[libc-commits] [libc] 42f1837 - [libc] Change sinf/cosf range reduction to mod pi/32 to be shared with tanf.
Tue Ly via libc-commits
libc-commits at lists.llvm.org
Thu Aug 11 06:41:53 PDT 2022
Author: Tue Ly
Date: 2022-08-11T09:41:45-04:00
New Revision: 42f183792c8c418da7a34f1c700755dc65cafdfc
URL: https://github.com/llvm/llvm-project/commit/42f183792c8c418da7a34f1c700755dc65cafdfc
DIFF: https://github.com/llvm/llvm-project/commit/42f183792c8c418da7a34f1c700755dc65cafdfc.diff
LOG: [libc] Change sinf/cosf range reduction to mod pi/32 to be shared with tanf.
Change sinf/cosf range reduction to mod pi/32 to be shared with tanf,
since polynomial approximations for tanf on subintervals of length pi/16 do not
provide enough accuracy.
Reviewed By: orex
Differential Revision: https://reviews.llvm.org/D131652
Added:
Modified:
libc/docs/math.rst
libc/src/math/generic/cosf.cpp
libc/src/math/generic/range_reduction.h
libc/src/math/generic/range_reduction_fma.h
libc/src/math/generic/sincosf.cpp
libc/src/math/generic/sincosf_utils.h
libc/src/math/generic/sinf.cpp
Removed:
################################################################################
diff --git a/libc/docs/math.rst b/libc/docs/math.rst
index f3bab2633e621..cf04f6aadf213 100644
--- a/libc/docs/math.rst
+++ b/libc/docs/math.rst
@@ -200,7 +200,7 @@ Performance
| +-----------+-------------------+-----------+-------------------+ +------------+-------------------------+--------------+---------------+
| | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) | | CPU | OS | Compiler | Special flags |
+==============+===========+===================+===========+===================+=====================================+============+=========================+==============+===============+
-| cosf | 14 | 32 | 56 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+| cosf | 13 | 32 | 53 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
| coshf | 23 | 20 | 73 | 49 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
@@ -230,9 +230,9 @@ Performance
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
| log2f | 13 | 10 | 57 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| sinf | 13 | 25 | 54 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+| sinf | 12 | 25 | 51 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| sincosf | 20 | 30 | 62 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+| sincosf | 19 | 30 | 57 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
| sinhf | 23 | 64 | 73 | 141 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
diff --git a/libc/src/math/generic/cosf.cpp b/libc/src/math/generic/cosf.cpp
index e0824006582bc..58f499ff5afed 100644
--- a/libc/src/math/generic/cosf.cpp
+++ b/libc/src/math/generic/cosf.cpp
@@ -53,21 +53,21 @@ LLVM_LIBC_FUNCTION(float, cosf, (float x)) {
// Range reduction:
// For |x| > pi/16, we perform range reduction as follows:
// Find k and y such that:
- // x = (k + y) * pi/16
+ // x = (k + y) * pi/32
// k is an integer
// |y| < 0.5
- // For small range (|x| < 2^46 when FMA instructions are available, 2^22
+ // For small range (|x| < 2^45 when FMA instructions are available, 2^22
// otherwise), this is done by performing:
- // k = round(x * 16/pi)
- // y = x * 16/pi - k
+ // k = round(x * 32/pi)
+ // y = x * 32/pi - k
// For large range, we will omit all the higher parts of 16/pi such that the
- // least significant bits of their full products with x are larger than 31,
- // since cos((k + y + 32*i) * pi/16) = cos(x + i * 2pi) = cos(x).
+ // least significant bits of their full products with x are larger than 63,
+ // since cos((k + y + 64*i) * pi/32) = cos(x + i * 2pi) = cos(x).
//
- // When FMA instructions are not available, we store the digits of 16/pi in
+ // When FMA instructions are not available, we store the digits of 32/pi in
// chunks of 28-bit precision. This will make sure that the products:
- // x * SIXTEEN_OVER_PI_28[i] are all exact.
- // When FMA instructions are available, we simply store the digits of 16/pi in
+ // x * THIRTYTWO_OVER_PI_28[i] are all exact.
+ // When FMA instructions are available, we simply store the digits of 32/pi in
// chunks of doubles (53-bit of precision).
// So when multiplying by the largest values of single precision, the
// resulting output should be correct up to 2^(-208 + 128) ~ 2^-80. By the
@@ -80,11 +80,11 @@ LLVM_LIBC_FUNCTION(float, cosf, (float x)) {
//
// Once k and y are computed, we then deduce the answer by the cosine of sum
// formula:
- // cos(x) = cos((k + y)*pi/16)
- // = cos(y*pi/16) * cos(k*pi/16) - sin(y*pi/16) * sin(k*pi/16)
- // The values of sin(k*pi/16) and cos(k*pi/16) for k = 0..31 are precomputed
- // and stored using a vector of 32 doubles. Sin(y*pi/16) and cos(y*pi/16) are
- // computed using degree-7 and degree-8 minimax polynomials generated by
+ // cos(x) = cos((k + y)*pi/32)
+ // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
+ // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
+ // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
+ // computed using degree-7 and degree-6 minimax polynomials generated by
// Sollya respectively.
