[libc][math][c23] Add sqrtf16 C23 math function

libc/config/gpu/entrypoints.txt

@@ -567,6 +567,8 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.llogbf16
     libc.src.math.llrintf16
     libc.src.math.llroundf16
+    libc.src.math.log10f16
+    libc.src.math.log2f16
     libc.src.math.logbf16
     libc.src.math.logf16
     libc.src.math.lrintf16
@@ -588,6 +590,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.setpayloadf16
     libc.src.math.setpayloadsigf16
     libc.src.math.sinhf16
+    libc.src.math.sqrtf16
     libc.src.math.tanhf16
     libc.src.math.totalorderf16
     libc.src.math.totalordermagf16

libc/config/linux/aarch64/entrypoints.txt

@@ -680,6 +680,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.setpayloadf16
     libc.src.math.setpayloadsigf16
     libc.src.math.sinpif16
+    libc.src.math.sqrtf16
     libc.src.math.totalorderf16
     libc.src.math.totalordermagf16
     libc.src.math.truncf16

libc/config/linux/x86_64/entrypoints.txt

@@ -660,6 +660,8 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.llogbf16
     libc.src.math.llrintf16
     libc.src.math.llroundf16
+    libc.src.math.log10f16
+    libc.src.math.log2f16
     libc.src.math.logbf16
     libc.src.math.logf16
     libc.src.math.lrintf16
@@ -682,6 +684,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
     libc.src.math.setpayloadsigf16
     libc.src.math.sinhf16
     libc.src.math.sinpif16
+    libc.src.math.sqrtf16
     libc.src.math.tanhf16
     libc.src.math.totalorderf16
     libc.src.math.totalordermagf16

libc/docs/math/index.rst

@@ -312,13 +312,13 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | log       | |check|          | |check|         |                        | |check|              |                        | 7.12.6.11              | F.10.3.11                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| log10     | |check|          | |check|         |                        |                      |                        | 7.12.6.12              | F.10.3.12                  |
+| log10     | |check|          | |check|         |                        | |check|              |                        | 7.12.6.12              | F.10.3.12                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | log10p1   |                  |                 |                        |                      |                        | 7.12.6.13              | F.10.3.13                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | log1p     | |check|          | |check|         |                        |                      |                        | 7.12.6.14              | F.10.3.14                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| log2      | |check|          | |check|         |                        |                      |                        | 7.12.6.15              | F.10.3.15                  |
+| log2      | |check|          | |check|         |                        | |check|              |                        | 7.12.6.15              | F.10.3.15                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | log2p1    |                  |                 |                        |                      |                        | 7.12.6.16              | F.10.3.16                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
@@ -344,7 +344,7 @@ Higher Math Functions
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | sinpi     | |check|          |                 |                        |  |check|             |                        | 7.12.4.13              | F.10.1.13                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
-| sqrt      | |check|          | |check|         | |check|                |                      | |check|                | 7.12.7.10              | F.10.4.10                  |
+| sqrt      | |check|          | |check|         | |check|                | |check|              | |check|                | 7.12.7.10              | F.10.4.10                  |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
 | tan       | |check|          | |check|         |                        |                      |                        | 7.12.4.7               | F.10.1.7                   |
 +-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+

libc/spec/stdc.td

@@ -642,12 +642,14 @@ def StdC : StandardSpec<"stdc"> {
 
           FunctionSpec<"log10", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"log10f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+          GuardedFunctionSpec<"log10f16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
 
           FunctionSpec<"log1p", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"log1pf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
 
           FunctionSpec<"log2", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"log2f", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
+          GuardedFunctionSpec<"log2f16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
 
           FunctionSpec<"log", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"logf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
@@ -752,6 +754,7 @@ def StdC : StandardSpec<"stdc"> {
           FunctionSpec<"sqrt", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,
           FunctionSpec<"sqrtf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
           FunctionSpec<"sqrtl", RetValSpec<LongDoubleType>, [ArgSpec<LongDoubleType>]>,
+          GuardedFunctionSpec<"sqrtf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,
           GuardedFunctionSpec<"sqrtf128", RetValSpec<Float128Type>, [ArgSpec<Float128Type>], "LIBC_TYPES_HAS_FLOAT128">,
 
