Skip to content

Commit

Permalink
[libc][math][c23] Add sinhf16 and coshf16 C23 math functions
Browse files Browse the repository at this point in the history
Part of #95250.
  • Loading branch information
overmighty committed Oct 15, 2024
1 parent e21264e commit f016204
Show file tree
Hide file tree
Showing 17 changed files with 756 additions and 2 deletions.
2 changes: 2 additions & 0 deletions libc/config/gpu/entrypoints.txt
Original file line number Diff line number Diff line change
Expand Up @@ -521,6 +521,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
libc.src.math.coshf16
libc.src.math.exp10f16
libc.src.math.exp10m1f16
libc.src.math.exp2f16
Expand Down Expand Up @@ -585,6 +586,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.scalbnf16
libc.src.math.setpayloadf16
libc.src.math.setpayloadsigf16
libc.src.math.sinhf16
libc.src.math.totalorderf16
libc.src.math.totalordermagf16
libc.src.math.truncf16
Expand Down
2 changes: 2 additions & 0 deletions libc/config/linux/x86_64/entrypoints.txt
Original file line number Diff line number Diff line change
Expand Up @@ -610,6 +610,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.canonicalizef16
libc.src.math.ceilf16
libc.src.math.copysignf16
libc.src.math.coshf16
libc.src.math.exp10f16
libc.src.math.exp10m1f16
libc.src.math.exp2f16
Expand Down Expand Up @@ -678,6 +679,7 @@ if(LIBC_TYPES_HAS_FLOAT16)
libc.src.math.scalbnf16
libc.src.math.setpayloadf16
libc.src.math.setpayloadsigf16
libc.src.math.sinhf16
libc.src.math.totalorderf16
libc.src.math.totalordermagf16
libc.src.math.truncf16
Expand Down
4 changes: 2 additions & 2 deletions libc/docs/math/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -278,7 +278,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cos | |check| | |check| | | | | 7.12.4.5 | F.10.1.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cosh | |check| | | | | | 7.12.5.4 | F.10.2.4 |
| cosh | |check| | | | |check| | | 7.12.5.4 | F.10.2.4 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| cospi | |check| | | | | | 7.12.4.12 | F.10.1.12 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
Expand Down Expand Up @@ -340,7 +340,7 @@ Higher Math Functions
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sincos | |check| | |check| | | | | | |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sinh | |check| | | | | | 7.12.5.5 | F.10.2.5 |
| sinh | |check| | | | |check| | | 7.12.5.5 | F.10.2.5 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
| sinpi | |check| | | | | | 7.12.4.13 | F.10.1.13 |
+-----------+------------------+-----------------+------------------------+----------------------+------------------------+------------------------+----------------------------+
Expand Down
4 changes: 4 additions & 0 deletions libc/spec/stdc.td
Original file line number Diff line number Diff line change
Expand Up @@ -792,7 +792,11 @@ def StdC : StandardSpec<"stdc"> {
FunctionSpec<"pow", RetValSpec<DoubleType>, [ArgSpec<DoubleType>, ArgSpec<DoubleType>]>,

FunctionSpec<"coshf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
GuardedFunctionSpec<"coshf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,

FunctionSpec<"sinhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
GuardedFunctionSpec<"sinhf16", RetValSpec<Float16Type>, [ArgSpec<Float16Type>], "LIBC_TYPES_HAS_FLOAT16">,

FunctionSpec<"tanhf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,

FunctionSpec<"acosf", RetValSpec<FloatType>, [ArgSpec<FloatType>]>,
Expand Down
4 changes: 4 additions & 0 deletions libc/src/math/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -89,8 +89,11 @@ add_math_entrypoint_object(copysignf128)

add_math_entrypoint_object(cos)
add_math_entrypoint_object(cosf)

add_math_entrypoint_object(cosh)
add_math_entrypoint_object(coshf)
add_math_entrypoint_object(coshf16)

add_math_entrypoint_object(cospif)

add_math_entrypoint_object(daddl)
Expand Down Expand Up @@ -480,6 +483,7 @@ add_math_entrypoint_object(sinpif)

add_math_entrypoint_object(sinh)
add_math_entrypoint_object(sinhf)
add_math_entrypoint_object(sinhf16)

add_math_entrypoint_object(sqrt)
add_math_entrypoint_object(sqrtf)
Expand Down
21 changes: 21 additions & 0 deletions libc/src/math/coshf16.h
Original file line number Diff line number Diff line change
@@ -0,0 +1,21 @@
//===-- Implementation header for coshf16 -----------------------*- C++ -*-===//
//
// 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
//
//===----------------------------------------------------------------------===//