// |x| < 0x1.0p-12f
@@ -128,8 +128,8 @@ LLVM_LIBC_FUNCTION(float, cosf, (float x)) {
}
// Combine the results with the sine of sum formula:
- // cos(x) = cos((k + y)*pi/16)
- // = cos(y*pi/16) * cos(k*pi/16) - sin(y*pi/16) * sin(k*pi/16)
+ // cos(x) = cos((k + y)*pi/32)
+ // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
// = cosm1_y * cos_k + sin_y * sin_k
// = (cosm1_y * cos_k + cos_k) + sin_y * sin_k
double sin_k, cos_k, sin_y, cosm1_y;
diff --git a/libc/src/math/generic/range_reduction.h b/libc/src/math/generic/range_reduction.h
index d9b41d739ecfb..095226608ee79 100644
--- a/libc/src/math/generic/range_reduction.h
+++ b/libc/src/math/generic/range_reduction.h
@@ -10,7 +10,6 @@
#define LLVM_LIBC_SRC_MATH_GENERIC_RANGE_REDUCTION_H
#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/FPUtil/nearest_integer.h"
@@ -22,83 +21,66 @@ static constexpr uint32_t FAST_PASS_BOUND = 0x4a80'0000U; // 2^22
static constexpr int N_ENTRIES = 8;
-// We choose to split bits of 16/pi into 28-bit precision pieces, so that the
-// product of x * SIXTEEN_OVER_PI_28[i] is exact.
+// We choose to split bits of 32/pi into 28-bit precision pieces, so that the
+// product of x * THIRTYTWO_OVER_PI_28[i] is exact.
// These are generated by Sollya with:
-// > a1 = D(round(16/pi, 28, RN)); a1;
-// > a2 = D(round(16/pi - a1, 28, RN)); a2;
-// > a3 = D(round(16/pi - a1 - a2, 28, RN)); a3;
-// > a4 = D(round(16/pi - a1 - a2 - a3, 28, RN)); a4;
+// > a1 = D(round(32/pi, 28, RN)); a1;
+// > a2 = D(round(32/pi - a1, 28, RN)); a2;
+// > a3 = D(round(32/pi - a1 - a2, 28, RN)); a3;
+// > a4 = D(round(32/pi - a1 - a2 - a3, 28, RN)); a4;
// ...
-static constexpr double SIXTEEN_OVER_PI_28[N_ENTRIES] = {
- 0x1.45f306ep+2, -0x1.b1bbeaep-29, 0x1.3f84ebp-58, -0x1.7056592p-88,
- 0x1.c0db62ap-117, -0x1.4cd8778p-146, -0x1.bef806cp-175, 0x1.63abdecp-205};
+static constexpr double THIRTYTWO_OVER_PI_28[N_ENTRIES] = {
+ 0x1.45f306ep+3, -0x1.b1bbeaep-28, 0x1.3f84ebp-57, -0x1.7056592p-87,
+ 0x1.c0db62ap-116, -0x1.4cd8778p-145, -0x1.bef806cp-174, 0x1.63abdecp-204};
// Exponents of the least significant bits of the corresponding entries in
-// SIXTEEN_OVER_PI_28.
-static constexpr int SIXTEEN_OVER_PI_28_LSB_EXP[N_ENTRIES] = {
- -25, -56, -82, -115, -144, -171, -201, -231};
+// THIRTYTWO_OVER_PI_28.
+static constexpr int THIRTYTWO_OVER_PI_28_LSB_EXP[N_ENTRIES] = {
+ -24, -55, -81, -114, -143, -170, -200, -230};
// Return k and y, where
// k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
static inline int64_t small_range_reduction(double x, double &y) {
- double prod = x * SIXTEEN_OVER_PI_28[0];
+ double prod = x * THIRTYTWO_OVER_PI_28[0];
double kd = fputil::nearest_integer(prod);
y = prod - kd;
- y = fputil::multiply_add(x, SIXTEEN_OVER_PI_28[1], y);
- y = fputil::multiply_add(x, SIXTEEN_OVER_PI_28[2], y);
+ y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[1], y);
+ y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[2], y);
return static_cast<int64_t>(kd);
}
// Return k and y, where
-// k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
-// For large range, there are at most 2 parts of SIXTEEN_OVER_PI_28 contributing
-// to the lowest 5 binary digits (k & 31). If the least significant bit of
-// x * the least significant bit of SIXTEEN_OVER_PI_28[i] >= 32, we can
-// completely ignore SIXTEEN_OVER_PI_28[i].
+// k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
+// For large range, there are at most 2 parts of THIRTYTWO_OVER_PI_28
+// contributing to the lowest 6 binary digits (k & 63). If the least
+// significant bit of x * the least significant bit of THIRTYTWO_OVER_PI_28[i]
+// >= 64, we can completely ignore THIRTYTWO_OVER_PI_28[i].
static inline int64_t large_range_reduction(double x, int x_exp, double &y) {
int idx = 0;
y = 0;
int x_lsb_exp_m4 = x_exp - fputil::FloatProperties<float>::MANTISSA_WIDTH;
- // Skipping the first parts of 16/pi such that:
- // LSB of x * LSB of SIXTEEN_OVER_PI_28[i] >= 32.
- while (x_lsb_exp_m4 + SIXTEEN_OVER_PI_28_LSB_EXP[idx] > 4)
+ // Skipping the first parts of 32/pi such that:
+ // LSB of x * LSB of THIRTYTWO_OVER_PI_28[i] >= 32.
