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321 lines
15 KiB
321 lines
15 KiB
//
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// Copyright (c) 2000, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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typedef enum
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{
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logl_zero=0, logl_negative, /* 0, 1 */
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log_zero, log_negative, /* 2, 3 */
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logf_zero, logf_negative, /* 4, 5 */
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log10l_zero, log10l_negative, /* 6, 7 */
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log10_zero, log10_negative, /* 8, 9 */
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log10f_zero, log10f_negative, /* 10, 11 */
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expl_overflow, expl_underflow, /* 12, 13 */
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exp_overflow, exp_underflow, /* 14, 15 */
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expf_overflow, expf_underflow, /* 16, 17 */
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powl_overflow, powl_underflow, /* 18, 19 */
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powl_zero_to_zero, /* 20 */
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powl_zero_to_negative, /* 21 */
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powl_neg_to_non_integer, /* 22 */
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powl_nan_to_zero, /* 23 */
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pow_overflow, pow_underflow, /* 24, 25 */
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pow_zero_to_zero, /* 26 */
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pow_zero_to_negative, /* 27 */
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pow_neg_to_non_integer, /* 28 */
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pow_nan_to_zero, /* 29 */
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powf_overflow, powf_underflow, /* 30, 31 */
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powf_zero_to_zero, /* 32 */
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powf_zero_to_negative, /* 33 */
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powf_neg_to_non_integer, /* 34 */
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powf_nan_to_zero, /* 35 */
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atan2l_zero, /* 36 */
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atan2_zero, /* 37 */
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atan2f_zero, /* 38 */
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expm1l_overflow, /* 39 */
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expm1l_underflow, /* 40 */
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expm1_overflow, /* 41 */
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expm1_underflow, /* 42 */
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expm1f_overflow, /* 43 */
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expm1f_underflow, /* 44 */
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hypotl_overflow, /* 45 */
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hypot_overflow, /* 46 */
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hypotf_overflow, /* 47 */
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sqrtl_negative, /* 48 */
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sqrt_negative, /* 49 */
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sqrtf_negative, /* 50 */
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scalbl_overflow, scalbl_underflow, /* 51,52 */
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scalb_overflow, scalb_underflow, /* 53,54 */
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scalbf_overflow, scalbf_underflow, /* 55,56 */
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acosl_gt_one, acos_gt_one, acosf_gt_one, /* 57, 58, 59 */
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asinl_gt_one, asin_gt_one, asinf_gt_one, /* 60, 61, 62 */
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coshl_overflow, cosh_overflow, coshf_overflow, /* 63, 64, 65 */
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y0l_zero, y0l_negative,y0l_gt_loss, /* 66, 67, 68 */
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y0_zero, y0_negative,y0_gt_loss, /* 69, 70, 71 */
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y0f_zero, y0f_negative,y0f_gt_loss, /* 72, 73, 74 */
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y1l_zero, y1l_negative,y1l_gt_loss, /* 75, 76, 77 */
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y1_zero, y1_negative,y1_gt_loss, /* 78, 79, 80 */
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y1f_zero, y1f_negative,y1f_gt_loss, /* 81, 82, 83 */
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ynl_zero, ynl_negative,ynl_gt_loss, /* 84, 85, 86 */
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yn_zero, yn_negative,yn_gt_loss, /* 87, 88, 89 */
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ynf_zero, ynf_negative,ynf_gt_loss, /* 90, 91, 92 */
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j0l_gt_loss, /* 93 */
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j0_gt_loss, /* 94 */
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j0f_gt_loss, /* 95 */
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j1l_gt_loss, /* 96 */
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j1_gt_loss, /* 97 */
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j1f_gt_loss, /* 98 */
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jnl_gt_loss, /* 99 */
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jn_gt_loss, /* 100 */
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jnf_gt_loss, /* 101 */
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lgammal_overflow, lgammal_negative,lgammal_reserve, /* 102, 103, 104 */
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lgamma_overflow, lgamma_negative,lgamma_reserve, /* 105, 106, 107 */
