@@ -43,6 +43,11 @@ Major new features:
fminimum_mag, fminimum_mag_num and corresponding functions for float,
long double, _FloatN and _FloatNx.
+* <math.h> macros for single-precision float constants are added as a
+ GNU extension: M_Ef, M_LOG2Ef, M_LOG10Ef, M_LN2f, M_LN10f, M_PIf,
+ M_PI_2f, M_PI_4f, M_1_PIf, M_2_PIf, M_2_SQRTPIf, M_SQRT2f and
+ M_SQRT1_2f.
+
* The __STDC_IEC_60559_BFP__ and __STDC_IEC_60559_COMPLEX__ macros are
predefined as specified in TS 18661-1:2014.
@@ -131,9 +131,10 @@ defined. The default set of features includes these constants.
@xref{Feature Test Macros}.
All values are of type @code{double}. As an extension, @theglibc{}
-also defines these constants with type @code{long double}. The
-@code{long double} macros have a lowercase @samp{l} appended to their
-names: @code{M_El}, @code{M_PIl}, and so forth. These are only
+also defines these constants with type @code{long double} and
+@code{float}. The @code{long double} macros have a lowercase @samp{l}
+while the @code{float} macros have a lowercase @samp{f} appended to
+their names: @code{M_El}, @code{M_PIl}, and so forth. These are only
available if @code{_GNU_SOURCE} is defined.
Likewise, @theglibc{} also defines these constants with the types
@@ -56,7 +56,7 @@ M_DECL_FUNC (__kernel_casinh) (CFLOAT x, int adj)
}
res = M_SUF (__clog) (y);
- __real__ res += (FLOAT) M_MLIT (M_LN2);
+ __real__ res += M_MLIT (M_LN2);
}
else if (rx >= M_LIT (0.5) && ix < M_EPSILON / 8)
{
@@ -1158,6 +1158,23 @@ iszero (__T __val)
# define M_SQRT1_2 0.70710678118654752440 /* 1/sqrt(2) */
#endif
+/* GNU extension to provide float constants with similar names. */
+#ifdef __USE_GNU
+# define M_Ef 2.7182818284590452354f /* e */
+# define M_LOG2Ef 1.4426950408889634074f /* log_2 e */
+# define M_LOG10Ef 0.43429448190325182765f /* log_10 e */
+# define M_LN2f 0.69314718055994530942f /* log_e 2 */
+# define M_LN10f 2.30258509299404568402f /* log_e 10 */
+# define M_PIf 3.14159265358979323846f /* pi */
+# define M_PI_2f 1.57079632679489661923f /* pi/2 */
+# define M_PI_4f 0.78539816339744830962f /* pi/4 */
+# define M_1_PIf 0.31830988618379067154f /* 1/pi */
+# define M_2_PIf 0.63661977236758134308f /* 2/pi */
+# define M_2_SQRTPIf 1.12837916709551257390f /* 2/sqrt(pi) */
+# define M_SQRT2f 1.41421356237309504880f /* sqrt(2) */
+# define M_SQRT1_2f 0.70710678118654752440f /* 1/sqrt(2) */
+#endif
+
/* The above constants are not adequate for computation using `long double's.
Therefore we provide as an extension constants with similar names as a
GNU extension. Provide enough digits for the 128-bit IEEE quad. */
@@ -32,7 +32,7 @@ M_DECL_FUNC (__cacos) (CFLOAT x)
{
y = M_SUF (__casin) (x);
- __real__ res = (FLOAT) M_MLIT (M_PI_2) - __real__ y;
+ __real__ res = M_MLIT (M_PI_2) - __real__ y;
if (__real__ res == 0)
__real__ res = 0;
__imag__ res = -__imag__ y;
@@ -106,7 +106,7 @@ M_DECL_FUNC (__catan) (CFLOAT x)
if (M_FABS (__imag__ x) == 1
&& M_FABS (__real__ x) < M_EPSILON * M_EPSILON)
__imag__ res = (M_COPYSIGN (M_LIT (0.5), __imag__ x)
- * ((FLOAT) M_MLIT (M_LN2)
+ * (M_MLIT (M_LN2)
- M_LOG (M_FABS (__real__ x))));
else
{
@@ -75,7 +75,7 @@ M_DECL_FUNC (__catanh) (CFLOAT x)
if (M_FABS (__real__ x) == 1
&& M_FABS (__imag__ x) < M_EPSILON * M_EPSILON)
__real__ res = (M_COPYSIGN (M_LIT (0.5), __real__ x)
- * ((FLOAT) M_MLIT (M_LN2)
+ * (M_MLIT (M_LN2)
- M_LOG (M_FABS (__imag__ x))));
else
{
@@ -72,7 +72,7 @@ M_DECL_FUNC (__clog10) (CFLOAT x)
if (absx == 1 && scale == 0)
{
__real__ result = (M_LOG1P (absy * absy)
- * ((FLOAT) M_MLIT (M_LOG10E) / 2));
