171 lines · plain
1//===----------------------------------------------------------------------===//2//3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.4// See https://llvm.org/LICENSE.txt for license information.5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception6//7//===----------------------------------------------------------------------===//8//9// Computes natural log(1+x). Algorithm based on:10// Ping-Tak Peter Tang11// "Table-driven implementation of the logarithm function in IEEE floating-point12// arithmetic" ACM Transactions on Mathematical Software (TOMS) Volume 16, Issue13// 4 (December 1990)14//15// Note that we use a lookup table of size 64 rather than 128, and compensate by16// having extra terms in the minimax polynomial for the kernel approximation.17//18//===----------------------------------------------------------------------===//19 20#if __CLC_FPSIZE == 3221 22_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_log1p(__CLC_GENTYPE x) {23 __CLC_GENTYPE w = x;24 __CLC_UINTN ux = __CLC_AS_UINTN(x);25 __CLC_UINTN ax = ux & EXSIGNBIT_SP32;26 27 // |x| < 2^-428 __CLC_GENTYPE u2 = MATH_DIVIDE(x, 2.0f + x);29 __CLC_GENTYPE u = u2 + u2;30 __CLC_GENTYPE v = u * u;31 // 2/(5 * 2^5), 2/(3 * 2^3)32 __CLC_GENTYPE zsmall =33 __clc_mad(-u2, x, __clc_mad(v, 0x1.99999ap-7f, 0x1.555556p-4f) * v * u) +34 x;35 36 // |x| >= 2^-437 ux = __CLC_AS_UINTN(x + 1.0f);38 39 __CLC_INTN m = __CLC_AS_INTN((ux >> EXPSHIFTBITS_SP32) & 0xff) - EXPBIAS_SP32;40 __CLC_GENTYPE mf = __CLC_CONVERT_GENTYPE(m);41 __CLC_UINTN indx = (ux & 0x007f0000) + ((ux & 0x00008000) << 1);42 __CLC_GENTYPE F = __CLC_AS_GENTYPE(indx | 0x3f000000);43 44 // x > 2^2445 __CLC_GENTYPE fg24 = F - __CLC_AS_GENTYPE(0x3f000000 | (ux & MANTBITS_SP32));46 47 // x <= 2^2448 __CLC_UINTN xhi = ux & 0xffff8000;49 __CLC_GENTYPE xh = __CLC_AS_GENTYPE(xhi);50 __CLC_GENTYPE xt = (1.0f - xh) + w;51 __CLC_UINTN xnm = ((~(xhi & 0x7f800000)) - 0x00800000) & 0x7f800000;52 xt = xt * __CLC_AS_GENTYPE(xnm) * 0.5f;53 __CLC_GENTYPE fl24 =54 F - __CLC_AS_GENTYPE(0x3f000000 | (xhi & MANTBITS_SP32)) - xt;55 56 __CLC_GENTYPE f = mf > 24.0f ? fg24 : fl24;57 58 indx = indx >> 16;59 __CLC_GENTYPE r = f * __CLC_USE_TABLE(log_inv_tbl, __CLC_CONVERT_INTN(indx));60 61 // 1/3, 1/262 __CLC_GENTYPE poly =63 __clc_mad(__clc_mad(r, 0x1.555556p-2f, 0x1.0p-1f), r * r, r);64 65 const __CLC_GENTYPE LOG2_HEAD = 0x1.62e000p-1f; // 0.69311523466 const __CLC_GENTYPE LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.000031946183367 68 __CLC_GENTYPE tv0 = __CLC_USE_TABLE(loge_tbl_lo, __CLC_AS_INTN(indx));69 __CLC_GENTYPE tv1 = __CLC_USE_TABLE(loge_tbl_hi, __CLC_AS_INTN(indx));70 __CLC_GENTYPE z1 = __clc_mad(mf, LOG2_HEAD, tv0);71 __CLC_GENTYPE z2 = __clc_mad(mf, LOG2_TAIL, -poly) + tv1;72 __CLC_GENTYPE z = z1 + z2;73 74 z = ax < 0x3d800000U ? zsmall : z;75 76 // Edge cases77 z = ax >= PINFBITPATT_SP32 ? w : z;78 z = w < -1.0f ? __CLC_GENTYPE_NAN : z;79 z = w == -1.0f ? __CLC_AS_GENTYPE((__CLC_UINTN)NINFBITPATT_SP32) : z;80 // Fix subnormals81 z = ax < 0x33800000 ? x : z;82 83 return z;84}85 86#elif __CLC_FPSIZE == 6487 88_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_log1p(__CLC_GENTYPE x) {89 // Process Inside the threshold now90 __CLC_ULONGN ux = __CLC_AS_ULONGN((__CLC_GENTYPE)1.0 + x);91 __CLC_INTN xexp =92 __CLC_CONVERT_INTN((ux >> EXPSHIFTBITS_DP64) & 0x7ff) - EXPBIAS_DP64;93 __CLC_GENTYPE f =94 __CLC_AS_GENTYPE((__CLC_ULONGN)ONEEXPBITS_DP64 | (ux & MANTBITS_DP64));95 96 __CLC_INTN j = __CLC_CONVERT_INTN(ux >> 45);97 j = ((0x80 | (j & 0x7e)) >> 1) + (j & 0x1);98 __CLC_GENTYPE f1 = __CLC_CONVERT_GENTYPE(j) * 0x1.0p-6;99 j -= 64;100 101 __CLC_GENTYPE f2temp = f - f1;102 __CLC_GENTYPE m2 =103 __CLC_AS_GENTYPE(__CLC_CONVERT_ULONGN(0x3ff - xexp) << EXPSHIFTBITS_DP64);104 __CLC_GENTYPE f2l = __clc_fma(m2, x, m2 - f1);105 __CLC_GENTYPE f2g = __clc_fma(m2, x, -f1) + m2;106 __CLC_GENTYPE f2 =107 __CLC_CONVERT_LONGN(xexp <= MANTLENGTH_DP64 - 1) ? f2l : f2g;108 f2 = __CLC_CONVERT_LONGN(xexp <= -2 || (xexp >= MANTLENGTH_DP64 + 8)) ? f2temp109 : f2;110 111 __CLC_GENTYPE z1 = __CLC_USE_TABLE(ln_tbl_lo, j);112 __CLC_GENTYPE q = __CLC_USE_TABLE(ln_tbl_hi, j);113 114 __CLC_GENTYPE u = MATH_DIVIDE(f2, __clc_fma(0.5, f2, f1));115 __CLC_GENTYPE v = u * u;116 117 __CLC_GENTYPE poly = v * __clc_fma(v,118 __clc_fma(v, 2.23219810758559851206e-03,119 1.24999999978138668903e-02),120 8.33333333333333593622e-02);121 122 // log2_lead and log2_tail sum to an extra-precise version of log(2)123 // 0x3fe62e42e0000000124 const __CLC_GENTYPE log2_lead = 6.93147122859954833984e-01;125 // 0x3e6efa39ef35793c126 const __CLC_GENTYPE log2_tail = 5.76999904754328540596e-08;127 128 __CLC_GENTYPE z2 = q + __clc_fma(u, poly, u);129 __CLC_GENTYPE dxexp = __CLC_CONVERT_GENTYPE(xexp);130 __CLC_GENTYPE r1 = __clc_fma(dxexp, log2_lead, z1);131 __CLC_GENTYPE r2 = __clc_fma(dxexp, log2_tail, z2);132 __CLC_GENTYPE result1 = r1 + r2;133 134 // Process Outside the threshold now135 __CLC_GENTYPE r = x;136 u = r / (2.0 + r);137 __CLC_GENTYPE correction = r * u;138 u = u + u;139 v = u * u;140 r1 = r;141 142 poly = __clc_fma(v,143 __clc_fma(v,144 __clc_fma(v, 4.34887777707614552256e-04,145 2.23213998791944806202e-03),146 1.25000000037717509602e-02),147 8.33333333333317923934e-02);148 149 r2 = __clc_fma(u * v, poly, -correction);150 151 // The values exp(-1/16)-1 and exp(1/16)-1152 const __CLC_GENTYPE log1p_thresh1 = -0x1.f0540438fd5c3p-5;153 const __CLC_GENTYPE log1p_thresh2 = 0x1.082b577d34ed8p-4;154 __CLC_GENTYPE result2 = r1 + r2;155 result2 = x < log1p_thresh1 || x > log1p_thresh2 ? result1 : result2;156 157 result2 = __clc_isinf(x) ? x : result2;158 result2 = x < -1.0 ? __CLC_GENTYPE_NAN : result2;159 result2 =160 x == -1.0 ? __CLC_AS_GENTYPE((__CLC_ULONGN)NINFBITPATT_DP64) : result2;161 return result2;162}163 164#elif __CLC_FPSIZE == 16165 166_CLC_OVERLOAD _CLC_DEF __CLC_GENTYPE __clc_log1p(__CLC_GENTYPE x) {167 return __CLC_CONVERT_GENTYPE(__clc_log1p(__CLC_CONVERT_FLOATN(x)));168}169 170#endif171