#ifndef LLVM_LIBC_SRC_MATH_COSHF16_H
#define LLVM_LIBC_SRC_MATH_COSHF16_H

#include "src/__support/macros/config.h"
#include "src/__support/macros/properties/types.h"

namespace LIBC_NAMESPACE_DECL {

float16 coshf16(float16 x);

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC_MATH_COSHF16_H
38 changes: 38 additions & 0 deletions libc/src/math/generic/CMakeLists.txt
Original file line number Diff line number Diff line change
Expand Up @@ -4199,6 +4199,25 @@ add_entrypoint_object(
-O3
)

add_entrypoint_object(
coshf16
SRCS
coshf16.cpp
HDRS
../coshf16.h
DEPENDS
.expxf16
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
COMPILE_OPTIONS
-O3
)

add_entrypoint_object(
sinhf
SRCS
Expand All @@ -4214,6 +4233,25 @@ add_entrypoint_object(
-O3
)

add_entrypoint_object(
sinhf16
SRCS
sinhf16.cpp
HDRS
../sinhf16.h
DEPENDS
.expxf16
libc.hdr.errno_macros
libc.hdr.fenv_macros
libc.src.__support.FPUtil.except_value_utils
libc.src.__support.FPUtil.fenv_impl
libc.src.__support.FPUtil.fp_bits
libc.src.__support.FPUtil.rounding_mode
libc.src.__support.macros.optimization
COMPILE_OPTIONS
-O3
)

add_entrypoint_object(
tanhf
SRCS
Expand Down
103 changes: 103 additions & 0 deletions libc/src/math/generic/coshf16.cpp
Original file line number Diff line number Diff line change
@@ -0,0 +1,103 @@
//===-- Half-precision cosh(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/coshf16.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/except_value_utils.h"
#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
#include "src/__support/macros/config.h"
#include "src/__support/macros/optimization.h"

namespace LIBC_NAMESPACE_DECL {

static constexpr fputil::ExceptValues<float16, 9> COSHF16_EXCEPTS_POS = {{
// x = 0x1.6ap-5, coshf16(x) = 0x1p+0 (RZ)
{0x29a8U, 0x3c00U, 1U, 0U, 1U},
// x = 0x1.8c4p+0, coshf16(x) = 0x1.3a8p+1 (RZ)
{0x3e31U, 0x40eaU, 1U, 0U, 0U},
// x = 0x1.994p+0, coshf16(x) = 0x1.498p+1 (RZ)
{0x3e65U, 0x4126U, 1U, 0U, 0U},
// x = 0x1.b6p+0, coshf16(x) = 0x1.6d8p+1 (RZ)
{0x3ed8U, 0x41b6U, 1U, 0U, 1U},
// x = 0x1.aap+1, coshf16(x) = 0x1.be8p+3 (RZ)
{0x42a8U, 0x4afaU, 1U, 0U, 1U},
// x = 0x1.cc4p+1, coshf16(x) = 0x1.23cp+4 (RZ)
{0x4331U, 0x4c8fU, 1U, 0U, 0U},
// x = 0x1.288p+2, coshf16(x) = 0x1.9b4p+5 (RZ)
{0x44a2U, 0x526dU, 1U, 0U, 0U},
// x = 0x1.958p+2, coshf16(x) = 0x1.1a4p+8 (RZ)
{0x4656U, 0x5c69U, 1U, 0U, 0U},
// x = 0x1.5fp+3, coshf16(x) = 0x1.c54p+14 (RZ)
{0x497cU, 0x7715U, 1U, 0U, 1U},
}};

static constexpr fputil::ExceptValues<float16, 4> COSHF16_EXCEPTS_NEG = {{
// x = -0x1.6ap-5, coshf16(x) = 0x1p+0 (RZ)
{0xa9a8U, 0x3c00U, 1U, 0U, 1U},
// x = -0x1.b6p+0, coshf16(x) = 0x1.6d8p+1 (RZ)
{0xbed8U, 0x41b6U, 1U, 0U, 1U},
// x = -0x1.288p+2, coshf16(x) = 0x1.9b4p+5 (RZ)
{0xc4a2U, 0x526dU, 1U, 0U, 0U},
// x = -0x1.5fp+3, coshf16(x) = 0x1.c54p+14 (RZ)
{0xc97cU, 0x7715U, 1U, 0U, 1U},
}};