+ * (M_MLIT (M_LOG10E) / 2));
math_check_force_underflow_nonneg (__real__ result);
}
else if (absx > 1 && absx < 2 && absy < 1 && scale == 0)
@@ -80,7 +80,7 @@ M_DECL_FUNC (__clog10) (CFLOAT x)
FLOAT d2m1 = (absx - 1) * (absx + 1);
if (absy >= M_EPSILON)
d2m1 += absy * absy;
- __real__ result = M_LOG1P (d2m1) * ((FLOAT) M_MLIT (M_LOG10E) / 2);
+ __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
}
else if (absx < 1
&& absx >= M_LIT (0.5)
@@ -88,7 +88,7 @@ M_DECL_FUNC (__clog10) (CFLOAT x)
&& scale == 0)
{
FLOAT d2m1 = (absx - 1) * (absx + 1);
- __real__ result = M_LOG1P (d2m1) * ((FLOAT) M_MLIT (M_LOG10E) / 2);
+ __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
}
else if (absx < 1
&& absx >= M_LIT (0.5)
@@ -96,7 +96,7 @@ M_DECL_FUNC (__clog10) (CFLOAT x)
&& absx * absx + absy * absy >= M_LIT (0.5))
{
FLOAT d2m1 = M_SUF (__x2y2m1) (absx, absy);
- __real__ result = M_LOG1P (d2m1) * ((FLOAT) M_MLIT (M_LOG10E) / 2);
+ __real__ result = M_LOG1P (d2m1) * (M_MLIT (M_LOG10E) / 2);
}
else
{
@@ -32,7 +32,7 @@ M_DECL_FUNC (__clog) (CFLOAT x)
if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO))
{
/* Real and imaginary part are 0.0. */
- __imag__ result = signbit (__real__ x) ? (FLOAT) M_MLIT (M_PI) : 0;
+ __imag__ result = signbit (__real__ x) ? M_MLIT (M_PI) : 0;
__imag__ result = M_COPYSIGN (__imag__ result, __imag__ x);
/* Yes, the following line raises an exception. */
__real__ result = -1 / M_FABS (__real__ x);
@@ -94,7 +94,7 @@ M_DECL_FUNC (__clog) (CFLOAT x)
else
{
FLOAT d = M_HYPOT (absx, absy);
- __real__ result = M_LOG (d) - scale * (FLOAT) M_MLIT (M_LN2);
+ __real__ result = M_LOG (d) - scale * M_MLIT (M_LN2);
}
__imag__ result = M_ATAN2 (__imag__ x, __real__ x);
@@ -27,9 +27,8 @@
#define M_STRTO_NAN __strtof_nan
#define M_USE_BUILTIN(c) USE_ ##c ##F_BUILTIN
-/* Standard/GNU macro literals do not exist for the float type. Use
- the double macro constants. */
-#define M_MLIT(c) c
+/* GNU extension float constant macros. */
+#define M_MLIT(c) c ## f
#include <libm-alias-float.h>
#include <math-nan-payload-float.h>
@@ -85,7 +85,7 @@ gammaf_positive (float x, int *exp2_adj)
float x_adj_frac = x_adj - x_adj_int;
int x_adj_log2;
float x_adj_mant = __frexpf (x_adj, &x_adj_log2);
- if (x_adj_mant < (float) M_SQRT1_2)
+ if (x_adj_mant < M_SQRT1_2f)
{
x_adj_log2--;
x_adj_mant *= 2.0f;
@@ -94,7 +94,7 @@ gammaf_positive (float x, int *exp2_adj)
float ret = (__ieee754_powf (x_adj_mant, x_adj)
* __ieee754_exp2f (x_adj_log2 * x_adj_frac)
* __ieee754_expf (-x_adj)
- * sqrtf (2 * (float) M_PI / x_adj)
+ * sqrtf (2 * M_PIf / x_adj)
/ prod);
exp_adj += x_eps * __ieee754_logf (x_adj);
float bsum = gamma_coeff[NCOEFF - 1];
@@ -176,11 +176,11 @@ __ieee754_gammaf_r (float x, int *signgamp)
if (frac > 0.5f)
frac = 1.0f - frac;
float sinpix = (frac <= 0.25f
- ? __sinf ((float) M_PI * frac)
- : __cosf ((float) M_PI * (0.5f - frac)));
+ ? __sinf (M_PIf * frac)
+ : __cosf (M_PIf * (0.5f - frac)));
int exp2_adj;
- float tret = (float) M_PI / (-x * sinpix
- * gammaf_positive (-x, &exp2_adj));
+ float tret = M_PIf / (-x * sinpix
+ * gammaf_positive (-x, &exp2_adj));
ret = __scalbnf (tret, -exp2_adj);
math_check_force_underflow_nonneg (ret);
}
@@ -233,7 +233,7 @@ j0f_near_root (float x, float z)
float index_f;
int index;
- index_f = roundf ((x - FIRST_ZERO_J0) / (float) M_PI);
+ index_f = roundf ((x - FIRST_ZERO_J0) / M_PIf);
/* j0f_asympt fails to give an error <= 9 ulps for x=0x1.324e92p+7
(index 48) thus we can't reduce SMALL_SIZE below 49. */
if (index_f >= SMALL_SIZE)
@@ -514,7 +514,7 @@ y0f_near_root (float x, float z)
