d06ea74 */ + 3.19656024605152215752e-05, /* 0x3f00c259bcc0ecc5 */ + 2.08687768377236501204e-04, /* 0x3f2b5a6647cf9016 */ + 4.84668088325403796299e-05, /* 0x3f09691adefb0870 */ + 1.17517985422733832468e-03, /* 0x3f53410fc29cde38 */ + 6.90830086959560562415e-04, /* 0x3f46a31a50b6fb3c */ + 1.45697262451506548420e-03, /* 0x3f57defc71805c40 */ + 2.99859023684906737806e-02, /* 0x3f9eb49fd80e0bab */ + 1.02538800507941396667e-02, /* 0x3f84fffc7bcd5920 */ + 1.26787628407699110022e-01, /* 0x3fc03a93b6c63435 */ + 6.86652479544033744752e-02, /* 0x3fb1940bb255fd1c */ + 4.81593627621056619148e-01, /* 0x3fded26e14260b50 */ + 1.70489513795397629181e+00, /* 0x3ffb47401fc9f2a2 */ + 1.12416073482258713767e+01, /* 0x40267bb3f55634f1 */ + 7.06579578070110514432e+00, /* 0x401c435ff8194ddc */ + 5.91244512999659974639e+01, /* 0x404d8fee052ba63a */ + 1.68921736147050694399e+02, /* 0x40651d7edccde3f6 */ + 2.60692936262073658327e+02, /* 0x40704b1644557d1a */ + 3.62419382134885609048e+02, /* 0x4076a6b5ca0a9dc4 */ + 4.07689930834187271103e+03, /* 0x40afd9cc72249aba */ + 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */ + 2.53720210371943067003e+04, /* 0x40d8c70158ac6363 */ + 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */ + 1.81871712615542812273e+05, /* 0x4106337db36fc718 */ + 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */ + 6.41374032312148716301e+05, /* 0x412392bc108b37cc */ + 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */ + 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */ + 7.63580561355670914054e+06}; /* 0x415d20d76744835c */ + + static const double cosh_lead[ 37] = { + 1.00000000000000000000e+00, /* 0x3ff0000000000000 */ + 1.54308062791824340820e+00, /* 0x3ff8b07550000000 */ + 3.76219564676284790039e+00, /* 0x400e18fa08000000 */ + 1.00676617622375488281e+01, /* 0x402422a490000000 */ + 2.73082327842712402344e+01, /* 0x403b4ee858000000 */ + 7.42099475860595703125e+01, /* 0x40528d6fc8000000 */ + 2.01715633392333984375e+02, /* 0x406936e678000000 */ + 5.48317031860351562500e+02, /* 0x4081228948000000 */ + 1.49047915649414062500e+03, /* 0x409749eaa8000000 */ + 4.05154199218750000000e+03, /* 0x40afa71580000000 */ + 1.10132329101562500000e+04, /* 0x40c5829dd0000000 */ + 2.99370708007812500000e+04, /* 0x40dd3c4488000000 */ + 8.13773945312500000000e+04, /* 0x40f3de1650000000 */ + 2.21206695312500000000e+05, /* 0x410b00b590000000 */ + 6.01302140625000000000e+05, /* 0x412259ac48000000 */ + 1.63450865625000000000e+06, /* 0x4138f0cca8000000 */ + 4.44305525000000000000e+06, /* 0x4150f2ebd0000000 */ + 1.20774762500000000000e+07, /* 0x4167093488000000 */ + 3.28299845000000000000e+07, /* 0x417f4f2208000000 */ + 8.92411500000000000000e+07, /* 0x419546d8f8000000 */ + 2.42582596000000000000e+08, /* 0x41aceb0888000000 */ + 6.59407856000000000000e+08, /* 0x41c3a6e1f8000000 */ + 1.79245641600000000000e+09, /* 0x41dab5adb8000000 */ + 4.87240166400000000000e+09, /* 0x41f226af30000000 */ + 1.32445608960000000000e+10, /* 0x4208ab7fb0000000 */ + 3.60024494080000000000e+10, /* 0x4220c3d390000000 */ + 9.78648043520000000000e+10, /* 0x4236c93268000000 */ + 2.66024116224000000000e+11, /* 0x424ef822f0000000 */ + 7.23128516608000000000e+11, /* 0x42650bba30000000 */ + 1.96566712320000000000e+12, /* 0x427c9aae40000000 */ + 5.34323724288000000000e+12, /* 0x4293704708000000 */ + 1.45244246507520000000e+13, /* 0x42aa6b7658000000 */ + 3.94814795284480000000e+13, /* 0x42c1f43fc8000000 */ + 1.07321789251584000000e+14, /* 0x42d866f348000000 */ + 2.91730863685632000000e+14, /* 0x42f0953e28000000 */ + 7.93006722514944000000e+14, /* 