+ while (x_lsb_exp_m4 + THIRTYTWO_OVER_PI_28_LSB_EXP[idx] > 5)
++idx;
- double prod_hi = x * SIXTEEN_OVER_PI_28[idx];
- // Get the integral part of x * SIXTEEN_OVER_PI_28[idx]
+ double prod_hi = x * THIRTYTWO_OVER_PI_28[idx];
+ // Get the integral part of x * THIRTYTWO_OVER_PI_28[idx]
double k_hi = fputil::nearest_integer(prod_hi);
- // Get the fractional part of x * SIXTEEN_OVER_PI_28[idx]
+ // Get the fractional part of x * THIRTYTWO_OVER_PI_28[idx]
double frac = prod_hi - k_hi;
- double prod_lo = fputil::multiply_add(x, SIXTEEN_OVER_PI_28[idx + 1], frac);
+ double prod_lo = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 1], frac);
double k_lo = fputil::nearest_integer(prod_lo);
// Now y is the fractional parts.
y = prod_lo - k_lo;
- y = fputil::multiply_add(x, SIXTEEN_OVER_PI_28[idx + 2], y);
- y = fputil::multiply_add(x, SIXTEEN_OVER_PI_28[idx + 3], y);
+ y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 2], y);
+ y = fputil::multiply_add(x, THIRTYTWO_OVER_PI_28[idx + 3], y);
return static_cast<int64_t>(k_hi) + static_cast<int64_t>(k_lo);
}
-// Exceptional cases.
-static constexpr int N_EXCEPTS = 3;
-
-static constexpr fputil::ExceptionalValues<float, N_EXCEPTS> SinfExcepts{
- /* inputs */ {
- 0x3fa7832a, // x = 0x1.4f0654p0
- 0x46199998, // x = 0x1.33333p13
- 0x55cafb2a, // x = 0x1.95f654p44
- },
- /* outputs (RZ, RU offset, RD offset, RN offset) */
- {
- {0x3f7741b5, 1, 0, 1}, // x = 0x1.4f0654p0, sin(x) = 0x1.ee836ap-1 (RZ)
- {0xbeb1fa5d, 0, 1, 0}, // x = 0x1.33333p13, sin(x) = -0x1.63f4bap-2 (RZ)
- {0xbf7e7a16, 0, 1,
- 1}, // x = 0x1.95f654p44, sin(x) = -0x1.fcf42cp-1 (RZ)
- }};
-
} // namespace generic
} // namespace __llvm_libc
diff --git a/libc/src/math/generic/range_reduction_fma.h b/libc/src/math/generic/range_reduction_fma.h
index 2cb56fec116c5..102c1d7a59254 100644
--- a/libc/src/math/generic/range_reduction_fma.h
+++ b/libc/src/math/generic/range_reduction_fma.h
@@ -11,92 +11,76 @@
#include "src/__support/FPUtil/FMA.h"
#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/nearest_integer.h"
namespace __llvm_libc {
namespace fma {
-static constexpr uint32_t FAST_PASS_BOUND = 0x5680'0000U; // 2^46
+static constexpr uint32_t FAST_PASS_BOUND = 0x5600'0000U; // 2^45
-// Digits of 1/pi, generated by Sollya with:
-// > a0 = D(16/pi);
-// > a1 = D(16/pi - a0);
-// > a2 = D(16/pi - a0 - a1);
-// > a3 = D(16/pi - a0 - a1 - a2);
-static constexpr double SIXTEEN_OVER_PI[5] = {
- 0x1.45f306dc9c883p+2, -0x1.6b01ec5417056p-52, -0x1.6447e493ad4cep-106,
- 0x1.e21c820ff28b2p-160, -0x1.508510ea79237p-215};
+// Digits of 32/pi, generated by Sollya with:
+// > a0 = D(32/pi);
+// > a1 = D(32/pi - a0);
+// > a2 = D(32/pi - a0 - a1);
+// > a3 = D(32/pi - a0 - a1 - a2);
+static constexpr double THIRTYTWO_OVER_PI[5] = {
+ 0x1.45f306dc9c883p+3, -0x1.6b01ec5417056p-51, -0x1.6447e493ad4cep-105,
+ 0x1.e21c820ff28b2p-159, -0x1.508510ea79237p-214};
// Return k and y, where
-// k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
-// Assume x is non-negative.
+// k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
static inline int64_t small_range_reduction(double x, double &y) {
- double kd = fputil::nearest_integer(x * SIXTEEN_OVER_PI[0]);
- y = fputil::fma(x, SIXTEEN_OVER_PI[0], -kd);
- y = fputil::fma(x, SIXTEEN_OVER_PI[1], y);
+ double kd = fputil::nearest_integer(x * THIRTYTWO_OVER_PI[0]);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[0], -kd);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[1], y);
return static_cast<int64_t>(kd);
}
// Return k and y, where
-// k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
+// k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
+// This is used for sinf, cosf, sincosf.
static inline int64_t large_range_reduction(double x, int x_exp, double &y) {
- // 2^46 <= |x| < 2^99
+ // 2^45 <= |x| < 2^99
if (x_exp < 99) {
- // - When x < 2^99, the full exact product of x * SIXTEEN_OVER_PI[0]
- // contains at least one integral bit <= 2^4.
- // - When 2^46 <= |x| < 2^56, the lowest 5 unit bits are contained
- // in the last 10 bits of double(x * SIXTEEN_OVER_PI[0]).
- // - When |x| >= 2^56, the LSB of double(x * SIXTEEN_OVER_PI[0]) is at least
- // 32.
- fputil::FPBits<double> prod_hi(x * SIXTEEN_OVER_PI[0]);
- prod_hi.bits &= (x_exp < 56) ? (~0xfffULL) : (~0ULL); // |x| < 2^56
+ // - When x < 2^99, the full exact product of x * THIRTYTWO_OVER_PI[0]
+ // contains at least one integral bit <= 2^5.
+ // - When 2^45 <= |x| < 2^55, the lowest 6 unit bits are contained
+ // in the last 12 bits of double(x * THIRTYTWO_OVER_PI[0]).
