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