           FunctionSpec<"trunc", RetValSpec<DoubleType>, [ArgSpec<DoubleType>]>,

libc/src/__support/FPUtil/generic/sqrt.h

@@ -139,7 +139,8 @@ sqrt(InType x) {
       for (InStorageType current_bit = ONE >> 1; current_bit;
            current_bit >>= 1) {
         r <<= 1;
-        InStorageType tmp = (y << 1) + current_bit; // 2*y(n - 1) + 2^(-n-1)
+        // 2*y(n - 1) + 2^(-n-1)
+        InStorageType tmp = static_cast<InStorageType>((y << 1) + current_bit);
         if (r >= tmp) {
           r -= tmp;
           y += current_bit;

libc/src/math/CMakeLists.txt

@@ -334,12 +334,14 @@ add_math_entrypoint_object(ldexpf128)
 
 add_math_entrypoint_object(log10)
 add_math_entrypoint_object(log10f)
+add_math_entrypoint_object(log10f16)
 
 add_math_entrypoint_object(log1p)
 add_math_entrypoint_object(log1pf)
 
 add_math_entrypoint_object(log2)
 add_math_entrypoint_object(log2f)
+add_math_entrypoint_object(log2f16)
 
 add_math_entrypoint_object(log)
 add_math_entrypoint_object(logf)
@@ -490,6 +492,7 @@ add_math_entrypoint_object(sinhf16)
 add_math_entrypoint_object(sqrt)
 add_math_entrypoint_object(sqrtf)
 add_math_entrypoint_object(sqrtl)
+add_math_entrypoint_object(sqrtf16)
 add_math_entrypoint_object(sqrtf128)
 
 add_math_entrypoint_object(tan)

libc/src/math/generic/CMakeLists.txt

@@ -2173,6 +2173,28 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  log10f16
+  SRCS
+    log10f16.cpp
+  HDRS
+    ../log10f16.h
+  DEPENDS
+    .expxf16
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.cpu_features
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   log1p
   SRCS
@@ -2250,6 +2272,28 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  log2f16
+  SRCS
+    log2f16.cpp
+  HDRS
+    ../log2f16.h
+  DEPENDS
+    .expxf16
+    libc.hdr.errno_macros
+    libc.hdr.fenv_macros
+    libc.src.__support.FPUtil.cast
+    libc.src.__support.FPUtil.except_value_utils
+    libc.src.__support.FPUtil.fenv_impl
+    libc.src.__support.FPUtil.fp_bits
+    libc.src.__support.FPUtil.multiply_add
+    libc.src.__support.FPUtil.polyeval
+    libc.src.__support.macros.optimization
+    libc.src.__support.macros.properties.cpu_features
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   log
   SRCS
@@ -3205,6 +3249,18 @@ add_entrypoint_object(
     -O3
 )
 
+add_entrypoint_object(
+  sqrtf16
+  SRCS
+    sqrtf16.cpp
+  HDRS
+    ../sqrtf16.h
+  DEPENDS
+    libc.src.__support.FPUtil.sqrt
+  COMPILE_OPTIONS
+    -O3
+)
+
 add_entrypoint_object(
   sqrtf128
   SRCS

libc/src/math/generic/expxf16.h

@@ -302,6 +302,34 @@ constexpr cpp::array<float, 32> LOGF_F = {
     0x1.41d8fep-1f, 0x1.4a4f86p-1f, 0x1.52a2d2p-1f, 0x1.5ad404p-1f,
 };
 
+// Generated by Sollya with the following commands:
+//   > display = hexadecimal;
+//   > for i from 0 to 31 do print(round(log2(1 + i * 2^-5), SG, RN));
+constexpr cpp::array<float, 32> LOG2F_F = {
+    0x0p+0f,        0x1.6bad38p-5f, 0x1.663f7p-4f,  0x1.08c588p-3f,
+    0x1.5c01a4p-3f, 0x1.acf5e2p-3f, 0x1.fbc16cp-3f, 0x1.24407ap-2f,
+    0x1.49a784p-2f, 0x1.6e221cp-2f, 0x1.91bba8p-2f, 0x1.b47ecp-2f,
+    0x1.d6753ep-2f, 0x1.f7a856p-2f, 0x1.0c105p-1f,  0x1.1bf312p-1f,
+    0x1.2b8034p-1f, 0x1.3abb4p-1f,  0x1.49a784p-1f, 0x1.584822p-1f,
+    0x1.66a008p-1f, 0x1.74b1fep-1f, 0x1.82809ep-1f, 0x1.900e62p-1f,
+    0x1.9d5dap-1f,  0x1.aa709p-1f,  0x1.b74948p-1f, 0x1.c3e9cap-1f,
+    0x1.d053f6p-1f, 0x1.dc899ap-1f, 0x1.e88c6cp-1f, 0x1.f45e08p-1f,
+};
+
+// Generated by Sollya with the following commands:
+//   > display = hexadecimal;
+//   > for i from 0 to 31 do print(round(log10(1 + i * 2^-5), SG, RN));
+constexpr cpp::array<float, 32> LOG10F_F = {
+    0x0p+0f,        0x1.b5e908p-7f, 0x1.af5f92p-6f, 0x1.3ed11ap-5f,
+    0x1.a30a9ep-5f, 0x1.02428cp-4f, 0x1.31b306p-4f, 0x1.5fe804p-4f,
+    0x1.8cf184p-4f, 0x1.b8de4ep-4f, 0x1.e3bc1ap-4f, 0x1.06cbd6p-3f,
+    0x1.1b3e72p-3f, 0x1.2f3b6ap-3f, 0x1.42c7e8p-3f, 0x1.55e8c6p-3f,
+    0x1.68a288p-3f, 0x1.7af974p-3f, 0x1.8cf184p-3f, 0x1.9e8e7cp-3f,
+    0x1.afd3e4p-3f, 0x1.c0c514p-3f, 0x1.d1653p-3f,  0x1.e1b734p-3f,
+    0x1.f1bdeep-3f, 0x1.00be06p-2f, 0x1.087a08p-2f, 0x1.101432p-2f,
+    0x1.178da6p-2f, 0x1.1ee778p-2f, 0x1.2622bp-2f,  0x1.2d404cp-2f,
+};
+
 // Generated by Sollya with the following commands:
 //   > display = hexadecimal;
 //   > for i from 0 to 31 do print(round(1 / (1 + i * 2^-5), SG, RN));

