#include <clc/clc.h>
#include "math.h"
#include "tables.h"
#include "../clcmacro.h"
/* Refer to the exp routine for the underlying algorithm */
_CLC_OVERLOAD _CLC_DEF float expm1(float x) {
const float X_MAX = 0x1.62e42ep+6f; // 128*log2 : 88.722839111673
const float X_MIN = -0x1.9d1da0p+6f; // -149*log2 : -103.27892990343184
const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657
const float R_LOG2_BY_64_LD = 0x1.620000p-7f; // log2/64 lead: 0.0108032227
const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388
uint xi = as_uint(x);
int n = (int)(x * R_64_BY_LOG2);
float fn = (float)n;
int j = n & 0x3f;
int m = n >> 6;
float r = mad(fn, -R_LOG2_BY_64_TL, mad(fn, -R_LOG2_BY_64_LD, x));
// Truncated Taylor series
float z2 = mad(r*r, mad(r, mad(r, 0x1.555556p-5f, 0x1.555556p-3f), 0.5f), r);
float m2 = as_float((m + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
float2 tv = USE_TABLE(exp_tbl_ep, j);
float two_to_jby64_h = tv.s0 * m2;
float two_to_jby64_t = tv.s1 * m2;
float two_to_jby64 = two_to_jby64_h + two_to_jby64_t;
z2 = mad(z2, two_to_jby64, two_to_jby64_t) + (two_to_jby64_h - 1.0f);
//Make subnormals work
z2 = x == 0.f ? x : z2;
z2 = x < X_MIN | m < -24 ? -1.0f : z2;
z2 = x > X_MAX ? as_float(PINFBITPATT_SP32) : z2;
z2 = isnan(x) ? x : z2;
return z2;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, expm1, float)
#ifdef cl_khr_fp64
#include "exp_helper.h"
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double expm1(double x) {
const double max_expm1_arg = 709.8;
const double min_expm1_arg = -37.42994775023704;
const double log_OnePlus_OneByFour = 0.22314355131420976; //0x3FCC8FF7C79A9A22 = log(1+1/4)
const double log_OneMinus_OneByFour = -0.28768207245178096; //0xBFD269621134DB93 = log(1-1/4)
const double sixtyfour_by_lnof2 = 92.33248261689366; //0x40571547652b82fe
const double lnof2_by_64_head = 0.010830424696223417; //0x3f862e42fefa0000
const double lnof2_by_64_tail = 2.5728046223276688e-14; //0x3d1cf79abc9e3b39
// First, assume log(1-1/4) < x < log(1+1/4) i.e -0.28768 < x < 0.22314
double u = as_double(as_ulong(x) & 0xffffffffff000000UL);
double v = x - u;
double y = u * u * 0.5;
double z = v * (x + u) * 0.5;
double q = fma(x,
fma(x,
fma(x,
fma(x,
fma(x,
fma(x,
fma(x,
fma(x,2.4360682937111612e-8, 2.7582184028154370e-7),
2.7558212415361945e-6),
2.4801576918453420e-5),
1.9841269447671544e-4),
1.3888888890687830e-3),
8.3333333334012270e-3),
4.1666666666665560e-2),
1.6666666666666632e-1);
q *= x * x * x;
double z1g = (u + y) + (q + (v + z));
double z1 = x + (y + (q + z));
z1 = y >= 0x1.0p-7 ? z1g : z1;
// Now assume outside interval around 0
int n = (int)(x * sixtyfour_by_lnof2);
int j = n & 0x3f;
int m = n >> 6;
double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j);
double f1 = tv.s0;
double f2 = tv.s1;
double f = f1 + f2;
double dn = -n;
double r = fma(dn, lnof2_by_64_tail, fma(dn, lnof2_by_64_head, x));
q = fma(r,
fma(r,
fma(r,
fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03),
4.16666666662260795726e-02),
1.66666666665260878863e-01),
5.00000000000000008883e-01);
q = fma(r*r, q, r);
double twopm = as_double((long)(m + EXPBIAS_DP64) << EXPSHIFTBITS_DP64);
double twopmm = as_double((long)(EXPBIAS_DP64 - m) << EXPSHIFTBITS_DP64);
// Computations for m > 52, including where result is close to Inf
ulong uval = as_ulong(0x1.0p+1023 * (f1 + (f * q + (f2))));
int e = (int)(uval >> EXPSHIFTBITS_DP64) + 1;
double zme1024 = as_double(((long)e << EXPSHIFTBITS_DP64) | (uval & MANTBITS_DP64));
zme1024 = e == 2047 ? as_double(PINFBITPATT_DP64) : zme1024;
double zmg52 = twopm * (f1 + fma(f, q, f2 - twopmm));
zmg52 = m == 1024 ? zme1024 : zmg52;
// For m < 53
double zml53 = twopm * ((f1 - twopmm) + fma(f1, q, f2*(1.0 + q)));
// For m < -7
double zmln7 = fma(twopm, f1 + fma(f, q, f2), -1.0);
z = m < 53 ? zml53 : zmg52;
z = m < -7 ? zmln7 : z;
z = x > log_OneMinus_OneByFour & x < log_OnePlus_OneByFour ? z1 : z;
z = x > max_expm1_arg ? as_double(PINFBITPATT_DP64) : z;
z = x < min_expm1_arg ? -1.0 : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, expm1, double)
#endif
_CLC_DEFINE_UNARY_BUILTIN_FP16(expm1)
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