+ // - When |x| >= 2^55, the LSB of double(x * THIRTYTWO_OVER_PI[0]) is at
+ // least 2^6.
+ fputil::FPBits<double> prod_hi(x * THIRTYTWO_OVER_PI[0]);
+ prod_hi.bits &= (x_exp < 55) ? (~0xfffULL) : (~0ULL); // |x| < 2^55
double k_hi = fputil::nearest_integer(static_cast<double>(prod_hi));
- double truncated_prod = fputil::fma(x, SIXTEEN_OVER_PI[0], -k_hi);
- double prod_lo = fputil::fma(x, SIXTEEN_OVER_PI[1], truncated_prod);
+ double truncated_prod = fputil::fma(x, THIRTYTWO_OVER_PI[0], -k_hi);
+ double prod_lo = fputil::fma(x, THIRTYTWO_OVER_PI[1], truncated_prod);
double k_lo = fputil::nearest_integer(prod_lo);
- y = fputil::fma(x, SIXTEEN_OVER_PI[1], truncated_prod - k_lo);
- y = fputil::fma(x, SIXTEEN_OVER_PI[2], y);
- y = fputil::fma(x, SIXTEEN_OVER_PI[3], y);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[1], truncated_prod - k_lo);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[2], y);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[3], y);
return static_cast<int64_t>(k_lo);
}
- // - When x >= 2^110, the full exact product of x * SIXTEEN_OVER_PI[0] does
- // not contain any of the lowest 5 unit bits, so we can ignore it completely.
- // - When 2^99 <= |x| < 2^110, the lowest 5 unit bits are contained
- // in the last 12 bits of double(x * SIXTEEN_OVER_PI[1]).
- // - When |x| >= 2^110, the LSB of double(x * SIXTEEN_OVER_PI[1]) is at
- // least 32.
- fputil::FPBits<double> prod_hi(x * SIXTEEN_OVER_PI[1]);
+ // - When x >= 2^110, the full exact product of x * THIRTYTWO_OVER_PI[0] does
+ // not contain any of the lowest 6 unit bits, so we can ignore it completely.
+ // - When 2^99 <= |x| < 2^110, the lowest 6 unit bits are contained
+ // in the last 12 bits of double(x * THIRTYTWO_OVER_PI[1]).
+ // - When |x| >= 2^110, the LSB of double(x * THIRTYTWO_OVER_PI[1]) is at
+ // least 64.
+ fputil::FPBits<double> prod_hi(x * THIRTYTWO_OVER_PI[1]);
prod_hi.bits &= (x_exp < 110) ? (~0xfffULL) : (~0ULL); // |x| < 2^110
double k_hi = fputil::nearest_integer(static_cast<double>(prod_hi));
- double truncated_prod = fputil::fma(x, SIXTEEN_OVER_PI[1], -k_hi);
- double prod_lo = fputil::fma(x, SIXTEEN_OVER_PI[2], truncated_prod);
+ double truncated_prod = fputil::fma(x, THIRTYTWO_OVER_PI[1], -k_hi);
+ double prod_lo = fputil::fma(x, THIRTYTWO_OVER_PI[2], truncated_prod);
double k_lo = fputil::nearest_integer(prod_lo);
- y = fputil::fma(x, SIXTEEN_OVER_PI[2], truncated_prod - k_lo);
- y = fputil::fma(x, SIXTEEN_OVER_PI[3], y);
- y = fputil::fma(x, SIXTEEN_OVER_PI[4], y);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[2], truncated_prod - k_lo);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[3], y);
+ y = fputil::fma(x, THIRTYTWO_OVER_PI[4], y);
return static_cast<int64_t>(k_lo);
}
-// Exceptional cases.
-static constexpr int N_EXCEPTS = 2;
-
-static constexpr fputil::ExceptionalValues<float, N_EXCEPTS> SinfExcepts{
- /* inputs */ {
- 0x3fa7832a, // x = 0x1.4f0654p0
- 0x55cafb2a, // x = 0x1.95f654p44
- },
- /* outputs (RZ, RU offset, RD offset, RN offset) */
- {
- {0x3f7741b5, 1, 0, 1}, // x = 0x1.4f0654p0, sin(x) = 0x1.ee836ap-1 (RZ)
- {0xbf7e7a16, 0, 1,
- 1}, // x = 0x1.95f654p44, sin(x) = -0x1.fcf42cp-1 (RZ)
- }};
-
} // namespace fma
} // namespace __llvm_libc
diff --git a/libc/src/math/generic/sincosf.cpp b/libc/src/math/generic/sincosf.cpp
index 3a1149f01bec6..25a59bd915e95 100644
--- a/libc/src/math/generic/sincosf.cpp
+++ b/libc/src/math/generic/sincosf.cpp
@@ -18,51 +18,35 @@
namespace __llvm_libc {
// Exceptional values
-static constexpr int N_EXCEPTS = 10;
+static constexpr int N_EXCEPTS = 6;
static constexpr uint32_t EXCEPT_INPUTS[N_EXCEPTS] = {
- 0x3b5637f5, // x = 0x1.ac6feap-9
- 0x3fa7832a, // x = 0x1.4f0654p0
