1#include <clc/clc.h> 2 3#include "math.h" 4#include "tables.h" 5#include "../clcmacro.h" 6 7/* Refer to the exp routine for the underlying algorithm */ 8 9_CLC_OVERLOAD _CLC_DEF float expm1(float x) { 10 const float X_MAX = 0x1.62e42ep+6f; // 128*log2 : 88.722839111673 11 const float X_MIN = -0x1.9d1da0p+6f; // -149*log2 : -103.27892990343184 12 13 const float R_64_BY_LOG2 = 0x1.715476p+6f; // 64/log2 : 92.332482616893657 14 const float R_LOG2_BY_64_LD = 0x1.620000p-7f; // log2/64 lead: 0.0108032227 15 const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388 16 17 uint xi = as_uint(x); 18 int n = (int)(x * R_64_BY_LOG2); 19 float fn = (float)n; 20 21 int j = n & 0x3f; 22 int m = n >> 6; 23 24 float r = mad(fn, -R_LOG2_BY_64_TL, mad(fn, -R_LOG2_BY_64_LD, x)); 25 26 // Truncated Taylor series 27 float z2 = mad(r*r, mad(r, mad(r, 0x1.555556p-5f, 0x1.555556p-3f), 0.5f), r); 28 29 float m2 = as_float((m + EXPBIAS_SP32) << EXPSHIFTBITS_SP32); 30 float2 tv = USE_TABLE(exp_tbl_ep, j); 31 32 float two_to_jby64_h = tv.s0 * m2; 33 float two_to_jby64_t = tv.s1 * m2; 34 float two_to_jby64 = two_to_jby64_h + two_to_jby64_t; 35 36 z2 = mad(z2, two_to_jby64, two_to_jby64_t) + (two_to_jby64_h - 1.0f); 37 //Make subnormals work 38 z2 = x == 0.f ? x : z2; 39 z2 = x < X_MIN | m < -24 ? -1.0f : z2; 40 z2 = x > X_MAX ? as_float(PINFBITPATT_SP32) : z2; 41 z2 = isnan(x) ? x : z2; 42 43 return z2; 44} 45 46_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, expm1, float) 47 48#ifdef cl_khr_fp64 49 50#include "exp_helper.h" 51 52#pragma OPENCL EXTENSION cl_khr_fp64 : enable 53 54_CLC_OVERLOAD _CLC_DEF double expm1(double x) { 55 const double max_expm1_arg = 709.8; 56 const double min_expm1_arg = -37.42994775023704; 57 const double log_OnePlus_OneByFour = 0.22314355131420976; //0x3FCC8FF7C79A9A22 = log(1+1/4) 58 const double log_OneMinus_OneByFour = -0.28768207245178096; //0xBFD269621134DB93 = log(1-1/4) 59 const double sixtyfour_by_lnof2 = 92.33248261689366; //0x40571547652b82fe 60 const double lnof2_by_64_head = 0.010830424696223417; //0x3f862e42fefa0000 61 const double lnof2_by_64_tail = 2.5728046223276688e-14; //0x3d1cf79abc9e3b39 62 63 // First, assume log(1-1/4) < x < log(1+1/4) i.e -0.28768 < x < 0.22314 64 double u = as_double(as_ulong(x) & 0xffffffffff000000UL); 65 double v = x - u; 66 double y = u * u * 0.5; 67 double z = v * (x + u) * 0.5; 68 69 double q = fma(x, 70 fma(x, 71 fma(x, 72 fma(x, 73 fma(x, 74 fma(x, 75 fma(x, 76 fma(x,2.4360682937111612e-8, 2.7582184028154370e-7), 77 2.7558212415361945e-6), 78 2.4801576918453420e-5), 79 1.9841269447671544e-4), 80 1.3888888890687830e-3), 81 8.3333333334012270e-3), 82 4.1666666666665560e-2), 83 1.6666666666666632e-1); 84 q *= x * x * x; 85 86 double z1g = (u + y) + (q + (v + z)); 87 double z1 = x + (y + (q + z)); 88 z1 = y >= 0x1.0p-7 ? z1g : z1; 89 90 // Now assume outside interval around 0 91 int n = (int)(x * sixtyfour_by_lnof2); 92 int j = n & 0x3f; 93 int m = n >> 6; 94 95 double2 tv = USE_TABLE(two_to_jby64_ep_tbl, j); 96 double f1 = tv.s0; 97 double f2 = tv.s1; 98 double f = f1 + f2; 99 100 double dn = -n; 101 double r = fma(dn, lnof2_by_64_tail, fma(dn, lnof2_by_64_head, x)); 102 103 q = fma(r, 104 fma(r, 105 fma(r, 106 fma(r, 1.38889490863777199667e-03, 8.33336798434219616221e-03), 107 4.16666666662260795726e-02), 108 1.66666666665260878863e-01), 109 5.00000000000000008883e-01); 110 q = fma(r*r, q, r); 111 112 double twopm = as_double((long)(m + EXPBIAS_DP64) << EXPSHIFTBITS_DP64); 113 double twopmm = as_double((long)(EXPBIAS_DP64 - m) << EXPSHIFTBITS_DP64); 114 115 // Computations for m > 52, including where result is close to Inf 116 ulong uval = as_ulong(0x1.0p+1023 * (f1 + (f * q + (f2)))); 117 int e = (int)(uval >> EXPSHIFTBITS_DP64) + 1; 118 119 double zme1024 = as_double(((long)e << EXPSHIFTBITS_DP64) | (uval & MANTBITS_DP64)); 120 zme1024 = e == 2047 ? as_double(PINFBITPATT_DP64) : zme1024; 121 122 double zmg52 = twopm * (f1 + fma(f, q, f2 - twopmm)); 123 zmg52 = m == 1024 ? zme1024 : zmg52; 124 125 // For m < 53 126 double zml53 = twopm * ((f1 - twopmm) + fma(f1, q, f2*(1.0 + q))); 127 128 // For m < -7 129 double zmln7 = fma(twopm, f1 + fma(f, q, f2), -1.0); 130 131 z = m < 53 ? zml53 : zmg52; 132 z = m < -7 ? zmln7 : z; 133 z = x > log_OneMinus_OneByFour & x < log_OnePlus_OneByFour ? z1 : z; 134 z = x > max_expm1_arg ? as_double(PINFBITPATT_DP64) : z; 135 z = x < min_expm1_arg ? -1.0 : z; 136 137 return z; 138} 139 140_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, expm1, double) 141 142#endif 143