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lgammaf_overflow, lgammaf_negative, lgammaf_reserve,/* 108, 109, 110 */
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gammal_overflow,gammal_negative, gammal_reserve, /* 111, 112, 113 */
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gamma_overflow, gamma_negative, gamma_reserve, /* 114, 115, 116 */
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gammaf_overflow,gammaf_negative,gammaf_reserve, /* 117, 118, 119 */
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fmodl_by_zero, /* 120 */
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fmod_by_zero, /* 121 */
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fmodf_by_zero, /* 122 */
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remainderl_by_zero, /* 123 */
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remainder_by_zero, /* 124 */
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remainderf_by_zero, /* 125 */
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sinhl_overflow, sinh_overflow, sinhf_overflow, /* 126, 127, 128 */
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atanhl_gt_one, atanhl_eq_one, /* 129, 130 */
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atanh_gt_one, atanh_eq_one, /* 131, 132 */
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atanhf_gt_one, atanhf_eq_one, /* 133, 134 */
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acoshl_lt_one, /* 135 */
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acosh_lt_one, /* 136 */
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acoshf_lt_one, /* 137 */
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log1pl_zero, log1pl_negative, /* 138, 139 */
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log1p_zero, log1p_negative, /* 140, 141 */
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log1pf_zero, log1pf_negative, /* 142, 143 */
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ldexpl_overflow, ldexpl_underflow, /* 144, 145 */
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ldexp_overflow, ldexp_underflow, /* 146, 147 */
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ldexpf_overflow, ldexpf_underflow, /* 148, 149 */
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logbl_zero, logb_zero, logbf_zero, /* 150, 151,152 */
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nextafterl_overflow, nextafter_overflow,
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nextafterf_overflow, /* 153, 154,155 */
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ilogbl_zero, ilogb_zero, ilogbf_zero, /* 156, 157,158 */
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exp2l_overflow, exp2l_underflow, /* 159, 160 */
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exp2_overflow, exp2_underflow, /* 161, 162 */
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exp2f_overflow, exp2f_underflow, /* 163, 164 */
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exp10l_overflow, exp10_overflow,
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exp10f_overflow, /* 165, 166, 167 */
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log2l_zero, log2l_negative, /* 168, 169 */
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log2_zero, log2_negative, /* 170, 171 */
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log2f_zero, log2f_negative, /* 172, 173 */
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log_nan = 1000, /* 1000 */
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log10_nan, /* 1001 */
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exp_nan, /* 1002 */
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atan_nan, /* 1003 */
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ceil_nan, /* 1004 */
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floor_nan, /* 1005 */
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pow_nan, /* 1006 */
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modf_nan /* 1007 */
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} error_types;
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void __libm_error_support(void*,void*,void*,error_types);
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#define BIAS_64 1023
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#define EXPINF_64 2047
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#define DOUBLE_HEX(HI, LO) 0x ## LO, 0x ## HI
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static const unsigned INF[] = {
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DOUBLE_HEX(7ff00000, 00000000),
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DOUBLE_HEX(fff00000, 00000000)
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};
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static const unsigned BIG[] = {
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DOUBLE_HEX(7fe00000, 00000000),
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DOUBLE_HEX(00200000, 00000000)
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};
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static const unsigned ZERO[] = {
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DOUBLE_HEX(00000000, 00000000),
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DOUBLE_HEX(80000000, 00000000)
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};
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static const unsigned INF_32[] = {0x7f800000,0xff800000 };
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static const unsigned NAN_32[] = {0x7fc00000,0xffc00000};
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static const unsigned ZERO_32[] = { 0, 0x80000000 };
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static const float libm_largef[] = { 1.0e+30f, -1.0e+30f };
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static const float libm_smallf[] = { 1.0e-30f, -1.0e-30f };
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static const double libm_small[] = { 1.0e-300, -1.0e-300 };
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#define INVALID (*((double*)&ZERO[0]) * *((double*)&INF[0]))