- 0x46199998, // x = 0x1.33333p13
- 0x55325019, // x = 0x1.64a032p43
- 0x55cafb2a, // x = 0x1.95f654p44
- 0x5922aa80, // x = 0x1.4555p51
- 0x5aa4542c, // x = 0x1.48a858p54
- 0x5f18b878, // x = 0x1.3170fp63
- 0x6115cb11, // x = 0x1.2b9622p67
- 0x7beef5ef, // x = 0x1.ddebdep120
+ 0x46199998, // x = 0x1.33333p13 x
+ 0x55325019, // x = 0x1.64a032p43 x
+ 0x5922aa80, // x = 0x1.4555p51 x
+ 0x5f18b878, // x = 0x1.3170fp63 x
+ 0x6115cb11, // x = 0x1.2b9622p67 x
+ 0x7beef5ef, // x = 0x1.ddebdep120 x
};
static constexpr uint32_t EXCEPT_OUTPUTS_SIN[N_EXCEPTS][4] = {
- {0x3b5637dc, 1, 0, 0}, // x = 0x1.ac6feap-9, sin(x) = 0x1.ac6fb8p-9 (RZ)
- {0x3f7741b5, 1, 0, 1}, // x = 0x1.4f0654p0, sin(x) = 0x1.ee836ap-1 (RZ)
{0xbeb1fa5d, 0, 1, 0}, // x = 0x1.33333p13, sin(x) = -0x1.63f4bap-2 (RZ)
{0xbf171adf, 0, 1, 1}, // x = 0x1.64a032p43, sin(x) = -0x1.2e35bep-1 (RZ)
- {0xbf7e7a16, 0, 1, 1}, // x = 0x1.95f654p44, sin(x) = -0x1.fcf42cp-1 (RZ)
{0xbf587521, 0, 1, 1}, // x = 0x1.4555p51, sin(x) = -0x1.b0ea42p-1 (RZ)
- {0x3f5f5646, 1, 0, 0}, // x = 0x1.48a858p54, sin(x) = 0x1.beac8cp-1 (RZ)
{0x3dad60f6, 1, 0, 1}, // x = 0x1.3170fp63, sin(x) = 0x1.5ac1ecp-4 (RZ)
{0xbe7cc1e0, 0, 1, 1}, // x = 0x1.2b9622p67, sin(x) = -0x1.f983cp-3 (RZ)
{0xbf587d1b, 0, 1, 1}, // x = 0x1.ddebdep120, sin(x) = -0x1.b0fa36p-1 (RZ)
};
static constexpr uint32_t EXCEPT_OUTPUTS_COS[N_EXCEPTS][4] = {
- {0x3f7fffa6, 1, 0, 0}, // x = 0x1.ac6feap-9, cos(x) = 0x1.ffff4cp-1 (RZ)
- {0x3e84aabf, 1, 0, 1}, // x = 0x1.4f0654p0, cos(x) = 0x1.09557ep-2 (RZ)
{0xbf70090b, 0, 1, 0}, // x = 0x1.33333p13, cos(x) = -0x1.e01216p-1 (RZ)
{0x3f4ea5d2, 1, 0, 0}, // x = 0x1.64a032p43, cos(x) = 0x1.9d4ba4p-1 (RZ)
- {0x3ddf11f3, 1, 0, 1}, // x = 0x1.95f654p44, cos(x) = 0x1.be23e6p-4 (RZ)
{0x3f08aebe, 1, 0, 1}, // x = 0x1.4555p51, cos(x) = 0x1.115d7cp-1 (RZ)
- {0x3efa40a4, 1, 0, 0}, // x = 0x1.48a858p54, cos(x) = 0x1.f48148p-2 (RZ)
{0x3f7f14bb, 1, 0, 0}, // x = 0x1.3170fp63, cos(x) = 0x1.fe2976p-1 (RZ)
{0x3f78142e, 1, 0, 1}, // x = 0x1.2b9622p67, cos(x) = 0x1.f0285cp-1 (RZ)
{0x3f08a21c, 1, 0, 0}, // x = 0x1.ddebdep120, cos(x) = 0x1.114438p-1 (RZ)
};
-// Fast sincosf implementation. Worst-case ULP is 0.5607, maximum relative
-// error is 0.5303 * 2^-23. A single-step range reduction is used for
-// small values. Large inputs have their range reduced using fast integer
-// arithmetic.
LLVM_LIBC_FUNCTION(void, sincosf, (float x, float *sinp, float *cosp)) {
using FPBits = typename fputil::FPBits<float>;
FPBits xbits(x);
@@ -71,25 +55,25 @@ LLVM_LIBC_FUNCTION(void, sincosf, (float x, float *sinp, float *cosp)) {
double xd = static_cast<double>(x);
// Range reduction:
- // For |x| > pi/16, we perform range reduction as follows:
+ // For |x| >= 2^-12, we perform range reduction as follows:
// Find k and y such that:
- // x = (k + y) * pi/16
+ // x = (k + y) * pi/32
// k is an integer
// |y| < 0.5
- // For small range (|x| < 2^46 when FMA instructions are available, 2^22
+ // For small range (|x| < 2^45 when FMA instructions are available, 2^22
// otherwise), this is done by performing:
- // k = round(x * 16/pi)
- // y = x * 16/pi - k
- // For large range, we will omit all the higher parts of 16/pi such that the
- // least significant bits of their full products with x are larger than 31,
+ // k = round(x * 32/pi)
+ // y = x * 32/pi - k
+ // For large range, we will omit all the higher parts of 32/pi such that the
+ // least significant bits of their full products with x are larger than 63,
// since:
- // sin((k + y + 32*i) * pi/16) = sin(x + i * 2pi) = sin(x), and
- // cos((k + y + 32*i) * pi/16) = cos(x + i * 2pi) = cos(x).
+ // sin((k + y + 64*i) * pi/32) = sin(x + i * 2pi) = sin(x), and
+ // cos((k + y + 64*i) * pi/32) = cos(x + i * 2pi) = cos(x).