LLVM_LIBC_FUNCTION(float16, coshf16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits x_bits(x);

uint16_t x_u = x_bits.uintval();
uint16_t x_abs = x_u & 0x7fffU;

// When |x| >= acosh(2^16), or x is NaN.
if (LIBC_UNLIKELY(x_abs >= 0x49e5U)) {
// cosh(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;
}

// When |x| >= acosh(2^16).
if (x_abs >= 0x49e5U) {
// cosh(+/-inf) = +inf
if (x_bits.is_inf())
return FPBits::inf().get_val();

switch (fputil::quick_get_round()) {
case FE_TONEAREST:
case FE_UPWARD:
fputil::set_errno_if_required(ERANGE);
fputil::raise_except_if_required(FE_OVERFLOW | FE_INEXACT);
return FPBits::inf().get_val();
default:
return FPBits::max_normal().get_val();
}
}
}

if (x_bits.is_pos()) {
if (auto r = COSHF16_EXCEPTS_POS.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
} else {
if (auto r = COSHF16_EXCEPTS_NEG.lookup(x_u); LIBC_UNLIKELY(r.has_value()))
return r.value();
}

return eval_sinh_or_cosh</*IsSinh=*/false>(x);
}

} // namespace LIBC_NAMESPACE_DECL
113 changes: 113 additions & 0 deletions libc/src/math/generic/expxf16.h
Original file line number Diff line number Diff line change
Expand Up @@ -174,6 +174,119 @@ LIBC_INLINE ExpRangeReduction exp10_range_reduction(float16 x) {
return {exp2_hi_mid, exp10_lo};
}

// Generated by Sollya with the following commands:
// > display = hexadecimal;
// > round(log2(exp(1)), SG, RN);
static constexpr float LOG2F_E = 0x1.715476p+0f;

// Generated by Sollya with the following commands:
// > display = hexadecimal;
// > round(log(2), SG, RN);
static constexpr float LOGF_2 = 0x1.62e43p-1f;

// Generated by Sollya with the following commands:
// > display = hexadecimal;
// > for i from 0 to 31 do printsingle(round(2^(i * 2^-5), SG, RN));
static constexpr cpp::array<uint32_t, 32> EXP2_MID_5_BITS = {
0x3f80'0000U, 0x3f82'cd87U, 0x3f85'aac3U, 0x3f88'980fU, 0x3f8b'95c2U,
0x3f8e'a43aU, 0x3f91'c3d3U, 0x3f94'f4f0U, 0x3f98'37f0U, 0x3f9b'8d3aU,
0x3f9e'f532U, 0x3fa2'7043U, 0x3fa5'fed7U, 0x3fa9'a15bU, 0x3fad'583fU,
0x3fb1'23f6U, 0x3fb5'04f3U, 0x3fb8'fbafU, 0x3fbd'08a4U, 0x3fc1'2c4dU,
0x3fc5'672aU, 0x3fc9'b9beU, 0x3fce'248cU, 0x3fd2'a81eU, 0x3fd7'44fdU,
0x3fdb'fbb8U, 0x3fe0'ccdfU, 0x3fe5'b907U, 0x3fea'c0c7U, 0x3fef'e4baU,
0x3ff5'257dU, 0x3ffa'83b3U,
};

// This function correctly calculates sinh(x) and cosh(x) by calculating exp(x)
// and exp(-x) simultaneously.
// To compute e^x, we perform the following range reduction:
// find hi, mid, lo such that:
// x = (hi + mid) * log(2) + lo, in which
// hi is an integer,
// 0 <= mid * 2^5 < 32 is an integer
// -2^(-5) <= lo * log2(e) <= 2^-5.
// In particular,
// hi + mid = round(x * log2(e) * 2^5) * 2^(-5).
// Then,
// e^x = 2^(hi + mid) * e^lo = 2^hi * 2^mid * e^lo.
// We store 2^mid in the lookup table EXP2_MID_5_BITS, and compute 2^hi * 2^mid
// by adding hi to the exponent field of 2^mid.
// e^lo is computed using a degree-3 minimax polynomial generated by Sollya:
// e^lo ~ P(lo)
// = 1 + lo + c2 * lo^2 + ... + c5 * lo^5
// = (1 + c2*lo^2 + c4*lo^4) + lo * (1 + c3*lo^2 + c5*lo^4)
// = P_even + lo * P_odd
// To compute e^(-x), notice that:
// e^(-x) = 2^(-(hi + mid)) * e^(-lo)
// ~ 2^(-(hi + mid)) * P(-lo)
// = 2^(-(hi + mid)) * (P_even - lo * P_odd)
// So:
// sinh(x) = (e^x - e^(-x)) / 2
// ~ 0.5 * (2^(hi + mid) * (P_even + lo * P_odd) -
// 2^(-(hi + mid)) * (P_even - lo * P_odd))
// = 0.5 * (P_even * (2^(hi + mid) - 2^(-(hi + mid))) +
// lo * P_odd * (2^(hi + mid) + 2^(-(hi + mid))))
// And similarly:
// cosh(x) = (e^x + e^(-x)) / 2
// ~ 0.5 * (P_even * (2^(hi + mid) + 2^(-(hi + mid))) +
// lo * P_odd * (2^(hi + mid) - 2^(-(hi + mid))))
// The main point of these formulas is that the expensive part of calculating
// the polynomials approximating lower parts of e^x and e^(-x) is shared and
// only done once.
template <bool IsSinh> LIBC_INLINE float16 eval_sinh_or_cosh(float16 x) {
float xf = x;
float kf = fputil::nearest_integer(xf * (LOG2F_E * 0x1.0p+5f));
int x_hi_mid_p = static_cast<int>(kf);
int x_hi_mid_m = -x_hi_mid_p;

