| |
| /* |
| * Copyright (C) 2008-2009 Advanced Micro Devices, Inc. All Rights Reserved. |
| * |
| * This file is part of libacml_mv. |
| * |
| * libacml_mv is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * libacml_mv is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| * Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public |
| * License along with libacml_mv. If not, see |
| * <http://www.gnu.org/licenses/>. |
| * |
| */ |
| |
| |
| #include "../inc/libm_amd.h" |
| #include "../inc/libm_util_amd.h" |
| |
| |
| /*#define USE_REMAINDER_PIBY2F_INLINE*/ |
| #define USE_VALF_WITH_FLAGS |
| #define USE_NANF_WITH_FLAGS |
| #define USE_HANDLE_ERRORF |
| #include "../inc/libm_inlines_amd.h" |
| #undef USE_VALF_WITH_FLAGS |
| #undef USE_NANF_WITH_FLAGS |
| /*#undef USE_REMAINDER_PIBY2F_INLINE*/ |
| #undef USE_HANDLE_ERRORF |
| |
| #ifdef WINDOWS |
| #include "../inc/libm_errno_amd.h" |
| #endif |
| |
| extern void __amd_remainder_piby2d2f(unsigned long long ux, double *r, int *region); |
| |
| /* tan(x) approximation valid on the interval [-pi/4,pi/4]. |
| If recip is true return -1/tan(x) instead. */ |
| static inline double tanf_piby4(double x, int recip) |
| { |
| double r, t; |
| |
| /* Core Remez [1,2] approximation to tan(x) on the |
| interval [0,pi/4]. */ |
| r = x*x; |
| t = x + x*r* |
| (0.385296071263995406715129e0 - |
| 0.172032480471481694693109e-1 * r) / |
| (0.115588821434688393452299e+1 + |
| (-0.51396505478854532132342e0 + |
| 0.1844239256901656082986661e-1 * r) * r); |
| |
| if (recip) |
| return -1.0 / t; |
| else |
| return t; |
| } |
| |
| #ifdef WINDOWS |
| #pragma function(tanf) |
| #endif |
| |
| float FN_PROTOTYPE(tanf)(float x) |
| { |
| double r, dx; |
| int region, xneg; |
| |
| unsigned long long ux, ax; |
| |
| dx = x; |
| |
| GET_BITS_DP64(dx, ux); |
| ax = (ux & ~SIGNBIT_DP64); |
| |
| if (ax <= 0x3fe921fb54442d18LL) /* abs(x) <= pi/4 */ |
| { |
| if (ax < 0x3f80000000000000LL) /* abs(x) < 2.0^(-7) */ |
| { |
| if (ax < 0x3f20000000000000LL) /* abs(x) < 2.0^(-13) */ |
| { |
| if (ax == 0x0000000000000000LL) |
| return x; |
| else |
| return valf_with_flags(x, AMD_F_INEXACT); |
| } |
| else |
| return (float)(dx + dx*dx*dx*0.333333333333333333); |
| } |
| else |
| return (float)tanf_piby4(x, 0); |
| } |
| else if ((ux & EXPBITS_DP64) == EXPBITS_DP64) |
| { |
| /* x is either NaN or infinity */ |
| if (ux & MANTBITS_DP64) |
| { |
| /* x is NaN */ |
| #ifdef WINDOWS |
| unsigned int ufx; |
| GET_BITS_SP32(x, ufx); |
| return handle_errorf("tanf", ufx|0x00400000, _DOMAIN, 0, |
| EDOM, x, 0.0F); |
| #else |
| return x + x; /* Raise invalid if it is a signalling NaN */ |
| #endif |
| } |
| else |
| { |
| /* x is infinity. Return a NaN */ |
| #ifdef WINDOWS |
| return handle_errorf("tanf", INDEFBITPATT_SP32, _DOMAIN, 0, |
| EDOM, x, 0.0F); |
| #else |
| return nanf_with_flags(AMD_F_INVALID); |
| #endif |
| } |
| } |
| |
| xneg = (int)(ux >> 63); |
| |
| if (xneg) |
| dx = -dx; |
| |
| if (dx < 5.0e5) |
| { |
| /* For these size arguments we can just carefully subtract the |
| appropriate multiple of pi/2, using extra precision where |
| dx is close to an exact multiple of pi/2 */ |
| static const double |
| twobypi = 6.36619772367581382433e-01, /* 0x3fe45f306dc9c883 */ |
| piby2_1 = 1.57079632673412561417e+00, /* 0x3ff921fb54400000 */ |
| piby2_1tail = 6.07710050650619224932e-11, /* 0x3dd0b4611a626331 */ |
| piby2_2 = 6.07710050630396597660e-11, /* 0x3dd0b4611a600000 */ |
| piby2_2tail = 2.02226624879595063154e-21, /* 0x3ba3198a2e037073 */ |
| piby2_3 = 2.02226624871116645580e-21, /* 0x3ba3198a2e000000 */ |
| piby2_3tail = 8.47842766036889956997e-32; /* 0x397b839a252049c1 */ |
| double t, rhead, rtail; |
| int npi2; |
| unsigned long long uy, xexp, expdiff; |
| xexp = ax >> EXPSHIFTBITS_DP64; |
| /* How many pi/2 is dx a multiple of? */ |
| if (ax <= 0x400f6a7a2955385eLL) /* 5pi/4 */ |
| { |
| if (ax <= 0x4002d97c7f3321d2LL) /* 3pi/4 */ |
| npi2 = 1; |
| else |
| npi2 = 2; |
| } |
| else if (ax <= 0x401c463abeccb2bbLL) /* 9pi/4 */ |
| { |
| if (ax <= 0x4015fdbbe9bba775LL) /* 7pi/4 */ |
| npi2 = 3; |
| else |
| npi2 = 4; |
| } |
| else |
| npi2 = (int)(dx * twobypi + 0.5); |
| /* Subtract the multiple from dx to get an extra-precision remainder */ |
| rhead = dx - npi2 * piby2_1; |
| rtail = npi2 * piby2_1tail; |
| GET_BITS_DP64(rhead, uy); |
| expdiff = xexp - ((uy & EXPBITS_DP64) >> EXPSHIFTBITS_DP64); |
| if (expdiff > 15) |
| { |
| /* The remainder is pretty small compared with dx, which |
| implies that dx is a near multiple of pi/2 |
| (dx matches the multiple to at least 15 bits) */ |
| t = rhead; |
| rtail = npi2 * piby2_2; |
| rhead = t - rtail; |
| rtail = npi2 * piby2_2tail - ((t - rhead) - rtail); |
| if (expdiff > 48) |
| { |
| /* dx matches a pi/2 multiple to at least 48 bits */ |
| t = rhead; |
| rtail = npi2 * piby2_3; |
| rhead = t - rtail; |
| rtail = npi2 * piby2_3tail - ((t - rhead) - rtail); |
| } |
| } |
| r = rhead - rtail; |
| region = npi2 & 3; |
| } |
| else |
| { |
| /* Reduce x into range [-pi/4,pi/4] */ |
| __amd_remainder_piby2d2f(ax, &r, ®ion); |
| } |
| |
| if (xneg) |
| return (float)-tanf_piby4(r, region & 1); |
| else |
| return (float)tanf_piby4(r, region & 1); |
| } |
| |
| weak_alias (__tanf, tanf) |