//
- // When FMA instructions are not available, we store the digits of 16/pi in
+ // When FMA instructions are not available, we store the digits of 32/pi in
// chunks of 28-bit precision. This will make sure that the products:
- // x * SIXTEEN_OVER_PI_28[i] are all exact.
- // When FMA instructions are available, we simply store the digits of 16/pi in
+ // x * THIRTYTWO_OVER_PI_28[i] are all exact.
+ // When FMA instructions are available, we simply store the digits of326/pi in
// chunks of doubles (53-bit of precision).
// So when multiplying by the largest values of single precision, the
// resulting output should be correct up to 2^(-208 + 128) ~ 2^-80. By the
@@ -102,13 +86,13 @@ LLVM_LIBC_FUNCTION(void, sincosf, (float x, float *sinp, float *cosp)) {
//
// Once k and y are computed, we then deduce the answer by the sine and cosine
// of sum formulas:
- // sin(x) = sin((k + y)*pi/16)
- // = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)
- // cos(x) = cos((k + y)*pi/16)
- // = cos(y*pi/16) * cos(k*pi/16) - sin(y*pi/16) * sin(k*pi/16)
- // The values of sin(k*pi/16) and cos(k*pi/16) for k = 0..31 are precomputed
- // and stored using a vector of 32 doubles. Sin(y*pi/16) and cos(y*pi/16) are
- // computed using degree-7 and degree-8 minimax polynomials generated by
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
+ // cos(x) = cos((k + y)*pi/32)
+ // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
+ // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..63 are precomputed
+ // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
+ // computed using degree-7 and degree-6 minimax polynomials generated by
// Sollya respectively.
// |x| < 0x1.0p-12f
@@ -195,12 +179,12 @@ LLVM_LIBC_FUNCTION(void, sincosf, (float x, float *sinp, float *cosp)) {
}
// Combine the results with the sine and cosine of sum formulas:
- // sin(x) = sin((k + y)*pi/16)
- // = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
// = sin_y * cos_k + (1 + cosm1_y) * sin_k
// = sin_y * cos_k + (cosm1_y * sin_k + sin_k)
- // cos(x) = cos((k + y)*pi/16)
- // = cos(y*pi/16) * cos(k*pi/16) - sin(y*pi/16) * sin(k*pi/16)
+ // cos(x) = cos((k + y)*pi/32)
+ // = cos(y*pi/32) * cos(k*pi/32) - sin(y*pi/32) * sin(k*pi/32)
// = cosm1_y * cos_k + sin_y * sin_k
// = (cosm1_y * cos_k + cos_k) + sin_y * sin_k
double sin_k, cos_k, sin_y, cosm1_y;
diff --git a/libc/src/math/generic/sincosf_utils.h b/libc/src/math/generic/sincosf_utils.h
index 06064c8fdb7c1..ebb248749f573 100644
--- a/libc/src/math/generic/sincosf_utils.h
+++ b/libc/src/math/generic/sincosf_utils.h
@@ -29,22 +29,34 @@ using __llvm_libc::generic::small_range_reduction;
namespace __llvm_libc {
-// Lookup table for sin(k * pi / 16) with k = 0, ..., 31.
+// Lookup table for sin(k * pi / 32) with k = 0, ..., 63.
// Table is generated with Sollya as follow:
// > display = hexadecimal;
-// > for k from 0 to 31 do { D(sin(k * pi/16)); };
-const double SIN_K_PI_OVER_16[32] = {
- 0x0.0000000000000p+0, 0x1.8f8b83c69a60bp-3, 0x1.87de2a6aea963p-2,
- 0x1.1c73b39ae68c8p-1, 0x1.6a09e667f3bcdp-1, 0x1.a9b66290ea1a3p-1,
- 0x1.d906bcf328d46p-1, 0x1.f6297cff75cb0p-1, 0x1.0000000000000p+0,
- 0x1.f6297cff75cb0p-1, 0x1.d906bcf328d46p-1, 0x1.a9b66290ea1a3p-1,
- 0x1.6a09e667f3bcdp-1, 0x1.1c73b39ae68c8p-1, 0x1.87de2a6aea963p-2,
- 0x1.8f8b83c69a60bp-3, 0x0.0000000000000p+0, -0x1.8f8b83c69a60bp-3,
- -0x1.87de2a6aea963p-2, -0x1.1c73b39ae68c8p-1, -0x1.6a09e667f3bcdp-1,
- -0x1.a9b66290ea1a3p-1, -0x1.d906bcf328d46p-1, -0x1.f6297cff75cb0p-1,
- -0x1.0000000000000p+0, -0x1.f6297cff75cb0p-1, -0x1.d906bcf328d46p-1,
- -0x1.a9b66290ea1a3p-1, -0x1.6a09e667f3bcdp-1, -0x1.1c73b39ae68c8p-1,
- -0x1.87de2a6aea963p-2, -0x1.8f8b83c69a60bp-3};