int x_hi_p = x_hi_mid_p >> 5;
int x_hi_m = x_hi_mid_m >> 5;
int x_mid_p = x_hi_mid_p & 0x1f;
int x_mid_m = x_hi_mid_m & 0x1f;

uint32_t exp2_hi_mid_bits_p =
EXP2_MID_5_BITS[x_mid_p] +
static_cast<uint32_t>(x_hi_p << fputil::FPBits<float>::FRACTION_LEN);
uint32_t exp2_hi_mid_bits_m =
EXP2_MID_5_BITS[x_mid_m] +
static_cast<uint32_t>(x_hi_m << fputil::FPBits<float>::FRACTION_LEN);
// exp2_hi_mid_p = 2^(hi + mid)
float exp2_hi_mid_p = fputil::FPBits<float>(exp2_hi_mid_bits_p).get_val();
// exp2_hi_mid_m = 2^(-(hi + mid))
float exp2_hi_mid_m = fputil::FPBits<float>(exp2_hi_mid_bits_m).get_val();

// exp2_hi_mid_sum = 2^(hi + mid) + 2^(-(hi + mid))
float exp2_hi_mid_sum = exp2_hi_mid_p + exp2_hi_mid_m;
// exp2_hi_mid_diff = 2^(hi + mid) - 2^(-(hi + mid))
float exp2_hi_mid_diff = exp2_hi_mid_p - exp2_hi_mid_m;

// lo = x - (hi + mid) = round(x * log2(e) * 2^5) * log(2) * (-2^(-5)) + x
float lo = fputil::multiply_add(kf, LOGF_2 * -0x1.0p-5f, xf);
float lo_sq = lo * lo;

// Degree-3 minimax polynomial generated by Sollya with the following
// commands:
// > display = hexadecimal;
// > P = fpminimax(expm1(x)/x, 2, [|SG...|], [-2^-5, 2^-5]);
// > 1 + x * P;
constexpr cpp::array<float, 4> COEFFS = {0x1p+0f, 0x1p+0f, 0x1.0004p-1f,
0x1.555778p-3f};
float half_p_odd =
fputil::polyeval(lo_sq, COEFFS[1] * 0.5f, COEFFS[3] * 0.5f);
float half_p_even =
fputil::polyeval(lo_sq, COEFFS[0] * 0.5f, COEFFS[2] * 0.5f);

// sinh(x) = lo * (0.5 * P_odd * (2^(hi + mid) + 2^(-(hi + mid)))) +
// (0.5 * P_even * (2^(hi + mid) - 2^(-(hi + mid))))
if constexpr (IsSinh)
return static_cast<float16>(fputil::multiply_add(
lo, half_p_odd * exp2_hi_mid_sum, half_p_even * exp2_hi_mid_diff));
// cosh(x) = lo * (0.5 * P_odd * (2^(hi + mid) - 2^(-(hi + mid)))) +
// (0.5 * P_even * (2^(hi + mid) + 2^(-(hi + mid))))
return static_cast<float16>(fputil::multiply_add(
lo, half_p_odd * exp2_hi_mid_diff, half_p_even * exp2_hi_mid_sum));
}

} // namespace LIBC_NAMESPACE_DECL

#endif // LLVM_LIBC_SRC_MATH_GENERIC_EXPXF16_H
Loading

0 comments on commit f016204

Please sign in to comment.