Message ID | 1513143801-3290-2-git-send-email-raji@linux.vnet.ibm.com |
---|---|

State | Superseded |

Delegated to: | Joseph Myers |

Headers |

## Commit Message

## Comments

diff --git a/sysdeps/ieee754/flt-32/s_cosf.c b/sysdeps/ieee754/flt-32/s_cosf.c index ac6d044449..d19397faca 100644 --- a/sysdeps/ieee754/flt-32/s_cosf.c +++ b/sysdeps/ieee754/flt-32/s_cosf.c @@ -20,6 +20,7 @@ #include <math.h> #include <math_private.h> #include <libm-alias-float.h> +#include "s_sincos.h" #ifndef COSF # define COSF_FUNC __cosf @@ -27,95 +28,6 @@ # define COSF_FUNC COSF #endif -/* Chebyshev constants for cos, range -PI/4 - PI/4. */ -static const double C0 = -0x1.ffffffffe98aep-2; -static const double C1 = 0x1.55555545c50c7p-5; -static const double C2 = -0x1.6c16b348b6874p-10; -static const double C3 = 0x1.a00eb9ac43ccp-16; -static const double C4 = -0x1.23c97dd8844d7p-22; - -/* Chebyshev constants for sin, range -PI/4 - PI/4. */ -static const double S0 = -0x1.5555555551cd9p-3; -static const double S1 = 0x1.1111110c2688bp-7; -static const double S2 = -0x1.a019f8b4bd1f9p-13; -static const double S3 = 0x1.71d7264e6b5b4p-19; -static const double S4 = -0x1.a947e1674b58ap-26; - -/* Chebyshev constants for cos, range 2^-27 - 2^-5. */ -static const double CC0 = -0x1.fffffff5cc6fdp-2; -static const double CC1 = 0x1.55514b178dac5p-5; - -/* PI/2 with 98 bits of accuracy. */ -static const double PI_2_hi = 0x1.921fb544p+0; -static const double PI_2_lo = 0x1.0b4611a626332p-34; - -static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */ - -#define FLOAT_EXPONENT_SHIFT 23 -#define FLOAT_EXPONENT_BIAS 127 - -static const double pio2_table[] = { - 0 * M_PI_2, - 1 * M_PI_2, - 2 * M_PI_2, - 3 * M_PI_2, - 4 * M_PI_2, - 5 * M_PI_2 -}; - -static const double invpio4_table[] = { - 0x0p+0, - 0x1.45f306cp+0, - 0x1.c9c882ap-28, - 0x1.4fe13a8p-58, - 0x1.f47d4dp-85, - 0x1.bb81b6cp-112, - 0x1.4acc9ep-142, - 0x1.0e4107cp-169 -}; - -static const double ones[] = { 1.0, -1.0 }; - -/* Compute the cosine value using Chebyshev polynomials where - THETA is the range reduced absolute value of the input - and it is less than Pi/4, - N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide - whether a sine or cosine approximation is more accurate and - the sign of the result. */ -static inline float -reduced (double theta, unsigned int n) -{ - double sign, cx; - const double theta2 = theta * theta; - - /* Determine positive or negative primary interval. */ - n += 2; - sign = ones[(n >> 2) & 1]; - - /* Are we in the primary interval of sin or cos? */ - if ((n & 2) == 0) - { - /* Here cosf() is calculated using sin Chebyshev polynomial: - x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */ - cx = S3 + theta2 * S4; - cx = S2 + theta2 * cx; - cx = S1 + theta2 * cx; - cx = S0 + theta2 * cx; - cx = theta + theta * theta2 * cx; - } - else - { - /* Here cosf() is calculated using cos Chebyshev polynomial: - 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */ - cx = C3 + theta2 * C4; - cx = C2 + theta2 * cx; - cx = C1 + theta2 * cx; - cx = C0 + theta2 * cx; - cx = 1. + theta2 * cx; - } - return sign * cx; -} - float COSF_FUNC (float x) { @@ -161,7 +73,7 @@ COSF_FUNC (float x) pio2_table must go to 5 (9 / 2 + 1). */ unsigned int n = (abstheta * inv_PI_4) + 1; theta = abstheta - pio2_table[n / 2]; - return reduced (theta, n); + return reduced_cos (theta, n); } else if (isless (abstheta, INFINITY)) { @@ -171,7 +83,7 @@ COSF_FUNC (float x) double x = n / 2; theta = (abstheta - x * PI_2_hi) - x * PI_2_lo; /* Argument reduction needed. */ - return reduced (theta, n); + return reduced_cos (theta, n); } else /* |theta| >= 2^23. */ { @@ -199,7 +111,7 @@ COSF_FUNC (float x) e += c; e += d; e *= M_PI_4; - return reduced (e, l + 1); + return reduced_cos (e, l + 1); } else { @@ -209,14 +121,14 @@ COSF_FUNC (float x) if (e <= 1.0) { e *= M_PI_4; - return reduced (e, l + 1); + return reduced_cos (e, l + 1); } else { l++; e -= 2.0; e *= M_PI_4; - return reduced (e, l + 1); + return reduced_cos (e, l + 1); } } } diff --git a/sysdeps/ieee754/flt-32/s_sincos.h b/sysdeps/ieee754/flt-32/s_sincos.h new file mode 100644 index 0000000000..b0110fc2af --- /dev/null +++ b/sysdeps/ieee754/flt-32/s_sincos.h @@ -0,0 +1,155 @@ +/* Used by sinf, cosf and sincosf functions. + Copyright (C) 2017 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +/* Chebyshev constants for cos, range -PI/4 - PI/4. */ +static const double C0 = -0x1.ffffffffe98aep-2; +static const double C1 = 0x1.55555545c50c7p-5; +static const double C2 = -0x1.6c16b348b6874p-10; +static const double C3 = 0x1.a00eb9ac43ccp-16; +static const double C4 = -0x1.23c97dd8844d7p-22; + +/* Chebyshev constants for sin, range -PI/4 - PI/4. */ +static const double S0 = -0x1.5555555551cd9p-3; +static const double S1 = 0x1.1111110c2688bp-7; +static const double S2 = -0x1.a019f8b4bd1f9p-13; +static const double S3 = 0x1.71d7264e6b5b4p-19; +static const double S4 = -0x1.a947e1674b58ap-26; + +/* Chebyshev constants for sin, range 2^-27 - 2^-5. */ +static const double SS0 = -0x1.555555543d49dp-3; +static const double SS1 = 0x1.110f475cec8c5p-7; + +/* Chebyshev constants for cos, range 2^-27 - 2^-5. */ +static const double CC0 = -0x1.fffffff5cc6fdp-2; +static const double CC1 = 0x1.55514b178dac5p-5; + +/* PI/2 with 98 bits of accuracy. */ +static const double PI_2_hi = 0x1.921fb544p+0; +static const double PI_2_lo = 0x1.0b4611a626332p-34; + +static const double SMALL = 0x1p-50; /* 2^-50. */ +static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */ + +#define FLOAT_EXPONENT_SHIFT 23 +#define FLOAT_EXPONENT_BIAS 127 + +static const double pio2_table[] = { + 0 * M_PI_2, + 1 * M_PI_2, + 2 * M_PI_2, + 3 * M_PI_2, + 4 * M_PI_2, + 5 * M_PI_2 +}; + +static const double invpio4_table[] = { + 0x0p+0, + 0x1.45f306cp+0, + 0x1.c9c882ap-28, + 0x1.4fe13a8p-58, + 0x1.f47d4dp-85, + 0x1.bb81b6cp-112, + 0x1.4acc9ep-142, + 0x1.0e4107cp-169 +}; + +static const double ones[] = { 1.0, -1.0 }; + +/* Compute the sine value using Chebyshev polynomials where + THETA is the range reduced absolute value of the input + and it is less than Pi/4, + N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide + whether a sine or cosine approximation is more accurate and + SIGNBIT is used to add the correct sign after the Chebyshev + polynomial is computed. */ +static inline float +reduced_sin (const double theta, const unsigned int n, + const unsigned int signbit) +{ + double sx; + const double theta2 = theta * theta; + /* We are operating on |x|, so we need to add back the original + signbit for sinf. */ + double sign; + /* Determine positive or negative primary interval. */ + sign = ones[((n >> 2) & 1) ^ signbit]; + /* Are we in the primary interval of sin or cos? */ + if ((n & 2) == 0) + { + /* Here sinf() is calculated using sin Chebyshev polynomial: + x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */ + sx = S3 + theta2 * S4; /* S3+x^2*S4. */ + sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */ + sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */ + sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */ + sx = theta + theta * theta2 * sx; + } + else + { + /* Here sinf() is calculated using cos Chebyshev polynomial: + 