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143 lines
4.5 KiB
143 lines
4.5 KiB
#include <clc/clc.h>
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#include "math.h"
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#include "tables.h"
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#include "../clcmacro.h"
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/* Refer to the exp routine for the underlying algorithm */
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_CLC_OVERLOAD _CLC_DEF float expm1(float x) {
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const float X_MAX = 0x1.62e42ep+6f; // 128*log2 : 88.722839111673
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const float X_MIN = -0x1.9d1da0p+6f; // -149*log2 : -103.27892990343184
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const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657
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const float R_LOG2_BY_64_LD = 0x1.620000p-7f; // log2/64 lead: 0.0108032227
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const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388
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uint xi = as_uint(x);
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int n = (int)(x * R_64_BY_LOG2);
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float fn = (float)n;
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int j = n & 0x3f;
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int m = n >> 6;
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float r = mad(fn, -R_LOG2_BY_64_TL, mad(fn, -R_LOG2_BY_64_LD, x));
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// Truncated Taylor series
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float z2 = mad(r*r, mad(r, mad(r, 0x1.555556p-5f, 0x1.555556p-3f), 0.5f), r);
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float m2 = as_float((m + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
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float2 tv = USE_TABLE(exp_tbl_ep, j);
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float two_to_jby64_h = tv.s0 * m2;
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float two_to_jby64_t = tv.s1 * m2;
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float two_to_jby64 = two_to_jby64_h + two_to_jby64_t;
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z2 = mad(z2, two_to_jby64, two_to_jby64_t) + (two_to_jby64_h - 1.0f);
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//Make subnormals work
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z2 = x == 0.f ? x : z2;
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z2 = x < X_MIN | m < -24 ? -1.0f : z2;
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z2 = x > X_MAX ? as_float(PINFBITPATT_SP32) : z2;
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z2 = isnan(x) ? x : z2;
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return z2;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, expm1, float)
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#ifdef cl_khr_fp64
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#include "exp_helper.h"
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#pragma OPENCL EXTENSION cl_khr_fp64 : enable
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_CLC_OVERLOAD _CLC_DEF double expm1(double x) {
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const double max_expm1_arg = 709.8;
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const double min_expm1_arg = -37.42994775023704;
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const double log_OnePlus_OneByFour = 0.22314355131420976; //0x3FCC8FF7C79A9A22 = log(1+1/4)
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const double log_OneMinus_OneByFour = -0.28768207245178096; //0xBFD269621134DB93 = log(1-1/4)
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const double sixtyfour_by_lnof2 = 92.33248261689366; //0x40571547652b82fe
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const double lnof2_by_64_head = 0.010830424696223417; //0x3f862e42fefa0000
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const double lnof2_by_64_tail = 2.5728046223276688e-14; //0x3d1cf79abc9e3b39
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// First, assume log(1-1/4) < x < log(1+1/4) i.e -0.28768 < x < 0.22314
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double u = as_double(as_ulong(x) & 0xffffffffff000000UL);
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double v = x - u;
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double y = u * u * 0.5;
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double z = v * (x + u) * 0.5;
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double q = fma(x,
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fma(x,
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fma(x,
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fma(x,
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fma(x,
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fma(x,
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fma(x,
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fma(x,2.4360682937111612e-8, 2.7582184028154370e-7),
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2.7558212415361945e-6),
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2.4801576918453420e-5),
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1.9841269447671544e-4),
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1.3888888890687830e-3),
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8.3333333334012270e-3),
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4.1666666666665560e-2),
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1.6666666666666632e-1);
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q *= x * x * x;
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double z1g = (u + y) + (q + (v + z));
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double z1 = x + (y + (q + z));
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z1 = y >= 0x1.0p-7 ? z1g : z1;
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// Now assume outside interval around 0
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int n = (int)(x * sixtyfour_by_lnof2);
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int j = n & 0x3f;
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int m = n >> 6;
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double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j);
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double f1 = tv.s0;
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double f2 = tv.s1;
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double f = f1 + f2;
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double dn = -n;
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double r = fma(dn, lnof2_by_64_tail, fma(dn, lnof2_by_64_head, x));
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q = fma(r,
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fma(r,
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fma(r,
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fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03),
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4.16666666662260795726e-02),
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1.66666666665260878863e-01),
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5.00000000000000008883e-01);
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q = fma(r*r, q, r);
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double twopm = as_double((long)(m + EXPBIAS_DP64) << EXPSHIFTBITS_DP64);
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double twopmm = as_double((long)(EXPBIAS_DP64 - m) << EXPSHIFTBITS_DP64);
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// Computations for m > 52, including where result is close to Inf
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ulong uval = as_ulong(0x1.0p+1023 * (f1 + (f * q + (f2))));
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int e = (int)(uval >> EXPSHIFTBITS_DP64) + 1;
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double zme1024 = as_double(((long)e << EXPSHIFTBITS_DP64) | (uval & MANTBITS_DP64));
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zme1024 = e == 2047 ? as_double(PINFBITPATT_DP64) : zme1024;
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double zmg52 = twopm * (f1 + fma(f, q, f2 - twopmm));
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zmg52 = m == 1024 ? zme1024 : zmg52;
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// For m < 53
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double zml53 = twopm * ((f1 - twopmm) + fma(f1, q, f2*(1.0 + q)));
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// For m < -7
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double zmln7 = fma(twopm, f1 + fma(f, q, f2), -1.0);
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z = m < 53 ? zml53 : zmg52;
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z = m < -7 ? zmln7 : z;
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z = x > log_OneMinus_OneByFour & x < log_OnePlus_OneByFour ? z1 : z;
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z = x > max_expm1_arg ? as_double(PINFBITPATT_DP64) : z;
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z = x < min_expm1_arg ? -1.0 : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, expm1, double)
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#endif
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