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#define INVALID_32 *(float *)&ZERO_32[0] * *(float *)&INF_32[0]
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#define LIBM_OVERFLOW (*((double*)&BIG[0]) * *((double*)&BIG[0]))
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#define LIBM_UNDERFLOW (*((double*)&BIG[2]) * *((double*)&BIG[2]))
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#define LIBM_OVERFLOWF (libm_largef[0] * libm_largef[0])
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#define LIBM_UNDERFLOWF (libm_smallf[0] * libm_smallf[0])
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#define PINF *((double*)&INF[0])
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#define NINF -PINF
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#define PINF_DZ (1.0/(*((double*)&ZERO[0]))
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struct _exception
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{
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int type;
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char *name;
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double arg1, arg2, retval;
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};
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#define MATHERR_D _matherr
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#define EXC_DECL_D _exception
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extern int MATHERR_D(struct EXC_DECL_D*);
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/* Set these appropriately to make thread Safe */
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#define ERRNO_RANGE errno = ERANGE
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#define ERRNO_DOMAIN errno = EDOM
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extern int (*_pmatherr)(struct EXC_DECL_D*);
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// This is a run-time variable and may affect
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// floating point behavior of the libm functions
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#define BIAS_32 127
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#define BIAS_64 1023
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#define BIAS_80 16383
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#define BIAS_128 16383
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#define MAXEXP_32 254
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#define MAXEXP_64 2046
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#define MAXEXP_80 32766
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#define MAXEXP_128 32766
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#define EXPINF_32 255
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#define EXPINF_64 2047
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#define EXPINF_80 32767
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#define EXPINF_128 32767
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/*****************************/
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/* memory format definitions */
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/*****************************/
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/*/// if you use /Zp2 option, or the following pragma... then the
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//// 80 bit FP objects will occupy only 10 bytes in memory - otherwise
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//// more generous alignments will "waste" memory.
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//// Use of -DPACKFP80 is NOT recommended.
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//// The same effect can be obtained using /Zp2 (again, NOT recommended).
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//// Otherwise the alignment will be a word, forcing the size to be
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//// 12 bytes (this means some memory will be wasted in exchange
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//// for better performance).
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//// Unfortunately, because -DPACKFP80 is implemented the same as /Zp2,
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//// all structures will be packed tighter in the entire program. */
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#ifdef PACKFP80
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#pragma warning(disable:4103)
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#pragma pack(2)
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#endif
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struct fp32 { /*// sign:1 exponent:8 significand:23 (implied leading 1)*/
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unsigned significand:23;
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unsigned exponent:8;
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unsigned sign:1;
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};
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struct fp64 { /*/ sign:1 exponent:11 significand:52 (implied leading 1)*/
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unsigned lo_significand:32;
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unsigned hi_significand:20;
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unsigned exponent:11;
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unsigned sign:1;
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};
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struct fp80 { /*/ sign:1 exponent:15 significand:64 (NO implied bits) */
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unsigned lo_significand;
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unsigned hi_significand;
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unsigned exponent:15;
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unsigned sign:1;
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};
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#ifdef __cplusplus
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extern "C" {