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */ + sx = C3 + theta2 * C4; /* C3+x^2*C4. */ + sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */ + sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */ + sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */ + sx = 1.0 + theta2 * sx; + } + + /* Add in the signbit and assign the result. */ + return sign * sx; +} + +/* Compute the cosine value using Chebyshev polynomials where + THETA is the range reduced absolute value of the input + and it is less than Pi/4, + N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide + whether a sine or cosine approximation is more accurate and + the sign of the result. */ +static inline float +reduced_cos (double theta, unsigned int n) +{ + double sign, cx; + const double theta2 = theta * theta; + + /* Determine positive or negative primary interval. */ + n += 2; + sign = ones[(n >> 2) & 1]; + + /* Are we in the primary interval of sin or cos? */ + if ((n & 2) == 0) + { + /* Here cosf() is calculated using sin Chebyshev polynomial: + x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */ + cx = S3 + theta2 * S4; + cx = S2 + theta2 * cx; + cx = S1 + theta2 * cx; + cx = S0 + theta2 * cx; + cx = theta + theta * theta2 * cx; + } + else + { + /* Here cosf() is calculated using cos Chebyshev polynomial: + 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */ + cx = C3 + theta2 * C4; + cx = C2 + theta2 * cx; + cx = C1 + theta2 * cx; + cx = C0 + theta2 * cx; + cx = 1. + theta2 * cx; + } + return sign * cx; +} diff --git a/sysdeps/ieee754/flt-32/s_sincosf.c b/sysdeps/ieee754/flt-32/s_sincosf.c index 4946a6eb54..b9f775d45b 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.c +++ b/sysdeps/ieee754/flt-32/s_sincosf.c @@ -1,7 +1,6 @@ /* Compute sine and cosine of argument. - Copyright (C) 1997-2017 Free Software Foundation, Inc. + Copyright (C) 2017 Free Software Foundation, Inc. This file is part of the GNU C Library. - Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. The GNU C Library is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public @@ -19,9 +18,9 @@ #include <errno.h> #include <math.h> - #include <math_private.h> #include <libm-alias-float.h> +#include "s_sincos.h" #ifndef SINCOSF # define SINCOSF_FUNC __sincosf @@ -32,50 +31,137 @@ void SINCOSF_FUNC (float x, float *sinx, float *cosx) { - int32_t ix; - - /* High word of x. */ - GET_FLOAT_WORD (ix, x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if (ix <= 0x3f490fd8) - { - *sinx = __kernel_sinf (x, 0.0, 0); - *cosx = __kernel_cosf (x, 0.0); - } - else if (ix>=0x7f800000) + double cx; + double theta = x; + double abstheta = fabs (theta); + /* If |x|< Pi/4. */ + if (isless (abstheta, M_PI_4)) { - /* sin(Inf or NaN) is NaN */ - *sinx = *cosx = x - x; - if (ix == 0x7f800000) - __set_errno (EDOM); + if (abstheta >= 0x1p-5) /* |x| >= 2^-5. */ + { + const double theta2 = theta * theta; + /* Chebyshev polynomial of the form for sin and cos. */ + cx = C3 + theta2 * C4; + cx = C2 + theta2 * cx; + cx = C1 + theta2 * cx; + cx = C0 + theta2 * cx; + cx = 1.0 + theta2 * cx; + *cosx = cx; + cx = S3 + theta2 * S4; + cx = S2 + theta2 * cx; + cx = S1 + theta2 * cx; + cx = S0 + theta2 * cx; + cx = theta + theta * theta2 * cx; + *sinx = cx; + } + else if (abstheta >= 0x1p-27) /* |x| >= 2^-27. */ + { + /* A simpler Chebyshev approximation is close enough for this range: + for sin: x+x^3*(SS0+x^2*SS1) + for cos: 1.0+x^2*(CC0+x^3*CC1). */ + const double theta2 = theta * theta; + cx = CC0 + theta * theta2 * CC1; + cx = 1.0 + theta2 * cx; + *cosx = cx; + cx = SS0 + theta2 * SS1; + cx = theta + theta * theta2 * cx; + *sinx = cx; + } + else + { + /* Handle some special cases. */ + if (theta) + *sinx = theta - (theta * SMALL); + else + *sinx = theta; + *cosx = 1.0 - abstheta; + } } - else + else /* |x| >= Pi/4. */ { - /* Argument reduction needed. */ - float y[2]; - int n; - - n = __ieee754_rem_pio2f (x, y); - switch (n & 3) + unsigned int signbit = isless (x, 0); + if (isless (abstheta, 9 * M_PI_4)) /* |x| < 9*Pi/4. */ + { + /* There are cases where FE_UPWARD rounding mode can + produce a result of abstheta * inv_PI_4 == 9, + where abstheta < 9pi/4, so the domain for + pio2_table must go to 5 (9 / 2 + 1). */ + unsigned int n = (abstheta * inv_PI_4) + 1; + theta = abstheta - pio2_table[n / 2]; + *sinx = reduced_sin (theta, n, signbit); + *cosx = reduced_cos (theta, n); + } + else if (isless (abstheta, INFINITY)) + { + if (abstheta < 0x1p+23) /* |x| < 2^23. */ + { + unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1; + double x = n / 2; + theta = (abstheta - x * PI_2_hi) - x * PI_2_lo; + /* Argument reduction needed. */ + *sinx = reduced_sin (theta, n, signbit); + *cosx = reduced_cos (theta, n); + } + else /* |x| >= 2^23. */ + { + x = fabsf (x); + int exponent; + GET_FLOAT_WORD (exponent, x); + exponent + = (exponent >> FLOAT_EXPONENT_SHIFT) - FLOAT_EXPONENT_BIAS; + exponent += 3; + exponent /= 28; + double a = invpio4_table[exponent] * x; + double b = invpio4_table[exponent + 1] * x; + double c = invpio4_table[exponent + 2] * x; + double d = invpio4_table[exponent + 3] * x; + uint64_t l = a; + l &= ~0x7; + a -= l; + double e = a + b; + l = e; + e = a - l; + if (l & 1) + { + e -= 1.0; + e += b; + e += c; + e += d; + e *= M_PI_4; + *sinx = reduced_sin (e, l + 1, signbit); + *cosx = reduced_cos (e, l + 1); + } + else + { + e += b; + e += c; + e += d; + if (e <= 1.0) + { + e *= M_PI_4; + *sinx = reduced_sin (e, l + 1, signbit); + *cosx = reduced_cos (e, l + 1); + } + else + { + l++; + e -= 2.0; + e *= M_PI_4; + *sinx = reduced_sin (e, l + 1, signbit); + *cosx = reduced_cos (e, l + 1); + } + } + } + } + else { - case 0: - *sinx = __kernel_sinf (y[0], y[1], 1); - *cosx = __kernel_cosf (y[0], y[1]); - break; - case 1: - *sinx = __kernel_cosf (y[0], y[1]); - *cosx = -__kernel_sinf (y[0], y[1], 1); - break; - case 2: - *sinx = -__kernel_sinf (y[0], y[1], 1); - *cosx = -__kernel_cosf (y[0], y[1]); - break; - default: - *sinx = -__kernel_cosf (y[0], y[1]); - *cosx = __kernel_sinf (y[0], y[1], 1); - break; + int32_t ix; + /* High word of x. */ + GET_FLOAT_WORD (ix, abstheta); + /* sin/cos(Inf or NaN) is NaN. */ + *sinx = *cosx = x - x; + if (ix == 0x7f800000) + __set_errno (EDOM); } } } diff --git a/sysdeps/ieee754/flt-32/s_sinf.c b/sysdeps/ieee754/flt-32/s_sinf.c index 418d4487c5..c682bc64fc 100644 --- a/sysdeps/ieee754/flt-32/s_sinf.c +++ b/sysdeps/ieee754/flt-32/s_sinf.c @@ -20,6 +20,7 @@ #include <math.h> #include <math_private.h> #include <libm-alias-float.h> +#include "s_sincos.h" #ifndef SINF # define SINF_FUNC __sinf @@ -27,100 +28,6 @@ # define SINF_FUNC SINF #endif -/* Chebyshev constants for cos, range -PI/4 - PI/4. */ -static const double C0 = -0x1.ffffffffe98aep-2; -static const double C1 = 0x1.55555545c50c7p-5; -static const double C2 = -0x1.6c16b348b6874p-10; -static const double C3 = 0x1.a00eb9ac43ccp-16; -static const double C4 = -0x1.23c97dd8844d7p-22; - -/* Chebyshev constants for sin, range -PI/4 - PI/4. */ -static const double S0 = -0x1.5555555551cd9p-3; -static const double S1 = 0x1.1111110c2688bp-7; -static const double S2 = -0x1.a019f8b4bd1f9p-13; -static const double S3 = 0x1.71d7264e6b5b4p-19; -static const double S4 = -0x1.a947e1674b58ap-26; - -/* Chebyshev