libc/src/math/generic/log10f16.cpp

@@ -0,0 +1,164 @@
+//===-- Half-precision log10(x) function ----------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "src/math/log10f16.h"
+#include "expxf16.h"
+#include "hdr/errno_macros.h"
+#include "hdr/fenv_macros.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/except_value_utils.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/common.h"
+#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/macros/properties/cpu_features.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+static constexpr size_t N_LOG10F16_EXCEPTS = 11;
+#else
+static constexpr size_t N_LOG10F16_EXCEPTS = 17;
+#endif
+
+static constexpr fputil::ExceptValues<float16, N_LOG10F16_EXCEPTS>
+    LOG10F16_EXCEPTS = {{
+        // (input, RZ output, RU offset, RD offset, RN offset)
+        // x = 0x1.e3cp-3, log10f16(x) = -0x1.40cp-1 (RZ)
+        {0x338fU, 0xb903U, 0U, 1U, 0U},
+        // x = 0x1.fep-3, log10f16(x) = -0x1.35p-1 (RZ)
+        {0x33f8U, 0xb8d4U, 0U, 1U, 1U},
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        // x = 0x1.394p-1, log10f16(x) = -0x1.b4cp-3 (RZ)
+        {0x38e5U, 0xb2d3U, 0U, 1U, 1U},
+#endif
+        // x = 0x1.ea8p-1, log10f16(x) = -0x1.31p-6 (RZ)
+        {0x3baaU, 0xa4c4U, 0U, 1U, 1U},
+        // x = 0x1.ebp-1, log10f16(x) = -0x1.29cp-6 (RZ)
+        {0x3bacU, 0xa4a7U, 0U, 1U, 1U},
+        // x = 0x1.f3p-1, log10f16(x) = -0x1.6dcp-7 (RZ)
+        {0x3bccU, 0xa1b7U, 0U, 1U, 1U},
+// x = 0x1.f38p-1, log10f16(x) = -0x1.5f8p-7 (RZ)
+#ifndef LIBC_TARGET_CPU_HAS_FMA
+        {0x3bceU, 0xa17eU, 0U, 1U, 1U},
+        // x = 0x1.fd8p-1, log10f16(x) = -0x1.168p-9 (RZ)
+        {0x3bf6U, 0x985aU, 0U, 1U, 1U},
+        // x = 0x1.ff8p-1, log10f16(x) = -0x1.bccp-12 (RZ)
+        {0x3bfeU, 0x8ef3U, 0U, 1U, 1U},
+        // x = 0x1.374p+0, log10f16(x) = 0x1.5b8p-4 (RZ)
+        {0x3cddU, 0x2d6eU, 1U, 0U, 1U},
+        // x = 0x1.3ecp+1, log10f16(x) = 0x1.958p-2 (RZ)
+        {0x40fbU, 0x3656U, 1U, 0U, 1U},
+#endif
+        // x = 0x1.4p+3, log10f16(x) = 0x1p+0 (RZ)
+        {0x4900U, 0x3c00U, 0U, 0U, 0U},
+        // x = 0x1.9p+6, log10f16(x) = 0x1p+1 (RZ)
+        {0x5640U, 0x4000U, 0U, 0U, 0U},
+        // x = 0x1.f84p+6, log10f16(x) = 0x1.0ccp+1 (RZ)
+        {0x57e1U, 0x4033U, 1U, 0U, 0U},
+        // x = 0x1.f4p+9, log10f16(x) = 0x1.8p+1 (RZ)
+        {0x63d0U, 0x4200U, 0U, 0U, 0U},
+        // x = 0x1.388p+13, log10f16(x) = 0x1p+2 (RZ)
+        {0x70e2U, 0x4400U, 0U, 0U, 0U},
+        // x = 0x1.674p+13, log10f16(x) = 0x1.03cp+2 (RZ)
+        {0x719dU, 0x440fU, 1U, 0U, 0U},
+    }};
+
+LLVM_LIBC_FUNCTION(float16, log10f16, (float16 x)) {
+  using FPBits = fputil::FPBits<float16>;
+  FPBits x_bits(x);
+
+  uint16_t x_u = x_bits.uintval();
+
+  // If x <= 0, or x is 1, or x is +inf, or x is NaN.
+  if (LIBC_UNLIKELY(x_u == 0U || x_u == 0x3c00U || x_u >= 0x7c00U)) {