0x430689e220000000 */ + 2.15561576592179200000e+15}; /* 0x431ea215a0000000 */ + + static const double cosh_tail[ 37] = { + 0.00000000000000000000e+00, /* 0x0000000000000000 */ + 6.89700037027478056904e-09, /* 0x3e3d9f5504c2bd28 */ + 4.43207835591715833630e-08, /* 0x3e67cb66f0a4c9fd */ + 2.33540217013828929694e-07, /* 0x3e8f58617928e588 */ + 5.17452463948269748331e-08, /* 0x3e6bc7d000c38d48 */ + 9.38728274131605919153e-07, /* 0x3eaf7f9d4e329998 */ + 2.73012191010840495544e-06, /* 0x3ec6e6e464885269 */ + 3.29486051438996307950e-06, /* 0x3ecba3a8b946c154 */ + 4.75803746362771416375e-06, /* 0x3ed3f4e76110d5a4 */ + 3.33050940471947692369e-05, /* 0x3f017622515a3e2b */ + 9.94707313972136215365e-06, /* 0x3ee4dc4b528af3d0 */ + 6.51685096227860253398e-05, /* 0x3f11156278615e10 */ + 1.18132406658066663359e-03, /* 0x3f535ad50ed821f5 */ + 6.93090416366541877541e-04, /* 0x3f46b61055f2935c */ + 1.45780415323416845386e-03, /* 0x3f57e2794a601240 */ + 2.99862082708111758744e-02, /* 0x3f9eb4b45f6aadd3 */ + 1.02539925859688602072e-02, /* 0x3f85000b967b3698 */ + 1.26787669807076286421e-01, /* 0x3fc03a940fadc092 */ + 6.86652631843830962843e-02, /* 0x3fb1940bf3bf874c */ + 4.81593633223853068159e-01, /* 0x3fded26e1a2a2110 */ + 1.70489514001513020602e+00, /* 0x3ffb4740205796d6 */ + 1.12416073489841270572e+01, /* 0x40267bb3f55cb85d */ + 7.06579578098005001152e+00, /* 0x401c435ff81e18ac */ + 5.91244513000686140458e+01, /* 0x404d8fee052bdea4 */ + 1.68921736147088438429e+02, /* 0x40651d7edccde926 */ + 2.60692936262087528121e+02, /* 0x40704b1644557e0e */ + 3.62419382134890611269e+02, /* 0x4076a6b5ca0a9e1c */ + 4.07689930834187453002e+03, /* 0x40afd9cc72249abe */ + 1.55377375868385224749e+04, /* 0x40ce58de693edab5 */ + 2.53720210371943103382e+04, /* 0x40d8c70158ac6364 */ + 4.78822310734952334315e+04, /* 0x40e7614764f43e20 */ + 1.81871712615542812273e+05, /* 0x4106337db36fc718 */ + 5.62892347580489004031e+05, /* 0x41212d98b1f611e2 */ + 6.41374032312148716301e+05, /* 0x412392bc108b37cc */ + 7.57809544070145115256e+06, /* 0x415ce87bdc3473dc */ + 3.64177136406482197344e+06, /* 0x414bc8d5ae99ad14 */ + 7.63580561355670914054e+06}; /* 0x415d20d76744835c */ + + unsigned long ux, aux, xneg; + double y, z, z1, z2; + int m; + + /* Special cases */ + + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + if (aux < 0x3e30000000000000) /* |x| small enough that cosh(x) = 1 */ + { + if (aux == 0) + /* with no inexact */ + return 1.0; + else + return val_with_flags(1.0, AMD_F_INEXACT); + } + else if (aux >= PINFBITPATT_DP64) /* |x| is NaN or Inf */ + { + if (aux > PINFBITPATT_DP64) /* x is NaN */ + return _handle_error("cosh", OP_COSH, ux|0x0008000000000000,_DOMAIN, + 0,EDOM, x, 0.0, 1); + else /* x is infinity */ + return infinity_with_flags(0); + } + + xneg = (aux != ux); + + y = x; + if (xneg) y = -x; + + if (y >= max_cosh_arg) + { + return _handle_error("cosh", OP_COSH, PINFBITPATT_DP64,_OVERFLOW, + AMD_F_INEXACT|AMD_F_OVERFLOW,ERANGE, x, 0.0, 1); + +// z = infinity_with_flags(AMD_F_OVERFLOW); + } + else if (y >= small_threshold) + { + /* In this range y is large enough so that + the negative exponential is negligible, + so cosh(y) is approximated by sign(x)*exp(y)/2. The + code below is an inlined version of that from + exp() with two changes (it operates on + y instead of x, and the division by 2 is + done by reducing m by 1). */ + + splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead, + log2_by_32_tail, &m, &z1, &z2); + m -= 1; + + if (m >= EMIN_DP64 && m <= EMAX_DP64) + z = scaleDouble_1((z1+z2),m); + else + z = scaleDouble_2((z1+z2),m); + } + else + { + /* In this range we find the integer part y0 of y + and the increment dy = y - y0. We then compute + + z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) + z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) + + where sinh(y0) and cosh(y0) are tabulated above. */ + + int ind; + double dy, dy2, sdy, cdy; + + ind = (int)y; + dy = y - ind; + + dy2 = dy*dy; + sdy = dy*dy2*(0.166666666666666667013899e0 + + (0.833333333333329931873097e-2 + + (0.198412698413242405162014e-3 + + (0.275573191913636406057211e-5 + + (0.250521176994133472333666e-7 + + (0.160576793121939886190847e-9 + + 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); + + cdy = dy2*(0.500000000000000005911074e0 + + (0.416666666666660876512776e-1 + + (0.138888888889814854814536e-2 + + (0.248015872460622433115785e-4 + + (0.275573350756016588011357e-6 + + (0.208744349831471353536305e-8 + + 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); + + /* At this point sinh(dy) is approximated by dy + sdy, and cosh(dy) is approximated by 1 + cdy. + Shift some significant bits from dy to cdy. */ +#if 0 + double sdy1,sdy2; + GET_BITS_DP64(dy, ux); + ux &= 0xfffffffff8000000; + PUT_BITS_DP64(ux, sdy1); // sdy1 is upper 53-27=26 significant bits of dy. + sdy2 = sdy + (dy - sdy1); // sdy2 is sdy + lower bits of dy + + z = ((((((cosh_tail[ind]*cdy + sinh_tail[ind]*sdy2) + + sinh_tail[ind]*sdy1) + cosh_tail[ind]) + + cosh_lead[ind]*cdy) + sinh_lead[ind]*sdy2) + + sinh_lead[ind]*sdy1) + cosh_lead[ind]; +#else + z = ((((((cosh_tail[ind]*cdy + sinh_tail[ind]*sdy) + + sinh_tail[ind]*dy) + cosh_tail[ind]) + + cosh_lead[ind]*cdy) + sinh_lead[ind]*sdy) + + sinh_lead[ind]*dy) + cosh_lead[ind]; +#endif + } + + return z; +} diff --git a/sdk/lib/crt/math/libm_sse2/coshf.c b/sdk/lib/crt/math/libm_sse2/coshf.c new file mode 100644 index 00000000000..6e7ad089c37 --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/coshf.c @@ -0,0 +1,247 @@ + +/******************************************************************************* +MIT License +----------- + +Copyright (c) 2002-2019 Advanced Micro Devices, Inc. + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this Software and associated documentaon files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in +all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +THE SOFTWARE. +*******************************************************************************/ + +#include "libm.h" +#include "libm_util.h" + +#define USE_SPLITEXP +#define USE_SCALEDOUBLE_1 +#define USE_SCALEDOUBLE_2 +#define USE_INFINITYF_WITH_FLAGS +#define USE_VALF_WITH_FLAGS +#define USE_HANDLE_ERRORF +#include "libm_inlines.h" +#undef USE_SPLITEXP +#undef USE_SCALEDOUBLE_1 +#undef USE_SCALEDOUBLE_2 +#undef USE_INFINITYF_WITH_FLAGS +#undef USE_VALF_WITH_FLAGS +#undef USE_HANDLE_ERRORF + +// Disable "C4163: not available as intrinsic function" warning that older +// compilers may issue here. +#pragma warning(disable:4163) +#pragma function(coshf) + +float coshf(float fx) +{ + /* + After dealing with special cases the computation is split into + regions as follows: + + abs(x) >= max_cosh_arg: + cosh(x) = sign(x)*Inf + + abs(x) >= small_threshold: + cosh(x) = sign(x)*exp(abs(x))/2 computed using the + splitexp and scaleDouble functions as for exp_amd(). + + abs(x) < small_threshold: + compute p = exp(y) - 1 and then z = 0.5*(p+(p/(p+1.0))) + cosh(x) is then sign(x)*z. */ + + static const double + /* The max argument of coshf, but stored as a double */ + max_cosh_arg = 8.94159862922329438106e+01, /* 0x40565a9f84f82e63 */ + thirtytwo_by_log2 = 4.61662413084468283841e+01, /* 0x40471547652b82fe */ + log2_by_32_lead = 2.16608493356034159660e-02, /* 0x3f962e42fe000000 */ + log2_by_32_tail = 5.68948749532545630390e-11, /* 0x3dcf473de6af278e */ + + small_threshold = 8*BASEDIGITS_DP64*0.30102999566398119521373889; +// small_threshold = 20.0; + /* (8*BASEDIGITS_DP64*log10of2) ' exp(-x) insignificant c.f. exp(x) */ + + /* Tabulated values of sinh(i) and cosh(i) for i = 0,...,36. */ + + static const double sinh_lead[ 37] = { + 0.00000000000000000000e+00, /* 0x0000000000000000 */ + 1.17520119364380137839e+00, /* 0x3ff2cd9fc44eb982 */ + 3.62686040784701857476e+00, /* 0x400d03cf63b6e19f */ + 1.00178749274099008204e+01, /* 0x40240926e70949ad */ + 2.72899171971277496596e+01, /* 0x403b4a3803703630 */ + 7.42032105777887522891e+01, /* 0x40528d0166f07374 */ + 2.01713157370279219549e+02, /* 0x406936d22f67c805 */ + 5.48316123273246489589e+02, /* 0x408122876ba380c9 */ + 1.49047882578955000099e+03, /* 0x409749ea514eca65 */ + 4.05154190208278987484e+03, /* 0x40afa7157430966f */ + 1.10132328747033916443e+04, /* 0x40c5829dced69991 */ + 2.99370708492480553105e+04, /* 0x40dd3c4488cb48d6 */ + 8.13773957064298447222e+04, /* 0x40f3de1654d043f0 */ + 2.21206696003330085659e+05, /* 0x410b00b5916a31a5 */ + 6.01302142081972560845e+05, /* 0x412259ac48bef7e3 */ + 1.63450868623590236530e+06, /* 0x4138f0ccafad27f6 */ + 4.44305526025387924165e+06, /* 0x4150f2ebd0a7ffe3 */ + 1.20774763767876271158e+07, /* 0x416709348c0ea4ed */ + 3.28299845686652474105e+07, /* 0x417f4f22091940bb */ + 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */ + 2.42582597704895108938e+08, /* 0x41aceb088b68e803 */ + 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */ + 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */ + 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */ + 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */ + 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */ + 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */ + 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */ + 7.23128532145737548828e+11, /* 0x42650bba3796379a */ + 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */ + 5.34323729076223046875e+12, /* 0x429370470aec28ec */ + 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */ + 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */ + 1.07321789892958031250e+14, /* 0x42d866f34a725782 */ + 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */ + 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */ + 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */ + + static const double cosh_lead[ 37] = { + 1.00000000000000000000e+00, /* 0x3ff0000000000000 */ + 1.54308063481524371241e+00, /* 0x3ff8b07551d9f550 */ + 3.76219569108363138810e+00, /* 0x400e18fa0df2d9bc */ + 1.00676619957777653269e+01, /* 0x402422a497d6185e */ + 2.73082328360164865444e+01, /* 0x403b4ee858de3e80 */ + 7.42099485247878334349e+01, /* 0x40528d6fcbeff3a9 */ + 2.01715636122455890700e+02, /* 0x406936e67db9b919 */ + 5.48317035155212010977e+02, /* 0x4081228949ba3a8b */ + 1.49047916125217807348e+03, /* 0x409749eaa93f4e76 */ + 4.05154202549259389343e+03, /* 0x40afa715845d8894 */ + 1.10132329201033226127e+04, /* 0x40c5829dd053712d */ + 2.99370708659497577173e+04, /* 0x40dd3c4489115627 */ + 8.13773957125740562333e+04, /* 0x40f3de1654d6b543 */ + 2.21206696005590405548e+05, /* 0x410b00b5916b6105 */ + 6.01302142082804115489e+05, /* 0x412259ac48bf13ca */ + 1.63450868623620807193e+06, /* 0x4138f0ccafad2d17 */ + 4.44305526025399193168e+06, /* 0x4150f2ebd0a8005c */ + 1.20774763767876680940e+07, /* 0x416709348c0ea503 */ + 3.28299845686652623117e+07, /* 0x417f4f22091940bf */ + 8.92411504815936237574e+07, /* 0x419546d8f9ed26e1 */ + 2.42582597704895138741e+08, /* 0x41aceb088b68e804 */ + 6.59407867241607308388e+08, /* 0x41c3a6e1fd9eecfd */ + 1.79245642306579566002e+09, /* 0x41dab5adb9c435ff */ + 4.87240172312445068359e+09, /* 0x41f226af33b1fdc0 */ + 1.32445610649217357635e+10, /* 0x4208ab7fb5475fb7 */ + 3.60024496686929321289e+10, /* 0x4220c3d3920962c8 */ + 9.78648047144193725586e+10, /* 0x4236c932696a6b5c */ + 2.66024120300899291992e+11, /* 0x424ef822f7f6731c */ + 7.23128532145737548828e+11, /* 0x42650bba3796379a */ + 1.96566714857202099609e+12, /* 0x427c9aae4631c056 */ + 5.34323729076223046875e+12, /* 0x429370470aec28ec */ + 1.45244248326237109375e+13, /* 0x42aa6b765d8cdf6c */ + 3.94814800913403437500e+13, /* 0x42c1f43fcc4b662c */ + 1.07321789892958031250e+14, /* 0x42d866f34a725782 */ + 2.91730871263727437500e+14, /* 0x42f0953e2f3a1ef7 */ + 7.93006726156715250000e+14, /* 0x430689e221bc8d5a */ + 2.15561577355759750000e+15}; /* 0x431ea215a1d20d76 */ + + unsigned long ux, aux, xneg; + unsigned int uhx; + double x = fx, y, z, z1, z2; + int m; + + /* Special cases */ + + GET_BITS_DP64(x, ux); + aux = ux & ~SIGNBIT_DP64; + if (aux < 0x3f10000000000000) /* |x| small enough that cosh(x) = 1 */ + { + if (aux == 0) return (float)1.0; /* with no inexact */ + if (LAMBDA_DP64 + x > 1.0) return valf_with_flags((float)1.0, AMD_F_INEXACT); /* with inexact */ + } + else if (aux >= PINFBITPATT_DP64) /* |x| is NaN or Inf */ + if (aux > PINFBITPATT_DP64) /* x is NaN */ + { + GET_BITS_SP32(fx, uhx); + return _handle_errorf("coshf",OP_COSH,uhx|0x00400000,_DOMAIN, 0, + EDOM, fx, 0.0, 1); + } + else /* x is infinity */ + return infinityf_with_flags(0); + xneg = (aux != ux); + + y = x; + if (xneg) y = -x; + + if (y >= max_cosh_arg) + /* Return +infinity with overflow flag. */ + return _handle_errorf("coshf",OP_COSH,PINFBITPATT_SP32,_OVERFLOW, + AMD_F_INEXACT|AMD_F_OVERFLOW,ERANGE, fx, 0.0, 1); +// z = infinity_with_flags(AMD_F_OVERFLOW); + else if (y >= small_threshold) + { + /* In this range y is large enough so that + the negative exponential is negligible, + so cosh(y) is approximated by sign(x)*exp(y)/2. The + code below is an inlined version of that from + exp() with two changes (it operates on + y instead of x, and the division by 2 is + done by reducing m by 1). */ + + splitexp(y, 1.0, thirtytwo_by_log2, log2_by_32_lead, + log2_by_32_tail, &m, &z1, &z2); + m -= 1; + + /* scaleDouble_1 is always safe because the argument x was + float, rather than double */ + z = scaleDouble_1((z1+z2),m); + } + else + { + /* In this range we find the integer part y0 of y + and the increment dy = y - y0. We then compute + + z = sinh(y) = sinh(y0)cosh(dy) + cosh(y0)sinh(dy) + z = cosh(y) = cosh(y0)cosh(dy) + sinh(y0)sinh(dy) + + where sinh(y0) and cosh(y0) are tabulated above. */ + + int ind; + double dy, dy2, sdy, cdy; + + ind = (int)y; + dy = y - ind; + + dy2 = dy*dy; + + sdy = dy + dy*dy2*(0.166666666666666667013899e0 + + (0.833333333333329931873097e-2 + + (0.198412698413242405162014e-3 + + (0.275573191913636406057211e-5 + + (0.250521176994133472333666e-7 + + (0.160576793121939886190847e-9 + + 0.7746188980094184251527126e-12*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); + + cdy = 1 + dy2*(0.500000000000000005911074e0 + + (0.416666666666660876512776e-1 + + (0.138888888889814854814536e-2 + + (0.248015872460622433115785e-4 + + (0.275573350756016588011357e-6 + + (0.208744349831471353536305e-8 + + 0.1163921388172173692062032e-10*dy2)*dy2)*dy2)*dy2)*dy2)*dy2); + + z = cosh_lead[ind]*cdy + sinh_lead[ind]*sdy; + } + +// if (xneg) z = - z; + return (float)z; +} diff --git a/sdk/lib/crt/math/libm_sse2/exp.asm b/sdk/lib/crt/math/libm_sse2/exp.asm new file mode 100644 index 00000000000..10fb7f48c6a --- /dev/null +++ b/sdk/lib/crt/math/libm_sse2/exp.asm @@ -0,0 +1,439 @@ +; +; MIT License +; ----------- +; +; Copyright (c) 2002-2019 Advanced Micro Devices, Inc. +; +; Permission is hereby granted, free of charge, to any person obtaining a copy +; of this Software and associated documentaon files (the "Software"), to deal +; in the Software without restriction, including without limitation the rights +; to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +; copies of the Software, and to permit persons to whom the Software is +; furnished to do so, subject to the following conditions: +; +; The above copyright notice and this permission notice shall be included in +; all copies or substantial portions of the Software. +; +; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +; OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN +; THE SOFTWARE. +; +; exp.asm +; +; An implementation of the exp libm function. +; +; Prototype: +; +; double exp(double x); +; + +; +; Algorithm: +; +; e^x = 2^(x/ln(2)) = 2^(x*(64/ln(2))/64) +; +; x*(64/ln(2)) = n + f, |f| <= 0.5, n is integer +; n = 64*m + j, 0 <= j < 64 +; +; e^x = 2^((64*m + j + f)/64) +; = (2^m) * (2^(j/64)) * 2^(f/64) +; = (2^m) * (2^(j/64)) * e^(f*(ln(2)/64)) +; +; f = x*(64/ln(2)) - n +; r = f*(ln(2)/64) = x - n*(ln(2)/64) +; +; e^x = (2^m) * (2^(j/64)) * e^r +; +; (2^(j/64)) is precomputed +; +; e^r = 1 + r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5! + (r^5)/5! +; e^r = 1 + q +; +; q = r + (r^2)/2! + (r^3)/3! + (r^4)/4! + (r^5)/5! + (r^5)/5! +; + +.const +ALIGN 16 +; these codes and the ones in the corresponding .c file have to match +__flag_x_nan DD 00000001 +__flag_y_zero DD 00000002 +__flag_y_inf DD 00000003 + +ALIGN 16 + +L__real_1_by_720 DQ 03f56c16c16c16c17h + DQ 03f56c16c16c16c17h ; 1/720 +L__real_1_by_120 DQ 03f81111111111111h + DQ 03f81111111111111h ; 1/120 +L__real_1_by_6 DQ 03fc5555555555555h + DQ 03fc5555555555555h ; 1/6 +L__real_1_by_2 DQ 03fe0000000000000h + DQ 03fe0000000000000h ; 1/2 +L__real_1_by_24 DQ 03fa5555555555555h + DQ 03fa5555555555555h ; 1/24 + +ALIGN 16 +L__log2_by_64_mtail_mhead DQ 0bf862e42fefa0000h, 0bd1cf79abc9e3b39h +L__ln_of_smallest_normal DQ 0C086232BDD7ABCD2h +L__zero DQ 00000000000000000h +L__max_exp_arg DQ 040862e42fefa39efh ; 709.78271289338397 +L__denormal_tiny_threshold DQ 0c0874046dfefd9d0h ; -744.03460681327306 +L__min_exp_arg DQ 0c0874910d52d3051h ; -745.13321910194111 +L__real_64_by_log2 DQ 040571547652b82feh ; 64/ln(2) +L__positive_infinity DQ 07ff0000000000000h +L__negative_infinity DQ 0fff0000000000000h +L__real_qnanbit DQ 0008000000000000h ; qnan set bit +L__real_x_near0_threshold DQ 3c00000000000000h +L__log2_by_64_mhead DQ 0bf862e42fefa0000h +L__log2_by_64_mtail DQ 0bd1cf79abc9e3b39h +L__real_smallest_denormal DQ 00000000000000001h +L__real_one DQ 03ff0000000000000h +L__2_to_neg_26 DQ 03E50000000000000h ; 2^-26 +L__min_normal DQ 00010000000000000h ; smallest normal + + +EXTRN __two_to_jby64_table:QWORD +EXTRN __two_to_jby64_head_table:QWORD +EXTRN __two_to_jby64_tail_table:QWORD +EXTRN __use_fma3_lib:DWORD + +; make room for fname_special to save things +dummy_space EQU 020h +stack_size EQU 038h + +include fm.inc + +fname TEXTEQU <exp> +fname_special TEXTEQU <_exp_special> + +;Define