diff options
Diffstat (limited to 'sysdeps/ieee754/flt-32/s_sincosf.h')
| -rw-r--r-- | sysdeps/ieee754/flt-32/s_sincosf.h | 171 |
1 files changed, 31 insertions, 140 deletions
diff --git a/sysdeps/ieee754/flt-32/s_sincosf.h b/sysdeps/ieee754/flt-32/s_sincosf.h index d3d7b4d6f3..1dcb04f235 100644 --- a/sysdeps/ieee754/flt-32/s_sincosf.h +++ b/sysdeps/ieee754/flt-32/s_sincosf.h @@ -1,5 +1,5 @@ /* Used by sinf, cosf and sincosf functions. - Copyright (C) 2017-2018 Free Software Foundation, Inc. + Copyright (C) 2018 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 @@ -20,145 +20,6 @@ #include <math.h> #include "math_config.h" -/* 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; -} - - /* 2PI * 2^-64. */ static const double pi63 = 0x1.921FB54442D18p-62; /* PI / 4. */ @@ -217,6 +78,36 @@ sincosf_poly (double x, double x2, const sincos_t *p, int n, float *sinp, *cosp = c + x6 * c2; } +/* Return the sine of inputs X and X2 (X squared) using the polynomial P. + N is the quadrant, and if odd the cosine polynomial is used. */ +static inline float +sinf_poly (double x, double x2, const sincos_t *p, int n) +{ + double x3, x4, x6, x7, s, c, c1, c2, s1; + + if ((n & 1) == 0) + { + x3 = x * x2; + s1 = p->s2 + x2 * p->s3; + + x7 = x3 * x2; + s = x + x3 * p->s1; + + return s + x7 * s1; + } + else + { + x4 = x2 * x2; + c2 = p->c3 + x2 * p->c4; + c1 = p->c0 + x2 * p->c1; + + x6 = x4 * x2; + c = c1 + x4 * p->c2; + + return c + x6 * c2; + } +} + /* Fast range reduction using single multiply-subtract. Return the modulo of X as a value between -PI/4 and PI/4 and store the quadrant in NP. The values for PI/2 and 2/PI are accessed via P. Since PI/2 as a double |