constants for sin, range 2^-27 - 2^-5. */ -static const double SS0 = -0x1.555555543d49dp-3; -static const double SS1 = 0x1.110f475cec8c5p-7; - -/* PI/2 with 98 bits of accuracy. */ -static const double PI_2_hi = -0x1.921fb544p+0; -static const double PI_2_lo = -0x1.0b4611a626332p-34; - -static const double SMALL = 0x1p-50; /* 2^-50. */ -static const double inv_PI_4 = 0x1.45f306dc9c883p+0; /* 4/PI. */ - -#define FLOAT_EXPONENT_SHIFT 23 -#define FLOAT_EXPONENT_BIAS 127 - -static const double pio2_table[] = { - 0 * M_PI_2, - 1 * M_PI_2, - 2 * M_PI_2, - 3 * M_PI_2, - 4 * M_PI_2, - 5 * M_PI_2 -}; - -static const double invpio4_table[] = { - 0x0p+0, - 0x1.45f306cp+0, - 0x1.c9c882ap-28, - 0x1.4fe13a8p-58, - 0x1.f47d4dp-85, - 0x1.bb81b6cp-112, - 0x1.4acc9ep-142, - 0x1.0e4107cp-169 -}; - -static const double ones[] = { 1.0, -1.0 }; - -/* Compute the sine value using Chebyshev polynomials where - THETA is the range reduced absolute value of the input - and it is less than Pi/4, - N is calculated as trunc(|x|/(Pi/4)) + 1 and it is used to decide - whether a sine or cosine approximation is more accurate and - SIGNBIT is used to add the correct sign after the Chebyshev - polynomial is computed. */ -static inline float -reduced (const double theta, const unsigned int n, - const unsigned int signbit) -{ - double sx; - const double theta2 = theta * theta; - /* We are operating on |x|, so we need to add back the original - signbit for sinf. */ - double sign; - /* Determine positive or negative primary interval. */ - sign = ones[((n >> 2) & 1) ^ signbit]; - /* Are we in the primary interval of sin or cos? */ - if ((n & 2) == 0) - { - /* Here sinf() is calculated using sin Chebyshev polynomial: - x+x^3*(S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4)))). */ - sx = S3 + theta2 * S4; /* S3+x^2*S4. */ - sx = S2 + theta2 * sx; /* S2+x^2*(S3+x^2*S4). */ - sx = S1 + theta2 * sx; /* S1+x^2*(S2+x^2*(S3+x^2*S4)). */ - sx = S0 + theta2 * sx; /* S0+x^2*(S1+x^2*(S2+x^2*(S3+x^2*S4))). */ - sx = theta + theta * theta2 * sx; - } - else - { - /* Here sinf() is calculated using cos Chebyshev polynomial: - 1.0+x^2*(C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4)))). */ - sx = C3 + theta2 * C4; /* C3+x^2*C4. */ - sx = C2 + theta2 * sx; /* C2+x^2*(C3+x^2*C4). */ - sx = C1 + theta2 * sx; /* C1+x^2*(C2+x^2*(C3+x^2*C4)). */ - sx = C0 + theta2 * sx; /* C0+x^2*(C1+x^2*(C2+x^2*(C3+x^2*C4))). */ - sx = 1.0 + theta2 * sx; - } - - /* Add in the signbit and assign the result. */ - return sign * sx; -} - float SINF_FUNC (float x) { @@ -171,7 +78,7 @@ SINF_FUNC (float x) pio2_table must go to 5 (9 / 2 + 1). */ unsigned int n = (abstheta * inv_PI_4) + 1; theta = abstheta - pio2_table[n / 2]; - return reduced (theta, n, signbit); + return reduced_sin (theta, n, signbit); } else if (isless (abstheta, INFINITY)) { @@ -179,9 +86,9 @@ SINF_FUNC (float x) { unsigned int n = ((unsigned int) (abstheta * inv_PI_4)) + 1; double x = n / 2; - theta = x * PI_2_lo + (x * PI_2_hi + abstheta); + theta = (abstheta - x * PI_2_hi) - x * PI_2_lo; /* Argument reduction needed. */ - return reduced (theta, n, signbit); + return reduced_sin (theta, n, signbit); } else /* |x| >= 2^23. */ { @@ -209,7 +116,7 @@ SINF_FUNC (float x) e += c; e += d; e *= M_PI_4; - return reduced (e, l + 1, signbit); + return reduced_sin (e, l + 1, signbit); } else { @@ -219,14 +126,14 @@ SINF_FUNC (float x) if (e <= 1.0) { e *= M_PI_4; - return reduced (e, l + 1, signbit); + return reduced_sin (e, l + 1, signbit); } else { l++; e -= 2.0; e *= M_PI_4; - return reduced (e, l + 1, signbit); + return reduced_sin (e, l + 1, signbit); } } }