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#endif
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#define NONZERO_SIGNIFICAND(X) ((X)->hi_significand != 0 || (X)->lo_significand != 0)
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#define ZERO_SIGNIFICAND(X) ((X)->hi_significand == 0 && (X)->lo_significand == 0)
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#define SET_ZERO_SIGNIFICAND(X) (X)->hi_significand = 0; (X)->lo_significand = 0
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#define SET_LO_SIGNIFICAND(X, LO) (X)->lo_significand = (LO)
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#define SET_HI_SIGNIFICAND(X, HI) (X)->hi_significand = (HI)
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#define SET_SIGNIFICAND(X, HI, LO) (X)->hi_significand = (HI);(X)->lo_significand = (LO)
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#define SIGNIFICAND_EQUAL(X, HI, LO) (((X)->hi_significand == 0x ## HI) && ((X)->lo_significand == 0x ## LO))
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#define SIGNIFICAND_GREATER(X, HI, LO) ((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand > 0x ## LO))
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#define SIGNIFICAND_GREATER_EQ(X, HI, LO) ((X)->hi_significand > 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand >= 0x ## LO))
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#define SIGNIFICAND_LESS(X, HI, LO) ((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand < 0x ## LO))
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#define SIGNIFICAND_LESS_EQ(X, HI, LO) ((X)->hi_significand < 0x ## HI) || \
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(((X)->hi_significand == 0x ## HI) && ((X)->lo_significand <= 0x ## LO))
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#define HI_SIGNIFICAND_LESS(X, HI) ((X)->hi_significand < 0x ## HI)
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#define ISSIGNIFICAND_EQUAL(X, Y) (((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand == (Y)->lo_significand))
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#define ISSIGNIFICAND_GREATER(X, Y) ((X)->hi_significand > (Y)->hi_significand) || \
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(((X)->hi_significand == (Y)->hi_significand) && ((X)->lo_significand > (Y)->lo_significand))
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#define ADD_ULP(X) if(!++(X)->lo_significand) { \
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if(!++(X)->hi_significand) { \
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(X)->exponent++; }}
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#define SUB_ULP(X) if(!(X)->lo_significand--) { \
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if(!(X)->hi_significand--) { \
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(X)->exponent--; }}
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#define CLEAR_LOW_BITS(X,MASK) (X)->lo_significand &= 0x ## MASK
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#define FIX_N_HI_BITS(X, NBIT) (X)->lo_significand = 0; (X)->hi_significand &= (0xfffff << (20 - NBIT))
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#define HI_BITS_TO_INTEGER(X, NBIT) (1 << (NBIT)) | ((X)->hi_significand >> (20 - (NBIT)))
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#ifdef BIG_ENDIAN
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#define DOUBLE_HEX(HI, LO) 0x ## HI, 0x ## LO
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#define HI_WORD(NUM) (*((unsigned *)(NUM))) & 0x7fffffff
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#else
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#define DOUBLE_HEX(HI, LO) 0x ## LO, 0x ## HI
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#define HI_WORD(NUM) (*(((unsigned *)(NUM))+1)) & 0x7fffffff
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#endif
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#define SIGN_EXPAND(val,num) ((val) << (32-(num))) >> (32-(num)) /* sign expand of 'num' LSBs */
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#define VALUE_EQUAL(X,EXP,HI,LO) (((X)->exponent == (EXP)) && SIGNIFICAND_EQUAL(X, HI, LO))
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#define VALUE_GREATER(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GREATER(X, HI, LO))))
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#define VALUE_GREATER_EQ(X,EXP,HI,LO) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_GREATER_EQ(X, HI, LO))))
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#define VALUE_LESS(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LESS(X, HI, LO))))
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#define VALUE_LESS_EQ(X,EXP,HI,LO) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && (SIGNIFICAND_LESS_EQ(X, HI, LO))))
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#define ISVALUE_EQUAL(X, Y) \
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(((X)->exponent == (Y)->exponent) && ISSIGNIFICAND_EQUAL(X, Y))
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#define ISVALUE_GREATER(X, Y) \
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(((X)->exponent > (Y)->exponent) || (((X)->exponent == (Y)->exponent) && ISSIGNIFICAND_GREATER(X, Y)))
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#define VALUE_GREATERF(X,EXP,SIG) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && ((X)->significand > 0x##SIG)))
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#define VALUE_GREATER_EQF(X,EXP,SIG) (((X)->exponent > (EXP)) || \
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(((X)->exponent == (EXP)) && ((X)->significand >= 0x##SIG)))
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#define VALUE_LESSF(X,EXP,SIG) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && ((X)->significand < 0x##SIG)))
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#define VALUE_LESS_EQF(X,EXP,SIG) (((X)->exponent < (EXP)) || \
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(((X)->exponent == (EXP)) && ((X)->significand <= 0x##SIG)))
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