libc/src/math/generic/exp10f.cpp

   1 //===-- Single-precision 10^x function ------------------------------------===//
   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-exception
   6 //
   7 //===----------------------------------------------------------------------===//
   8
   9 #include "src/math/exp10f.h"
  10 #include "explogxf.h"
  11 #include "src/__support/FPUtil/BasicOperations.h"
  12 #include "src/__support/FPUtil/FEnvImpl.h"
  13 #include "src/__support/FPUtil/FPBits.h"
  14 #include "src/__support/FPUtil/PolyEval.h"
  15 #include "src/__support/FPUtil/multiply_add.h"
  16 #include "src/__support/FPUtil/nearest_integer.h"
  17 #include "src/__support/common.h"
  18 #include "src/__support/macros/optimization.h" // LIBC_UNLIKELY
  19
  20 #include <errno.h>
  21
  22 namespace __llvm_libc {
  23
  24 LLVM_LIBC_FUNCTION(float, exp10f, (float x)) {
  25   using FPBits = typename fputil::FPBits<float>;
  26   FPBits xbits(x);
  27
  28   uint32_t x_u = xbits.uintval();
  29   uint32_t x_abs = x_u & 0x7fff'ffffU;
  30
  31   // When |x| >= log10(2^128), or x is nan
  32   if (LIBC_UNLIKELY(x_abs >= 0x421a'209bU)) {
  33     // When x < log10(2^-150) or nan
  34     if (x_u > 0xc234'9e35U) {
  35       // exp(-Inf) = 0
  36       if (xbits.is_inf())
  37         return 0.0f;
  38       // exp(nan) = nan
  39       if (xbits.is_nan())
  40         return x;
  41       if (fputil::get_round() == FE_UPWARD)
  42         return static_cast<float>(FPBits(FPBits::MIN_SUBNORMAL));
  43       fputil::set_errno_if_required(ERANGE);
  44       fputil::raise_except_if_required(FE_UNDERFLOW);
  45       return 0.0f;
  46     }
  47     // x >= log10(2^128) or nan
  48     if (!xbits.get_sign() && (x_u >= 0x421a'209bU)) {
  49       // x is finite
  50       if (x_u < 0x7f80'0000U) {
  51         int rounding = fputil::get_round();
  52         if (rounding == FE_DOWNWARD || rounding == FE_TOWARDZERO)
  53           return static_cast<float>(FPBits(FPBits::MAX_NORMAL));
  54
  55         fputil::set_errno_if_required(ERANGE);
  56         fputil::raise_except_if_required(FE_OVERFLOW);
  57       }
  58       // x is +inf or nan
  59       return x + static_cast<float>(FPBits::inf());
  60     }
  61   }
  62
  63   // When |x| <= log10(2)*2^-6
  64   if (LIBC_UNLIKELY(x_abs <= 0x3b9a'209bU)) {
  65     if (LIBC_UNLIKELY(x_u == 0xb25e'5bd9U)) { // x = -0x1.bcb7b2p-27f
  66       if (fputil::get_round() == FE_TONEAREST)
  67         return 0x1.fffffep-1f;
  68     }
  69     // |x| < 2^-25
  70     // 10^x ~ 1 + log(10) * x
  71     if (LIBC_UNLIKELY(x_abs <= 0x3280'0000U)) {
  72       return fputil::multiply_add(x, 0x1.26bb1cp+1f, 1.0f);
  73     }
  74
  75     return static_cast<float>(Exp10Base::powb_lo(x));
  76   }
  77
  78   // Exceptional value.
  79   if (LIBC_UNLIKELY(x_u == 0x3d14'd956U)) { // x = 0x1.29b2acp-5f
  80     if (fputil::get_round() == FE_UPWARD)
  81       return 0x1.1657c4p+0f;
  82   }
  83
  84   // Exact outputs when x = 1, 2, ..., 10.
  85   // Quick check mask: 0x800f'ffffU = ~(bits of 1.0f | ... | bits of 10.0f)
  86   if (LIBC_UNLIKELY((x_u & 0x800f'ffffU) == 0)) {
  87     switch (x_u) {
  88     case 0x3f800000U: // x = 1.0f
  89       return 10.0f;
  90     case 0x40000000U: // x = 2.0f
  91       return 100.0f;
  92     case 0x40400000U: // x = 3.0f
  93       return 1'000.0f;
  94     case 0x40800000U: // x = 4.0f
  95       return 10'000.0f;
  96     case 0x40a00000U: // x = 5.0f
  97       return 100'000.0f;
  98     case 0x40c00000U: // x = 6.0f
  99       return 1'000'000.0f;
 100     case 0x40e00000U: // x = 7.0f
 101       return 10'000'000.0f;
 102     case 0x41000000U: // x = 8.0f
 103       return 100'000'000.0f;
 104     case 0x41100000U: // x = 9.0f
 105       return 1'000'000'000.0f;
 106     case 0x41200000U: // x = 10.0f
 107       return 10'000'000'000.0f;
 108     }
 109   }
 110
 111   // Range reduction: 10^x = 2^(mid + hi) * 10^lo
 112   //   rr = (2^(mid + hi), lo)
 113   auto rr = exp_b_range_reduc<Exp10Base>(x);
 114
 115   // The low part is approximated by a degree-5 minimax polynomial.
 116   // 10^lo ~ 1 + COEFFS[0] * lo + ... + COEFFS[4] * lo^5
 117   using fputil::multiply_add;
 118   double lo2 = rr.lo * rr.lo;
 119   // c0 = 1 + COEFFS[0] * lo
 120   double c0 = multiply_add(rr.lo, Exp10Base::COEFFS[0], 1.0);
 121   // c1 = COEFFS[1] + COEFFS[2] * lo
 122   double c1 = multiply_add(rr.lo, Exp10Base::COEFFS[2], Exp10Base::COEFFS[1]);
 123   // c2 = COEFFS[3] + COEFFS[4] * lo
 124   double c2 = multiply_add(rr.lo, Exp10Base::COEFFS[4], Exp10Base::COEFFS[3]);
 125   // p = c1 + c2 * lo^2
 126   //   = COEFFS[1] + COEFFS[2] * lo + COEFFS[3] * lo^2 + COEFFS[4] * lo^3
 127   double p = multiply_add(lo2, c2, c1);
 128   // 10^lo ~ c0 + p * lo^2
 129   // 10^x = 2^(mid + hi) * 10^lo
 130   //      ~ mh * (c0 + p * lo^2)
 131   //      = (mh * c0) + p * (mh * lo^2)
 132   return static_cast<float>(multiply_add(p, lo2 * rr.mh, c0 * rr.mh));
 133 }
 134
 135 } // namespace __llvm_libc