+// > for k from 0 to 63 do { D(sin(k * pi/32)); };
+const double SIN_K_PI_OVER_32[64] = {
+ 0x0.0000000000000p+0, 0x1.917a6bc29b42cp-4, 0x1.8f8b83c69a60bp-3,
+ 0x1.294062ed59f06p-2, 0x1.87de2a6aea963p-2, 0x1.e2b5d3806f63bp-2,
+ 0x1.1c73b39ae68c8p-1, 0x1.44cf325091dd6p-1, 0x1.6a09e667f3bcdp-1,
+ 0x1.8bc806b151741p-1, 0x1.a9b66290ea1a3p-1, 0x1.c38b2f180bdb1p-1,
+ 0x1.d906bcf328d46p-1, 0x1.e9f4156c62ddap-1, 0x1.f6297cff75cbp-1,
+ 0x1.fd88da3d12526p-1, 0x1.0000000000000p+0, 0x1.fd88da3d12526p-1,
+ 0x1.f6297cff75cbp-1, 0x1.e9f4156c62ddap-1, 0x1.d906bcf328d46p-1,
+ 0x1.c38b2f180bdb1p-1, 0x1.a9b66290ea1a3p-1, 0x1.8bc806b151741p-1,
+ 0x1.6a09e667f3bcdp-1, 0x1.44cf325091dd6p-1, 0x1.1c73b39ae68c8p-1,
+ 0x1.e2b5d3806f63bp-2, 0x1.87de2a6aea963p-2, 0x1.294062ed59f06p-2,
+ 0x1.8f8b83c69a60bp-3, 0x1.917a6bc29b42cp-4, 0x0.0000000000000p+0,
+ -0x1.917a6bc29b42cp-4, -0x1.8f8b83c69a60bp-3, -0x1.294062ed59f06p-2,
+ -0x1.87de2a6aea963p-2, -0x1.e2b5d3806f63bp-2, -0x1.1c73b39ae68c8p-1,
+ -0x1.44cf325091dd6p-1, -0x1.6a09e667f3bcdp-1, -0x1.8bc806b151741p-1,
+ -0x1.a9b66290ea1a3p-1, -0x1.c38b2f180bdb1p-1, -0x1.d906bcf328d46p-1,
+ -0x1.e9f4156c62ddap-1, -0x1.f6297cff75cbp-1, -0x1.fd88da3d12526p-1,
+ -0x1.0000000000000p+0, -0x1.fd88da3d12526p-1, -0x1.f6297cff75cbp-1,
+ -0x1.e9f4156c62ddap-1, -0x1.d906bcf328d46p-1, -0x1.c38b2f180bdb1p-1,
+ -0x1.a9b66290ea1a3p-1, -0x1.8bc806b151741p-1, -0x1.6a09e667f3bcdp-1,
+ -0x1.44cf325091dd6p-1, -0x1.1c73b39ae68c8p-1, -0x1.e2b5d3806f63bp-2,
+ -0x1.87de2a6aea963p-2, -0x1.294062ed59f06p-2, -0x1.8f8b83c69a60bp-3,
+ -0x1.917a6bc29b42cp-4,
+};
static inline void sincosf_eval(double xd, uint32_t x_abs, double &sin_k,
double &cos_k, double &sin_y, double &cosm1_y) {
@@ -58,29 +70,29 @@ static inline void sincosf_eval(double xd, uint32_t x_abs, double &sin_k,
k = large_range_reduction(xd, x_bits.get_exponent(), y);
}
- // After range reduction, k = round(x * 16 / pi) and y = (x * 16 / pi) - k.
+ // After range reduction, k = round(x * 32 / pi) and y = (x * 32 / pi) - k.
// So k is an integer and -0.5 <= y <= 0.5.
- // Then sin(x) = sin((k + y)*pi/16)
- // = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)
+ // Then sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
- sin_k = SIN_K_PI_OVER_16[k & 31];
- // cos(k * pi/16) = sin(k * pi/16 + pi/2) = sin((k + 8) * pi/16).
- // cos_k = y * cos(k * pi/16)
- cos_k = SIN_K_PI_OVER_16[(k + 8) & 31];
+ sin_k = SIN_K_PI_OVER_32[k & 63];
+ // cos(k * pi/32) = sin(k * pi/32 + pi/2) = sin((k + 16) * pi/32).
+ // cos_k = cos(k * pi/32)
+ cos_k = SIN_K_PI_OVER_32[(k + 16) & 63];
double ysq = y * y;
- // Degree-6 minimax even polynomial for sin(y*pi/16)/y generated by Sollya
+ // Degree-6 minimax even polynomial for sin(y*pi/32)/y generated by Sollya
// with:
- // > Q = fpminimax(sin(y*pi/16)/y, [|0, 2, 4, 6|], [|D...|], [0, 0.5]);
- sin_y = y * fputil::polyeval(ysq, 0x1.921fb54442d17p-3, -0x1.4abbce6256adp-10,
- 0x1.466bc5a5ac6b3p-19, -0x1.32bdcb4207562p-29);
- // Degree-8 minimax even polynomial for cos(y*pi/16) generated by Sollya with:
- // > P = fpminimax(cos(x*pi/16), [|0, 2, 4, 6, 8|], [|1, D...|], [0, 0.5]);
- // Note that cosm1_y = cos(y*pi/16) - 1.
- cosm1_y =
- ysq * fputil::polyeval(ysq, -0x1.3bd3cc9be45dcp-6, 0x1.03c1f081b08ap-14,
- -0x1.55d3c6fb0fb6ep-24, 0x1.e1d3d60f58873p-35);
+ // > Q = fpminimax(sin(y*pi/32)/y, [|0, 2, 4, 6|], [|D...|], [0, 0.5]);
+ sin_y =
+ y * fputil::polyeval(ysq, 0x1.921fb54442d18p-4, -0x1.4abbce625abb1p-13,
+ 0x1.466bc624f2776p-24, -0x1.32c3a619d4a7ep-36);
+ // Degree-8 minimax even polynomial for cos(y*pi/32) generated by Sollya with:
+ // > P = fpminimax(cos(x*pi/32), [|0, 2, 4, 6|], [|1, D...|], [0, 0.5]);
+ // Note that cosm1_y = cos(y*pi/32) - 1.