name and any external functions being called +EXTERN fname_special : PROC + +.code +PUBLIC fname +fname PROC FRAME + StackAllocate stack_size + .ENDPROLOG + + ; We need to avoid unwanted exceptions from a NaN argument. + ; It could be argued that a signaling NaN should raise an exception, + ; but the existing library doesn't. At any rate, the comparison operations + ; don't seem to like quiet NaN either, so... + movd rdx, xmm0 + btr rdx, 63 + cmp rdx, L__positive_infinity + jge Lexp_x_is_nan_or_inf + + cmp DWORD PTR __use_fma3_lib, 0 + jne Lexp_fma3 + + movapd xmm2, xmm0 + movapd xmm3, xmm0 + + ; Some hardware has problems with too many branches in a single + ; 16- or 32-byte window, so let's peel off the common case into + ; a single branch. + cmplesd xmm2, L__max_exp_arg ; xmm2 <-- 0xFFFFFFFF is x is not too big positive + cmpnltsd xmm3, L__denormal_tiny_threshold ; xmm3 <-- 0xFFFFFFFF if x is not too big negative + andps xmm2, xmm3 ; xmm2 <-- 0xFFFFFFFF if x is in range, 0 otherwise + ucomisd xmm2, xmm2 ; note that FFF... is NaN, so this comparison should set PF for in-range x + jp Lexp_y_is_finite + + ucomisd xmm0, L__max_exp_arg + ja Lexp_y_is_inf + ; Since we peeled off the cases with normal result, + ; there is only one possibility remaining: + jmp Lexp_y_is_denormal_or_zero + +ALIGN 16 +Lexp_y_is_finite: + ; x * (64/ln(2)) + movapd xmm1, xmm0 + btr rdx, 63 ; rdx <-- |x| + cmp rdx, L__2_to_neg_26 + jbe Lexp_return_1_plus_x + mulsd xmm1, L__real_64_by_log2 + + ; n = int( x * (64/ln(2)) ) + cvttpd2dq xmm2, xmm1 ; xmm2 = (int)n + cvtdq2pd xmm1, xmm2 ; xmm1 = (double)n + movd ecx, xmm2 + movapd xmm2, xmm1 + + ; r1 = x - n * ln(2)/64 head + mulsd xmm1, L__log2_by_64_mhead + + ; j = n & 0x3f + mov rax, 03fh + and eax, ecx ; eax = j + ; m = (n - j) / 64 + sar ecx, 6 ; ecx = m + + + ; r2 = - n * ln(2)/64 tail + mulsd xmm2, L__log2_by_64_mtail + addsd xmm0, xmm1 ; xmm0 = r1 + + ; r1+r2 + addsd xmm2, xmm0 ; xmm2 = r + + ; q = r + r^2*1/2 + r^3*1/6 + r^4 *1/24 + r^5*1/120 + r^6*1/720 + ; q = r + r*r*(1/2 + r*(1/6+ r*(1/24 + r*(1/120 + r*(1/720))))) + movapd xmm3, L__real_1_by_720 ; xmm3 = 1/720 + mulsd xmm3, xmm2 ; xmm3 = r*1/720 + movapd xmm0, L__real_1_by_6 ; xmm0 = 1/6 + movapd xmm1, xmm2 ; xmm1 = r + mulsd xmm0, xmm2 ; xmm0 = r*1/6 + addsd xmm3, L__real_1_by_120 ; xmm3 = 1/120 + (r*1/720) + mulsd xmm1, xmm2 ; xmm1 = r*r + addsd xmm0, L__real_1_by_2 ; xmm0 = 1/2 + (r*1/6) + movapd xmm4, xmm1 ; xmm4 = r*r + mulsd xmm4, xmm1 ; xmm4 = (r*r) * (r*r) + mulsd xmm3, xmm2 ; xmm3 = r * (1/120 + (r*1/720)) + mulsd xmm0, xmm1 ; xmm0 = (r*r)*(1/2 + (r*1/6)) + addsd xmm3, L__real_1_by_24 ; xmm3 = 1/24 + (r * (1/120 + (r*1/720))) + addsd xmm0, xmm2 ; xmm0 = r + ((r*r)*(1/2 + (r*1/6))) + mulsd xmm3, xmm4 ; xmm3 = ((r*r) * (r*r)) * (1/24 + (r * (1/120 + (r*1/720)))) + addsd xmm0, xmm3 ; xmm0 = r + ((r*r)*(1/2 + (r*1/6))) + ((r*r) * (r*r)) * (1/24 + (r * (1/120 + (r*1/720)))) + + ;(f)*(q) + f2 + f1 + cmp ecx, 0fffffc02h ; -1022 + lea rdx, __two_to_jby64_table + lea r11, __two_to_jby64_tail_table + lea r10, __two_to_jby64_head_table + mulsd xmm0, QWORD PTR [rdx+rax * 8 ] + addsd xmm0, QWORD PTR [r11+rax * 8 ] + addsd xmm0, QWORD PTR [r10+rax * 8 ] + + jle Lexp_process_denormal +Lexp_process_normal: + shl rcx, 52 + movd xmm2, rcx + paddq xmm0, xmm2 + StackDeallocate stack_size + ret + +ALIGN 16 +Lexp_process_denormal: + jl Lexp_process_true_denormal + ucomisd xmm0, L__real_one + jae Lexp_process_normal +Lexp_process_true_denormal: + ; here ( e^r < 1 and m = -1022 ) or m <= -1023 + add ecx, 1074 + mov rax, 1 + shl