float index_f;
int index;
- index_f = roundf ((x - FIRST_ZERO_Y0) / (float) M_PI);
+ index_f = roundf ((x - FIRST_ZERO_Y0) / M_PIf);
if (index_f >= SMALL_SIZE)
return y0f_asympt (x);
index = (int) index_f;
@@ -243,7 +243,7 @@ j1f_near_root (float x, float z)
x = -x;
sign = -1.0f;
}
- index_f = roundf ((x - FIRST_ZERO_J1) / (float) M_PI);
+ index_f = roundf ((x - FIRST_ZERO_J1) / M_PIf);
if (index_f >= SMALL_SIZE)
return sign * j1f_asympt (x);
index = (int) index_f;
@@ -525,7 +525,7 @@ y1f_near_root (float x, float z)
float index_f;
int index;
- index_f = roundf ((x - FIRST_ZERO_Y1) / (float) M_PI);
+ index_f = roundf ((x - FIRST_ZERO_Y1) / M_PIf);
if (index_f >= SMALL_SIZE)
return y1f_asympt (x);
index = (int) index_f;
@@ -134,7 +134,7 @@ __ieee754_jnf(int n, float x)
tmp = n;
v = two/x;
tmp = tmp*__ieee754_logf(fabsf(v*tmp));
- if(tmp<(float)8.8721679688e+01) {
+ if(tmp<8.8721679688e+01f) {
for(i=n-1,di=(float)(i+i);i>0;i--){
temp = b;
b *= di;
@@ -165,9 +165,9 @@ static float
lg_sinpi (float x)
{
if (x <= 0.25f)
- return __sinf ((float) M_PI * x);
+ return __sinf (M_PIf * x);
else
- return __cosf ((float) M_PI * (0.5f - x));
+ return __cosf (M_PIf * (0.5f - x));
}
/* Compute cos (pi * X) for -0.25 <= X <= 0.5. */
@@ -176,9 +176,9 @@ static float
lg_cospi (float x)
{
if (x <= 0.25f)
- return __cosf ((float) M_PI * x);
+ return __cosf (M_PIf * x);
else
- return __sinf ((float) M_PI * (0.5f - x));
+ return __sinf (M_PIf * (0.5f - x));
}
/* Compute cot (pi * X) for -0.25 <= X <= 0.5. */
@@ -92,7 +92,7 @@ __log1pf(float x)
if(k==0) return zero;
else {c += k*ln2_lo; return k*ln2_hi+c;}
}
- R = hfsq*((float)1.0-(float)0.66666666666666666*f);
+ R = hfsq*(1.0f-0.66666666666666666f*f);
if(k==0) return f-R; else
return k*ln2_hi-((R-(k*ln2_lo+c))-f);
}
Converting double precision constants to float is now affected by the runtime dynamic rounding mode instead of being evaluated at compile time with default rounding mode (except static object initializers). This can change the computed result and cause performance regression. The known correctness issues (increased ulp errors) are already fixed, this patch fixes remaining cases of unnecessary runtime conversions. Add float M_* macros to math.h as new GNU extension API. To avoid conversions the new M_* macros are used and instead of casting double literals to float, use float literals (only required if the conversion is inexact). The patch was tested on aarch64 where the following symbols had new spurious conversion instructions that got fixed: __clog10f __gammaf_r_finite@GLIBC_2.17 __j0f_finite@GLIBC_2.17 __j1f_finite@GLIBC_2.17 __jnf_finite@GLIBC_2.17 __kernel_casinhf __lgamma_negf __log1pf __y0f_finite@GLIBC_2.17 __y1f_finite@GLIBC_2.17 cacosf cacoshf casinhf catanf catanhf clogf gammaf_positive Fixes bug 28713. Reviewed-by: Paul Zimmermann <Paul.Zimmermann@inria.fr> --- v2: added NEWS entry. --- NEWS | 5 +++++ manual/math.texi | 7 ++++--- math/k_casinh_template.c | 2 +- math/math.h | 17 +++++++++++++++++ math/s_cacos_template.c | 2 +- math/s_catan_template.c | 2 +- math/s_catanh_template.c | 2 +- math/s_clog10_template.c | 8 ++++---- math/s_clog_template.c | 4 ++-- sysdeps/generic/math-type-macros-float.h | 5 ++--- sysdeps/ieee754/flt-32/e_gammaf_r.c | 12 ++++++------ sysdeps/ieee754/flt-32/e_j0f.c | 4 ++-- sysdeps/ieee754/flt-32/e_j1f.c | 4 ++-- sysdeps/ieee754/flt-32/e_jnf.c | 2 +- sysdeps/ieee754/flt-32/lgamma_negf.c | 8 ++++---- sysdeps/ieee754/flt-32/s_log1pf.c | 2 +- 16 files changed, 54 insertions(+), 32 deletions(-)