+    // log10(NaN) = NaN
+    if (x_bits.is_nan()) {
+      if (x_bits.is_signaling_nan()) {
+        fputil::raise_except_if_required(FE_INVALID);
+        return FPBits::quiet_nan().get_val();
+      }
+
+      return x;
+    }
+
+    // log10(+/-0) = −inf
+    if ((x_u & 0x7fffU) == 0U) {
+      fputil::raise_except_if_required(FE_DIVBYZERO);
+      return FPBits::inf(Sign::NEG).get_val();
+    }
+
+    if (x_u == 0x3c00U)
+      return FPBits::zero().get_val();
+
+    // When x < 0.
+    if (x_u > 0x8000U) {
+      fputil::set_errno_if_required(EDOM);
+      fputil::raise_except_if_required(FE_INVALID);
+      return FPBits::quiet_nan().get_val();
+    }
+
+    // log10(+inf) = +inf
+    return FPBits::inf().get_val();
+  }
+
+  if (auto r = LOG10F16_EXCEPTS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
+    return r.value();
+
+  // To compute log10(x), we perform the following range reduction:
+  //   x = 2^m * 1.mant,
+  //   log10(x) = m * log10(2) + log10(1.mant).
+  // To compute log10(1.mant), let f be the highest 6 bits including the hidden
+  // bit, and d be the difference (1.mant - f), i.e., the remaining 5 bits of
+  // the mantissa, then:
+  //   log10(1.mant) = log10(f) + log10(1.mant / f)
+  //                 = log10(f) + log10(1 + d/f)
+  // since d/f is sufficiently small.
+  // We store log10(f) and 1/f in the lookup tables LOG10F_F and ONE_OVER_F_F
+  // respectively.
+
+  int m = -FPBits::EXP_BIAS;
+
+  // When x is subnormal, normalize it.
+  if ((x_u & FPBits::EXP_MASK) == 0U) {
+    // Can't pass an integer to fputil::cast directly.
+    constexpr float NORMALIZE_EXP = 1U << FPBits::FRACTION_LEN;
+    x_bits = FPBits(x_bits.get_val() * fputil::cast<float16>(NORMALIZE_EXP));
+    x_u = x_bits.uintval();
+    m -= FPBits::FRACTION_LEN;
+  }
+
+  uint16_t mant = x_bits.get_mantissa();
+  // Leading 10 - 5 = 5 bits of the mantissa.
+  int f = mant >> 5;
+  // Unbiased exponent.
+  m += x_u >> FPBits::FRACTION_LEN;
+
+  // Set bits to 1.mant instead of 2^m * 1.mant.
+  x_bits.set_biased_exponent(FPBits::EXP_BIAS);
+  float mant_f = x_bits.get_val();
+  // v = 1.mant * 1/f - 1 = d/f
+  float v = fputil::multiply_add(mant_f, ONE_OVER_F_F[f], -1.0f);
+
+  // Degree-3 minimax polynomial generated by Sollya with the following
+  // commands:
+  //   > display = hexadecimal;
+  //   > P = fpminimax(log10(1 + x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
+  //   > x * P;
+  float log10p1_d_over_f =
+      v * fputil::polyeval(v, 0x1.bcb7bp-2f, -0x1.bce168p-3f, 0x1.28acb8p-3f);
+  // log10(1.mant) = log10(f) + log10(1 + d/f)
+  float log10_1_mant = LOG10F_F[f] + log10p1_d_over_f;
+  return fputil::cast<float16>(
+      fputil::multiply_add(static_cast<float>(m), LOG10F_2, log10_1_mant));
+}
+
+} // namespace LIBC_NAMESPACE_DECL