+ cosm1_y = ysq * fputil::polyeval(ysq, -0x1.3bd3cc9be430bp-8,
+ 0x1.03c1f070c2e27p-18, -0x1.55cc84bd942p-30);
}
} // namespace __llvm_libc
diff --git a/libc/src/math/generic/sinf.cpp b/libc/src/math/generic/sinf.cpp
index bc725ea4dd5d4..cae25a74381b5 100644
--- a/libc/src/math/generic/sinf.cpp
+++ b/libc/src/math/generic/sinf.cpp
@@ -12,7 +12,6 @@
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/common.h"
@@ -20,14 +19,8 @@
#if defined(LIBC_TARGET_HAS_FMA)
#include "range_reduction_fma.h"
-// using namespace __llvm_libc::fma;
-using __llvm_libc::fma::N_EXCEPTS;
-using __llvm_libc::fma::SinfExcepts;
#else
#include "range_reduction.h"
-// using namespace __llvm_libc::generic;
-using __llvm_libc::generic::N_EXCEPTS;
-using __llvm_libc::generic::SinfExcepts;
#endif
namespace __llvm_libc {
@@ -41,23 +34,23 @@ LLVM_LIBC_FUNCTION(float, sinf, (float x)) {
double xd = static_cast<double>(x);
// Range reduction:
- // For |x| > pi/16, we perform range reduction as follows:
+ // For |x| > pi/32, we perform range reduction as follows:
// Find k and y such that:
- // x = (k + y) * pi/16
+ // x = (k + y) * pi/32
// k is an integer
// |y| < 0.5
- // For small range (|x| < 2^46 when FMA instructions are available, 2^22
+ // For small range (|x| < 2^45 when FMA instructions are available, 2^22
// otherwise), this is done by performing:
- // k = round(x * 16/pi)
- // y = x * 16/pi - k
- // For large range, we will omit all the higher parts of 16/pi such that the
- // least significant bits of their full products with x are larger than 31,
- // since sin((k + y + 32*i) * pi/16) = sin(x + i * 2pi) = sin(x).
+ // k = round(x * 32/pi)
+ // y = x * 32/pi - k
+ // For large range, we will omit all the higher parts of 32/pi such that the
+ // least significant bits of their full products with x are larger than 63,
+ // since sin((k + y + 64*i) * pi/32) = sin(x + i * 2pi) = sin(x).
//
- // When FMA instructions are not available, we store the digits of 16/pi in
+ // When FMA instructions are not available, we store the digits of 32/pi in
// chunks of 28-bit precision. This will make sure that the products:
- // x * SIXTEEN_OVER_PI_28[i] are all exact.
- // When FMA instructions are available, we simply store the digits of 16/pi in
+ // x * THIRTYTWO_OVER_PI_28[i] are all exact.
+ // When FMA instructions are available, we simply store the digits of 32/pi in
// chunks of doubles (53-bit of precision).
// So when multiplying by the largest values of single precision, the
// resulting output should be correct up to 2^(-208 + 128) ~ 2^-80. By the
@@ -70,11 +63,11 @@ LLVM_LIBC_FUNCTION(float, sinf, (float x)) {
//
// Once k and y are computed, we then deduce the answer by the sine of sum
// formula:
- // sin(x) = sin((k + y)*pi/16)
- // = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)
- // The values of sin(k*pi/16) and cos(k*pi/16) for k = 0..31 are precomputed
- // and stored using a vector of 32 doubles. Sin(y*pi/16) and cos(y*pi/16) are
- // computed using degree-7 and degree-8 minimax polynomials generated by
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
+ // The values of sin(k*pi/32) and cos(k*pi/32) for k = 0..31 are precomputed
+ // and stored using a vector of 32 doubles. Sin(y*pi/32) and cos(y*pi/32) are
+ // computed using degree-7 and degree-6 minimax polynomials generated by
// Sollya respectively.
// |x| <= pi/16
@@ -129,12 +122,13 @@ LLVM_LIBC_FUNCTION(float, sinf, (float x)) {
return xd * result;
}
- using ExceptChecker = typename fputil::ExceptionChecker<float, N_EXCEPTS>;
- {
- float result;
- if (ExceptChecker::check_odd_func(SinfExcepts, x_abs, xbits.get_sign(),
- result))
- return result;
+ if (unlikely(x_abs == 0x4619'9998U)) { // x = 0x1.33333p13
+ float r = -0x1.63f4bap-2f;
+ int rounding = fputil::get_round();
+ bool sign = xbits.get_sign();
+ if ((rounding == FE_DOWNWARD && !sign) || (rounding == FE_UPWARD && sign))
+ r = -0x1.63f4bcp-2f;
+ return xbits.get_sign() ? -r : r;
}
if (unlikely(x_abs >= 0x7f80'0000U)) {
@@ -147,8 +141,8 @@ LLVM_LIBC_FUNCTION(float, sinf, (float x)) {
}
// Combine the results with the sine of sum formula:
- // sin(x) = sin((k + y)*pi/16)
- // = sin(y*pi/16) * cos(k*pi/16) + cos(y*pi/16) * sin(k*pi/16)
+ // sin(x) = sin((k + y)*pi/32)
+ // = sin(y*pi/32) * cos(k*pi/32) + cos(y*pi/32) * sin(k*pi/32)
// = sin_y * cos_k + (1 + cosm1_y) * sin_k
// = sin_y * cos_k + (cosm1_y * sin_k + sin_k)
double sin_k, cos_k, sin_y, cosm1_y;
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