rax, cl + movd xmm2, rax + mulsd xmm0, xmm2 + jmp Lexp_finish + +Lexp_y_is_one: + movsd xmm0, L__real_one + jmp Lexp_finish + +ALIGN 16 +Lexp_x_is_nan_or_inf: + movd rax, xmm0 + cmp rax, L__positive_infinity + je Lexp_finish + cmp rax, L__negative_infinity + je Lexp_return_zero_without_exception + or rax, L__real_qnanbit + movd xmm1, rax + mov r8d, __flag_x_nan + call fname_special + jmp Lexp_finish + +ALIGN 16 +Lexp_y_is_inf: + mov rax, 07ff0000000000000h + movd xmm1, rax + mov r8d, __flag_y_inf + call fname_special + jmp Lexp_finish + +ALIGN 16 +Lexp_y_is_denormal_or_zero: + ucomisd xmm0, L__min_exp_arg + jbe Lexp_y_is_zero + movapd xmm0, L__real_smallest_denormal + jmp Lexp_finish + +ALIGN 16 +Lexp_y_is_zero: + pxor xmm1, xmm1 + mov r8d, __flag_y_zero + call fname_special + jmp Lexp_finish + +ALIGN 16 +Lexp_return_1_plus_x: + cmp rdx, L__min_normal + jbe Lexp_return_1_plus_eps + addsd xmm0, L__real_one + StackDeallocate stack_size + ret 0 + +; Some hardware really does not like subnormals. Try to avoid them. +ALIGN 16 +Lexp_return_1_plus_eps: + movsd xmm0, L__real_one + addsd xmm0, L__min_normal ; make sure inexact is set + StackDeallocate stack_size + ret 0 + +ALIGN 16 +Lexp_return_zero_without_exception: + pxor xmm0,xmm0 + StackDeallocate stack_size + ret 0 + + +ALIGN 16 +Lexp_finish: + StackDeallocate stack_size + ret 0 + +ALIGN 16 +Lexp_fma3: + ; Some hardware has problems with too many branches in a single + ; 16- or 32-byte window, so let's peel off the common case into + ; a single branch. + vcmplesd xmm2, xmm0, L__max_exp_arg ; xmm2 <-- 0xFFFFFFFF is x is not too big positive + vcmpnltsd xmm3, xmm0, L__denormal_tiny_threshold ; xmm3 <-- 0xFFFFFFFF if x is not too big negative + vandps xmm2, xmm3, xmm2 ; xmm2 <-- 0xFFFFFFFF if x is in range, 0 otherwise + vucomisd xmm2, xmm2 ; note that FFF... is NaN, so this comparison should set PF for in-range x + jp Lexp_fma3_y_is_finite + + vucomisd xmm0,L__max_exp_arg + ja Lexp_fma3_y_is_inf + ; Since we peeled off the cases with normal result, + ; there is only one possibility remaining: + jmp Lexp_fma3_y_is_zero + +; vpsllq xmm1, xmm0, 1 +; vpsrlq xmm1, xmm1, 1 +; vucomisd xmm1, L__real_x_near0_threshold ; 2^-63 +; jb Lexp_fma3_y_is_one + +ALIGN 16 +Lexp_fma3_y_is_finite: + vmovq rdx, xmm0 + btr rdx, 63 ; rdx <-- |x| + cmp rdx, L__2_to_neg_26 + jbe Lexp_fma3_return_1_plus_x + + ; x * (64/ln(2)) + vmulsd xmm1,xmm0,L__real_64_by_log2 + + ; n = int( x * (64/ln(2)) ) + vcvttpd2dq xmm2,xmm1 ;xmm2 = (int)n + vcvtdq2pd xmm1,xmm2 ;xmm1 = (double)n ;can use round + vmovd ecx,xmm2 + + ; r1 = x - n * ln(2)/64 head + ; r2 = - n * ln(2)/64 tail + ; r = r1+r2 + vmovlhps xmm1,xmm1,xmm1 ;xmm1 = (double (double)n,)n + vmovq xmm0,xmm0 ;xmm0 = 0,x ;zero out the upper part + vfmadd132pd xmm1,xmm0,L__log2_by_64_mtail_mhead + vhaddpd xmm2,xmm1,xmm1 ;xmm2 = r,r + + ;j = n & 03fh + mov rax,03fh + and eax,ecx ;eax = j + ; m = (n - j) / 64 + sar ecx,6 ;ecx = m + + ; q = r + r^2*1/2 + r^3*1/6 + r^4 *1/24 + r^5*1/120 + r^6*1/720 + ; q = r + r*r*(1/2 + r*(1/6+ r*(1/24 + r*(1/120 + r*(1/720))))) + vmovapd xmm3,L__real_1_by_720 + vfmadd213sd xmm3,xmm2,L__real_1_by_120 + vfmadd213sd xmm3,xmm2,L__real_1_by_24 + vfmadd213sd xmm3,xmm2,L__real_1_by_6 + vfmadd213sd xmm3,xmm2,L__real_1_by_2 + vmulsd xmm0,xmm2,xmm2 + vfmadd213sd xmm0,xmm3,xmm2 + + ; (f)*(q) + f2 + f1 + cmp ecx,0fffffc02h ; -1022 + lea rdx,__two_to_jby64_table + lea r11,__two_to_jby64_tail_table + lea r10,__two_to_jby64_head_table + vmulsd xmm2,xmm0,QWORD PTR[rdx + rax * 8] ... 17978 lines suppressed ...
-
Timo Kreuzer